Volumetric Properties and Viscosity of Fluid Mixtures at High Pressures: Lubricants and Ionic

Liquids

James Scott Dickmann

Dissertation submitted to the faculty of the Virginia Polytechnic Institute and State University in

partial fulfillment of the requirements for the degree of

Doctor of Philosophy

In

Chemical Engineering

Erdogan Kiran, Chair

Richey M. Davis

Stephen M. Martin

Hongliang Xin

April 26, 2019

Blacksburg, VA

Keywords: Viscosity, Density, Lubricants, Ionic liquids, High pressure, Viscometer, Modeling,

Compressibility, Solubility parameter

Volumetric Properties and Viscosity of Fluid Mixtures at High Pressures: Lubricants and

Ionic Liquids

James Dickmann

Abstract

The present thesis explores the volumetric and transport properties of complex fluid

mixtures under pressure in order to develop a better, more holistic understanding of the

relationship between the volumetric properties, derived thermodynamic properties, and viscosity.

To accomplish this broad objective, two different categories of fluid mixtures were examined

using a combination of experimental data and models. These included base oils and their

mixtures with polymeric additives, used in lubricants and ionic liquids, with cosolvent addition,

for use in biomass and polymer processing. Experimental density data were collected using a

variable-volume view-cell at pressures up to 40 MPa and temperatures up to 398 K. A unique

high pressure rotational viscometer was developed to study the effect of pressure, temperature,

and shear rate on viscosity while also allowing for the simultaneous examination of phase

behavior. Viscosity data were collected at pressures up to 40 MPa, temperatures up to 373 K,

and shear rates up to 1270 s-1. Experimental density and viscosity data were fit to a pair of

coupled model equations, the Sanchez-Lacombe equation of state and the free volume theory

respectively. From density, derived thermodynamic properties, namely isothermal

compressibility, isobaric thermal expansion coefficient, and internal pressure, were calculated.

By generating these models, viscosity could be viewed in terms of density, allowing for a direct

link with thermodynamic properties.

In the first part of the study, the effect of composition on density, thermodynamic

properties, and viscosity was examined for base oils used in automotive lubricants. Six different

base oils, four mineral oils and two synthetic oils, were studied to develop a better understanding

on how the thermodynamic properties, particularly isothermal compressibility and internal

pressure, vary with the concentration of cyclic molecules in the oil stock. Isothermal

compressibility was found to decrease with cycloalkane content, while internal pressure

increased. Additionally, the effect of two different polymeric additives on the volumetric

properties and viscosity of a base oil composed of poly(α olefins) was examined. Both additives

are polymethacrylate based, one with amine functionality, and are used as viscosity index

modifiers in engine oils and automatic transmission fluids. The polymer with amine

functionality was found to have a significant effect on internal pressure, seen as a large drop at

high polymer concentration (7 mass percent), due to the addition of repulsive intermolecular

interactions.

In the second part of the study, six ionic liquids with the 1-alkyl-3-methylimidazolium

cation and their mixtures with ethanol were examined. Two anions were used, chloride and

acetate. The effect of ethanol addition on the derived thermodynamic properties and viscosity

was studied in terms of chain length of the alkyl group on the cation. In addition, a method of

estimating Hildebrand solubility parameter was employed, allowing for solubility parameter to

be put in terms of pressure, temperature, and composition. The effect of cosolvent addition on

the thermodynamic properties was changed by the length of the alkyl group on the cation. As the

cation became bulkier, anion-cation interactions weakened, allowing for an increase in the anion-

cosolvent interactions.

Volumetric Properties and Viscosity of Fluid Mixtures at High Pressures: Lubricants and

Ionic Liquids

James Dickmann

General Audience Abstract

The present thesis aims to understand both the density and viscosity of various fluid

mixtures at high pressures and temperatures through both experiments and modeling. By

studying these properties simultaneously, a more holistic view of a fluid can be developed to

predict its usefulness for a specific application. This is especially important in the case of fluid

mixtures, where, in addition to temperature and pressure, composition needs to be taken into

account. To accomplish the experimental portion of this work, a new high pressure rotational

viscometer was developed to measure viscosity as a function of temperature and pressure in

conjunction with a preexisting technique for measuring density. This experimental data was

used to create models, allowing for a better understanding of the effect of temperature, pressure,

and composition on both density and viscosity along with certain thermodynamic properties.

In the first part of the study, oils and additives used to make lubricants with automotive

applications, such as engine oils and automatic transmission fluids, were studied. By studying

the properties of these mixtures under pressure, a better understanding of how properties key to

lubricant effectiveness are related to temperature, pressure, and composition can be developed.

In the second part of the study, ionic liquids, salts with melting points below 100oC, and

their mixtures with ethanol were studied. Ionic liquids have unique properties and have been

studied for use in batteries, polymer processing, biomass processing, and gas capture. Due to the

wide range of potential ionic liquids with various properties that can be made, these salts have

been described as tailorable solvents. By adding an additional solvent, the resulting mixture can

be tuned through temperature, pressure, and composition. Using the set of tools employed in the

present work, important properties for process design were calculated. In particular, the

Hildebrand solubility parameter was estimated as a function of temperature, pressure, and

composition. The solubility parameter is a useful tool in predicting whether or not a material

will dissolve in the solvent of choice.

v

Acknowledgments

A number of people have been instrumental in the completion of the body of work found

in the current thesis. I would like to express my appreciation to my advisor Dr. Erdogan Kiran

for his help in the work presented in the present thesis. His help and reassurance through both

the successes and failures in the long road of developing the high pressure rotational viscometer

were instrumental in getting it to the place it is today. His consistent encouragement has been

key in getting me this far in my professional life. I would also like to thank Mrs. Gunin Kiran

for her encouragement and the many wonderful meals she provided for the lab group over the

years.

I would like to offer a special thanks to Dr. John Hassler. His help in coding in Python®

and in troubleshooting the viscometer, especially the software and electronics involved, has

made a major impact on this work. Additionally, without his early groundwork on the use of

Python® for the Sanchez-Lacombe equation of state, the modeling section of this work would

not have been possible. My grateful thanks are also extended to Michael Vaught and Kevin

Holshouser, without whom, the viscometer would never be completed.

In addition, I would like to acknowledge the Afton Chemical Corp for sponsoring much

of this research, especially Dr. Mark Devlin, whose interactions always provided an excellent

learning opportunity into a field I was not as familiar with.

I wish to extend my thanks to the other members of the Supercritical Fluids Lab that I

have worked alongside over the past six years: Mary McCorkill and Katrina Avery for their help

in generating the final series of experimental results, Dr. Joon-Hyuk Yim for working alongside

of me on parts of the ionic liquid research, Michael Williams and Joseph Sarver for agreeing to

help edit this thesis, Dr. Heather Grandelli, Dr. Sulamith Frerich, and Shinya Takahashi for

training me at the start of my degree, and Daniel Aube, KwangHae Noh, Mai Ngo, Macy

Lupton, Lauren Pironis, Jenna Sumey, Carter Berry, Scott Holahan, Josh Rasco, and Morgan

Whitfield for their continued support over the course of this work.

Finally, I would like to thank my parents, Norb and Marion Dickmann, who have been

there every step of the way in my journey to finish this thesis.

vi

Table of Contents

Chapter I Introduction and Survey of the Literature 1

I.1 A Brief Description of the Scope of the Thesis 1

I.2 A Brief Overview of the Literature 3

I.2.1 Experimental Determination of Viscosity at High Pressure 7

I.2.1.A Falling Body/Rolling Ball Viscometers 7

I.2.1.B Capillary Viscometers 8

I.2.1.C Vibrating Wire Viscometers 9

I.2.1.D Oscillating Quartz Viscometers 9

I.2.1.E Oscillating Piston Viscometers 10

I.2.1.F Rotational Viscometers 10

I.2.1.G Other 11

I.2.1.H Density and High Pressure Viscosity 11

I.2.1.I Limitations 12

I.2.2 Modeling of Pressure Effects on Viscosity 13

I.2.2.A Modeling Viscosity of Gases 13

I.2.2.B Free Volume Theory 15

I.2.2.C Friction Theory 16

I.2.2.D Scaling Factors 16

I.2.2.E Molecular Dynamics Simulations 17

I.2.2.F Other models 17

I.2.2.G Modeling of Density and Phase Behavior 18

I.2.2.H Limitations 19

I.2.3 Oils, Lubricants, and Fuels 19

I.2.3.A Lubricants 20

I.2.3.B Fuels 21

I.2.3.C Oil Recovery 21

I.2.4 Ionic Liquids 22

I.2.5 Gas Expanded Liquids 23

I.2.6 Polymers 24

vii

I.2.6.A Plasticizers 24

I.2.6.B Foams 25

I.2.7 Geological Effects 25

I.3 A Brief Rationale for the Present Study 26

I.4 References 27

Chapter II Experiments 35

II.1 Variable-Volume View-Cell 35

II.2 High Pressure Rotational Viscometer 39

III.3 References 60

Chapter III Analysis and Modeling 51

III.1 Volumetric properties and lattice fluid models 51

III.2 Modeling mixtures 53

III.3 Derived thermodynamic properties 55

III.4 Viscosity and free volume 56

III.5 Statistical analysis of model fits 57

III.6 References 58

Chapter IV Base Oils 60

IV.1 Introduction 70

IV.1.1 Objectives 61

IV.2 Materials and Methods 61

IV.3 Results and Discussion 64

IV.3.1 PVT Data and Modeling 64

IV.3.2 Derived Thermodynamic Properties 66

IV.3.3 Viscosity and Modelling 73

IV.4 Conclusions 77

IV.5 References 77

Chapter V Base Oil Additives 79

V.1 Introduction 79

V.1.1 Objectives 79

V.2 Materials and Methods 80

V.3 Results and Discussion 81

viii

V.3.1 Viscosity Index Modifiers 81

V.3.2 Automatic Transmission Fluids 92

V.4 Conclusions 96

V.5 References 97

Chapter VI Ionic Liquids 98

VI.1 Introduction 98

VI.1.1 Objectives 98

VI.2 Materials and Methods 99

VI.2.1 Synthesis 101

VII.3 Results and Discussion 103

VI.3.1 1-Alkyl-3-methylimidazolium Chlorides and their Mixtures with

Ethanol

103

VI.3.1.A Derived Thermodynamic Properties of [RMIM]Cl + Ethanol 109

VI.3.2 1-Alkyl-3-methylimidazolium Acetates and their Mixtures with

Ethanol

118

VI.3.2.A Derived Thermodynamic Properties of [RMIM]Ac + Ethanol 121

VI.3.2.B Viscosity of [RMIM]Ac + Ethanol 128

VI.3.3 Hildebrand Solubility Parameters of Ionic Liquids 130

VI.4 Conclusions 135

VI.5 References 136

Chapter VII Conclusions 138

VII.1 Future Work 139

VII.2 References 140

Appendix A: Publications Represented in the Present Thesis 141

Appendix B: Calibration and Verification of Density and Viscosity Measurements 142

Appendix C: Density, Derived Thermodynamic Properties, and Viscosity of Base

Oils

151

Appendix D: Density, Derived Thermodynamic Properties, and Viscosity of

Mixtures of Base Oils with Additives and Automatic Transmission Fluids

166

Appendix E: Density, Derived Thermodynamic Properties, and Viscosity of Ionic

Liquids and Their Mixtures with Ethanol

191

ix

List of Tables

Table I.1. Base oil categories as laid out by the American Petroleum Institute

guidelines.

20

Table II.1. Cannon Instrument Company calibration standards used to calibrate the

high pressure rotational viscometer.

45

Table IV.1. Characteristics of the base oils studied. 62

Table IV.2. Sanchez-Lacombe parameters of base oils. 65

Table IV.3. Parameters for the free volume theory of viscosity. 75

Table V.1. S-L parameters for mixtures of PAO 4 with Polymer 1. 83

Table V.2. S-L parameters for mixtures of PAO 4 with Polymer 2. 84

Table V.3. Parameters for the free volume theory of viscosity for mixtures of PAO 4

and viscosity index modifier Polymer 1.

90

Table V.4. Parameters for the free volume theory of viscosity for mixtures of PAO 4

and viscosity index modifier Polymer 2.

91

Table V.5. Tait equation parameters for automatic transmission fluids. 93

Table VI.1. Melting Points of the ILs used in this study. 101

Table VI.2. S-L EOS characteristic parameters for ethanol, [EMIM]Cl, [PMIM]Cl,

[BMIM]Cl, and [HMIM]Cl.

104

Table VI.3. Comparison of Root Mean Squared Deviations (RSME) for different

models of the binary interaction parameter used in mixing rules for the S-L EOS.

106

Table VI.4. S-L EOS characteristic parameters for [EMIM]Cl + ethanol mixtures. 106

Table VI.5. S-L EOS characteristic parameters for [PMIM]Cl + ethanol mixtures. 107

Table VI.6. S-L EOS characteristic parameters for [BMIM]Cl + ethanol mixtures. 107

Table VI.7. S-L EOS characteristic parameters for [HMIM]Cl + ethanol mixtures. 107

Table VI.8. S-L EOS characteristic parameters for [EMIM]Ac and [BMIM]Ac. 119

Table VI.9. Comparison of Root Mean Squared Deviations (RSME) for different

models of the binary interaction parameter used in mixing rules for the S-L EOS for

[EMIM]Ac and [BMIM]Ac.

120

Table VI.10. S-L EOS characteristic parameters for [EMIM]Ac + ethanol mixtures. 120

Table VI.11. S-L EOS characteristic parameters for [BMIM]Ac + ethanol mixtures. 121

x

Table VI.12. Parameters for the free volume theory of viscosity. 129

Table VI.13. Solubility parameters of ionic liquids at 298 K and 0.1 MPa. 135

xi

List of Figures

Figure I.1. Journal articles published every year from 2000-2018 using search terms

Viscosity + High Pressure on Web of Science.

4

Figure I.2. Journal articles published every year from 2000-2018 using search terms

Viscosity + High Pressure + Lubricant on Web of Science.

4

Figure I.3. Journal articles published every year from 2000-2018 using search terms

Viscosity + High Pressure + Ionic Liquid on Web of Science.

5

Figure I.4. Journal articles published every year from 2000-2018 using search terms

Viscosity + High Pressure + Polymer on Web of Science.

5

Figure I.5. Journal articles published every year from 2000-2018 using search terms

Viscosity + High Pressure + Supercritical Fluid on Web of Science.

6

Figure II.1. External diagram of the variable-volume view-cell. 36

Figure II.2. Internal diagram of the variable-volume view-cell. 37

Figure II.3. Dimensions of the variable-volume view-cell. 37

Figure II.4. Evaluation of a sample run of ethanol in the variable-volume view-cell at

a fixed temperature of 298 K.

38

Figure II.5. Comparison of experimental (circles) data for a validation run to

literature values (diamonds).

39

Figure II.6. External diagram of the high pressure rotational viscometer. 41

Figure II.7. Internal diagram of the high pressure rotational viscometer. 41

Figure II.8. Internal geometries of the high pressure rotational viscometer. 42

Figure II.9. Torque versus time (left) and average torque versus rotational speed

(right) for Cannon Instrument Company calibration standard N14 at 298 K and

ambient pressure.

46

Figure II.10. Torque versus time for Cannon Instrument Company calibration

standard N14 at 298 K and ambient pressure.

46

Figure II.11. Viscosity versus average corrected torque/rotational speed for Cannon

Instrument Company calibration standard N14.

47

Figure II.12. Viscosity versus average corrected torque/rotational speed for all

calibration standards in Table III.1.

47

xii

Figure II.13. Viscosity versus time for a validation run at ambient pressure for a

silicone oil (Canon Instruments S60).

48

Figure II.14. Evaluation of a sample run in the high pressure rotational viscometer,

involving a base oil composed of poly(alpha olefins) at 298 K and 500 rpm.

49

Figure III.1. Two-dimensional representation of the lattice fluid model. 53

Figure IV.1. Composition of base oils IIA (left) and IIB (right). 62

Figure IV.2. Composition of base oils IIIA (left) and IIIB (right). 63

Figure IV.3. Composition of base oils PAO 4 (left) and PAO 8 (right). 63

Figure IV.4. Examples of the primary poly(α-olefins) found in PAO 4 and PAO 8, a

trimer (A) and tetramer (B) of 1-decene.

64

Figure IV.5. Density versus pressure for the base oil IIB at isotherms 298, 323, 348,

373, and 398 K.

65

Figure IV.6. Density versus pressure for six base oils at 323 K (left) and 373 K

(right).

66

Figure IV.7. Isothermal compressibility versus pressure (left) and isobaric thermal

expansion coefficient versus temperature (right) for IIB as calculated from the S-L

EOS.

67

Figure IV.8. Internal pressure versus pressure for IIB calculated from the S-L EOS. 67

Figure IV.9. Isothermal compressibility versus pressure for six base oils at 323 K

(left) and 373 K (right).

68

Figure IV.10. Isothermal compressibility versus mass percent cycloparaffin content

at 373 K and 10 MPa for all base oils.

69

Figure IV.11. Isobaric thermal expansion coefficient versus temperature for six base

oils at 10 MPa (left) and 40 MPa (right).

70

Figure IV.12. Isobaric thermal expansion coefficient versus mass percent

cycloparaffin content at 373 K and 10 MPa for all base oils.

70

Figure IV.13. Internal pressure versus pressure for six base oils at 323 K (left) and

373 K (right).

71

Figure IV.14. Internal pressure versus mass percent cycloparaffin content at 373 K

and 10 MPa for all base oils.

72

xiii

Figure IV.15. Viscosity versus pressure for base oil IIB at 500 rpm (300 rpm for the

298 K run).

73

Figure IV.16. Viscosity versus pressure (left) and average shear stress at 10 MPa

versus shear rate (right) for IIB at 323 K

74

Figure IV.17. Viscosity versus pressure for base oil IIB at 500 rpm (300 rpm for the

298 K run). Free volume correlation fit is represented by black dots.

76

Figure IV.18. Viscosity versus pressure for six base oils at 323 K and 500 rpm. Free

volume correlation fit is represented by black dots.

76

Figure V.1. Structure of viscosity index modifier Polymer 1. 80

Figure V.2. Structure of viscosity index modifier Polymer 2. 81

Figure V.3. Density versus pressure for PAO 4 and its mixtures with viscosity index

modifier Polymer 1 at 323 K.

82

Figure V.4. Density versus pressure for PAO 4 and its mixtures with viscosity index

modifier Polymer 2 at 323 K.

83

Figure V.5. Isothermal compressibility versus pressure for PAO 4 and its mixtures

with viscosity index modifiers Polymer 1 (left) and Polymer 2 (right) at 323 K.

85

Figure V.6. Isothermal compressibility versus mass percent polymer at 323 K and 10

MPa for mixtures of PAO 4 with viscosity index modifiers Polymer 1 and Polymer 2.

85

Figure V.7. Isobaric thermal expansion coefficient versus temperature for PAO 4

and its mixtures with viscosity index modifiers Polymer 1 (left) and Polymer 2 (right)

at 10 MPa.

86

Figure V.8. Isobaric thermal expansion coefficient versus mass percent polymer at

323 K and 10 MPa for mixtures of PAO 4 with viscosity index modifiers Polymer 1

and Polymer 2.

87

Figure V.9. Internal pressure versus pressure for PAO 4 and its mixtures with

viscosity index modifiers Polymer 1 (left) and Polymer 2 (right) at 323 K.

88

Figure V.10. Internal pressure versus mass percent polymer at 323 K and 10 MPa for

mixtures of PAO 4 with viscosity index modifiers Polymer 1 and Polymer 2.

88

Figure V.11. Viscosity versus pressure for mixtures of PAO 4 with viscosity index

modifiers Polymer 1 (left) and Polymer 2 (right) at 298 K and 500 rpm.

89

xiv

Figure V.12. Viscosity versus pressure for mixtures of PAO 4 with viscosity index

modifiers Polymer 1 (left) and Polymer 2 (right) at 323 K and 500 rpm.

90

Figure V.13. Density versus pressure for an experimental and a commercial ATF at

323 K (left) and 373 K (right). Tait equation fits are shown as black diamonds.

93

Figure V.14. Isothermal compressibility versus pressure for an experimental and a

commercial ATF at 323 K (left) and 373 K (right).

94

Figure V.15. Isobaric thermal expansion coefficient versus temperature for an

experimental and a commercial ATF at 10 MPa (left) and 40 MPa (right).

94

Figure V.16. Internal pressure versus pressure for an experimental and a commercial

ATF at 323 K (left) and 373 K (right).

95

Figure V.17. Viscosity versus pressure for an experimental ATF (left) and a

commercial ATF (right).

95

Figure V.18. Viscosity versus pressure for an experimental and a commercial ATF at

323 K and 500 rpm.

96

Figure VI.1. 1-Alkyl-3-methylimidazolium cation and the chloride and acetate

anions. R is an alkyl group (ranging in length from 2 to 6 in the present thesis).

99

Figure VI.2. Route of synthesis for 1-alkyl-3-methylimidazolium chloride. R

represents either a propyl or hexyl group.

102

Figure VI.3. FTIR comparison of the synthesized [HMIM]Cl to commercial

[HMIM]Cl (purity 97 %) and spectra from the Bio-Rad database.

102

Figure VI.4. Density versus pressure for ILs [EMIM]Cl (top left), [PMIM]Cl (top

right), [BMIM]Cl (bottom left), and [HMIM]Cl (bottom right).

105

Figure VI.5. Density versus pressure for mixtures of [EMIM]Cl (top left), [PMIM]Cl

(top right), [BMIM]Cl (bottom left), and [HMIM]Cl (bottom right) with ethanol at

348 K.

108

Figure VI.6. Isothermal compressibility versus pressure for 50% [EMIM]Cl + 50%

ethanol (left) and various concentrations of [EMIM]Cl + ethanol at 348 K (right).

109

Figure VI.7. Isothermal compressibility versus pressure for 50% [PMIM]Cl + 50%

ethanol (left) and various concentrations of [PMIM]Cl + ethanol at 348 K (right).

110

Figure VI.8. Isothermal compressibility versus pressure for 50% [BMIM]Cl + 50%

ethanol (left) and various concentrations of [BMIM]Cl + ethanol at 348 K (right).

110

xv

Figure VI.9. Isothermal compressibility versus pressure for 50% [HMIM]Cl + 50%

ethanol (left) and various concentrations of [HMIM]Cl + ethanol at 348 K (right).

111

Figure VI.10. Isothermal compressibility versus mass percent IL for mixtures of

[EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl + ethanol at 348 K and 10 MPa.

111

Figure VI.11. Isobaric expansivity versus temperature for 50% [EMIM]Cl + 50%

ethanol (left) and various concentrations of [EMIM]Cl + ethanol at 10 MPa (right).

112

Figure VI.12. Isobaric expansivity versus temperature for 50% [PMIM]Cl + 50%

ethanol (left) and various concentrations of [PMIM]Cl + ethanol at 10 MPa (right).

113

Figure VI.13. Isobaric expansivity versus temperature for 50% [BMIM]Cl + 50%

ethanol (left) and various concentrations of [BMIM]Cl + ethanol at 10 MPa (right).

113

Figure VI.14. Isobaric expansivity versus temperature for 50% [HMIM]Cl + 50%

ethanol (left) and various concentrations of [HMIM]Cl + ethanol at 10 MPa (right).

114

Figure VI.15. Isobaric thermal expansion coefficient versus mass percent IL for

mixtures of [EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl + ethanol at 348 K

and 10 MPa.

114

Figure VI.16. Internal pressure versus pressure for 50% [EMIM]Cl + 50% ethanol

(left) and various concentrations of [EMIM]Cl + ethanol at 348 K (right).

116

Figure VI.17. Internal pressure versus pressure for 50% [PMIM]Cl + 50% ethanol

(left) and various concentrations of [PMIM]Cl + ethanol at 348 K (right).

116

Figure VI.18. Internal pressure versus pressure for 50% [BMIM]Cl + 50% ethanol

(left) and various concentrations of [BMIM]Cl + ethanol at 348 K (right).

117

Figure VI.19. Internal pressure versus pressure for 50% [HMIM]Cl + 50% ethanol

(left) and various concentrations of [HMIM]Cl + ethanol at 348 K (right).

117

Figure VI.20. Internal pressure versus mass percent IL for mixtures of [EMIM]Cl,

[PMIM]Cl, [BMIM]Cl, and [HMIM]Cl + ethanol at 348 K and 10 MPa.

118

Figure VI.21. Density versus pressure for ILs [EMIM]Ac (left) and [BMIM]Ac

(right).

119

Figure VI.22. Density versus pressure for mixtures of [EMIM]Ac (left) and

[BMIM]Ac (right) with ethanol at 348 K.

121

Figure VI.23. Isothermal compressibility versus pressure for 50% [EMIM]Ac + 50%

ethanol (left) and various concentrations of [EMIM]Ac + ethanol at 348 K (right).

122

xvi

Figure VI.24. Isothermal compressibility versus pressure for 50% [BMIM]Ac + 50%

ethanol (left) and various concentrations of [BMIM]Ac + ethanol at 348 K (right).

123

Figure VI.25. Isothermal compressibility versus mass percent IL for mixtures of

[EMIM]Ac and [BMIM]Ac + ethanol at 348 K and 10 MPa.

123

Figure VI.26. Isobaric expansivity versus temperature for 50% [EMIM]Ac + 50%

ethanol (left) and various concentrations of [EMIM]Ac + ethanol at 10 MPa (right).

124

Figure VI.27. Isobaric expansivity versus temperature for 50% [BMIM]Ac + 50%

ethanol (left) and various concentrations of [BMIM]Ac + ethanol at 10 MPa (right).

125

Figure VI.28. Isobaric thermal expansion coefficient versus mass percent IL for

mixtures of [EMIM]Ac and [BMIM]Ac + ethanol at 348 K and 10 MPa.

125

Figure VI.29. Internal pressure versus pressure for 50% [EMIM]Ac + 50% ethanol

(left) and various concentrations of [EMIM]Ac + ethanol at 348 K (right).

127

Figure VI.30. Internal pressure versus pressure for 50% [BMIM]Ac + 50% ethanol

(left) and various concentrations of [BMIM]Ac + ethanol at 348 K (right).

127

Figure VI.31. Internal pressure versus mass percent IL for mixtures of [EMIM]Ac

and [BMIM]Ac + ethanol at 348 K and 10 MPa.

128

Figure VI.32. Viscosity versus pressure for [EMIM]Ac from 298-373 K (left) and

mixtures of [EMIM]Ac with ethanol at 323 K and 500 rpm (right).

129

Figure VI.33. Viscosity versus pressure for [BMIM]Ac from 298-373 K (left) and

mixtures of [BMIM]Ac with ethanol at 323 K and 500 rpm (right).

130

Figure VI.34. Solubility parameter versus pressure for mixtures of [EMIM]Cl (top

left), [PMIM]Cl (top right), [BMIM]Cl (bottom left), and [HMIM]Cl (bottom right)

with ethanol at 348 K.

132

Figure VI.35. Solubility parameter versus pressure for mixtures of [EMIM]Ac (left)

and [BMIM]Ac (right) with ethanol at 348 K.

133

Figure VI.36. Solubility parameter versus mass % IL for mixtures of [EMIM]Cl,

[PMIM]Cl, [BMIM]Cl and [HMIM]Cl with ethanol at 298 K and (left) and 348 K

and (right) and 10 MPa.

133

Figure VI.37. Solubility parameter versus mass % IL for mixtures of [EMIM]Ac and

[BMIM]Ac with ethanol at 298 K and (left) and 348 K and (right) and 10 MPa.

134

xvii

Figure VI.38. Solubility parameter versus temperature at ambient pressure as

estimated in the current work using the S-L EOS and estimated through

chromatographic techniques in the literature.

134

1

I. Introduction and Survey of the Literature

I.1 A Brief Description of the Scope of the Thesis

The broad aim of this thesis is to investigate the thermodynamic and transport properties

of complex fluid mixtures under pressure. With this in mind, the present study has been

designed with the objectives of generating fundamental volumetric data, reliable viscosity data,

and descriptive models. Experiments were carried out to examine the effect of pressure and

temperature on density, and pressure, temperature, and shear rate on viscosity for a range of fluid

mixtures. The primary focus has been on two categories of mixtures, namely base oils and their

mixtures with polymeric additives which are of high significance as lubricants, and ionic liquids

and their mixtures with organic solvents which are of high significance in applications such as

biomass processing. Modeling in the form of the free volume theory of viscosity paired with the

Sanchez-Lacombe equation of state was employed in conjunction with experimentally

determined data to aid in the development of a more holistic understanding of how viscosity

relates to density, and with it, to the derived thermodynamic properties. With a complete

understanding of the interconnection between these thermodynamic properties and viscosity, a

better understanding of how these mixtures function as both lubricants and solvents can be

developed.

While there is extensive literature on viscosity determination techniques and viscosity

data at ambient conditions, there is still a need for a greater understanding of the effect of

pressure on the viscosity of fluids. This applies to both the design of experimental systems to

collect viscosity data at high pressure conditions and the models used to analyze and, if possible,

carry out predictions. A major effort in the present study was devoted the development of a

novel high pressure rotational viscometer. This new instrument combines the ability to collect

viscosity data across a range of pressures and temperatures with the ability to control and

measure the shear rate while at the same time assessing the phase-state of the system. The

viscometer design incorporates features for assessment of density along with viscosity which is

expected to be put into operation in future studies. In the present study, an independent

variable-volume view-cell was used to collect density data at the same temperature and pressure

2

conditions where viscosity determinations were carried out. The experimental systems are

described in Chapter II.

The research completed in this thesis can be divided into two different areas of focus:

oils for use in automotive lubricants and ionic liquids as specialty solvents for polymeric

systems.

In the first focus area, base oils and their mixtures with select additives were studied.

These oils and additives are all constituents in automotive lubricants: engine oils and automatic

transmission fluids. The effects of both pressure and temperature on viscosity and density were

studied and modeled. In addition, the derived thermodynamic properties isothermal

compressibility, isobaric thermal expansion coefficient, and internal pressure were calculated.

By looking at these oils holistically, relating viscosity to density and thermodynamic properties

related to intermolecular interactions, a better understanding of how these mixtures function as

effective lubricants can be determined. These are discussed in detail in Chapters IV and V of the

thesis.

In the second focus area, ionic liquids were studied to determine the effect of cation ion

modification and anion choice on the solvent properties of these molten salts. A series of ionic

liquids with varying length alkyl functional groups on the imidazolium cation were used to study

the effect of modifications on the viscosity and density across a range of pressures and

temperatures. The effects of two different anions were studied, chloride and acetate. Viscosity

and density data were collected and modeled for mixtures of these ionic liquids with ethanol.

This in turn allowed for the estimation of Hildebrand solubility parameters as a function of

pressure, temperature, and composition. Knowing both the solubility parameter and viscosity

across a range of pressures, temperatures, and compositions allows for the determination of the

usefulness of these mixtures as solvents, especially for use with polymeric systems, such as the

dissolution and separation of lignocellulosic materials.

In the following sections, a brief overview of the literature is presented. Viscosity is of

particular interest due to its effects in mass transfer, heat transfer, flow behavior, and

elastohydrodynamic lubrication.1-5 There is a growing demand for high pressure viscosity data

and for their modeling. Since a major effort in the present thesis was devoted to the development

of a new instrument to measure this particular fluid property and its importance in the relevant

fields of interest, the primary emphasis of the next section is on the review of the current

3

literature with regards to the viscosity of fluids under high pressure conditions. While density

determinations at high pressure is also a major part of this thesis, the method that was employed

in this study is the same as used previously which is described in detail in Chapter II. The

modeling of density is described in Chapter III. More extensive literature background on

automotive lubricants and ionic liquids are included in the chapters relevant to these areas of

focus.

I.2 A Brief Overview of the Literature

With growth in fields such as lubricant design, diesel fuel and engine optimization, oil

recovery, ionic liquids, and polymer processing, interest in viscosity data of complex and

polymeric mixtures at high pressures has increased, especially after 1991. This trend can easily

be seen in the literature. Searching the Web of Science for the keywords viscosity and high

pressure yielded a total of 14,020 publications covering the period from 1920 to 2018. Of these

13881 have been published since 1990. While 24 articles had appeared in 1990, there was a

drastic increase in the number of publications in 1991, up to 159. This increase continued, with

311 articles published in 2000, all the way up to 1090 in 2018. Figure I.1 shows the increase in

articles published per year from 2000-2018. Figures I.2 – I.5 show the publication trends from

2000-2018 by narrowing the search topics with an additional term: lubricant, ionic liquids,

polymer, or supercritical fluid. A search of high pressure viscosity for lubricants showed an

increase from 13 articles in 2000 to 35 articles in 2018. Replacing lubricant with ionic liquid

showed a dramatic increase from 4 articles published in 2000, to 75 in 2018. Articles involving

polymeric systems showed an increase from 43 articles in 2000 to 102 articles in 2018. Finally,

adding the parameter supercritical fluid to a search of high pressure viscosity showed an increase

from 7 articles published in 2000 to 36 articles in 2018.

4

Figure I.1. Journal articles published every year from 2000-2018 using search terms Viscosity +

High Pressure on Web of Science.

Figure I.2. Journal articles published every year from 2000-2018 using search terms Viscosity +

High Pressure + Lubricant on Web of Science.

0

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400

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1000

1200

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Viscosity + High Pressure

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Viscosity + High Pressure +

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5

Figure I.3. Journal articles published every year from 2000-2018 using search terms Viscosity +

High Pressure + Ionic Liquid on Web of Science.

Figure I.4. Journal articles published every year from 2000-2018 using search terms Viscosity +

High Pressure + Polymer on Web of Science.

0

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40

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ers

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shed

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Viscosity + High Pressure +

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Viscosity + High Pressure +

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6

Figure I.5. Journal articles published every year from 2000-2018 using search terms Viscosity +

High Pressure + Supercritical Fluid on Web of Science.

A close examination of the articles cited in the Web of Science shows that interest in

viscosity at high pressure conditions covers a wide range of applications, including but not

limited to food processing and pasteurization,6,7 estimating the properties of molten rock in the

Earth’s mantle,8,9 and oil recovery and CO2 sequestration.4,10-15 There are also distinct trends that

have been displayed over the past few years. Areas of particular interest that have been noted in

more recent publications include lubricants and fuels used in the automotive industry,1,16-27 ionic

liquids for such applications as high pressure CO2 or SO2 capture,28-41 gas expanded liquids as

tunable solvents,42-48 and polymer processing (including polymer foams).49-67

The following sections provide a brief overview of the literature on the methods of

viscosity measurement, analysis, and select areas of interest:

I.2.1 Experimental Determination of Viscosity at High Pressures

I.2.2 Modeling of Pressure Effects on Viscosity

I.2.3 Oils, Lubricants, and Fuels

I.2.4 Ionic Liquids

I.2.5 Gas Expanded Liquids

0

5

10

15

20

25

30

35

40

Pap

ers

Pu

bli

shed

Year

Viscosity + High Pressure +

Supercritical Fluid

7

I.2.6 Polymers, Foams, and Plasticizers

I.2.7 Geological Effects

I.2.1 Experimental Determination of Viscosity at High Pressure

A variety of experimental techniques have been employed in the literature to determine

viscosity as a function of both temperature and pressure. Due to the difficulties involved with

performing measurements under high pressure conditions, all techniques employed have

different advantages and limitations. While not an exhaustive list, the most common techniques

are described below.

I.2.1.A Falling Body/Rolling Ball Viscometers

Falling body viscometers are commonly used in high pressure applications in the

literature.3,4,30,32,39,43,44,54,68-71 The concept is simple. A sinker is allowed to fall through a fluid in

a tube. Based on the geometry of the system, and the viscosity of the fluid being measured, the

sinker will reach a terminal velocity. If the density of both the sinker (ρs) and fluid (ρf) are

known, and the terminal velocity (Vt) can be measured, viscosity can be determined from:

𝜂 = 𝐶(𝜌𝑠 − 𝜌𝑓)1

𝑉𝑡 I.1

where C is a constant that needs to be experimentally determined.43,44,68 To determine terminal

velocity, an accurate method of measuring sinker position in real time is needed. This has been

accomplished through a variety of means: visually under a microscope,9 using x-ray scattering

paired with a high speed camera,8 or magnetic detectors such as a linear variable differential

transformer (LVDT).68 These viscometers can be designed to operate in the range of hundreds of

MPa16 with some implementations for determining viscosities of magmatic melts reaching up to

7.5 GPa.9 While these instruments have simple operating principles and incredibly high pressure

ranges, they do have drawbacks. Due to the design, it is difficult to control the shear rate applied

to the measured fluid, often limiting these instruments to low shear or Newtonian conditions. In

addition, for highly viscous fluids, fall times can be extremely long, leading to difficulties in

8

measuring the terminal velocity.56 Rolling ball viscometers operate on a similar principle by

measuring the fall time of a ball submerged in the measured fluid rolling down an incline due to

gravitational forces and relating it to viscosity through a relation to sinker and fluid density, such

as equation I.1.34,72 One challenge with rolling ball viscometers is ensuring that no skidding or

sliding occurs.

I.2.1.B Capillary Viscometers

Another technique employed in the literature involves using capillary viscometers that

determine viscosity by measuring the pressure drop of a fluid at a steady flow rate through a

long, narrow tube.52,73-76 When fluid through a cylindrical tube is fully developed and laminar,

viscosity, η, can be determined from the Hagen-Poiseuille equation:

𝜂 =𝜋𝑟4Δ𝑃

8𝐿𝑞 I.2

where r is the radius of the tube, ΔP is the pressure drop across the capillary, L is the length of

the capillary, and q is the flow rate.73 The difficulty of the design for high pressure instruments

is having a steady flow rate in an instrument with high pressure requirements. Due to the

requirement of laminar flow, only conditions in which the measured fluid flow exhibits low

Reynolds numbers are valid for measurement. Additionally, depending on the design of the

instrument, end effects may need to be taken into account.75,76 Examples of this style instrument

operating up to 0.6 GPa have been reported in the literature.74

In addition to standard capillary viscometers, capillary dies and slit rheometers can be

used in conjunction with extruders to determine the viscosity of polymer melts.53,55,59,61,64,67

These systems seem useful in measuring the viscosity of polymers in the presence of a

supercritical or compressible fluid, such as CO2, as a plasticizer or foaming agent, but have their

short comings. Due to the pressure differential across the capillary, it can be difficult to

determine the actual concentration or homogeneity of plasticizer in the melt.64 To reduce this

pressure differential, many of these instruments include a counter pressure chamber at the end of

the die. This counter pressure chamber allows for greater control of the pressure differential

9

involved with the viscosity determination while also preventing the compressible fluid from

separating out of the polymer being measured.67

I.2.1.C Vibrating Wire Viscometers

Vibrating wire viscometers use a submerged wire that is exposed to a permanent

magnetic field. By passing a sinusoidal current through the wire, the wire is vibrated.1,25,26,77,78

By measuring the voltage applied to the wire, viscosity can be determined. There are

instruments in the literature capable of reaching pressures into the GPa range.78 These

instruments can be complex to calibrate and utilize, requiring the correct wire chosen for the

viscosity range being measured. A limitation of this style instrument is that while shear rates can

be varied by changing the frequency of vibration, the shear rates are not necessarily defined with

any degree of accuracy.

I.2.1.D Oscillating Quartz Viscometers

Another design based on vibrational effects utilizes a piezoelectric sensor submerged in

the fluid being measured. By comparing the frequency dampening by the fluid, viscosity can be

determined:

𝑓0 − 𝑓𝑟𝑒𝑠 = 𝑘(𝜋𝑓𝑟𝑒𝑠𝜂𝜌𝑓) I.3

where f0 is the oscillation of the quartz, fres is the frequency of oscillation while the quartz is

submerged, k is a constant, and ρf is the density of the fluid.3 Similar to the vibrating wire

viscometer, the effect of shear rate can be determined by varying the voltage applied to the

crystal. This allows for the determination of Newtonian versus non-Newtonian behavior of a

fluid.

10

I.2.1.E Oscillating Piston Viscometers

Oscillating piston viscometers operate by measuring the time it takes for a magnetically

driven piston to move a specified distance through the fluid being measured. The viscosity range

that can be resolved depends on the magnetic field used in the experiment.42 They have been

employed in high pressure conditions,29,35,42 up to 300 bar at temperatures up to 110oC. These

instruments are known for requiring a small amount of fluid to assess viscosity. At high pressure

conditions, such viscometers are known to be capable of performing measurements up to 10,000

mPa s.42

I.2.1.F Rotational Viscometers

Rotational viscometers use a rotating element compared to a fixed element with the

measured fluid in between, such as parallel plates or concentric cylinders, to determine

viscosity.12,13,18,57,58,65,79 There are commercial instruments available of this type, but many of

them are limited to pressures below 20 MPa, with at least one example capable of reaching

pressures up to 40 MPa.13 Viscosity is calculated by determining torque and shear rate. Shear

rate is easily controlled and determined, though the viscosity range that can be effectively

measured is affected by the geometry of the instrument.18 These instruments often have a lower

viscosity limit that can be effectively measured. With moving parts that need to be coupled to a

torque transducer and/or motor, a layer of complexity is added into instrument design,

particularly involving sealing at high pressures. The instrument either needs to be sealed across

moving parts, or some form of magnetic coupling needs to be employed. Either method adds in

frictional effects that need to be compensated for in the viscosity determinations. For many

magnetically coupled designs, the inner rotating shaft needs to be set on sapphire bearings. The

lubrication effects need to be considered in the final calculations. This can be done in one of two

ways. One approach is to add a drop of the fluid to the bearings and perform a calibration run to

get a baseline to eliminate in the viscosity calculations.13 This approach is limited to single

phase or saturated fluids. Another approach is to perform an ambient pressure scan across a

range of shear rates of the fluid being measured at the temperature of interest. Resulting torque

versus shear rate data can be fit and the intercept taken as the baseline to be eliminated from final

11

calculations.18 In the present thesis, viscosity measurements were carried out using a specially

designed rotational viscometer which will be described in more detail in Chapter II.

I.2.1.G Other

A variety of other methods of determining viscosity have been described in the literature.

These are usually custom designed and of limited implementation. An acoustic levitation

method was used to study the viscosity of squalene + CO2 at pressures up to 16 MPa and

temperatures up to 433 K.13 A sound wave is sent through the CO2 medium to a reflector. The

waves from the source interfere with those coming back from the reflector, causing pressure

zones in which a drop of squalene is levitated. A high speed camera allows for the oscillations in

the drop to be observed and converted to both viscosity and interfacial tension.13 An instrument

using a magnetically levitated sphere was developed to look at samples of viscosities up to 100

Pa s and pressures up to 42 MPa.60 A sphere is held in place by an electromagnet while the outer

cylinder is moved, inducing flow around the sphere. By comparing the current needed to keep

the sphere in place during fluid flow compared to a stationary fluid phase, viscosity is

determined.60 Another unique instrument, a torsional vibrating viscometer uses measurements of

the damping of oscillations of a cylinder submerged in a fluid to calculate viscosity. This

method is similar to quartz or vibrating wire viscometers. One particular example was capable

of measurements up to 15 MPa and 373 K.63

I.2.1.H Density and High Pressure Viscosity

In addition to generating high pressure viscosity data, many techniques either directly

integrate, or are run in conjunction with, a method for determining density. Additionally, there

are several models utilized in the literature, discussed in Section I.3, that require knowledge of

density effects to describe how viscosity varies with pressure. Many of the techniques used in

determining viscosity (such as falling body viscometers) also require knowledge of the density of

the fluid at the specific temperature and pressure of each run. To determine density at these high

pressure conditions, a variety of techniques are employed, such as vibrating tube

densitometers30,80 and variable-volume methods.3,18 Variable-volume methods involving bellows

12

based apparatuses or movable pistons operate on the principle of a closed system in which the

internal volume can be changed as a function of temperature and pressure. By knowing the mass

loaded and having a method to determine the position of the piston or bellows, and with it the

volume, density can be determined.18 A detailed description of a variable-volume view-cell

employed in the present thesis is provided in Chapter II.

I.2.1.I Limitations

Each experimental design comes with its limitations. As with any high pressure

instrument, seal design plays an important role in determining the pressure and temperature

range of operation. While certain designs, such as falling body viscometers, have specific

implementations that can reach incredibly high pressures (in the range of GPas), not every such

instrument found in the literature are designed for such applications. Some designs, such as

rotational viscometers, have pressure limitations due to the need for specialty sealing

arrangements to compensate for moving parts. Additionally, design has an impact on the

viscosity range that can be accurately resolved, with some viscometers being capable of allowing

modifications from run to run to change the measurable range. In falling body viscometers, this

may be achieved by using sinkers of different densities. Oscillating piston viscometers have

limited viscosity ranges based off a replaceable magnet in the system. Other designs require

implementing methods to provide and control a consistent flow rate, such as capillary type

viscometers. One major limitation common to most high pressure viscometer implementations is

the lack of ability to accurately control and measure the shear rate. Falling body viscometers are

simple and allow for measurements up to high pressures, but it is difficult to control shear rate,

often limiting these instruments to studying fluids at low shear or Newtonian conditions.

Methods based on vibrations, such as vibrating wire or oscillating quartz viscometers, can

provide a range of shear rates, allowing for the detection of the presence of non-Newtonian

behavior. While shear rate can be varied, it appears that accurate shear rates are not reported

using this method in the literature. Rotational viscometers, in spite of their limitations in

pressure and viscosity ranges, are the most suitable viscometers for the assessment of shear rates

and their effect on viscous behavior under high pressure conditions.

13

I.2.2 Modeling of Pressure Effects on Viscosity

Experimental techniques for the determination of viscosity data at high pressure are

subject to limitations as described in the previous sections. Additionally, due to time and cost, it

would be impossible to generate this data for every possible pure component and mixture

experimentally. Many of the fluids utilized in high pressure scenarios, particularly fuels and

lubricants, are not pure components. They are complex mixtures composed of many species.

While there is no replacement for experimental data, there are several models available in the

literature that provide descriptions of viscous behavior with a possibility of predictions. For

gases at low pressures, theoretical models derived from kinetic theory can be used.10,81 For

dense or liquid fluids, however, modeling is not as simple. In these situations, empirical or semi-

empirical models have been used, including free volume theory, friction theory, and density

scaling approaches.10,37-41,82,83 In addition to experimental data, molecular dynamics simulations

have been used to provide estimations of the needed viscosity data.21,45-48,84

I.2.2.A Modeling Viscosity of Gases

Many models utilized in the determination of viscosity of fluids at high pressures,

especially free volume and friction theory, include a term to represent the dilute gas viscosity at

the zero density limit (η0). From the kinetic theory of gases, an equation has been derived:

𝜂0 =𝑘𝐵𝑇

⟨𝑣⟩

𝑓𝜂(𝑛)

𝔖

I.4

where T is temperature, kB is Boltzmann’s constant, ⟨𝑣⟩ is the average relative thermal speed, 𝔖

is the generalized cross section, and fη(n) is a correction factor.81 While theoretically derived, this

form requires specific knowledge of intermolecular interactions that may not be readily available

for all fluids. By modeling a fluid as a collection of rigid, non-attractive spheres, a more specific

equation was proposed:

𝜂0 = 26.69√𝑀𝑇

𝜎2

I.5

14

where M is molecular weight and σ is the sphere diameter.10 Chapman-Enskog theory adds

collision effects to the above model. Further modification by Chung et al.85 results in a model

that puts the zero density limit viscosity in terms of temperature and critical point values of the

species in question:10,14,41

𝜂0 = 40.785√𝑀𝑇

𝑉𝑐2/3Ω∗𝑇∗𝐹𝑐

I.6

𝑇∗ = 𝑇/𝑇𝑐 I.7

where TC and VC are the critical temperature and volume respectively, Ω* is the collision

integral, and FC is a correction factor:10,14,41

Ω∗ =1.16145

𝑇∗+

0.52487

𝑒0.77320𝑇∗ +

2.1678

𝑒2.43787𝑇∗

−6345 × 10−4(𝑇∗)0.014784 sin[18.0323(𝑇∗)−0.76830 − 7.2731]

I.8

𝐹𝑐 = 1 − 0.2756𝜔 + 0.059035𝜇𝑟4 + 𝜅′ I.9

where κ’ corrects for hydrogen bonding, ω is the accentric factor, and μr is a reduced dipole

moment calculated from the dipole moment μ:10,14,41

𝜇𝑟 =131.3𝜇

√𝑉𝑐𝑇𝑐 I.10

The viscosities calculated for η0 are very low, in the μPa s range. For many studies, the specific

model used for calculating the zero density limit viscosity is often the weakest part of the model,

or is neglected all together, due to the negligible effect that η0 has on overall viscosity for many

dense fluids at high pressure conditions.18,41

15

I.2.2.B Free Volume Theory

Viscosity is often interpreted in terms of and linked to free volume.82 This concept of

relating the viscosity to the spacing between molecules allows for the linking of viscosity to

density. An early approach to relating viscosity to density is given by the Doolittle equation:82,86

𝜂 = 𝐴𝑒𝑥𝑝 (𝐵

1−𝑉0𝜌) I.11

where ρ is density, V0 is close packed volume of the fluid, and A and B are constants. This

approach is empirical in nature and has been applied to high pressure systems, including those

involving polymeric materials.57,87 This equation has been expanded by Allal et al.82 to add more

physical significance to the model. The full form of the free volume theory is thus represented

by the equation:82

𝜂 = 𝜂0 +𝜌𝜄(𝛼𝜌+

𝑃𝑀

𝜌)

√3𝑅𝑇𝑀𝑒𝐵(

𝛼𝜌+𝑃𝑀𝜌

𝑅𝑇)

3 2⁄

I.12

where η0 is the dilute gas viscosity at the zero density limit (as previously described), R is the gas

constant, M is molecular weight, T is temperature, ι is the characteristic molecular length, α is

related to the energy barrier molecules must overcome to diffuse, and B is a dimensionless

parameter that represents free volume effects. The use of this model requires coupling with an

equation of state to generate the required density values. Studies in the literature have coupled

the above equation with a variety of equations of state, such as PC-SAFT (perturbed-chain

statistical associating fluid theory)14,41 and Sanchez-Lacombe.18 A limitation of this model is the

need for experimental data to determine the parameters ι, α, and B.10 Free volume theory and its

implementation in this thesis will be discussed in greater detail in Chapter III.

16

I.2.2.C Friction Theory

As with the free volume theory, friction theory divides viscosity into two contributions,

viscosity at the zero density limit (η0) and in the dense state (ηf):10,83,88

𝜂(𝑇, 𝑃) = 𝜂0(𝑇) + 𝜂𝐹(𝑇, 𝑃) I.13

The viscosity term for dense states is then related to the attractive (pa) and repulsive (pr) pressure

contributions as predicted by a Van der Waals based model:

𝜂𝐹 = 𝜅𝑎𝑝𝑎 + 𝜅𝑟𝑝𝑟 + 𝜅𝑟𝑟𝑝𝑟2 I.14

where κa, κr, and κrr are friction coefficients paired with the attractive pressure (pa), repulsive

pressure (pr), and square of the repulsive pressure (pr2) contributions respectively. These three

coefficients are functions of temperature.83,88 The pressure terms are generally calculated from

cubic equations of state, such as Peng-Robinson or Soave-Redlich-Kwong, though in principle

this model can be paired with any EOS, including SAFT (statistical associating fluid theory).10,83

It should be noted that the friction coefficients are determined by fitting with experimental data

in conjunction with the EOS of choice. This leads to the coefficients used being dependent on

the EOS used.10

I.2.2.D Scaling Factors

One more approach to relate viscosity to density effects is through the use of scaling

factors. Viscosity can be expressed in terms of a function (f) that combines both temperature and

density:

𝜂(𝑇, 𝜌) = 𝑓(𝑇𝜌−𝛾) I.15

where γ is a scaling factor.37-40,89 The value of gamma is chosen in such a way that causes the

viscosity data to superimpose into one master curve. The effectiveness of the model is then

17

dependent on the function (f) chosen. The value of gamma is useful in assessing the types of

intermolecular forces, with lower values representing stronger attractive effects, such as

hydrogen bonding.37 It is known that for certain fluids, such as water, this method does not work

across a wide range of temperatures and pressures as there is no value of gamma that causes all

values of viscosity to collapse into a single curve.37 In these cases, modifications to the model

may be needed, such as using a reduced value of viscosity instead.37 This scaling parameter

approach is not only useful for modeling viscous effects, it has been used in the literature to also

model relaxation times, diffusion coefficients, thermal conductivities, and electrical

conductivities.37

I.2.2.E Molecular Dynamics Simulations

While these empirical models for liquid and dense fluids require some experimental data

to fit to the necessary equations, molecular dynamics simulations offer a potential supplement by

providing estimations of viscosity data when experiments have not been performed. Such

simulations have been performed for a number of high pressure systems, especially CO2 and CO2

expanded systems.46-48,84 The quality of the results of a molecular dynamics simulation can vary

depending on the simplifications used to reduce computing time. Due to this, viscosity

predictions by such modeling are often only accurate to within an order of magnitude.10 With

such a disparity, predictive values from molecular dynamics simulations still need a way to

validate the reasonableness of the results, such as with experimental data.

I.2.2.F Other models

There are a number of other models available to describe viscosity under high pressure

conditions. Eyring’s absolute rate theory models Newtonian fluids in similar terms as a chemical

reaction:10

𝜂 =ℎ𝑁𝑎

𝑉𝑒

𝐹

𝑅𝑇 I.16

18

where h is Planck’s constant, Na is Avogadro’s number, V is molar volume, R is the gas

constant, and F is the molar free energy of activation of flow. This basic model has been

modified to model both binary mixtures of organic solvents and ionic liquids among other

applications.36,90

One work attempted to use a semi-theoretical approach to do predictive modeling with a

rough hard sphere model in conjunction with an artificial neural network to examine viscosity at

high pressure for biodiesels and their constituents.24

I.2.2.G Modeling of Density and Phase Behavior

Three of the viscosity models described above are dependent on either density or values

dependent on an equation of state: free volume theory, friction theory, and density scaling

approaches. Understanding how viscosity is related to fluid density is important in

understanding how viscosity is in turn related to pressure. As pressure changes, so do the

intermolecular interactions, affecting viscosity. Due to this, many studies by necessity

incorporate density modeling by equations of state such as SAFT models14,41 or lattice fluid

models, such as the Sanchez-Lacombe equation of state,18 in their analysis. Also important in

the determination of viscosity are compositional effects. Utilizing equations of state allows for

the modeling of phase composition in situations where phase separation can occur, such as the

use of compressible fluids as plasticizers in polymer processing64 or in the case of gas expanded

liquids.42 Another benefit of modeling density effects through an equation of state alongside

viscosity is that other properties can also be determined: isothermal compressibility, isobaric

thermal expansion coefficient, and internal pressure. These derived thermodynamic properties

can aid in providing a complete picture of the intermolecular forces affecting a fluid system.

These properties, such as compressibility, are also useful for determining the effectiveness of a

fluid as a lubricant, for which viscosity plays an important role.17,18 Modeling of density data by

the Sanchez-Lacombe equation of state and the calculation of derived thermodynamic properties

has been a major component of the present research and is described in greater detail in Chapter

III.

19

I.2.2.H Limitations

The empirical or semi-empirical nature of the models employed in the literature requires

experimental viscosity data to be used for any fitting parameters to be determined. There have

been cases where it has been possible to use data from an analogous species as a starting point

for the determination of model parameters where high pressure data of the material in question

are not available.42 This is especially relevant for situations where there are several similar

species in a series, such as alkanes or ionic liquids with the same anion and a cation that varies

by alkyl chain length. It is difficult to effectively model viscous effects for dense fluids as a

function of temperature without experimental data. Additionally, most of these models do not

take into account shear effects. For non-Newtonion fluids, either zero shear viscosity needs to be

determined, or some modification must be done to account for the shear rate. Due to the above

reasons, there is currently no effective way to replace experimental data. Many of the models

require coupling with an equation of state to model density. This adds an additional requirement

to either generate, or have available in the literature, accurate density data at high pressures.

Finally, many of these models require assumptions to be made that may not hold true, such as

that each molecule can be treated as a hard sphere, which reduce the physical significance of the

models.

I.2.3 Oils, Lubricants, and Fuels

Crude oil and oil derivatives are used in a variety of applications that require exposure to

high pressure conditions. While studies have been performed on model systems, the entire story

is more complex, with crude oils and their derivative fuels and mineral oils being composed of a

multitude of components.14,18 Even synthetic derivatives are blends of different components,

such as poly(α-olefins) of varying lengths.17,18 Specific applications where high pressure

viscosity data for these mixtures of hydrocarbons are needed include lubricant development,

engine design to incorporate specific fuel mixtures (such as diesel and natural gas), and CO2

assisted oil recovery. Two review articles on fluid properties under high pressure conditions of

hydrocarbons have been published at the end of 2017: on pure hydrocarbons and their viscosity

models by Baled et al.,10 and more generally (including experimentation) by Mallepally et al.4

20

I.2.3.A Lubricants

There is a need in the automotive industry to increase fuel efficiency. One suggested

approach to solve this issue is to improve the effectiveness of the lubricants used: both engine

oils and automatic transmission fluids.91 By using lower viscosity oils in the formulation of

these lubricants, fuel efficiency can be increased.17,92,93 Under standard operating conditions,

these oils are exposed to high pressures (in the GPa range) and shear rates (up to 105 s-1).17,94,95

While it is known that using low viscosity lubricants improves fuel efficiency,

elastohydrodynamic lubrication effects occur at these extreme conditions. There is a need in

understanding the effect of pressure on viscosity, along with other parameters, such as isothermal

compressibility.17,18 Each engine oil is composed of a base oil (the majority component) and 10

or more additives.18 Base oils are fit into a series of categories, with Group I-III oils all being

mineral oils, with each category dependent on composition and viscosity index (a measure of the

temperature dependence of viscosity). Group IV oils are synthetic oils. Group V oils do not fit

into the other four groups based on hydrocarbons.18 These classifications are laid out in Table

I.1. Additives include viscosity index modifiers, detergents, dispersants, friction modifiers, and

anti-wear modifiers.96-98

Table I.1. Base oil categories as laid out by the American Petroleum Institute guidelines.18

Sulfur Content Saturates Viscosity Index Additional Information

Group I > 0.03% < 90% 80-120 Group II < 0.03% > 90% 80-120 Group III < 0.03% > 90% > 120 Group IV 0% 100% NA Synthetic oils composed of PAOs

Group V NA NA NA All oils that don't fit into Groups I-IV

Recent publications have studied the effect of pressure on viscosity using both

experimental and modeling techniques. Mixtures of polyalkylene glycol with CO2 were modeled

under high pressure conditions. By adding a compressible fluid, an adaptive lubricant is made

that can have its lubricant effectiveness easily modified by pressure in response to changing

pressure conditions.19 Another area of importance is examining the effect of additive, such as

graphene, for the formation of nanoliquids.21 Actual experimentation has also been run on

21

hydraulic oils and their constituents22 and the base oil stocks that make up the majority of a

lubricant.99

I.2.3.B Fuels

Recent work dealing with hydrocarbons for fuel purposes involves studying viscosity of

these mixtures at high pressures.1,23,25,100 A number of fuels either need to be stored at high

pressures, such as natural gas, or are exposed to high pressure situations during operation, such

as diesel. Mixtures simulating natural gas, both with and without CO2, were studied by a

vibrating wire viscometer.1,25 In addition to natural gas, there is a need for high pressure data for

rocket fuel. Using a capillary viscometer, viscosity for the fuel RP-1 was studied up to 60 MPa

and higher than standard temperatures of 744 K.23 In diesel engines, viscosity has a significant

effect on fuel atomization during fuel injection.20 With new fuel blends based around high

viscosity biodiesels gaining more notice, having actual data to design engines and injectors for

these new fuel types is necessary. Both model and experimental data have been generated to

help fill the blanks in the literature.20,100

I.2.3.C Oil Recovery

A final area involving the effect of pressure on the viscosity of hydrocarbon based fluids

is oil recovery. There is a need to modify the transport properties of crude oil that has yet to be

extracted from reservoirs, especially the reduction of viscosity.101 Supercritical CO2 has found

use in enhanced oil recovery.11,13,102 One way an understanding of these systems has been

accomplished is by studying CO2 solubility and its effect on viscosity for model hydrocarbons

such as squalene (C30H50).13 Understanding both solubility and viscosity at operating conditions

is necessary due to the challenges associated with enhanced oil recovery. Low density and

viscosity CO2 can displace the oil in an unfavorable way, causing oil recovery to decrease,

instead of increasing as desired. By adding viscosity thickeners, this effect can be mitigated.102

One potential side effect to operating oil wells at higher pressures involves the phase behavior

with water contamination in the oil. As pressure increases, water miscibility in the oil increases,

further complicating the determination of the viscous behavior of the recovered product.12 There

22

are attempts in the literature to model oil/solvent mixtures using a cubic model103 and free

volume theory.14

I.2.4 Ionic Liquids

Ionic liquids (ILs) are a class of salts with melting points below 100oC.104 These molten

salts owe their low melting points due to their composition, a bulky, often asymmetrical organic

cation matched with an anion that is often also organic, which prevents packing. Known for

their negligible vapor pressure and interesting solvent capabilities, there has been interest in the

literature in using ILs as replacements for volatile organic compounds.104-106 The choice of

cation, anion, and any functional groups associated with the cation is critical in determining the

physical properties of the salt used.107,108 It has been estimated that there are potentially 1012

possible combinations of ions that would form an ionic liquid.104 Due to this, these materials are

often considered to be designer solvents.107,108 Additionally, cosolvents can be used to modify

solvent capabilities and add compressibility to the fluid, allowing for pressure to be used as a

tuning parameter.109 Due to their unique properties, these fluids have been investigated for use

in polymer processing and synthesis,110-114 CO2 or SO2 capture,28,34,35 battery electrolytes,115 and

biomass processing.116-118

There has been much work in the literature to characterize ionic liquids and determine

their physical properties, including viscosity. Many of these molten salts have much higher

viscosities than the volatile organic solvents they are meant to replace, making it crucial to

understand how ionic liquid structure affects viscosity when designing one for a particular

process. In spite of the large number of publications on viscosity, very few record viscosity data

at high pressure conditions. This is especially surprising due to the interest in using ionic liquids

under high pressure conditions for CO2 capture. A few examples of ionic liquids with high

pressure viscosity data are available in the literature. Harris et al.30 used a falling body

viscometer to study triethylpentylphosphonium bis(trifluoromethanesulfonyl)imide (273-363 K,

up to 243 MPa). Gacino et al.33 used a falling body viscometer to study 1-ethyl-3-

methylimidazolium ethylsulfate and two pyrrolidinium based salts with the anion

bis(trifluoromethanesulfonyl)imide (313-363 K, up to 150 MPa). Ahosseini and Scurto29 used an

oscillating piston viscometer to study imidazolium based ionic liquids with the anions

23

bis(trifluoromethanesulfonyl)imide, tetrafluoroborate, and hexafluorophosphate (298-343 K, up

to 126 MPa). There are some examples of viscosity data for mixtures of ionic liquids with CO2

as well: imidazoliums with the hexaflurophosphate34 and bis(trifluoromethanesulfonyl)imide35

anions. To help remedy this lack of experimental data, there has been an emphasis on the

effective modeling of pressure and temperature effects on the viscosity of ionic liquids. There

are a number of examples of the utilization of density scaling methods available in the

literature.37-40 Additionally, free volume theory paired with ePC-SAFT (electrolyte PC-SAFT)

was used to model a wide range of ionic liquids by Sun et al.41 By examining broad trends

affiliated with ionic liquids, especially those with similar structures, it was shown that it is

possible to improve the predictive properties of some of these model fits without a full set of

high pressure data. Anion effects appear to be dominant in determining the viscosity of an ionic

liquid.41 Also, with the same anion and same cation type, viscosity changes with the addition or

adjustment of functional groups on the cation. An example of this is that viscosity increases with

alkyl chain length.41 With the same anion, minor variations in the cation, such as alkyl chain

length, can be modeled using free volume theory using high pressure data from just a small

sample size of ionic liquids.41

I.2.5 Gas Expanded Liquids

A class of mixtures referred to as gas expanded liquids have been gaining popularity in

the literature. By combining a liquid with a compressible gas, such as CO2, the volume can be

increased with pressure as increasing amounts of CO2 are dissolved in the liquid. The resulting

mixture properties then become adjustable with pressure. Some examples of gas expanded

liquids utilizing CO2 as the compressible fluid portion in the literature include alkanes

(methane,48 n-hexane, n-decane, and n-tetradecane42), alkyl acetates,47 ethanol,44 acetone,43 and

acetonitrile.45,46 These mixtures have properties between pure liquids and supercritical fluids.42-

48 Common experimental techniques for measuring the viscosity in these systems include falling

body43,44 and oscillating piston viscometers.42 Due to the wide range of possible combinations of

liquids to compressible gases, combined with the fact that these are binary mixtures compared to

other complex fluids such as mineral oils or diesel fuels, a number of molecular dynamics

simulations have been run to provide estimations of the viscosities of these mixtures.47,48

24

I.2.6 Polymers

Polymer processing requires knowledge of transport properties and flow behavior at high

shear rates and potentially high pressures. Polymeric materials are highly viscous due to their

high molecular weights and entanglement effects.55 The viscosity of polymers is affected by

more than the standard intermolecular interactions as the long chain nature of these

macromolecules allow for the mers that make up the polymer to interact with each other on the

same chain. This leads to elastic effects and non-Newtonian behavior.55 Modeling in terms of

free volume is especially important for polymeric systems as an increase in molecular spacing

leads to an increase in chain mobility (decrease in viscosity). Increasing free volume, thereby

decreasing viscosity and increasing processability, in polymer melts can be accomplished by

decreasing pressure, increasing temperature, or adding a plasticizer.56,87 To reduce the

temperature requirements needed to examine polymer melts, many studies have employed model

systems. Polydimethylsiloxane in particular is commonly used to model melt conditions and

validate viscometers due to its ability to exist as a melt at room temperature conditions.61

In addition to techniques utilized for low molecular weight systems, such as oscillating

quartz and rotational viscometers, capillary die rheometers are used in the literature for

examining polymer melts.53,55,59,61,64,67 Polymer viscosity data is needed at operating conditions,

especially at high shear rates, making it advantageous to incorporate the measurement device

directly into an extruder or injection molder.53

I.2.6.A Plasticizers

While increasing temperature is one method to decrease viscosity in polymer melts, this

is not an effective solution for every situation. The temperature requirements to reduce the

viscosity of many biocompatible polymers (such as poly(lactic acid)) to processable levels is

high enough to lead to degradation of the polymer, or any drug molecules that may be

impregnated into the polymer.55-65 For situations where viscosity needs to be decreased without

increasing temperature, plasticizers can be used. Due to its cost, nontoxicity, solubility in

polymer, and ease of removal, supercritical CO2 has been considered as a potential plasticizer in

the literature.55-65 One potential downside of using CO2 is the time of uptake. Adding an

25

additional plasticizer can help overcome this difficulty. In the case of poly(lactic acid), adding

poly(ethylene glycol) can further reduce viscosity and increase the rate at which CO2 is sorbed

into the polymer melt.65

I.2.6.B Foams

Polymers are extensively used in the production of foams.57,66 In certain industries, such

as the production of automobiles, there is a need for lightweight parts that still meet standards for

strength.57 These components are often injected molded. For these systems, it is necessary to

maintain the pressure during extrusion to keep the blowing agent in solution until the actual

injection. This adds an extra layer of complexity in accurately determining the viscosity of the

polymer solution. The inclusion of a counter pressure chamber to maintain high pressure

conditions at the end of the capillary can help keep the foaming agent in solution during

measurement.57

I.2.7 Geological Effects

One particular field that benefits from high pressure and temperature instrumentation is

geology. Due to the need to study highly viscous melts at temperatures above 1000oC and

pressures in the range of GPas, the instrumentation involved pushes the limits of what high

pressure viscometers found in the literature are capable of. Understanding viscosity at these

extreme conditions allows for the development of a better understanding of phenomena below

the Earth’s crust, where direct observation is impossible.8,9 Two recent studies show the current

capabilities of experimentation in this field. Stagno et al.8 measured viscosities of sodium

carbonate melts at temperatures as high at 1700oC and pressure up to 4.6 GPa. Viscosities for

sodium carbonate at these conditions went as high as 0.0073 Pa s. Additionally, Persikov et al.9

determined viscosities for haplokimberlitic and basaltic melts at temperatures up to 1950oC and

7.5 GPa. Viscosities were in a range up to 1.5 Pa s. Both studies employed falling body

techniques to determine viscosity.

26

I.3 A Brief Rationale for the Present Study

Over the past two decades, there has been a significant increase in the literature on high

pressure viscosity determination and modelling. There is, however, much room for further

growth. Modeling endeavors have grown with increasing need to generate data when

experiments cannot be run. That being said, due to the nature of the available models and their

limitations, experimental data cannot be replaced. However, experimental apparatuses are also

limited in some fashion. While this is not likely to change due to the nature of high pressure

instrumentation, these limitations can be mitigated somewhat by understanding the appropriate

use cases of the fluids being measured and the design of new instrumentation. There is a need

for improved instruments capable of shear rate control and determination during the

measurement process. Rotational viscometers are capable of providing this shear rate control,

but at the cost of pressure limitations. The development of rotational viscometers that can reach

higher pressures than most commercial instruments, incorporates the ability to measure density,

and allows for the observation of phase behavior would be very useful and has been a primary

focus in this thesis. Since most semi-empirical descriptions of viscosity (free volume theory,

friction theory, and density scaling) involve density, having methods of generating PVT data in

the same study, preferably simultaneously with the viscosity determinations, is important.

Without this capability, studies are either limited in their description of the system being

measured, or are limited to systems with well defined PVT data and models.

Two particular fields that could greatly benefit from further expansion of available high

pressure viscosity data are those of automotive lubricants and ionic liquids. Lubricant oils are

complex mixtures, leading to difficulties in accurately modeling these fluids without detailed

experimental data. Additionally, these lubricants include additives, including polymeric

modifiers, whose effects on the system as a whole need to be characterized. By determining both

viscosity and density as a function of temperature and pressure, a holistic understanding of the

flow behavior, film formation, and thermodynamics can be produced. In the case of ionic

liquids, high pressure viscosity and density measurements allows for the simultaneous

determination of the transport behavior and solvent capabilities through PVT data. This

information is needed if ionic liquids are to be successfully used as replacements for traditional

solvents in any sort of chemical engineering applications.

27

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35

II. Experiments

II.1 Variable-Volume View-Cell

A variable-volume view-cell was used to generate density data across a range of

temperatures and pressures. The details of this instrument have been previously published.1-5

However, for completeness, a description of the instrument and how it was used in the present

thesis is provided below. Figures II.1 and II.2 are diagrams of the apparatus. The instrument

uses a pair of sapphire windows to allow for visual or optical observation of the phase behavior.

Real time measurements of phase behavior are possible by utilizing an optical sensor in

conjunction with a light source. By passing light through the sample and measuring the

transmittance, the temperature and pressure at which phase separation or miscibility occurs can

be determined. The variable-volume portion allows for the control and measurement of volume

in the cell. With knowledge of the volume and mass loaded, density is determined.

The variable-volume portion consists of a piston with a back-pressure fluid, ethanol,

controlling the piston movement. Pressure in the back-pressure line is controlled by a motorized

pressure generator, allowing for steady pressure scans (typical runs are performed at a pressure

scan rate of 0.5 MPa/s) at a constant temperature. Piston position, and with it, volume in the cell,

is measured using a linear variable differential transformer (LVDT), manufactured by TE

Connectivity (model HR2000). This LVDT monitors the position of a magnetic core attached to

the piston. This system allows for the determination of volume in the cell to within ± 0.1 cm3

across a range of 11 to 23 cm3. Temperature in the cell is measured by a J-type thermocouple (±

1.1 K) while pressure is measured by a Dynisco diaphragm pressure transducer (model

#TPT432A-10M-6/18, up to 70 MPa, ± 0.07 MPa). Density is determined to within ± 1%.

Heating of the cell is achieved by four electric cartridge heaters (75 W heaters from ProTherm

Industries, model #TD25030AA) controlled by an Omega Engineering CN76000 temperature

controller. Figure II.3 shows the inner dimensions of the variable-volume view-cell. Mixing in

the cell is achieved with a magnetic stir bar.

In a typical experiment, the cell is loaded with 12-15 g of sample. For mixtures, each

constituent is loaded separately until the desired composition is reached. Components with low

volatility at ambient conditions (such as solids or liquids with high boiling points) are loaded into

36

the apparatus with a syringe before the cell is closed. Once the cell is closed, vacuum is pulled

on the internal volume to eliminate the effects of air on the density measurements. Volatile

components are pumped into the closed cell from a secondary container. The mass of all

constituents loaded is measured by a Mettler PM6100 balance (± 0.005 g). Once the variable-

volume view-cell is loaded, isothermal pressure scans are performed at temperatures of 298, 323,

348, 373, and 398 K across a range of 10-40 MPa.

Figure II.4 shows a typical run in the variable-volume view-cell, performed for ethanol at

298 K. The voltage of the LVDT and pressure are recorded with time. The LVDT reading is

directly related to piston position, and with it volume. With the mass loaded into the instrument

known, density is determined. Once density has been calculated across the isotherm, it can be

related to pressure. In the present thesis, this process was repeated for four more isotherms up to

398 K.

The variable-volume view-cell was validated with a series of additional ethanol runs.

The density of ethanol at the conditions evaluated has been also reported in the literature.6-10

Figure II.5 shows a comparison of an ethanol validation run compared to select points from the

literature.6 The experimental density of ethanol fell within ± 1% of the literature values, with the

average deviation determined to be 0.50 %. Further information on the validation of the

variable-volume view-cell can be found in Appendix B.

Figure II.1. External diagram of the variable-volume view-cell.

Thermocouple

Pressure Transducer

PGN

LVDT

Sapphire Window

37

Figure II.2. Internal diagram of the variable-volume view-cell.

Figure II.3. Dimensions of the variable-volume view-cell.

30.6 mm

12.9 mm 36.9 mm

15.7 mm

92.6 mm

Thermocouple

Pressure Transducer

PGN

LVDT

Magnetic Core Piston

Stir Bar

Magnetic

Stir Plate

38

Figure II.4. Evaluation of a sample run of ethanol in the variable-volume view-cell at a fixed

temperature of 298 K. Pressure (top left) and LVDT readings (top right) are collected

simultaneously during the run. LVDT reading relates to piston position, and with it, volume and

density (bottom left). Once density is determined, it can be related to pressure along the

isotherm (bottom right).

0

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100

Pre

ssu

re (

MP

a)

Time (s)

Ethanol

298 K

0.2

0.21

0.22

0.23

0.24

0.25

0.26

0.27

0.28

0 20 40 60 80 100

LV

DT

Rea

din

g (

V)

Time (s)

Ethanol

298 K

0.76

0.77

0.78

0.79

0.8

0.81

0.82

0.83

0 20 40 60 80 100

Den

sity

(g/c

m3)

Time (s)

Ethanol

298 K

0.76

0.77

0.78

0.79

0.8

0.81

0.82

0.83

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

Ethanol

298 K

39

Figure II.5. Comparison of experimental (circles) data for a validation run to literature values

(diamonds). Literature values used were from Abdulagatov et al.6

II.2 High Pressure Rotational Viscometer

A high pressure rotational viscometer was developed in the present thesis to examine

viscosity as a function of temperature, pressure, and shear rate. A detailed description of this

instrument and how it was used in the present thesis is provided below. The system has been

described in our recent publication.5 The operation of rotational viscometers is dependent on the

geometry of the instrument. Examples of potential inner geometries of rotational viscometers

include coaxial cylinders, cone and plate, and parallel plate.11-13 This particular instrument is

based on the coaxial cylinder geometry, with the viscosity determined by the flow of fluid

between two concentric cylinders. Depending on design, either the inner (Searle) or outer

(Couette) cylinder can act as the rotating element.11-14 For this instrument, a Searle type design

was used, with the inner rotating shaft driven by a motor combined with a torque transducer.

The outer cylinder is built into the main body of the high pressure cell as a cylindrical cavity.

Figures II.6 and II.7 show the layout of this instrument. To avoid having to seal across

moving parts, the inner shaft is magnetically coupled to the torque transducer/motor. A

Thermofisher Haake Viscotester 550 (± 0.00015 N m) has been modified to serve as both the

torque transducer and motor. While this arrangement allows for the operation of the viscometer

0.65

0.67

0.69

0.71

0.73

0.75

0.77

0.79

0.81

0.83

0.85

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

Ethanol

298 K

323 K

348 K

373 K

398 K

40

at high pressures, the use of magnetic coupling adds a number of complications in the

determination of viscosity. Rotating a magnetic field over the steel portions of the high pressure

cell induces eddy currents in the system. This in turn creates a magnetic field that is picked up

by the torque transducer. The effect of this magnetic term needs to be taken into account in

calibrating the instrument. There is also a limit in the viscosity that can be reached before the

magnets decouple. In the present system, if the torque required to maintain a constant rotational

speed is too high, above 0.02 N m, the inner rotating shaft ceases to move. In addition to the

magnetic effects, the unusual geometry of the high pressure cell further modifies the

interpretation of the final results. Figure II.8 shows the measurements and proportions of the

instrument. The cylindrical cavity in the main body is not fully cylindrical for its full length due

to the presence of the sapphire windows and variable volume portions of the cell. However,

these irregular portions are small compared to the portions that are indeed cylindrical, with the

overall length being 136.9 mm and the length of the irregular portions being 41 mm, making the

interactive length 95.9 mm.

In addition to serving as a viscometer, this instrument is also a variable-volume view-cell.

Two pairs of sapphire windows allow for visual observations of the phase behavior inside the

viscometer. Additionally, there are two variable-volume portions, with movable pistons that

allows for the control of the volume and pressure in the cell. LVDTs (TE Connectivity XS-A

1003) are used to measure the position of both pistons. Here also, ethanol was used as the back-

pressure fluid. A 60,000 psi pressure generator from High Pressure Equipment Company was

used to control the pressure of the back pressure line. Using two pistons insures that the internal

volume range of the cell is wide enough to allow for the instrument to be usable in performing

measurements on compressible fluids. Additionally, the arrangement of the two pistons, one on

either side, allows for viscous multicomponent fluids to be forced back and forth across the

rotating shaft, ensuring proper mixing. Temperature and pressure are measured by a J-type

thermocouple (± 1.1 K) and an Omega PX91N0-60KSV pressure transducer (full range of 400

MPa, ± 0.4 MPa). Heating for the instrument was performed by four electric heating cartridges

(150 W heaters from ProTherm Industries, model #TD25060AA) controlled by an Omega

Engineering CN78000 temperature controller.

41

Figure II.6. External diagram of the high pressure rotational viscometer.

Figure II.7. Internal diagram of the high pressure rotational viscometer.

Torque

Transducer/Motor

LVDT

PGN PGN

LVDT

Sapphire

Windows

Pressure

Transducer

J Thermocouple

LVDT

Coupling

Magnets

Hole

LVDT

Piston

Magnetic Core

Thermocouple

Sapphire

bearings

42

Figure II.8. Internal geometries of the high pressure rotational viscometer.

To calculate viscosity, shear stress and shear rate are needed, which are calculated from

torque and rotational speed according to the following relationships:14

𝜏 =𝑀𝑇

2𝜋𝑟𝑖2𝐻

II.1

=2𝑟𝑜

2

(𝑟𝑜2−𝑟𝑖

2)Ω II.2

where τ is the shear stress, is the shear rate, ri is the inner radius, ro is the outer radius, H is

height, MT is measured torque, and Ω is rotational speed. Viscosity is then calculated from the

shear stress and shear rate:11-12

𝜂 =𝜏

II.3

However, due to the effects of the friction, magnetic fields and the inner geometry, equation II.3

cannot be simply used in conjunction with equations II.1 and II.2. During operation, the inner

rotating shaft sits in between two sapphire bearings, one at each end, to keep the shaft centered.

The friction addition from these physical contact points change depending on the fluid in the cell,

54.0 mm

20.5 mm 152.4 mm

23.8 mm

18.9 mm

23.6 mm

18.7 mm

136.9 mm

14.1 mm 16.7 mm

43

due to lubrication effects. For each fluid and temperature, a correction factor needs to be

determined. Additionally, the magnetic eddy currents and nonuniform geometry requires the use

of an empirical fit determined through calibration with fluids of known viscosity. For a

Newtonian fluid, viscosity is calculated from rotational speed and measured torque using

equation:

𝜂 = 𝐴 (𝐶𝑇

Ω) − 𝐵 II.4

where η is viscosity, CT is the corrected torque, Ω is rotational speed, and A and B are constants.

Constants A and B were determined with silicone and mineral oil standards from the Cannon

Instrument Company shown in Table II.1.

For each calibration standard, ambient pressure runs were performed at temperatures at

which the standards had been characterized by the manufacturer (298 K, 323 K, 353 K, and 373

K for two oils, 273 K and 313 K for the rest). All of these standards were Newtonian in nature.

The viscosity and density at each temperature at which a calibration run was performed can be

found in Table II.1. At each rotational speed, from 100-800 rpm, torque was measured for one

minute. The average torque at each rotational speed was plotted versus rotational speed to

determine the y-intercept. Figure II.9 shows this process for a mineral oil based calibration

standard N14 at 298 K and ambient pressure. The calculated y-intercept for each temperature

and each standard was used as the correction factor to compensate for friction and lubrication

effects pertaining to mechanical contact of the rotating shaft with the sapphire bearings. The

correction factor was subtracted from the measured torque values to determine the corrected

torque. Figure II.10 shows this correction process at 500 rpm and the corrected torque for all

rotational values for calibration standard N14 at 298 K and ambient pressure. Finally, the known

viscosity can be compared to average corrected torque/rotational speed (ACT/Ω). The constants

for equation II.4 were determined by through a linear fit of viscosity versus ACT/Ω for all

calibration standards. Figure II.11 shows the comparison of viscosity and ACT/Ω for standard

N14 at all measured temperatures (298 K, 323 K, 353 K, and 373 K), ambient pressure, and all

rotational speeds. Figure II.12 shows the final calibration curve using all calibration standards in

Table II.1. Plots of the measured torque and torque corrections for each calibration standard at

each temperature can be found in Appendix B.

44

Comparing data collected at ambient pressures to oil standards, the uncertainty was found

to be ± 5% for runs at 300 rpm or above at viscosities above 3 cP. Figure II.13 shows an

example of a validation run using silicone oil S60 from Canon Instrument Company at ambient

pressure at rotational speeds of 300-800 rpm. This was a separate run from those performed for

the calibration of the instrument. With the calibration and validation completed at ambient

pressures, a similar procedure can be used to determine the viscosity of fluids at high pressure

conditions. For each individual experiment at each temperature, a correction run is completed.

Once the temperature in the viscometer has come to a stable equilibrium, a run at each rotational

speed up to 800 rpm, or when the rotating shaft decoupled, was completed at ambient pressure.

As with the calibration runs, average torque for each one minute run was plotted versus

rotational speed. The y-intercept of the resulting linear fit is subtracted from the measured

torque to calculate the corrected torque for each run at that temperature for the loaded fluid.

Once the correction run is completed, pressure scans at each rotational speed can be done across

the isotherm. The full process for converting measured torque to viscosity for an experimental

run is shown in Figure II.14 for an oil (a base oil composed of poly(alpha olefins)) at 298 K and

500 rpm.

Once calibrations are done, typical viscosity measurements were performed at constant

temperatures of 298, 323, 348, and 373 K across a pressure range of 10-40 MPa. The pressure

scan rate was typically 0.3 MPa/s. Runs were performed at rotational speeds ranging from 300-

800 rpm. Unlike the variable-volume view-cell, the high pressure viscometer is not operational

at 398 K, with 373 K being the maximum operating temperature. Additionally, at low rotational

speeds, below 300 rpm, there was an instability leading to high scatter of the data (± 3 mPa s).

This limitation was ignored for certain runs at high viscosities (above 80 mPa s) where

decoupling of the magnets occurred at 300 rpm and above. For typical experiments, shear rates

were estimated to range from 480 to 1270 s-1.

45

Table II.1. Cannon Instrument Company calibration standards used to calibrate the high

pressure rotational viscometer. Viscosity and density values are specific to the actual sample

used, with values provided by the manufacturer.

Standard T (K) η (mPa s) ρ (g/cm3) Oil Type

N14 298 21.68 0.8103 Mineral

323 8.909 0.7944

353 4.127 0.7752

373 2.774 0.7624

S60 298 102.0 0.8619 Silicone

323 29.03 0.8468

353 10.16 0.8282

373 6.052 0.8158

RT50 298 46.65 0.9592 Silicone

313 35.05 0.9459

RT100 298 90.33 0.9625 Silicone

313 67.91 0.9491

46

Figure II.9. Torque versus time (left) and average torque versus rotational speed (right) for

Cannon Instrument Company calibration standard N14 at 298 K and ambient pressure.

Figure II.10. Torque versus time for Cannon Instrument Company calibration standard N14 at

298 K and ambient pressure. The friction correction for the 500 rpm run is shown on the left

while the corrected torque for all rotational speeds is shown on the right.

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80

Torq

ue

(N m

)

Times (s)

N14

298 K

0.1 MPa

100 rpm

200 rpm

300 rpm

400 rpm

500 rpm

600 rpm

700 rpm

800 rpm

0

0.005

0.01

0.015

0.02

0.025

0.03

0 200 400 600 800 1000

Aver

age

Torq

ue

(N m

)

Rotational Speed (rpm)

N14

298 K

0.1 MPa

AT = 2.1391E-05Ω + 0.0022050

R2 = 0.9999

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80

Torq

ue

(N m

)

Time (s)

N14

298 K

0.1 MPa

500 rpm

Measured Torque

Corrected Torque

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80

Corr

ecte

d T

orq

ue

(N m

)

Time (s)

N14

298 K

0.1 MPa

100 rpm

200 rpm

300 rpm

400 rpm

500 rpm

600 rpm

700 rpm

800 rpm

47

Figure II.11. Viscosity versus average corrected torque/rotational speed for Cannon Instrument

Company calibration standard N14 at 0.1 MPa.

Figure II.12. Viscosity versus average corrected torque/rotational speed for all calibration

standards in Table II.1. The final calibration curve used to determine the constants in equation

II.4 is represented by the dashed line.

0

5

10

15

20

25

0.00001 0.000015 0.00002 0.000025

Vis

cosi

ty (

mP

a s

)

ACT/Ω (N m min)

N14

0.1 MPa

298 K

323 K

353 K

373 K

0

20

40

60

80

100

120

0 0.00002 0.00004 0.00006

Vis

cosi

ty (

mP

a s

)

ACT/Ω (N m min)

η = 2.6600E6ACT/Ω - 31.497

R2 = 0.997

48

Figure II.13. Viscosity versus time for a validation run at ambient pressure for a silicone oil

(Canon Instruments S60). Blue circles represent collected data and orange lines are the actual

values as specified by the manufacturer.

0

20

40

60

80

100

120

140

0 20 40 60 80

Vis

cosi

ty (

mP

a s

)

Time (s)

Silicone Oil S60

300-800 rpm

298 K

(300 rpm)

323 K

348 K373 K

49

Figure II.14. Evaluation of a sample run in the high pressure rotational viscometer, involving a

base oil composed of poly(alpha olefins) at 298 K and 500 rpm. Torque values are compared to

rotational speeds at low pressures to generate a correction plot (top left). This base line is then

subtracted from the torque values from a run (top right). Corrected torque is then converted to

viscosity (bottom).

y = 2E-05x + 0.0004R² = 0.9998

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 200 400 600 800

Torq

ue

(N m

)

Rotational Speed (rpm)

PAO 4

298 K

0.012

0.013

0.014

0.015

0.016

0.017

0.018

0 10 20 30 40 50

Torq

ue

(N m

)

Pressure (MPa)

PAO 4

298 K

500 rpm

Torque

Correction

Original

Corrected

30

35

40

45

50

55

60

65

70

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

PAO 4

298 K

500 rpm

50

II.3 References

1. H.E. Grandelli, E. Kiran, High pressure density, miscibility and compressibility of

poly(lactide-co-glycolide) solutions in acetone and acetone + CO2 binary fluid mixtures,

Journal of Supercritical Fluids, 75 (2013) 159-171.

2. J.M. Milanesio, J.C. Hassler, E. Kiran, Volumetric Properties of Propane, n-Octane, and

Their Binary Mixtures at High Pressures, Ind. Eng. Chem. Res., 52 (2013) 6592-6609.

3. H.E. Grandelli, J.S. Dickmann, M.T. Devlin, J.C. Hassler, E. Kiran, Volumetric

Properties and Internal Pressure of Poly(alpha-olefin) Base Oils, Industrial &

Engineering Chemistry Research, 52 (2013) 17725-17734.

4. J.S. Dickmann, J.C. Hassler, E. Kiran, Modeling of the volumetric properties and

estimation of the solubility parameters of ionic liquid plus ethanol mixtures with the

Sanchez-Lacombe and Simha-Somcynsky equations of state: [EMIM]Ac plus ethanol

and [EMIM]Cl plus ethanol mixtures, Journal of Supercritical Fluids, 98 (2015) 86-101.

5. J.S. Dickmann, J.C. Hassler, E. Kiran, High Pressure Volumetric Properties and

Viscosity of Base Oils Used in Automotive Lubricants and Their Modeling, Industrial &

Engineering Chemistry Research, 57 (2018) 17266-17275.

6. I.M. Abdulagatov, F.Sh. Aliyev, M.A. Talibov, J.T. Safarov, A.N. Shahverdiyev, E.P.

Hassel, High-pressure densities and derived volumetric properties (excess and partial

molar volumes, vapor-pressures) of binary methanol + ethanol mixtures, Thermochimica

Acta, 476 (2008) 51-62.

7. D. Pecar, V. Dolecek, Volumetric properties of ethanol-water mixtures under high

temperatures and pressures, Fluid Phase Equilibria, 230 (2005) 36-44.

8. Y. Takiguchi, M. Uematsu, Densities for liquid ethanol in the temperature range from

310 K to 480 K at pressures up to 200 MPa, J. Chem. Thermodynamics, 28 (1996) 7-16.

9. H. Pohler, E. Kiran, Volumetric Properties of Carbon Dioxide + Ethanol at High

Pressures, J. Chem. Eng. Data, 42 (1997) 384-388.

10. C.K. Zeberg-Mikkelsen, L. Lugo, J. Garcia, J. Fernandez, Volumetric properties under

pressure for the binary system ethanol + toluene, Fluid Phase Equilibria, 235 (2005) 139-

151.

11. W.H. Deen, Analysis of Transport Phenomena, second ed., Oxford University Press, New

York, 2011.

12. R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, second ed., John Wiley

& Sons, New York, 2002.

13. S. Bair, High Pressure Rheology for Quantitative Elastohydrodynamics, first ed.,

Elsevier, New York, 2007.

14. A. Blanco, C. Negro, E. Fuente, J. Tijero, Rotor selection for a Searle-type device to

study the rheology of paper pulp suspensions, Chemical Engineering and Processing, 46

(2007) 37-44.

51

III. Analysis and Modeling

III.1 Volumetric properties and lattice fluid models

In addition to determination through experimental means, density at high pressure

conditions can be modelled. By utilizing a model to fit collected density data, it is possible to

generate a better understanding of both the temperature and pressure effects on density and

calculate derived thermodynamic properties. There are a number of methods used in the

literature to model PVT data, ranging from empirical fits1-4 to detailed equations of state.3-8

A common method used to fit experimental density data is the semi-empirical Tait

equation:9,10

𝜌0

𝜌= 1 −

1

1+𝐾0′ ln [1 +

𝑃

𝐾0(1 + 𝐾0

′)] III.1

where ρ is density, ρ0 is reference density, K0 is the bulk modulus, and K0’ is the pressure

derivative of the bulk modulus. Temperature dependence is added to the Tait equation through

the modulus and reference density terms:10

𝐾0 = 𝐾00exp(−𝛽𝐾𝑇) III.2

𝜌0 = 𝜌𝑅 (1 − 𝑎𝜌(𝑇 − 𝑇𝑅)) III.3

where K00, βK, and aρ are constants and ρR is the density at reference temperature TR. It is

assumed that K0’ is temperature independent. This model has been employed in the analysis of a

wide range of systems, including lubricants10,11 and ionic liquids.12,13 While the Tait equation is

commonly employed, it has its limitations.4 This semi-empirical equation is often modified for

the model to fit the data, adding extra required parameters, and its terms have limited physical

significance. Instead, in this thesis study we employed a lattice fluid model, the Sanchez-

Lacombe equation of state (S-L EOS). In the S-L EOS, the fluid is modeled as fitting into a

lattice, where each lattice site is occupied by either a molecule or polymer segment, or a vacant

site.14,15 Figure III.1 shows a two-dimensional representation of the model. The S-L EOS is

represented by the equation:14,15

52

2 + + (ln(1 − ) + (1 −1

𝑟) ) = 0 III.4

where , , and are reduced values of density, pressure, and temperature, while r represents

the number of lattice sites a molecule fills:

=𝜌

𝜌∗, =

𝑃

𝑃∗, =

𝑇

𝑇∗,𝑟 =

𝑀𝑊𝑃∗

𝑅𝑇∗𝜌∗ III.5

where ρ is density, P is pressure, T is temperature, MW is molecular weight, R is gas constant,

and ρ*, T*, and P* are the characteristic parameters of the S-L EOS. The equation can also be

put in terms of intermolecular effects represented by molecular segment interaction parameter

(ε*) and close-packed volume of each segment (ν*):

𝑇∗ =𝜀∗

𝑘 𝑃∗ =

𝜀∗

𝑣∗ III.6

where k is Boltzmann’s constant.14,15 From its earliest use, the S-L EOS has been employed in

literature to model both molecular solvents14 and polymers.15 This thesis includes some of the

first work on the application of the S-L EOS for the modeling of ionic liquids.16 In recent years,

the use of this model to describe ionic liquids has increased.13,17

53

Figure III.1. Two-dimensional representation of the lattice fluid model.

III.2 Modeling mixtures

Equations III.4 – 5 can simply be fit to data for a single component system. The S-L

EOS is not limited to single component systems, however. In order to model multicomponent

systems, mixing rules must be used.15 The S-L parameters for a multicomponent mixture can be

calculated based on concentration:

𝑃𝑚𝑖𝑥∗ = ∑ ∑ 𝜙𝑖𝜙𝑗𝑃𝑖𝑗

∗𝑗𝑖 III.7

where ϕi is the close pack volume fraction, calculated from mass fraction of the components (wj)

and characteristic density of each component (𝜌𝑗∗):

𝜙𝑖 =

𝑤𝑖𝜌𝑖∗

∑ (𝑤𝑗

𝜌𝑗∗)𝑗

III.8

The term 𝑃𝑖𝑗∗ is a cross parameter:

54

𝑃𝑖𝑗∗ = (1 − 𝑘𝑖𝑗) ∗ √𝑃𝑖

∗𝑃𝑗∗

III.9

where 𝑃𝑗∗ is the characteristic pressure for a component and kij is an empirical interaction

parameter. Once 𝑃𝑚𝑖𝑥∗ has been calculated, 𝑇𝑚𝑖𝑥

∗ can be calculated:

𝑇𝑚𝑖𝑥∗ = 𝑃𝑚𝑖𝑥

∗ ∑ 𝜙𝑖0

𝑖𝑇𝑖∗

𝑃𝑖∗

III.10

where 𝑇𝑖∗ is the characteristic temperature of a single component and 𝜙𝑖

0 is the average close

packed mer volume fraction:

𝜙𝑖0 =

𝜙𝑖𝑃𝑖∗

𝑇𝑖∗

∑ 𝜙𝑗

𝑃𝑗∗

𝑇𝑗∗𝑗

III.11

Once 𝑃𝑚𝑖𝑥∗ and 𝑇𝑚𝑖𝑥

∗ have been calculated, 𝜌𝑚𝑖𝑥∗ and rmix need to be determined in order to use

equations III.4 and 5 to model a mixture. A value for rmix can be calculated using the equation:

1

𝑟𝑚𝑖𝑥= ∑

𝜙𝑗

𝑟𝑗𝑗 III.12

In conjunction with an average molecular weight:

1

𝑀𝑊𝑚𝑖𝑥= ∑

𝑤𝑖

𝑀𝑊𝑖𝑖 III.13

the parameter 𝜌𝑚𝑖𝑥∗ can be calculated using equations III.12 in conjunction with the equation for r

in equation III.5 to derive:

1

𝜌𝑚𝑖𝑥∗ = ∑

𝑤𝑖

𝜌𝑖∗𝑖 III.14

55

Once the pure component values have been determined for the S-L EOS, equations III.7 – III.14

can be used to determine S-L characteristic parameters for a mixture at a fixed composition. By

utilizing mixing rules, density can be modeled in terms of composition, in addition to

temperature and pressure.15,18

IV.3 Derived thermodynamic properties

Once PVT data have been fit to a model equation, derived thermodynamic properties can

be determined. Isothermal compressibility and isobaric thermal expansion coefficient can be

determined from the partial derivatives of density with respect of pressure (compressibility) and

temperature (expansion):16,19

𝜅𝑇 = −1

𝑉(𝜕𝑉

𝜕𝑃)𝑇=

1

𝜌(𝜕𝜌

𝜕𝑃)𝑇

III.15

𝛽𝑃 =1

𝑉(𝜕𝑉

𝜕𝑇)𝑃= −

1

𝜌(𝜕𝜌

𝜕𝑇)𝑃

III.16

Using the S-L EOS in conjunction with these equations leads to:16

𝜅𝑇 =2

𝑃([1

−1+1

𝑟]−2)

III.17

𝛽𝑃 =1+2

𝑇([1

−1+1

𝑟]−2)

III.18

Once isothermal compressibility and thermal expansion coefficient have been calculated, internal

pressure can be calculated. Internal pressure is a measure of the overall attractive and repulsive

interactions in the system:1,20-23

𝜋 = (𝜕𝑈

𝜕𝑉)𝑇= 𝑇 (

𝜕𝑃

𝜕𝑇)𝑉− 𝑃 = 𝑇 (

𝛽𝑃

𝜅𝑇) − 𝑃 III.19

56

With an understanding of the intermolecular interactions, it is possible to estimate solvent

capabilities of a fluid or mixture. It has indeed been suggested in the literature that the

Hildebrand solubility parameter can be estimated using internal pressure.23,24 Used as an

estimate of the miscibility of two different species, the solubility parameter provides a method of

determining the effectiveness of a solvent for a particular process before experimentation has

been carried out. The solubility parameter is defined as the square root of the cohesive energy

density (CED) and traditionally requires knowledge on the heat of vaporization of a species:

𝜎 = 𝐶𝐸𝐷1 2⁄ = (𝑈

𝑉)1 2⁄

= (∆𝐻𝑣−𝑅𝑇

𝑉)1 2⁄

III.20

where U is internal energy, V is volume, ΔHv is heat of vaporization, R is gas constant, and T is

temperature.25 While heat of vaporization is readily measurable for volatile organic solvents,

this is not the case for many materials with low or negligible volatilities, such as polymers, ionic

liquids, or base oils. While internal pressure is not directly equivalent to cohesive energy

density, it can be used as a substitute for many substances:23,24

𝜎 ≅ √𝜋 III.21

Thus, by utilizing internal pressure, PVT data can be used to estimate the Hildebrand solubility

parameter of both pure components and mixtures as a function of temperature and pressure.

III.4 Viscosity and free volume

Viscosity can be modeled alongside density and the derived thermodynamic properties.

As previously discussed in Chapter I, one possible approach is to examine viscosity through the

lens of free volume, and with it, density. An early approach to relating viscosity to free volume

and density is the empirical Doolittle equation (Equation I.11).26,27 A later model by Allal et

al.,27,28 shown in equation I.12, provides a more detailed relationship of density and free volume

effects on viscosity. In this study, equation I.12 was further simplified. All experiments in this

study were carried out on dense liquids, both lubricants and ionic liquids. The term η0,

representing the gas viscosity at infinite dilution, is small compared to the overall viscosities of

57

these fluids. For the experiments carried out in the high pressure rotational viscometer described

in Chapter II, it was assumed that η >> η0, allowing for the equation to be simplified to three

parameters:

𝜂 =𝜌𝜄(𝛼𝜌+

𝑃𝑀𝑊

𝜌)

√3𝑅𝑇𝑀𝑊𝑒𝐵(

𝛼𝜌+𝑃𝑀𝑊𝜌

𝑅𝑇)

3 2⁄

III.22

where ι is the characteristic molecular length, α relates to intermolecular energy, and B

represents free volume effects. Once the parameters ι, α, and B, which are treated at constants,

have been calculated, viscosity can be calculated in conjunction with an EOS for determining

density, such as the S-L EOS (Equation III.4).29

IV.5 Statistical analysis of model fits

Python® programs were written to fit density data of both pure components and mixtures

to the S-L EOS (Equations III.4 and III.5) and viscosity data to equation III.22. For both density

and viscosity models, root mean squared deviation (RMSE), percent absolute deviation (%

AAD), and bias (ℬ) were evaluated:

𝑅𝑀𝑆𝐸 = √∑(𝑥𝑐,𝑖−𝑥𝑖)

2

𝑛

III.23

𝑑𝑖 = (1 −𝑥𝑐,𝑖

𝑥) ∗ 100% III.24

%𝐴𝐴𝐷 =1

𝑛∑|𝑑𝑖| III.25

ℬ =1

𝑛∑𝑑𝑖 III.26

Equations III.23 – 26 allow for the determination of the quality of fit these models provide to the

experimental data collected as described in Chapter II.

58

III.6 References

1. H.E. Grandelli, J.S. Dickmann, M.T. Devlin, J.C. Hassler, E. Kiran, Volumetric

Properties and Internal Pressure of Poly(alpha-olefin) Base Oils, Industrial &

Engineering Chemistry Research, 52 (2013) 17725-17734.

2. C.C. Sampson, X. Yang, J. Xu, M. Richter, Measurement and correlation of the (p, ρ, T)

behavior of liquid propylene glycol at temperatures from (272.7 to 393.0) K and

pressures up to 91.4 MPa, J. Chem. Thermodynamics, 131 (2019) 206-218.

3. I. Abala, F.E.M. Alaoui, Y. Chhiti, A.S. Eddine, N.M. Rujas, F. Aguilar, Experimental

density and PC-SAFT modeling of biofuel mixtures (DBE + 1-Heptanol) at temperatures

from (298.15 to 393.15) K and at pressures up to 140 MPa, J. Chem. Thermodynamics,

131 (2019) 269-285.

4. R. Mohammadkhani, A. Paknejad, H. Zarei, Thermodynamic Properties of Amines under

High Temperature and Pressure: Experimental Results Correlating with a New Modified

Tait-like Equation and PC-SAFT, Ind. Eng. Chem. Res., 57 (2018) 16978-16988.

5. J.A. Sarabando, P.J.M. Magano, A.G.M. Ferreira, J.B. Santos, P.J. Carvalho, S. Mattedi,

I.M.A. Fonseca, M. Santos, Influence of temperature and pressure of the density and

speed of sound of N-ethyl-2-hydroxyethylammonium propionate ionic liquid, J. Chem.

Thermodynamics, 131 (2019) 303-313.

6. M. Ebrahiminejadhasanabadi, W.M. Nelson, P. Naidoo, A.H. Mohammadi, D.

Ramjugernath, Experimental measurement of carbon dioxide solubility in 1-

methypyrrolidin-2-one (NMP) + 1-butyl-3-methyl-1H-imidazol-3-ium tetrafluoroborate

([bmim][BF4]) mixtures using a new static-synthetic cell, Fluid Phase Equilibria, 477

(2018) 62-77.

7. J. Hekayati, A. Roost, J. Javanmardi, Volumetric properties of supercritical carbon

dioxide from volume-translated and modified Peng-Robinson equations of state, Korean

J. Chem. Eng., 33(2016) 3231-3244.

8. M.R. Curras, M.M. Mato, P.B. Sanchez, J. Garcia, Experimental densities of 2,2,2-

trifluoroethanol with 1-butyl-3-methylimidazolium hexafluorophosphate at high

pressures and modelling with PC-SAFT, J. Chem. Thermodynamics, 113 (2017) 29-40.

9. J.H. Dymond, The Tait equation: 100 years on, International Journal of Thermophysics,

9 (1996) 941-951.

10. W. Habchi, S. Bair, Quantitative Compressibility Effects in Thermal Elastohydrodynamic

Circular Contacts, J. Tribology, 135 (2013) 011502-1 – 011502-10.

11. I. Krupka, P. Kumar, S. Bair, M.M. Khonsari, M. Hartl, The Effect of Load (Pressure) for

Quantitative EHL Film Thickness, Tribol. Lett., 37 (2010) 613-622.

12. Y. Hiraga, S. Hagiwara, Y. Sato, R.L. Smith, Measurement and Correlation of High-

Pressure Densities and Atmospheric Viscosities of Ionic Liquids: 1-Butyl-1-

methylpyrrolidinium Bis(trifluoromethylsulfonyl)imide), 1-Allyl-3-methylimidazolium

Bis(trifluoromethylsulfonyl)imide, 1-Ethyl-3-methylimidazolium Tetracyanoborate, and

1-Hexyl-3-methylimidazolium Tetracyanoborate, J. Chem. Eng. Data, 63 (2018) 972-

980.

13. Y. Hiraga, M. Goto, Y. Sato, R.L. Smith, Measurement of high pressure densities and

atmospheric pressure viscosities of alkyl phosphate anion ionic liquids and correlation

59

with the ε*-modified Sanchez-Lacombe equation of state, J. Chem. Thermodynamics,

104 (2017) 73-81.

14. I.C. Sanchez, R.H. Lacombe, An Elementary Molecular Theory of Classical Fluids. Pure

Fluids, J. Phys. Chem., 80 (1976) 2352–2362.

15. I.C. Sanchez, R.H. Lacombe, Statistical Thermodynamics of Polymer Solutions,

Macromolecules, 11 (1978) 1145-1156.

16. J.S. Dickmann, J.C. Hassler, E. Kiran, Modeling of the volumetric properties and

estimation of the solubility parameters of ionic liquid plus ethanol mixtures with the

Sanchez-Lacombe and Simha-Somcynsky equations of state: [EMIM]Ac plus ethanol

and [EMIM]Cl plus ethanol mixtures, Journal of Supercritical Fluids, 98 (2015) 86-101.

17. H. Machida, Y. Sato, R.L. Smith, Simple modification of the temperature dependence of

the Sanchez-Lacombe equation of state, Fluid Phase Equilibria, 297 (2010) 205-209.

18. Y. Hiraga, K. Koyama, Y. Sato, R.L. Smith, High pressure densities for mixed ionic

liquids having different functionalities: 1-butyl-3-methylimidazolium chloride and 1-

butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, J. Chem.

Thermodynamics, 108 (2017) 7-17.

19. K.G. Nayar, M.H. Sharqawy, L.D. Banchik, J.H. Lienhard V, Thermophysical properties

of seawater: A review and new correlations that include pressure dependence,

Desalination, 390 (2016) 1-24.

20. B.O. Ahrstrom, S. Lindqvist, E. Hoglund, K.G. Sundin, Modified split Hopkinson

pressure bar method for determination of the dilation –pressure relationship of lubricants

used in elastohydrodynamic lubrication, Proceedings of the Institution of Mechanical

Engineers Part J – Journal of Engineering Tribology, 216 (2002) 63-73.

21. A.Vadakkepatt, A. Martini, Confined fluid compressibility predicted using molecular

dynamic simulation, Tribology International, 44 (2011) 330-335.

22. S. Verdier, S.I. Anderson, Internal pressure and solubility parameter as a function of

pressure, Fluid Phase Equilibria, 231(2005) 125-137.

23. E. Zorebski, Internal pressure as a function of pressure, Molecular and Quantum

acoustics, 27 (2006) 327-336.

24. M.M. Alavianmehr, S.M. Hosseini, A.A. Mohsenipour, J. Moghadasi, Further property of

ionic liquids: Hildebrand solubility parameter from new molecular thermodynamic

model, Journal of Molecular Liquids, 218 (2016) 332-341.

25. S.H. Lee, S.B. Lee, The Hildebrand solubility parameters, cohesive energy densities and

internal energies of 1-alkyl-3-methylimidazolium-based room temperature ionic liquids,

Chem. Commun., (2005) 3469-3471.

26. A.K. Doolittle, Studies in Newtonian Flow. II. The Dependence of the Viscosity of

Liquids on Free-Space, J. Appl. Phys., 1951, 22, 1471-1475

27. A. Allal, C. Boned, A. Baylaucq, Free-Volume Viscosity Model for Fluids in the Dense

and Gaseous States, Phys. Rev. E, 2001, 64, 1-10

28. M. Yoshimura, C. Boned, A. Baylaucq, G. Galliero, H. Ushiki, Influence of the Chain

Length on the Dynamic Viscosity at High Pressure of Some Amines: Measurements and

Comparison Study of Some Models, J. Chem. Thermodyn., 2009, 41, 291-300.

29. J.S. Dickmann, J.C. Hassler, E. Kiran, High Pressure Volumetric Properties and

Viscosity of Base Oils Used in Automotive Lubricants and Their Modeling, Industrial &

Engineering Chemistry Research, 57 (2018) 17266-17275.

60

IV. Base Oils

IV.1 Introduction

In this chapter, we discuss the volumetric properties and viscosity of several mineral and

synthetic base oils used in the manufacturing of automotive lubricants. There is a growing need

in the automotive industry to increase fuel efficiency. One way this can be accomplished is by

the choice of the lubricant used as engine oils and automatic transmission fluids.1 A reduction in

viscosity of the lubricant used often leads to an improvement in the lubricant effectiveness and

fuel efficiency.2-4 These lubricants operate under conditions that expose them to very high

pressures, in the range of GPas, and shear rates, in the range of 105 s-1. It is thus important to

understand the effect of pressure and shear on the flow behavior of these fluids.2,5,6 As described

in Chapter I in section I.2.3, while much work has been done at ambient pressures, there is a

growing need to understand the effect of pressure on both viscosity and thermodynamic

properties.

These engine oils and transmission fluids are complex mixtures, primarily composed of a

base oil, which itself is generally made up of many hydrocarbon-based constituents. In addition

to the base oil, these automotive lubricants contain a number of additives, often ten or more.

These additives allow for the lubricants to be tailored to meet the requirements needed for

effective use by modifying physical properties, like the temperature dependence of viscosity,

controlling the formation of deposits on mechanical parts, and reducing wear. These additives

include viscosity index modifiers, detergents, dispersants, friction modifiers and anti-wear

additives.7-10 Given that they are the primary components in automotive lubricants,

understanding the properties of base oils is necessary for the development of a successful

lubricant. The system for classifying these base oils as laid out by the American Petroleum

Institute was presented in Chapter I in Table I.1.

One of the major defining traits of these oils is the viscosity index. Viscosity index is a

measure of the temperature dependence of viscosity as compared to known standards at 40oC and

100oC.11 As viscosity index increases, the effect of temperature on viscosity decreases. Group I-

III oils are mineral oils and are categorized by viscosity index. Group I oils are generally made

by a solvent extraction of crude oil. Group II oils are group I oils that have been hydrotreated to

61

remove sulfur containing and aromatic compounds, leading to an increase in viscosity index. By

further treating the mineral oil, both opening the rings of cycloalkanes through hydrocracking

and further increasing viscosity index, Group III oils are made.12 Group IV and V oils are not

defined by viscosity index. Instead, Group IV oils are all synthetic oils composed of poly(α-

olefins), while Group V oils are anything that does not fit into Groups I-IV.

IV.1.1 Objectives

To gain a greater understanding of these oils, density and viscosity measurements were

carried out as a function of temperature, pressure, and in the case of viscosity also as a function

of shear rate for six base oils including two Group II, two Group III, and two Group IV oils. The

data were collected over a pressure and temperature range of 10-40 MPa and 298-398 K

respectively for density measurements and a range of 10-40 MPa and 298-373 K for viscosity

measurements.

The objective was to use the data to develop and test a holistic model to describe both

density and viscosity, while also allowing for the evaluation of the thermodynamic properties, of

these base oils. Density data were fit to the Sanchez-Lacombe equation of state, and the

thermodynamic properties isothermal compressibility, isobaric thermal expansion coefficient,

and internal pressure were calculated as a function of temperature and pressure. Viscosity data

were modeled by the free volume theory in conjunction with the Sanchez-Lacombe models

developed to describe the volumetric behavior.

IV.2 Materials and Methods

The base oils that were explored were provided by Afton Chemical Corp. They were

used as received. Basic properties for all six oils can be found in Table IV.1. These include the

kinematic viscosity at 373 K, viscosity index, and average molecular weight. The kinematic

viscosities and viscosity indexes were indicated to be as specified by the manufacturers of these

oils using ASTM tests D445 and D2270 respectively.

Figures IV.1-3 show the compositions of all six oils, which were provided by Afton

Chemical Corp based on GC-MS analysis. The technique is described in the literature.13 All six

62

oils fall into the base oil categories as laid out by the American Petroleum Institute guidelines,

described in Table I.1. Oils IIA and IIB are Group II oils composed of approximately 30 wt%

paraffins, 60 wt% cycloalkanes, and the remainder aromatic compounds. Oils IIIA and IIIB are

Group III oils composed of approximately 50 wt% paraffins, 45 wt% cycloalkanes, with the

remainder aromatics. Oils PAO 4 and PAO 8 are both Group IV oils, which are synthetic oils

composed solely of poly(α-olefins).

Table IV.1. Characteristics of the base oils studied.14

Kinematic Viscosity at 373 K

(cSt)

Viscosity

Index

Average Molecular Weight (g/mol)

IIA 4.1 103 354

IIB 6.4 103-109 445

IIIA 3.1 112 333

IIIB 6.5 131 474

PAO 4 4.1 126 489

PAO 8 7.9 139 526

Figure IV.1. Composition of base oils IIA (left) and IIB (right).14

0

10

20

30

40

50

60

70

80

90

100

Mass

Per

cen

t

IIA

0

10

20

30

40

50

60

70

80

90

100

Mass

Per

cen

t

IIB

63

Figure IV.2. Composition of base oils IIIA (left) and IIIB (right).14

Figure IV.3. Composition of base oils PAO 4 (left) and PAO 8 (right).14

0

10

20

30

40

50

60

70

80

90

100M

ass

Per

cen

t

IIIA

0

10

20

30

40

50

60

70

80

90

100

Mass

Per

cen

t

IIIB

0

10

20

30

40

50

60

70

80

90

100

Mass

Per

cen

t

PAO 4

0

10

20

30

40

50

60

70

80

90

100

Mass

Per

cen

t

PAO 8

64

Figure IV.4. Examples of the primary poly(α-olefins) found in PAO 4 and PAO 8, a trimer (A)

and tetramer (B) of 1-decene.

IV.3 Results and Discussions

The findings that are presented in the following sections are also described in our recent

publication in the journal Industrial & Engineering Chemistry Research.14

IV.3.1 PVT Data and Modeling

Density data were collected experimentally (oils IIA, IIB, IIIA, and IIIB) in the present

study and in an earlier study also conducted in our lab (oils PAO 4 and PAO 8).2 Figure IV.5

shows an example of the full range of data collected for oil IIB. The experimental data was fit to

the Sanchez-Lacombe equation of state (S-L EOS) laid out in equations III.4 and III.5. Table

IV.2 includes the parameters for the S-L EOS along with the root mean square deviation

(RSME), percent absolute average deviation (% AAD), and bias (% ℬ) for all six oils. The %

AAD was found to range from 0.130 to 0.204 %. A visual comparison of the S-L model fits to

the experimental data for oil IIB is show in Figure IV.4. The experimental density data and S-L

model fits for the remaining five oils are included in Appendix C. Figure IV.6 compares the

densities and S-L fits of all six oils at both 323 and 373 K. The Group II oils (IIA and IIB) were

found to have higher densities than the other four oils, with oil IIB having the highest densities

across the full range of temperatures and pressures represented in this study. Oil III B has

A) B)

65

slightly higher densities than the remaining three oils, which all had similar values in the

measured range.

Table IV.2. Sanchez-Lacombe parameters of base oils

IIA IIB IIIA IIIB PAO 4 PAO 8

P* (MPa) 506.42 501.44 488.06 499.53 433.62 418.46

T* (K) 553.4 556.03 538.91 548.92 544.10 548.24

ρ* (g/cm3) 0.95617 0.96258 0.91726 0.91979 0.91160 0.90929

MW (g/mol) 354 445 333 474 489 526

RMSE (g/cm3) 0.00140 0.00176 0.00157 0.00156 0.00198 0.00198

% AAD 0.130 0.171 0.160 0.156 0.201 0.204

% ℬ -0.00000860 -0.104 -0.000579 0.0000785 -0.000177 0.000285

Figure IV.5. Density versus pressure for the base oil IIB at isotherms 298, 323, 348, 373, and

398 K. Sanchez-Lacombe EOS fits are represented by black dots.

0.79

0.81

0.83

0.85

0.87

0.89

0.91

0.93

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

IIB

298 K

323 K

348 K

373 K

398 K

66

Figure IV.6. Density versus pressure for six base oils at 323 K (left) and 373 K (right).

Sanchez-Lacombe EOS fits are represented by black dots.

IV.3.2 Derived Thermodynamic Properties

Once the density data were fit to the S-L equation of state, the derived thermodynamic

properties isothermal compressibility, isobaric thermal expansion coefficient, and internal

pressure were calculated using equations III.17-19. Figures IV.7 and IV.8 show the calculated

thermodynamic properties for oil IIB across the temperature and pressure range in which the

density measurements were made. The thermodynamic properties across the full range of

temperatures and pressures examined in this study for the remaining five oils can be found in

Appendix C. For all six oils, the same trends with regards to temperature and pressure were

seen. Isothermal compressibility was found to increase with temperature and decrease with

pressure. Isobaric thermal expansion coefficient was also seen to increase with temperature and

decrease with pressure. Internal pressure had inverse trends, decreasing with temperature and

increasing with pressure.

0.77

0.79

0.81

0.83

0.85

0.87

0.89

0.91

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

323 K

IIB IIA

IIIA

IIIB

PAO 4

PAO 8

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

373 K

IIBIIA

IIIA

IIIB

PAO 4

PAO 8

67

Figure IV.7. Isothermal compressibility versus pressure (left) and isobaric thermal expansion

coefficient versus temperature (right) for IIB as calculated from the S-L EOS.

Figure IV.8. Internal pressure versus pressure for IIB calculated from the S-L EOS.

A comparison of the isothermal compressibilities of all six oils displays identifiable

trends. Figure IV.9 compares the compressibilities for the six oils in this study at two selected

temperatures, 323 and 373 K. The Group IV oils (PAOs) were found to have the highest

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

IIB

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

IIB

300

320

340

360

380

400

420

440

460

480

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

IIB

68

compressibilities followed by the Group III oils, then the Group II oils. The order of the oils was

found to be PAO 8 ≈ PAO 4 > IIIA > IIIB > IIA > IIB, with the differences between IIIB, IIA,

and IIB being relatively low. A similar trend was reported in Guimarey et al.,15 with the poly(α-

olefin) based oil (Group IV) they studied being more compressible than the reference Group III

oil in the study.

The differences in isothermal compressibility across these oils can be attributed to

composition. Figure IV.10 shows a comparison of compressibility versus cyclic molecule

content in the base oil. Group II oils have the highest content of cycloalkanes, followed by

Group III oils (Figures IV.1 and IV.2). Group IV oils have no cyclic molecule content as they

are synthetic oils. Given the trend, Group IV > Group III > Group II, it appears that isothermal

compressibility increases with decreasing cycloalkane content, indicating that these cyclic

molecules potentially pack in a manner that reduces compression effects compared to noncyclic

paraffins.

Figure IV.9. Isothermal compressibility versus pressure for six base oils at 323 K (left) and 373

K (right).

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

IIB

IIA

IIIB

IIIA

PAO 4

PAO 8

323 K

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

0.0013

0.0014

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

IIB

IIA

IIIB

IIIA

PAO 4PAO 8

373 K

69

Figure IV.10. Isothermal compressibility versus mass percent cycloparaffin content at 373 K

and 10 MPa for all base oils.

When comparing the thermal expansion coefficients for the oils studied, there were no

clear trends to be found. While oil IIIA had noticeably higher values for the expansion

coefficient, the other five oils had similar values. Figure IV.11 shows a comparison of thermal

expansion coefficient versus temperature for all six oils at two selected pressures, 10 and 40

MPa, while Figure IV.12 shows expansion coefficient versus composition. Unlike isothermal

compressibility, there is no clear effect of the cycloalkane content on the thermal expansion

coefficient.

0.0008

0.0009

0.001

0.0011

0.0012

0.0013

0.0014

0 20 40 60 80

κT

(1/M

Pa)

Mass % Cycloalkanes

373 K

10 MPa

70

Figure IV.11. Isobaric thermal expansion coefficient versus temperature for six base oils at 10

MPa (left) and 40 MPa (right).

Figure IV.12. Isobaric thermal expansion coefficient versus mass percent cycloparaffin content

at 373 K and 10 MPa for all base oils.

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

IIB

IIA

IIIAIIIB

PAO 4

PAO 8

10 MPa

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

250 300 350 400 450

βP

(1/K

)

Temperature (K)

IIB

IIAIIIA

IIIBPAO 4

PAO 8

40 MPa

0.0009

0.00092

0.00094

0.00096

0.00098

0.001

0.00102

0.00104

0.00106

0.00108

0.0011

0 20 40 60 80

βP

(1/K

)

Mass % Cycloalkanes

373 K

10 MPa

71

With isothermal compressibility and isobaric thermal expansion coefficient determined,

internal pressure can be calculated using equation III.19. Figure IV.13 compares internal

pressure of all six oils at both 323 and 373 K. As shown in equations III.19, the internal pressure

is proportional to the inverse of isothermal compressibility. Due to this, the trends associated

with internal pressure were also found to be inverted. Base oil IIA was found to have the highest

values across the range of temperatures and pressures examined in this study. The overall order

of the oils studied in terms of internal pressure was found to be IIA > IIB > IIIB > IIIA > PAO 4

> PAO 8. The group IV oils, PAO 4 and PAO 8, had much lower values of internal pressure

than the other four oils. Figure IV.14 shows the effect of composition on internal pressure.

Internal pressure was shown to increase with cycloalkane content.

Figure IV.13. Internal pressure versus pressure for six base oils at 323 K (left) and 373 K

(right).

320

340

360

380

400

420

440

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

IIB

IIA

IIIA

IIIB

PAO 4

PAO 8

323 K

300

310

320

330

340

350

360

370

380

390

400

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

IIB

IIA

IIIA

IIIB

PAO 4

PAO 8

373 K

72

Figure IV.14. Internal pressure versus mass percent cycloparaffin content at 373 K and 10 MPa

for all base oils.

The isothermal compressibility and internal pressure were found to be dependent on oil

composition, specifically cycloalkane content. This compositional effect was not found in the

isobaric thermal expansion coefficient. Isothermal compressibility is proportional to the partial

derivative of density with respect to pressure, while thermal expansion coefficient is related to

the partial derivative of density with respect to temperature (equations III.17 and III.18). The

effect of composition appears to change the sensitivity of the density of these base oils with

respect to pressure. The ring structures potentially allow for more efficient packing, reducing the

effect of pressure on density of the Group II and Group III oils, and with it, isothermal

compressibility. Given that lubricants operate by forming thin films under high pressure and

shear conditions, the change in the effect of pressure potentially affects this film formation.

Being inversely related to compressibility, internal pressure has also been shown to be affected

by the amount of cycloalkanes in the oil. Internal pressure is a measure of the overall effect of

the attractive and repulsive intermolecular forces. As internal pressure increases, attractive

forces become more dominant. As the amount of cyclic content increases, the more efficient

packing in the oil causes an increase in attractive intermolecular forces versus repulsive forces.

250

270

290

310

330

350

370

390

410

0 20 40 60 80

Inte

rnal

Pre

ssu

re (

MP

a)

Mass % Cycloalkanes

373 K

10 MPa

73

IV.3.3. Viscosity and Modelling

Viscosity data for all six base oils were collected in the high pressure rotational

viscometer described in Chapter II. Due to the high viscosities at 298 K, decoupling occurred for

several oils. At 298 K, viscosity data were collected for oils PAO 4 and IIIA from 300-800 rpm,

for oil IIA from 300-700 rpm, and for oils IIB, IIIB, and PAO 8 from 100-400 rpm. Figure

IV.15 shows the viscosity for oil IIB at 500 rpm (except at 298 K, where 300 rpm data were

shown). For all six oils, viscosity was shown to decrease with temperature and increase with

pressure. Figure IV.16 compares viscosity versus pressure collected at all rotational speeds and

shear stress to shear rate for oil IIB at 323 K. The isothermal viscosity data overlapped for all

rotational speeds, showing Newtonian behavior. All six oils were found to be Newtonian in

behavior in the measured range of shear rates.

Figure IV.15. Viscosity versus pressure for base oil IIB at 500 rpm (300 rpm for the 298 K run).

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

298 K

(300 rpm)

323 K

348 K373 K

IIB

500 rpm

74

Figure IV.16. Viscosity versus pressure (left) and average shear stress at 10 MPa versus shear

rate (right) for IIB at 323 K. All data points at rotational speeds from 300 to 800 rpm are

represented in the figure on the left. The linearity of shear stress versus shear rate shows the oil

is Newtonian in behavior.

With viscosity data collected, and the Newtonian behavior of the six oils studied in the

measured range confirmed, the temperature and pressure effects were modeled. Free volume

theory, described in detail in Chapter III and represented by equation III.22, was used. Due to

the Newtonian behavior of the oils studied, only the viscosity data for the 500 rpm runs were

fitted to the model equation. The exception to this were oils IIB, IIIB, and PAO 8 at 298 K as

the 500 rpm data could not be generated due to decoupling. For these oils at 298 K, 300 rpm

data were used (500 rpm data was used for all other temperatures). The fitted parameters are

shown in Table IV.3 for all six oils, along with values for root mean squared deviation (RSME),

percent absolute average deviation (% AAD), and the bias (% ℬ). Figure IV.17 shows the free

volume theory fit for oil IIB compared to the experimental data at all temperatures and 500 rpm.

The viscosity and free volume fits for the remaining five oils can be found in Appendix C. With

the exception of oils IIA and IIIA, the % AAD for each of the studied oils was below 10 %. Oils

IIA and IIIA had lower viscosities than the other four, with the 373 K values falling below the

threshold of sensitivity of the viscometer used, 3 mPa s. The high level of error in the low

temperature measurements could account for the high values of % AAD involved in the model

20

25

30

35

40

45

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

IIB

323 K

300-800 RPM

R² = 0.9995

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 500 1000 1500

Sh

ear

Str

ess

(N/m

2)

Shear Rate (1/s)

IIB

323 K

10 MPa

75

for these two oils. Figure IV.18 compares both the data and their fits at 323 K and 500 rpm for

all six oils studied.

Unlike isothermal compressibility and internal pressure, there is no clear trend relating

viscosity to the concentration of cyclic compounds in the oils. The viscosity is more closely

related to molecular weight for the oils studied, indicating that there are differences in what

intermolecular interactions influence the derived thermodynamic properties compared to viscous

effects. These differences indicate that it is necessary to examine both viscosity and the

volumetric effects simultaneously as both viscosity and compressibility are useful in the design

of lubricants for mechanical systems such as automobiles.

Table IV.3. Parameters for the free volume theory of viscosity.

IIA IIB IIIA IIIB PAO 4 PAO 8

L (cm) X 105 8.09 2.49 18.7 12.2 31.8 10.3

α (MPa*cm6/g*mol) 413600 1089000 447200 638600 728400 936200

B X 103 4.44 1.17 3.480 2.46 1.57 1.44

RMSE (mPa s) 0.845 1.21 0.735 0.922 1.06 1.79

% AAD 28.8 10.0 25.3 5.07 8.98 5.53

% ℬ -23.5 8.15 -20.5 -0.885 5.28 4.15

76

Figure IV.17. Viscosity versus pressure for base oil IIB at 500 rpm (300 rpm for the 298 K run).

Free volume correlation fit is represented by black dots.

Figure IV.18. Viscosity versus pressure for six base oils at 323 K and 500 rpm. Free volume

correlation fit is represented by black dots.

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

298 K

(300 rpm)

323 K

348 K373 K

IIB

500 rpm

0

10

20

30

40

50

60

70

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

PAO 4

PAO 8

IIA

IIB

IIIA

IIIB

323 K

500 rpm

77

IV.4 Conclusions

Density data for six base oils were collected across a range of temperatures and pressures

and modeled using the Sanchez-Lacombe equation of state. Absolute average deviations were

found to be in range of 0.130 to 0.204 %. Both isothermal compressibility and internal pressure

were found to be concentration dependent, specifically affected by the concentration of cyclic

compounds in the base oils. This dependency was not seen in the thermal expansion

coefficients. These trends appear to indicate that pressure effects are particularly impacted by

the packing of these cycloalkanes compared to chained paraffins.

All six base oils were found to be Newtonian in nature in the measured range. The

viscosity data were then fit to the free volume theory in conjunction with the Sanchez-Lacombe

equation of state. For all but two of the oils, the absolute average deviations for the free volume

theory fits of the viscosity were found to be below 10 %. For oils IIA and IIIA, absolute average

deviation was around 25 % due to the low viscosities of these two oils at 373 K compared to the

sensitivity of the instrument. Viscosity was found not to be driven by the same concentration

effects as isothermal compressibility and internal pressure, indicating that the intermolecular

interactions driving viscosity are more complex.

IV.5 References

1. R.I. Taylor, R.C. Coy, Improved Fuel Efficiency by Lubricant Design: A Review, Proc.

Inst. Mech. Eng. J., 2000, 214, 1-15.

2. H.E. Grandelli, J.S. Dickmann, M.T. Devlin, J.C. Hassler, E. Kiran, Volumetric

Properties and Internal Pressure of Poly(alpha-olefin) Base Oils, Ind. Eng. Chem. Res.,

2013, 52, 17725-17734.

3. G.D. Yadav, N.S. Doshi, Development of a Green Process for Poly-α-olefin Based

Lubricants, Green Chem., 2002, 4, 528-540.

4. P.W. Michael, J.M. Garcia, S.S. Bair, M.T. Devlin, A. Martini, Lubricant Chemistry and

Rheology Effects on Hydraulic Motor Starting Efficiency, Tribol. Trans. 2002, 55,

549−557.

5. R. Feng, K.T. Ramesh, On the Compressibility of Elastohydrodynamic Lubricants, J.

Tribology, 1993, 115, 557-559.

6. K.T. Ramesh, The Short-Time Compressibility of Elastohydrodynamic Lubricants, J.

Tribology, 1991, 113, 361-371.

7. E.H. Okrent, The Effect of Lubricant Viscosity and Composition on Engine Friction and

Bearing Wear, ASLE Trans., 1961, 4, 97-108.

78

8. K. Inoue, H. Watanabe, Interactions of Engine Oil Additives, ASLE Transactions, 1982,

26, 189-199.

9. J.J. Rodgers, N.E. Gallopoulos, Friction Characteristics of Some Automatic Transmission

Fluid Components, ASLE Trans., 1966, 10, 102-114.

10. M. Nobelen, S. Hoppe, C. Fonteix, F. Pla, M. Dupire, B. Jacques, Modeling of the

Rheological Behavior of Polyethylene/Supercritical CO2 Solutions, Chem. Eng. Sci.,

2006, 61, 5334-5345.

11. J.W. Robinson, Y. Zhou, J. Qu, R. Erck, L. Cosimbescu, Effects of Star-Shaped

Poly(alkyl methacrylate) Arm Uniformity on Lubricant Properties, J. Appl. Polym. Sci.,

2016, 133, 1-11.

12. N. Chandak, A. George, A.A. Hamadi, M. Berthod, Optimization of Hydrocracker Pilot

Plant Operation for Base Oil Production, Catal. Today, 2016, 271, 199-206.

13. I. Dzidic, H.A. Peterson, P.A. Wadsworth, H.V. Hart, Townsend Discharge Nitric Oxide

Chemical Ionization Gas Chromatography/Mass Spectrometry for Hydrocarbon Analysis

of the Middle Distillates. Anal. Chem., 1992, 64, 2227.

14. J.S. Dickmann, J.C. Hassler, E. Kiran, High Pressure Volumetric Properties and

Viscosity of Base Oils Used in Automotive Lubricants and Their Modeling, Industrial &

Engineering Chemistry Research, 57 (2018) 17266-17275.

15. M.J.G. Guimarey, M.J.P. Comunas, E.R. Lopez, A. Amigo, J. Fernandez, Volumetric

Behavior of Some Motor and Gear-Boxes Oils at High Pressure: Compressibility

Estimation at EHL Conditions, Ind. Eng. Chem. Res., 2017, 56, 10877-10885.

79

V. Base Oils with Additives

V.1 Introduction

In this chapter, we discuss the volumetric properties and viscosity of a base oil modified

by the addition of polymeric additive along with two automatic transmission fluids (ATFs). As

discussed in Chapter I and Chapter IV, the choice of lubricants in automotive applications can

have a significant effect on fuel efficiency.1 Engine oils and ATFs are not simple fluids. These

lubricants are composed of a base oil with a number of additives meant to fulfill specific roles

they have been tailored to, including detergents, dispersants, friction modifiers, and anti-wear

additives.2-4 One particular class of additive is the viscosity index modifier.

As stated earlier, the viscosity index is an empirical measure of the effect of temperature

on viscosity. The higher the viscosity index, the less effect temperature has on viscosity. With

the viscosity of a lubricant being important in determining fuel efficiency,5-7 it is important to

lower the viscosity range across the temperatures at which the engine or transmission operate at

to ensure uniform performance. Viscosity index is calculated by comparing the kinematic

viscosities of an oil at 313 K and 373 K to known standards:

𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦𝐼𝑛𝑑𝑒𝑥 = 100𝜈𝑉𝐼0−𝜈313

𝜈𝑉𝐼0−𝜈𝑉𝐼100 V.1

where ν313 is the kinematic viscosity of the measured oil at 313 K, νVI 0 is the kinematic viscosity

at 313 K of an oil standard with a viscosity index of 0 and the same kinematic viscosity as the

measured oil at 373 K, and νVI 100 is the kinematic viscosity at 313 K of an oil standard with a

viscosity index of 100 and the same kinematic viscosity as the measured oil at 373 K.8

V.1.1 Objectives

To understand the effect of viscosity index modifying polymers on the properties of base

oils, density measurements were carried out over a pressure range of 10-40 MPa and a

temperature range of 298-398 K on mixtures of base oil PAO 4 with two polymeric additives, up

to 7.12 mass percent. Alongside the density measurements, viscosity measurements were carried

80

out across a pressure range of 10-40 MPa, a temperature range of 298-373 K, and rotational

speeds from 300-800 rpm. Additionally, densities and viscosities were determined for two fully

formulated automatic transmission fluids.

The objective was again to use the collected data to apply a holistic approach, described

in Chapter IV, to describe the density, derived thermodynamic properties, and viscosity. To

accomplish this, following the methodology described in Chapter III, density data were fit to the

Sanchez-Lacombe equation of state (S-L EOS) while viscosity data were fit to a coupled model,

the free volume theory. Using the S-L EOS fits, the derived thermodynamic properties were

calculated. By examining all these properties simultaneously, the effect of polymeric additives

on base oils could be assessed. Finally, the density of two ATFs was modeled. Due to an

incomplete description of the compositions of the ATFs, instead of the S-L EOS, the Tait

equation was used in modeling these lubricants.

V.2 Materials and Methods

Mixtures of synthetic base oil PAO 4, composed completely of poly(α-olefins), with

viscosity index modifiers were provided by Afton Chemical Corp. These mixtures were used as

received. These mixtures were made using two different viscosity index modifiers. These

viscosity index modifiers were indicated to be both polymethacrylate based polymers. Both

additives have alkyl chains of varying length coming off the methacrylate mers. The difference

between the two additives is the existence of amine end-groups on some of these alkyl chains for

Polymer 1 (3-4% of these chains contain a N(CH3)2 group), while Polymer 2 had no amine

functionality at all. Figures V.1 and V.2 shows the structure of these two additives.

Figure V.1. Structure of viscosity index modifier Polymer 1.

81

Figure V.2. Structure of viscosity index modifier Polymer 2.

In addition to mixtures of a base oil with an individual additive, fully formulated

automatic transmission fluids were studied. Two ATFs were provided by Afton Chemical Corp,

one experimental and one commercial. They were used as received.

V.3 Results and Discussion

V.3.1 Viscosity Index Modifiers

Experimental density data for mixtures of base oil PAO 4 with two polymer additives at

concentrations up to 7 mass % (4 mixtures with each polymer) were analyzed. Figures V.3 and

V.4 compare the densities of PAO 4 and its mixtures with both viscosity index modifiers at 323

K. Densities for PAO 4 were determined experimentally in a previous study conducted in our

lab.5 Additionally, these mixtures were treated as pseudo-single component fluids and modeled

with the Sanchez-Lacombe equation of state. The S-L EOS parameters, and derived

thermodynamic properties, for base oil PAO 4 were calculated in our previous publication in

Industrial & Engineering Chemistry Research.9 To effectively model these mixtures, knowledge

of the molecular weight is needed. As all mixtures were composed of concentrations of > 90

mass % PAO 4, the average molecular weight of the pure base oil (MW of 489 g/mol) was used

in all fits. Tables V.1 and V.2 show the calculated S-L parameters for these mixtures along with

root mean squared deviation (RSME), percent absolute average deviation (% AAD), and bias (%

ℬ). The S-L EOS fits for all these mixtures were found to have % AADs less than 0.3 For all

82

mixtures, both with Polymer 1 and Polymer 2, a small reduction of density is seen. The densities

of these mixtures are within 1 % of each other, the error associated with these measurements,

making it difficult to determine a trend in the effect of polymer concentration on density. The

experimental densities and resulting S-L EOS fits for all mixtures can be found in Appendix D.

Figure V.3. Density versus pressure for PAO 4 and its mixtures with viscosity index modifier

Polymer 1 at 323 K.

0.78

0.79

0.8

0.81

0.82

0.83

0.84

0.85

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

Polymer 1

323 K PAO 4

0.71 %

7.12 %

1.42 %

2.85 %

83

Figure V.4. Density versus pressure for PAO 4 and its mixtures with viscosity index modifier

Polymer 2 at 323 K.

Table V.1. S-L parameters for mixtures of PAO 4 with Polymer 1

PAO 4 0.71 % 1.42 % 2.85 % 7.12 %

P* (MPa) 433.62 447.50 455.80 473.49 311.29

T* (K) 544.10 530.08 529.95 523.17 576.05

ρ* (g/cm3) 0.91160 0.89343 0.90072 0.90447 0.88624

RMSE (g/cm3) 0.00198 0.00185 0.00206 0.00284 0.00213

% AAD 0.201 0.195 0.212 0.298 0.221

% ℬ -0.000177 -0.000260 -0.00086 -0.0283 -0.00066

0.79

0.795

0.8

0.805

0.81

0.815

0.82

0.825

0.83

0.835

0.84

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

Polymer 2

323 KPAO 4

0.70 %

1.40 %

2.80 %

7.01 %

84

Table V.2. S-L parameters for mixtures of PAO 4 with Polymer 2

PAO 4 0.70 % 1.40 % 2.80 % 7.01 %

P* (MPa) 433.62 496.64 547.29 460.72 402.04

T* (K) 544.10 516.55 469.18 535.53 522.81

ρ* (g/cm3) 0.91160 0.90588 0.89350 0.89927 0.90184

RMSE (g/cm3) 0.00198 0.00190 0.00182 0.00166 0.00266

% AAD 0.201 0.190 0.182 0.167 0.277

% ℬ -0.000177 0.0362 -0.00066 -0.00027 -0.00089

Once the density data were fit to the S-L equation of state, the derived thermodynamic

properties for these mixtures were calculated using equations III.17-19. The thermodynamic

properties across the full range of temperatures and pressures examined in this study for the

mixtures of PAO 4 with viscosity index modifiers can be found in Appendix D.

As with the pure base oils from Chapter IV, isothermal compressibility was found to

increase with temperature and decrease with pressure. Additionally, compressibility was found

to be influenced by composition. Figure V.5 shows a comparison of isothermal compressibility

versus pressure at 323 K for all mixtures. Figure V.6 shows isothermal compressibility versus

mass % polymer at 323 K and 10 MPa. Compressibility was found to be slightly high in

mixtures with Polymer 1 up to concentrations of 2.85 mass % polymer. Isothermal

compressibility was found to increase upon addition of around 7 mass % polymer for both

additives.

85

Figure V.5. Isothermal compressibility versus pressure for PAO 4 and its mixtures with

viscosity index modifiers Polymer 1 (left) and Polymer 2 (right) at 323 K.

Figure V.6. Isothermal compressibility versus mass percent polymer at 323 K and 10 MPa for

mixtures of PAO 4 with viscosity index modifiers Polymer 1 and Polymer 2.

As with the pure base oils, isobaric thermal expansion coefficient for these mixtures was

found to increase with temperature and decrease with pressure. Thermal expansion coefficient

0.0005

0.00055

0.0006

0.00065

0.0007

0.00075

0.0008

0.00085

0.0009

0.00095

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

Polymer 1

323 K

7.12%

0.71%

2.85%

1.42%

PAO 4

0.0005

0.00055

0.0006

0.00065

0.0007

0.00075

0.0008

0.00085

0.0009

0.00095

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

Polymer 2

323 K

7.01%

0.70%

2.80%

1.40%

PAO 4

0.0007

0.00075

0.0008

0.00085

0.0009

0.00095

0 2 4 6 8

κT

(1/M

Pa)

Mass % Polymer

323 K

10 MPa

Polymer 1

Polymer 2

86

was found to be affected by polymer composition. Figure V.7 shows isobaric thermal expansion

coefficient versus temperature at 10 MPa for mixtures of PAO 4 with Polymer 1 and Polymer 2.

Figure V.8 shows thermal expansion coefficient versus mass percent polymer of both additives.

The thermal expansion coefficient showed an initial increase upon the addition of a small amount

of either polymer (0.7 mass %). For Polymer 1, expansivity continued to increase with polymer

concentration up to 2.85 mass % polymer, then dropped at the high concentration mixture (7

mass %). For Polymer 2, After the initial increase in expansivity, as polymer concentration

increased thermal expansion coefficient stabilized at a value between the pure PAO 4 and 0.70

mass % polymer mixture.

Figure V.7. Isobaric thermal expansion coefficient versus temperature for PAO 4 and its

mixtures with viscosity index modifiers Polymer 1 (left) and Polymer 2 (right) at 10 MPa.

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

0.0013

250 300 350 400 450

βP

(1/K

)

Temperature (K)

Polymer 1

10 MPa

PAO 4

7.12%

2.85%

0.71%

1.42%

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

0.0013

250 300 350 400 450

βP

(1/K

)

Temperature (K)

Polymer 2

10 MPa

PAO 4

7.01%

2.80%

0.70%

1.40%

87

Figure V.8. Isobaric thermal expansion coefficient versus mass percent polymer at 323 K and

10 MPa for mixtures of PAO 4 with viscosity index modifiers Polymer 1 and Polymer 2.

The internal pressure for these mixtures was found to decrease with temperature and

increase with pressure. As with isothermal compressibility and thermal expansion coefficient,

internal pressure was found to be affected by polymer composition. Figure V.9 shows internal

pressure versus pressure at 323 K for mixtures of PAO 4 with both additives Polymer 1 and

Polymer 2. Figure V.10 shows internal pressure versus mass percent polymer of both additives.

For mixtures with Polymer 1, internal pressure increased with additive concentration up to 2.85

mass % polymer. Internal pressure decreased to significantly lower than the pure base oil value

upon the addition of 7 mass % polymer. For mixtures with polymer 2, internal pressure initially

increased with polymer addition (0.7 mass % polymer). After that initial increase, internal

pressure decreased with increasing concentration of Polymer 2. Additionally, the internal

pressures were found to be higher for mixtures with Polymer 2 than those with Polymer 1,

indicating that the overall attractive intermolecular interactions were stronger in the mixtures

with Polymer 2. This could indicate that the addition of the amine groups on Polymer 1 adds

additional repulsive interactions into the lubricant system.

0.0007

0.00075

0.0008

0.00085

0.0009

0.00095

0.001

0 2 4 6 8

βP

(1/K

)

Mass % Polymer

323 K

10 MPaPolymer 1

Polymer 2

88

Figure V.9. Internal pressure versus pressure for PAO 4 and its mixtures with viscosity index

modifiers Polymer 1 (left) and Polymer 2 (right) at 323 K.

Figure V.10. Internal pressure versus mass percent polymer at 323 K and 10 MPa for mixtures

of PAO 4 with viscosity index modifiers Polymer 1 and Polymer 2.

Viscosity data for mixtures of base oil PAO 4 with two polymer additives at

concentrations up to 7 mass % were collected across a range of 10-40 MPa and 300-800 rpm at

250

270

290

310

330

350

370

390

410

430

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

Polymer 1

323 K

7.12%

PAO 40.71%

1.42%

2.85%

250

270

290

310

330

350

370

390

410

430

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

Polymer 1

323 K

7.01%

PAO 4

0.70%

1.40% 2.80%

250

275

300

325

350

375

400

0 2 4 6 8

Inte

rnal

Pre

ssu

re (

MP

a)

Mass % Polymer

323 K

10 MPaPolymer 2

Polymer 1

89

isotherms of 298, 323, 348, and 373 K. All mixtures of PAO 4 with Polymer 1 and Polymer 2

were Newtonian in nature. Figures V.11 and V.12 compare the viscosities of these mixtures at

both 298 and 323 K and 500 rpm. At 298 K, there is a decrease in viscosity with the addition of

these polymeric additives at lower concentrations (below 2.85 mass %), with viscosity

decreasing by approximately 3.5 mPa s at all concentrations for Polymer 1 and 5 mPa s at

concentrations of 0.70 and 1.40 mass %, and 3 mPa s at a concentration of 2.80 mass %, for

Polymer 2. At temperatures of 323 K and above, this decrease in viscosity was not readily seen.

For the mixtures involving high concentrations of polymer, above 7 mass %, the viscosity

increased at all temperatures, with an increase of 20 mPa s for Polymer 1 and 16 mPa s for

Polymer 2 at 298 K. In addition, viscosity data was fit to the free volume theory (equation

III.22) in conjunction with the Sanchez-Lacombe equation of state. As with the S-L EOS fits,

these mixtures were treated as pseudo-single component. Tables V.3 and V.4 show the fitted

parameters for the free volume theory along with RSME, % AAD, and % ℬ. The full range of

viscosity data and corresponding free volume theory fits for the mixtures studied in this chapter

can be found in Appendix D.

Figure V.11. Viscosity versus pressure for mixtures of PAO 4 with viscosity index modifiers

Polymer 1 (left) and Polymer 2 (right) at 298 K and 500 rpm.

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

PAO 4 + Polymer 1

298 K

500 rpm 7.12 %

0.71 %

1.42 %2.85 %

PAO 4

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

PAO 4 + Polymer 2

298 K

500 rpm 7.01 %

0.70 %1.40 %2.80 %

PAO 4

90

Figure V.12. Viscosity versus pressure for mixtures of PAO 4 with viscosity index modifiers

Polymer 1 (left) and Polymer 2 (right) at 323 K and 500 rpm.

Table V.3. Parameters for the free volume theory of viscosity for mixtures of PAO 4 and

viscosity index modifier Polymer 1.

PAO 4 0.71 % 1.42 % 2.85 % 7.12 %

L (cm) X 105 31.8 18.8 67.2 43.8 44.8

α (MPa*cm6/g*mol) 728000 779000 596000 715000 830000

B X 103 1.57 1.56 1.94 1.77 1.31

RMSE (mPa s) 1.06 0.417 1.24 0.586 0.795

% AAD 8.98 5.17 12.4 4.69 4.64

% ℬ 5.28 0.565 2.01 1.73 -0.34

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

PAO 4 + Polymer 1

323 K

500 rpm7.12 %

0.71 %

1.42 %

2.85 %

PAO 4

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

PAO 4 + Polymer 2

323 K

500 rpm

7.01 %

0.70 %1.40 %

2.40 %

PAO 4

91

Table V.4. Parameters for the free volume theory of viscosity for mixtures of PAO 4 and

viscosity index modifier Polymer 2.

PAO 4 0.70 % 1.40 % 2.80 % 7.01 %

L (cm) X 105 31.8 48.1 80.5 39.7 55.6

α (MPa*cm6/g*mol) 728000 621000 571000 611000 728000

B X 103 1.57 1.89 2.01 2.02 1.57

RMSE (mPa s) 1.06 0.573 1.07 0.537 0.901

% AAD 8.98 5.67 8.87 6.21 5.36

% ℬ 5.28 0.582 5.14 -2.91 2.99

The addition of these viscosity index modifiers has an effect on volumetric,

thermodynamic, and transport properties of the original base oils they are added to. Of particular

interest is the increase in isothermal compressibility at higher polymer concentrations. Knowing

how pressure effects the change in density, and volume, is important for understanding film

formation of these mixtures under lubrication conditions. Additionally, isobaric thermal

expansion coefficient and internal pressure were found to initially increase with a small amount

of polymer additive, with both properties dropping as polymer concentration increased. Internal

pressure is a measure of the overall intermolecular interactions. The higher values of internal

pressure for mixtures with Polymer 1 versus Polymer 2 can be attributed to the lack of amine

groups. The alkyl chains interact with the poly(α-olefins) of the pure base oil, while the amine

groups disrupt these interactions to a degree. Additionally, isobaric thermal expansion

coefficient (equation III.18) is proportional to the partial derivative of density with regards to

temperature. The initial addition of polymer causes a change in the effect of temperature on the

fluid. At higher concentrations, the thermal expansion coefficient drops as the polymer

interactions start to become more dominant.

This is the inverse of viscosity, which decreases at 298 K at low concentrations. These

additives are meant to change the viscosity index, a measure of the effect of temperature on

viscosity. These oils are selected due to their low viscosities at higher temperatures, leading to

an increase fuel efficiency. Even so, these oils need to operate over a range of temperatures,

making it necessary to reduce the effect of temperature on viscosity. By reducing viscosity at

92

low temperature conditions while keeping them constant at higher temperatures, viscosity index

can be increased without changing the performance at high temperature conditions the base oil

was selected for. At higher concentrations, in the case of this study above 7 mass %, polymeric

interactions take over leading to an increase in viscosity at all temperatures. The addition of

these additives has a particular effect on the effect of temperature on these fluids.

V.3.2 Automatic Transmission Fluids

The effect of temperature and pressure on the volumetric properties and viscosity of two

ATFs, an experimental blend and a commercial sample, was analyzed. The use of the S-L EOS

requires knowledge of the molecular weights of the constituents. These ATFs are composed of a

base oil (already a complex mixture) and numerous additives. Without a detailed description of

the composition of these ATFs, it is difficult to employ the S-L EOS. Due to the complexity of

these fluids, the Tait equation (equations III.1-3) were used instead of the S-L EOS in the

modeling of these ATFs. Figure V.13 shows density versus pressure for these ATFs at 323 and

373 K. Table V.5 shows the Tait equation parameters along with RSME, % AAD, and % ℬ.

The commercial ATF was shown to have higher densities than the experimental blend at the

temperatures and pressures in which measurements were carried out. The % AADs of both fits

were found to be approximately 0.1 %.

Utilizing the Tait equation fits, isothermal compressibility, isobaric thermal expansion

coefficient, and internal pressure were calculated. Figures V.14-16 show comparisons of the

derived thermodynamic properties of both ATFs. Isothermal compressibility was found to be

similar for both samples. The experimental ATF was found to have higher values of isobaric

thermal expansion coefficient and internal pressure. The full densities, Tait equation fits, and

derived thermodynamic properties for both ATFs can be found in Appendix D.

Figures V.17 and V.18 show viscosity versus pressure for these ATFs. Both the

experimental and commercial ATF samples were found to exhibit Newtonian behavior. The

commercial ATF was found to have higher viscosities than the experimental one, though at 323

K, this difference was within the 5 % error associated with the viscosity measurement. Due to

lack of compositional information, these viscosities were not modeled with the free volume

theory. Select viscosities are tabulated in Appendix D.

93

Figure V.13. Density versus pressure for an experimental and a commercial ATF at 323 K (left)

and 373 K (right). Tait equation fits are shown as black diamonds.

Table V.5. Tait equation parameters for automatic transmission fluids

Experimental

ATF

Commercial

ATF

aρ (1/K) 0.000934 0.000884

ρR (g/cm3) 0.860 0.870

Tr (K) 298 298

K0' 10.0 10.0

K00 (MPa) 9070 8270

βK (1/K) 0.00586 0.00561

RSME 0.00114 0.000972

% AAD 0.111 0.0936

% ℬ -0.000740 0.00400

0.84

0.845

0.85

0.855

0.86

0.865

0.87

0.875

0.88

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

323 KCommercial ATF

Experimental ATF

0.8

0.81

0.82

0.83

0.84

0.85

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

373 KCommercial ATF

Experimental ATF

94

Figure V.14. Isothermal compressibility versus pressure for an experimental and a commercial

ATF at 323 K (left) and 373 K (right).

Figure V.15. Isobaric thermal expansion coefficient versus temperature for an experimental and

a commercial ATF at 10 MPa (left) and 40 MPa (right).

0.0005

0.00055

0.0006

0.00065

0.0007

0.00075

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

323 K

Commercial ATF

Experimental ATF

0.00065

0.0007

0.00075

0.0008

0.00085

0.0009

0.00095

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

373 KExperimental ATF

Commercial ATF

0.0008

0.00082

0.00084

0.00086

0.00088

0.0009

0.00092

0.00094

0.00096

0.00098

0.001

250 300 350 400 450

Isob

ari

c E

xp

an

sivit

y (

1/K

)

Temperature (K)

10 MPa Experimental ATF

Commercial ATF

0.00075

0.00077

0.00079

0.00081

0.00083

0.00085

0.00087

0.00089

250 300 350 400 450

Isob

ari

c (1

/K)

Pressure (MPa)

40 MPa

Experimental ATF

Commercial ATF

95

Figure V.16. Internal pressure versus pressure for an experimental and a commercial ATF at

323 K (left) and 373 K (right).

Figure V.17. Viscosity versus pressure for an experimental ATF (left) and a commercial ATF

(right).

350

360

370

380

390

400

410

420

430

440

450

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

323 KExperimental ATF

Commercial ATF

350

360

370

380

390

400

410

420

430

440

450

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

373 K

Experimental ATF

Commercial ATF

0

20

40

60

80

100

120

0 10 20 30 40 50

Vis

cosi

ty (

cP)

Pressure (MPa)

Experimental ATF

500 RPM

298 K (400 RPM)

323 K

348 K

373 K0

20

40

60

80

100

120

0 10 20 30 40 50

Vis

cosi

ty (

cP)

Pressure (MPa)

Commercial ATF

500 RPM

298 K (400 RPM)

323 K

348 K

373 K

96

Figure V.18. Viscosity versus pressure for an experimental and a commercial ATF at 323 K and

500 rpm. Viscosity data are shown on the left, while error bars, showing that both ATFs have

similar viscosities within the measurement error, are shown on the right.

V.4 Conclusions

Isothermal compressibility was found to increase at higher polymer concentrations

(around 7 mass % polymer). Isobaric thermal expansion coefficient and internal pressure

initially increased with the addition of a small amount of polymer (around 0.7 mass %), followed

by an eventual drop in both properties as polymer concentration increased. Internal pressure was

found to be higher for mixtures with Polymer 2 than additive Polymer 1. This could be due to

the presence of a small number of amine functional groups disrupting carbon-carbon interactions

between the poly(α-olefins) of the base oil used and the polymeric additives in the case of

Polymer 1. Viscosity was found to initially drop at 298 K, while staying the same within the

error associated with the viscosity measurements at higher temperatures (323 K and above), for

concentrations below 3 mass % polymer. This should correspond with an increase in viscosity

index. At 7 mass % polymer, for both additives, viscosity increased at all temperatures as the

polymer chains interact with each other instead of just the base oil at these higher concentrations.

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

323 K

500 rpmCommercial ATF

Experimental ATF

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

323 K

500 rpmCommercial ATF

Experimental ATF

97

For the automatic transmission fluids, the Tait equation was used model density. A

comparison of the derived thermodynamic properties revealed that while there were differences

in isobaric thermal expansion coefficient and internal pressure, both of these transmission fluids

had similar isothermal compressibilities and viscosities. Knowledge of compressibility and

viscosity is needed for the design of effective lubricants.

V.5 References

1. R.I. Taylor, R.C. Coy, Improved Fuel Efficiency by Lubricant Design: A Review, Proc.

Inst. Mech. Eng. J., 2000, 214, 1-15.

2. E.H. Okrent, The Effect of Lubricant Viscosity and Composition on Engine Friction and

Bearing Wear, ASLE Trans., 1961, 4, 97-108.

3. K. Inoue, H. Watanabe, Interactions of Engine Oil Additives, ASLE Transactions, 1982,

26, 189-199.

4. J.J. Rodgers, N.E. Gallopoulos, Friction Characteristics of Some Automatic Transmission

Fluid Components, ASLE Trans., 1966, 10, 102-114.

5. H.E. Grandelli, J.S. Dickmann, M.T. Devlin, J.C. Hassler, E. Kiran, Volumetric

Properties and Internal Pressure of Poly(alpha-olefin) Base Oils, Ind. Eng. Chem. Res.,

2013, 52, 17725-17734.

6. G.D. Yadav, N.S. Doshi, Development of a Green Process for Poly-α-olefin Based

Lubricants, Green Chem., 2002, 4, 528-540.

7. P.W. Michael, J.M. Garcia, S.S. Bair, M.T. Devlin, A. Martini, Lubricant Chemistry and

Rheology Effects on Hydraulic Motor Starting Efficiency, Tribol. Trans. 2002, 55,

549−557.

8. J.W. Robinson, Y. Zhou, J. Qu, R. Erck, L. Cosimbescu, Effects of Star-Shaped

Poly(alkyl methacrylate) Arm Uniformity on Lubricant Properties, J. Appl. Polym. Sci.,

2016, 133, 1-11.

9. J.S. Dickmann, J.C. Hassler, E. Kiran, High Pressure Volumetric Properties and

Viscosity of Base Oils Used in Automotive Lubricants and Their Modeling, Industrial &

Engineering Chemistry Research, 57 (2018) 17266-17275.

98

VI. Ionic Liquids

VI.1 Introduction

Ionic liquids (ILs) are a class of salts with melting points below 100oC that are known for

their unique properties, such as negligible vapor pressure, electrochemical properties, and

potential thermal stability.1-3 The choice of cation and anion, along with the modification of any

functional groups on the ions, has a significant effect on the physical and solvent properties of

these salts. The properties associated with these fluids, specifically the low melting points but

also including viscosity and solubility parameter, are attributed to the structure of the ions, with

the cations being composed of bulky, often asymmetric, organic structures that inhibit the

association between the cation and ion, preventing crystallization.1 It has been estimated that

there are at least 1012 possible combinations of cation and anion that can form an IL.1 Due to the

number of possible ion pairs alongside the wide range of variation of the physical and solvent

properties of these materials, ILs have been described as designer solvents.4,5

The negligible vapor pressures and designer nature of these potential solvents has led to

increasing interest in using these ILs as replacements for volatile organic compounds.1 More

specifically, there has been growing body of work in the literature on the utilization of ILs in a

wide range of applications, including polymer processing and synthesis, CO2 capture, lithium ion

batteries, and biomass processing.6-17 In addition to utilizing ILs as a designer solvent, it can be

beneficial to add a cosolvent as a parameter to tune the solvent properties of the IL.18 The

addition of a cosolvent also adds the potential to increase the compressibility of a system,

allowing for the use of pressure as an additional tuning parameter. Due to the range of possible

options, effectively choosing an IL and cosolvent for a process requires knowledge of the

volumetric properties and viscosity of these mixtures across a range of temperatures and

pressures.

VI.1.1 Objectives

To determine the effect of cation and anion choice, along with the addition of a

cosolvent, on the solvent properties of ILs, density measurements were carried out in the

99

variable-volume view-cell on a series of ILs and their mixtures with ethanol. These ILs were

composed of four different variants of 1-alkyl-3-methylimidazolium with two different anions,

chloride and acetate. In addition to the density measurements, viscosity measurements were

carried out on two different ILs and select mixtures of ethanol. Figure VI.1 shows the structures

of the 1-alkyl-3-methylimidazolium cation and chloride and acetate anions that have been

studied.

The density data was modeled as a function of temperature, pressure, and composition

with the Sanchez-Lacombe equation of state (S-L EOS), while the free volume model was used

to describe viscosity. The S-L EOS fits were used to calculate derived thermodynamic

properties, which were in turn used to estimate the Hildebrand solubility parameter. The

solubility parameter was described in terms of alkyl chain length on the cation, anion, along with

temperature, pressure, and ethanol concentration. Finally, the effect of temperature, pressure,

ethanol concentration, and alkyl chain length on viscosity was examined.

Figure VI.1. 1-Alkyl-3-methylimidazolium cation and the chloride and acetate anions. R is an

alkyl group (ranging in length from 2 to 6 in the present thesis).

VI.2 Materials and Methods

ILs 1-ethyl-3-methylimidazolium chloride ([EMIM]Cl, ≥ 95 % purity), 1-ethyl-3-

methylimidazolium acetate ([EMIM]Ac, ≥ 95 % purity), 1-butyl-3-methylimidazolium chloride

([BMIM]Cl, ≥ 95 % purity), and 1-butyl-3-methylimidazolium acetate ([BMIM]Ac, ≥ 95 %

purity) were purchase from Sigma Aldrich. The ILs [EMIM]Ac and [BMIM]Ac were used as

received. [EMIM]Cl and [BMIM]Cl were dried for 48 hours at 343 K in a vacuum oven before

use. ILs 1-propyl-3-methylimidazolium chloride ([PMIM]Cl) and 1-hexyl-3-imidazolium

100

chloride ([HMIM]Cl) were synthesized for use in this study. Ethanol at 100% purity was

purchased from Decon Labs, Inc. 1-Methylimidazole, 1-chloropropane, 1-chlorohexane, and

ethyl acetate were used in the synthesis of ILs. 1-Methylimidazole (≥ 99 % purity), 1-

chloropropane (≥ 98 % purity), and 1-chlorohexane (≥ 99 % purity) were purchased from Sigma-

Aldrich. Ethyl acetate of purity 99.9 % was purchased from Fisher Scientific. Table VI.1 shows

the melting points of these ILs. The melting points were provided by Ionic Liquids Technologies

GmbH and Sigma-Aldrich.

Density data for these six ILs, ethanol, and mixtures of IL with ethanol were collected in

the variable-volume view-cell. Experiments were run from 10-40 MPa along isotherms of 298,

323, 348, 373, and 398 K. Viscosity data for [EMIM]Ac and [BMIM]Ac and their mixtures with

ethanol were collected in the high pressure rotational viscometer from 10-40 MPa at isotherms of

298, 323, 348, and 373 K. Due to restrictions arising from the decoupling of the magnetic

coupling, at certain temperatures, low rotational speeds were used. For [EMIM]Ac, runs were

performed at 100 and 200 rpm at 298 K, 300-800 rpm for all other temperatures. For

[BMIM]Ac, runs were performed at 50 rpm at 298 K, 100-300 rpm at 323 K, and 300-800 rpm at

348 and 373 K. Experimental details on the collection of density and viscosity can be found in

Chapter II. Experimental density data of the pure ILs and ethanol were fit to the S-L EOS.

Mixing rules were employed alongside the pure component values of the equation of state to

model mixtures with ethanol. With the S-L EOS parameters determined, derived thermodynamic

properties isothermal compressibility, isobaric thermal expansion coefficient, and internal

pressure were calculated. Additionally, the free volume theory was used to fit viscosity of the

pure ILs. The use of these models and the resulting calculations are described in further detail in

Chapter III.

101

Table VI.1. Melting Points of the ILs used in this study.

Ionic Liquid Melting Point (K)

[EMIM]Cl 360

[PMIM]Cl 333

[BMIM]Cl 338

[HMIM]Cl 198

[EMIM]Ac 303

[BMIM]Ac 253

VI.2.1 Synthesis

[PMIM]Cl and [HMIM]Cl were synthesized by reacting 1-methylimidazole with 1-

chloroalkane. Ethyl acetate was used as the reaction medium. Figure VI.2 shows the route of

synthesis for [RMIM]Cl, where R represents a propyl or hexyl group. The reaction was carried

out at the boiling point of ethyl acetate (350 K) for 48 hours in a reflux set up. Ice water was

circulated through the reflux column, which was open to the atmosphere. A magnetic stir bar

provided mixing during the reaction. Both [PMIM]Cl and [HMIM]Cl are insoluble in ethyl

acetate. As the reaction progressed, two phases were formed as the IL separated out of the ethyl

acetate. After the reaction was completed, leftover ethyl acetate was removed using a separation

funnel. To remove any unreacted reagents from the IL phase, clean ethyl acetate was added to

the IL and mixing applied. Again, a separation funnel was used to remove the ethyl acetate

phase. This wash step was repeated 5 times. Once the ethyl acetate washing was completed, the

resulting IL was dried in the vacuum oven for 48 hours at 343 K, then stored in a desiccant

chamber.

To determine if the IL was successfully synthesized, and to test for purity, FTIR was run

on the final products. A commercial sample of [HMIM]Cl was purchased from Sigma-Aldrich

(97 % purity) and dried at 343 K for 48 hours in a vacuum oven. The spectra for the synthesized

[HMIM]Cl was compared to both the commercial sample and a reference spectra from Bio-

Rad,19 as seen in Figure VI.3. The commercial sample from Sigma Aldrich was found to have

additional peaks not seen in the synthesized or reference spectra, at 1264, 1095, and 1017 cm-1,

102

indicating that the commercial sample had some unknown impurity not present in the

synthesized sample used in this study. According the Bio-Rad FTIR database, the presence of

these unknown peaks may be attributed to a catalyst.19 The FTIR spectra for [PMIM]Cl can be

found in Appendix E.

Figure VI.2. Route of synthesis for 1-alkyl-3-methylimidazolium chloride. R represents either

a propyl or hexyl group.

Figure VI.3. FTIR comparison of the synthesized [HMIM]Cl to commercial [HMIM]Cl (purity

97 %) and spectra from the Bio-Rad database.19

Commercial

Synthesized

Bio-Rad

103

VI.3 Results and Discussion

VI.3.1 1-Alkyl-3-methylimidazolium Chlorides and their Mixtures with Ethanol

The experimental densities for four ILs with the chloride anion, ethanol, and mixtures of

IL + ethanol (25, 50, and 75 mass percent IL) were compared. Due to the high melting point of

[EMIM]Cl (356 K), data was only collected at 348 K and above for both the pure IL and 75 mass

percent IL mixture with ethanol. While [PMIM]Cl and [BMIM]Cl both have melting points well

above room temperature, density data was collected across the full temperature range, though the

pure [BMIM]Cl run was limited to a pressure of 28 MPa at 298 K. Although the measurement

range for these three ILs included temperatures below the melting point, these ILs are capable of

existing as subcooled melts. This allows for the collection of liquid densities below their melting

points. The density data for the IL [EMIM]Cl and its mixtures with ethanol along with the S-L

EOS parameters for the IL and ethanol have been previously reported in our publication in The

Journal of Supercritical Fluids.18 The S-L EOS characteristic parameters for [EMIM]Cl,

[PMIM]Cl, [BMIM]Cl, and [HMIM]Cl can be found in Table VI.2, along with root mean

squared deviation (RSME), percent absolute average deviation (% AAD), and bias (% ℬ).

Figure VI.4 shows the density data and corresponding S-L EOS fits for both ILs. The % AADs

for [EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl were found to be 0.130 %, 0.170 %,

0.145 %, and 0.165 % respectively.

To model the mixtures of IL + ethanol, mixing rules were employed. The mixing rules

employed are described in Chapter III by equations III.7-14. Interaction parameter kij was

determined for all four IL + ethanol systems. Using a constant kij produced reasonable results

for the mixtures involving [EMIM]Cl. However, the RSME of the overall fits to the mixture

data increased with increasing alkyl chain length, from 0.00370 g/cm3 to 0.00906 g/cm3. Due to

this increased error, a concentration dependent kij was used:

𝑘𝑖𝑗 = 𝑘𝐴𝜙𝑖 − 𝑘𝐵 VI.1

where kA and kB are constants and ϕi is the close packed volume fraction of component i as

described by equation III.8. In the case of the present work, kij is represented in terms of the

104

close packed volume fraction of the IL. The constants needed to determine kij can be found in

Table VI.3. Using this concentration dependent kij in conjunction with the mixing rules

described in Chapter III reduces the RSME for [HMIM]Cl by 64% from 0.00906 to 0.00322

g/cm3. The S-L EOS parameters, along with RSME, % AAD, and % ℬ, calculated using mixing

rules for each mixture of [EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl with ethanol can be

found in Tables VI.4-7. Figure VI.5 shows density versus pressure for all four ILs and their

mixtures with ethanol at 348 K, along with the corresponding S-L EOS fits. Density was found

to increase with increasing IL concentration. The full range of densities for all mixtures of

[EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl with ethanol can be found in Appendix E.

Table VI.2. S-L EOS characteristic parameters for ethanol, [EMIM]Cl, [PMIM]Cl, [BMIM]Cl,

and [HMIM]Cl

Ethanol [EMIM]Cl [PMIM]Cl [BMIM]Cl [HMIM]Cl

P* (Mpa) 464.54 612.51 410.51 440.25 377.06

T* (K) 549.03 623.35 709.66 714.79 699.82

rho* (g/cm3) 0.88699 1.1834 1.1566 1.1181 1.0990

MW (g/mol) 46.07 146.62 160.65 174.69 202.71

RSME (g/cm3) 0.00138 0.00173 0.00231 0.00186 0.00212

% AAD 0.151 0.130 0.170 0.145 0.165

% ℬ -0.00774 -0.00173 0.00198 0.000429 0.00202

105

Figure VI.4. Density versus pressure for ILs [EMIM]Cl (top left), [PMIM]Cl (top right),

[BMIM]Cl (bottom left), and [HMIM]Cl (bottom right). S-L EOS fits are represented by black

diamonds.

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

[EMIM]Cl

348 K

373 K

398 K

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.1

1.11

1.12

1.13

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

[PMIM]Cl298 K

323 K

348 K

373 K

398 K

1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.1

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

BMIM]Cl

348K

373K

398K

323 K

298 K

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

[HMIM]Cl 298 K

323 K

348 K

373 K

398 K

106

Table VI.3. Comparison of Root Mean Squared Deviations (RSME) for different models of the

binary interaction parameter used in mixing rules for the S-L EOS.

IL Mixing Rule Fit Parameter Parameter Value RSME (g/cm3)

[EMIM]Cl Constant Parameter kij 0.03383 0.00370

Volume Fraction

Dependent kij*

kA 0.07612 0.00310

kB 0.00248

[PMIM]Cl Constant Parameter kij -0.030331 0.00538

Volume Fraction

Dependent kij*

kA 0.06019 0.00479

kB -0.64970

[BMIM]Cl Constant Parameter kij -0.09405 0.00628

Volume Fraction

Dependent kij*

kA 0.26520 0.00397

kB -0.20947

[HMIM]Cl Constant Parameter kij -0.17651 0.00906

Volume Fraction

Dependent kij*

kA 0.79783 0.00322

kB -0.46194

*Equation VI.1

Table VI.4. S-L EOS characteristic parameters for [EMIM]Cl + ethanol mixtures.

Mass % IL 25 50 75

P* (Mpa) 489.47 516.26 552.24

T* (K) 560.42 570.72 587.12

rho* (g/cm3) 0.94624 1.0140 1.0922

r 6.0596 7.2780 9.4776

RSME (g/cm3) 0.00400 0.00324 0.00251

% AAD 0.406 0.269 0.216

% ℬ -0.102 0.180 -0.0262

107

Table VI.5. S-L EOS characteristic parameters for [PMIM]Cl + ethanol mixtures.

Mass % IL 25 50 75

P* (Mpa) 498.10 505.62 479.43

T* (K) 623.21 692.21 726.91

rho* (g/cm3) 0.94189 1.0040 1.0749

r 5.8222 6.5788 7.7244

RSME (g/cm3) 0.00663 0.00602 0.00485

% AAD 0.673 0.594 0.380

% ℬ 0.673 -0.507 0.378

Table VI.6. S-L EOS characteristic parameters for [BMIM]Cl + ethanol mixtures.

Mass % IL 25 50 75

P* (Mpa) 482.45 474.28 451.65

T* (K) 604.59 637.23 660.29

rho* (g/cm3) 0.93532 0.98923 1.0497

r 5.9627 6.9574 8.5600

RSME (g/cm3) 0.00309 0.00422 0.00506

% AAD 0.318 0.374 0.443

% ℬ -0.204 0.0720 -0.102

Table VI.7. S-L EOS characteristic parameters for [HMIM]Cl + ethanol mixtures.

Mass % IL 25 50 75

P* (Mpa) 486.18 446.19 383.91

T* (K) 622.53 629.45 610.71

rho* (g/cm3) 0.93194 0.98169 1.0371

r 5.9940 7.0387 8.7322

RSME (g/cm3) 0.00329 0.00345 0.0619

% AAD 0.322 0.344 6.21

% ℬ -0.0808 -0.215 6.21

108

Figure VI.5. Density versus pressure for mixtures of [EMIM]Cl (top left), [PMIM]Cl (top

right), [BMIM]Cl (bottom left), and [HMIM]Cl (bottom right) with ethanol at 348 K. S-L EOS

fits are represented by black diamonds.

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

[EMIM]Cl

348 K

ethanol

25%

50%

75%

IL

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

[PMIM]Cl

348 KIL

75% IL

50% IL

25% IL

ethanol

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

IL

75%

50%

25%

ethanol

[BMIM]Cl

348 K

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

[HMIM]Cl

348 K

IL

ethanol

50%

25%

75%

109

VI.3.1.A Derived Thermodynamic Properties of [RMIM]Cl + Ethanol

With the S-L EOS parameters determined for all four ILs and their mixtures with ethanol,

the derived thermodynamic properties isothermal compressibility, isobaric thermal expansion

coefficient, and internal pressure were calculated. The full range of derived thermodynamic

properties for [EMIM]Cl, [PMIM]Cl, [BMIM]Cl, [HMIM]Cl and their mixtures with ethanol can

be found in Appendix E.

Figures VI.6-9 show isothermal compressibility versus pressure for the ILs and their

mixtures with ethanol. Compressibility was found to increase with temperature and decrease

with pressure for all ILs and their mixtures with ethanol. For [EMIM]Cl, isothermal

compressibility was found to decrease with increasing IL concentration. For the remaining three

ILs, this trend was more complicated. Figure VI.10 shows isothermal compressibility versus

mass % IL for all four ILs at 348 K and 10 MPa. For mixtures of [PMIM]Cl with ethanol,

compressibility goes through a minimum at 75 mass % IL in a parabolic fashion. For mixtures

of [BMIM]Cl and [HMIM]Cl with ethanol, the apparent trend starts to look like a third order

polynomial. This is especially visible for [HMIM]Cl, with a minimum at 50 mass % IL and a

maximum at 75 mass % IL.

Figure VI.6. Isothermal compressibility versus pressure for 50% [EMIM]Cl + 50% ethanol

(left) and various concentrations of [EMIM]Cl + ethanol at 348 K (right).

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

50% [EMIM]Cl

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

[EMIM]Cl

348 K

ethanol

25%

50%

75%

IL

110

Figure VI.7. Isothermal compressibility versus pressure for 50% [PMIM]Cl + 50% ethanol

(left) and various concentrations of [PMIM]Cl + ethanol at 348 K (right).

Figure VI.8. Isothermal compressibility versus pressure for 50% [BMIM]Cl + 50% ethanol

(left) and various concentrations of [BMIM]Cl + ethanol at 348 K (right).

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

50% [PMIM]Cl

298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

[PMIM]Cl

348 Kethanol

25% IL

50% IL

75% IL

IL

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

298K

323K

348K

373K

398K

50% [BMIM]Cl

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

[BMIM]Cl

348Kethanol

25%

50%

75%

IL

111

Figure VI.9. Isothermal compressibility versus pressure for 50% [HMIM]Cl + 50% ethanol

(left) and various concentrations of [HMIM]Cl + ethanol at 348 K (right).

Figure VI.10. Isothermal compressibility versus mass percent IL for mixtures of [EMIM]Cl,

[PMIM]Cl, [BMIM]Cl, and [HMIM]Cl + ethanol at 348 K and 10 MPa.

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

50% [HMIM]Cl

298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

[HMIM]Cl

348 Kethanol

25%

50%IL

75%

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 20 40 60 80 100

κT

(1/M

Pa)

Mass % IL

348 K

10 MPa

[HMIM]Cl

[BMIM]Cl

[PMIM]Cl

[EMIM]Cl

112

Figures VI.11-14 show isobaric thermal expansion coefficient versus temperature for

mixtures of 50 mass % IL with ethanol at all isotherms and all mixtures at 348 K for both

[EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl. Thermal expansion coefficient was found

to increase with temperature and decrease with pressure for the ILs and their mixtures with

ethanol. Thermal expansion coefficient was found to be higher for [EMIM]Cl than the other

three ILs. As with isothermal compressibility, the addition of ethanol affected the expansivity of

these ILs. Figure VI.15 shows isobaric thermal expansion coefficient versus mass % IL for both

ILs at 348 K and 10 MPa. For [EMIM]Cl, the coefficient was found to decrease with increasing

IL concentration in a near linear manner. For [BMIM]Cl, expansivity decreased with IL

concentration, but the linearity was less than clear. [PMIM]Cl went through a minimum at 75

mass % IL, while [HMIM]Cl went through a minimum at 50 mass % IL then a maximum at 75

mass % IL, before dropping to the pure IL value.

Figure VI.11. Isobaric expansivity versus temperature for 50% [EMIM]Cl + 50% ethanol (left)

and various concentrations of [EMIM]Cl + ethanol at 10 MPa (right).

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

0.0013

0.0014

0.0015

0.0016

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

50% [EMIM]Cl

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

0.0022

250 300 350 400 450

βP

(1/K

)

Temperature (K)

[EMIM]Cl

10 MPa ethanol

25%

50%

75%

IL

113

Figure VI.12. Isobaric expansivity versus temperature for 50% [PMIM]Cl + 50% ethanol (left)

and various concentrations of [PMIM]Cl + ethanol at 10 MPa (right).

Figure VI.13. Isobaric expansivity versus temperature for 50% [BMIM]Cl + 50% ethanol (left)

and various concentrations of [BMIM]Cl + ethanol at 10 MPa (right).

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

250 300 350 400 450

βP

(1/K

)

Temperature (K)

50% [PMIM]Cl

10 MPa

20 MPa

30 MPa

40 MPa

0

0.0005

0.001

0.0015

0.002

0.0025

250 300 350 400 450

βP

(1/K

)

Temperature (K)

[PMIM]Cl

10 MPaethanol

25%

50%

75%IL

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Pressure (MPa)

50% [BMIM]Cl

10 MPa

20 MPa

30 MPa

40 MPa

0

0.0005

0.001

0.0015

0.002

0.0025

250 300 350 400 450

βP

(1/K

)

Temperature (K)

ethanol

25%

50%

75%

IL

[BMIM]Cl

348K

114

Figure VI.14. Isobaric expansivity versus temperature for 50% [HMIM]Cl + 50% ethanol (left)

and various concentrations of [HMIM]Cl + ethanol at 10 MPa (right).

Figure VI.15. Isobaric thermal expansion coefficient versus mass percent IL for mixtures of

[EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl + ethanol at 348 K and 10 MPa.

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

50% [HMIM]Cl10 MPa

20 MPa

30 MPa

40 MPa

0

0.0005

0.001

0.0015

0.002

0.0025

250 300 350 400 450

Isob

ari

c E

xp

an

sivit

y (

1/K

)

Temperature (K)

[HMIM]Cl

10 MPaethanol

25%

50%

IL

75%

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 20 40 60 80 100

βP

(1/K

)

Mass % IL

348 K

10 MPa

[EMIM]Cl

[PMIM]Cl

[BMIM]Cl

[HMIM]Cl

115

Internal pressure was found to decrease with temperature while increasing with pressure.

Figures VI.16-19 show internal pressures across a range of temperatures and pressures for

mixtures of 50 mass % IL with ethanol for [EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl

along with internal pressures at 348 K for all four ILs and their mixtures with ethanol. Trends

were seen with regards to the effect of ethanol on internal pressure. For mixtures of [EMIM]Cl

with ethanol, internal pressure increased with increasing mass % IL. For mixtures of [PMIM]Cl

with ethanol, internal pressure followed a parabolic trend with a maximum at 50 mass % IL.

Both [BMIM]Cl, and [HMIM]Cl went through a maximum at 50 mass % IL and 25 mass % IL

respectively, before dropping to a minimum at 75 mass % IL, then settling at the pure IL value.

The difference between the maximum and minimum was more pronounced in the case of

[HMIM]Cl. The comparison between both ILs on the effect of IL concentration on internal

pressure at 348 K and 10 MPa is shown in Figure VI.20.

The changing effect of ethanol on internal pressure appears to be dependent on the alkyl

chain length on the cation. The length of the alkyl functional group on the imidazolium cation

leads to a further dissociation of the acetate anion. This can be seen by the general trend of

decreasing melting point with increasing alkyl chain length, as seen in Table VI.1, with melting

point dropping from 360 K for [EMIM]Cl to 206 K for [HMIM]Cl. This could provide an

explanation of the unusual effect the addition of a polar cosolvent has on the derived

thermodynamic properties of [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl. As the interaction

between the constituent ions weaken, the negatively charged anion has a greater potential to

interact with the ethanol cosolvent through hydrogen bonding. Additionally, as the alkyl chain

length increases, the potential for the cation to interact with the ethyl group on the alcohol

increases. This potentially allows for the formation of short range order in the liquid phase,

explaining the concentration dependence on both the thermodynamics and the interaction

parameter needed to employ the mixing rules for the S-L EOS.

116

Figure VI.16. Internal pressure versus pressure for 50% [EMIM]Cl + 50% ethanol (left) and

various concentrations of [EMIM]Cl + ethanol at 348 K (right).

Figure VI.17. Internal pressure versus pressure for 50% [PMIM]Cl + 50% ethanol (left) and

various concentrations of [PMIM]Cl + ethanol at 348 K (right).

300

320

340

360

380

400

420

440

460

480

500

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

50% [EMIM]Cl

300

350

400

450

500

550

600

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

[EMIM]Cl

348 K

IL

75%

50%

25%

ethanol

350

370

390

410

430

450

470

490

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

50% [PMIM]Cl

298 K

323 K

348 K

373 K

398 K

300

325

350

375

400

425

450

475

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

[PMIM]Cl

348 K

ethanol

25% IL

50% IL

75% IL

IL

117

Figure VI.18. Internal pressure versus pressure for 50% [BMIM]Cl + 50% ethanol (left) and

various concentrations of [BMIM]Cl + ethanol at 348 K (right).

Figure VI.19. Internal pressure versus pressure for 50% [HMIM]Cl + 50% ethanol (left) and

various concentrations of [HMIM]Cl + ethanol at 348 K (right).

300

320

340

360

380

400

420

440

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

50% [BMIM]Cl298K

323K

348K

373K

398K

300

320

340

360

380

400

420

440

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

[BMIM]Cl

348K

IL75%

50%

25%

ethanol

300

320

340

360

380

400

420

440

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

50% [HMIM]Cl

298 K

323 K

348 K

373 K

398 K

300

325

350

375

400

425

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

[HMIM]Cl

348 K

ethanol

25% IL

50% IL

IL

75%

118

Figure VI.20. Internal pressure versus mass percent IL for mixtures of [EMIM]Cl, [PMIM]Cl,

[BMIM]Cl, and [HMIM]Cl + ethanol at 348 K and 10 MPa.

VI.3.2 1-Alkyl-3-methylimidazolium Acetates and their Mixtures with Ethanol

The experimental densities for two ILs with the acetate anion and their mixtures with

ethanol were compared. The density data for the IL [EMIM]Ac and its mixtures with ethanol

along with the S-L EOS parameters for the IL and ethanol have been previously reported in our

publication in The Journal of Supercritical Fluids.18 The S-L EOS characteristic parameters for

[EMIM]Ac and [BMIM]Ac can be found in Table VI.8, along with RSME, % AAD, and % ℬ.

Figure VI.21 shows the density data and corresponding S-L EOS fits for both ILs. The % AADs

for [EMIM]Ac and [BMIM]Ac were found to be 0.258 % and 0.190 % respectively. Density

was found to decrease as the alkyl functional group changed from ethyl to butyl. Additionally,

mixing rules were employed in the fitting of the mixture data to the S-L EOS. A concentration

dependent interaction parameter, kij, was used as described in equation VI.1. The constants

needed to determine kij can be found in Table VI.9. The S-L EOS parameters calculated using

mixing rules for each mixture with ethanol studied in the present thesis can be found in Tables

VI.10 and 11. Figure VI.22 shows the densities as a function of pressure for both ILs and their

mixtures with ethanol at 348 K, along with the corresponding S-L EOS fits. Density was found

200

250

300

350

400

450

500

550

600

0 20 40 60 80 100

Inte

rnal

Pre

ssu

re (

MP

a)

Mass % IL

348 K

10 MPa

[EMIM]Cl

[PMIM]Cl

[BMIM]Cl

[HMIM]Cl

119

to increase with increasing IL concentration. The full range of densities for all mixtures of

[BMIM]Ac with ethanol can be found in Appendix E.

Table VI.8. S-L EOS characteristic parameters for [EMIM]Ac and [BMIM]Ac

[EMIM]Ac [BMIM]Ac

P* (Mpa) 614.59 528.62

T* (K) 557.54 590.64

rho* (g/cm3) 1.1897 1.138

MW (g/mol) 170.21 198.26

RSME (g/cm3) 0.00329 0.00241

% AAD 0.258 0.190

% ℬ 0.000312 -0.00218

Figure VI.21. Density versus pressure for ILs [EMIM]Ac (left) and [BMIM]Ac (right). S-L

EOS fits are represented by black diamonds.

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

298 K[EMIM]Ac

323 K

348 K

373 K

398 K

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

[BMIM]Ac

298K

323K

348K

373K

398K

120

Table VI.9. Comparison of Root Mean Squared Deviations (RSME) for different models of the

binary interaction parameter used in mixing rules for the S-L EOS for [EMIM]Ac and

[BMIM]Ac.

IL Mixing Rule Fit Parameter Parameter Value RSME (g/cm3)

[EMIM]Ac Constant Parameter kij -0.02439 0.00820

Volume Fraction

Dependent kij*

kA 0.19329 0.00718

kB -0.10101

[BMIM]Ac Constant Parameter kij -0.17989 0.0114

Volume Fraction

Dependent kij*

kA 0.58770 0.00481

kB -0.49625

*Equation VI.1

Table VI.10. S-L EOS characteristic parameters for [EMIM]Ac + ethanol mixtures.

Mass % IL 5 15 25 50 75

P* (Mpa) 473.46 489.53 503.39 530.89 558.56

T* (K) 553.25 558.89 561.12 555.59 545.92

rho* (g/cm3) 0.89842 0.92219 0.94725 1.0163 1.0962

r 5.4833 5.9268 6.4484 8.2674 11.516

RSME (g/cm3) 0.00642 0.00825 0.0034 0.00789 0.0078

% AAD 0.772 1.00 0.359 0.785 0.741

% ℬ -0.772 -1.00 -0.135 0.783 -0.643

121

Table VI.11. S-L EOS characteristic parameters for [BMIM]Ac + ethanol mixtures.

Mass % IL 5 14.9 25 50 75

P* (MPa) 481.55 509.72 528.86 539.81 520.64

T* (K) 569.56 599.93 619.23 623.32 591.95

ρ* (g/cm3) 0.89641 0.91668 0.93834 0.99662 1.0626

r 5.435 5.7992 6.2413 7.8143 10.81

RSME (g/cm3) 0.00302 0.00746 0.00507 0.00614 0.00911

% AAD 0.257 0.855 0.505 0.617 0.932

% ℬ 0.188 -0.784 -0.00542 -0.0579 -0.932

Figure VI.22. Density versus pressure for mixtures of [EMIM]Ac (left) and [BMIM]Ac (right)

with ethanol at 348 K. S-L EOS fits are represented by black diamonds.

VI.3.2.A Derived Thermodynamic Properties of [RMIM]Ac + Ethanol

With the S-L EOS parameters determined for both ILs and their mixtures with ethanol,

the derived thermodynamic properties isothermal compressibility, isobaric thermal expansion

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

[EMIM]Ac

348 KIL

75%

50%

25%

15%5%

ethanol

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

IL

75%

50%

25%

14.9%

5%

ethanol

[BMIM]Ac

348 K

122

coefficient, and internal pressure were calculated. The full range of derived thermodynamic

properties for the ILs and their mixtures with ethanol can be found in Appendix E.

Figures VI.23 and 24 show isothermal compressibility versus pressure for mixtures of 50

mass % IL with ethanol at all isotherms and all mixtures at 348 K for both [EMIM]Ac and

[BMIM]Ac. Compressibility was found to increase with temperature and decrease with pressure

for both ILs and all mixtures with ethanol. Both ILs were found to have similar values of

isothermal compressibility, with differences in compressibility ranging from around 1.0 %

difference at 298 K and 10 MPa, up to a maximum of 5.5 % difference at 398 K and 40 MPa,

with [EMIM]Ac having slightly high values. In spite of the similarities of the two ILs in their

pure states, differences begin to appear when these ILs are mixed with a cosolvent, in this case

ethanol. For [EMIM]Ac, isothermal compressibility was found to decrease with increasing IL

concentration. For [BMIM]Ac, this trend was only visible up to 50 mass % IL. Figure VI.25

shows isothermal compressibility versus mass % IL for both ILs at 348 K and 10 MPa. For

mixtures of [BMIM]Ac with ethanol, compressibility goes through a local minimum at 50 mass

% IL. Compressibility increases again to the 75 mass % IL point before dropping to the value

for the pure IL.

Figure VI.23. Isothermal compressibility versus pressure for 50% [EMIM]Ac + 50% ethanol

(left) and various concentrations of [EMIM]Ac + ethanol at 348 K (right).

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

50% [EMIM]Ac

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

[EMIM]Ac

348 K

ethanol

5%

15%

25%50%

75%

IL

123

Figure VI.24. Isothermal compressibility versus pressure for 50% [BMIM]Ac + 50% ethanol

(left) and various concentrations of [BMIM]Ac + ethanol at 348 K (right).

Figure VI.25. Isothermal compressibility versus mass percent IL for mixtures of [EMIM]Ac

and [BMIM]Ac + ethanol at 348 K and 10 MPa.

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

298K

323K

348K

373K

398K

50% [BMIM]Ac

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

[BMIM]Ac

348 Kethanol

5%

14.9%

25%

50%75%

IL

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0 20 40 60 80 100

κT

(1/M

Pa)

Mass % IL

348 K

10 MPa

[EMIM]Ac

[BMIM]Ac

124

Figures VI.26 and 27 show isobaric thermal expansion coefficient versus temperature for

a mixture of 50 mass % IL with ethanol at all isotherms and all mixtures at 348 K for both

[EMIM]Ac and [BMIM]Ac. As with isothermal compressibility, thermal expansion coefficient

was found to increase with temperature and decrease with pressure for both ILs and their

mixtures with ethanol. However, thermal expansion coefficient was found to be higher for

[EMIM]Ac than [BMIM]Ac. Additionally, the addition of ethanol affected the expansivity of

these ILs. For [EMIM]Ac, the coefficient was found to decrease with increasing IL

concentration. For [BMIM]Ac, this trend was only visible up to 50 mass % IL. Figure VI.28

shows isobaric thermal expansion coefficient versus mass % IL for both ILs at 348 K and 10

MPa. For mixtures of [BMIM]Ac with ethanol, thermal expansion coefficient goes through a

local minimum at 50 mass % IL and a local maximum at 75 mass % IL before dropping to the

value for the pure IL.

Figure VI.26. Isobaric expansivity versus temperature for 50% [EMIM]Ac + 50% ethanol (left)

and various concentrations of [EMIM]Ac + ethanol at 10 MPa (right).

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

0.0013

0.0014

0.0015

0.0016

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

50% [EMIM]Ac

0

0.0005

0.001

0.0015

0.002

0.0025

250 300 350 400 450

βP

(1/K

)

Temperature (K)

[EMIM]Ac

10 MPaethanol

5%

15%

25%50%

75%

IL

125

Figure VI.27. Isobaric expansivity versus temperature for 50% [BMIM]Ac + 50% ethanol (left)

and various concentrations of [BMIM]Ac + ethanol at 10 MPa (right).

Figure VI.28. Isobaric thermal expansion coefficient versus mass percent IL for mixtures of

[EMIM]Ac and [BMIM]Ac + ethanol at 348 K and 10 MPa.

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

50% [BMIM]Ac 10 MPa

20 MPa

30 MPa

40 MPa

0

0.0005

0.001

0.0015

0.002

0.0025

250 300 350 400 450

βP

(1/K

)

Temperature (K)

ethanol

5%

14.9%25%

50%75%

IL

[BMIM]Ac

10 MPa

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0 20 40 60 80 100

βP

(1/K

)

Mass % IL

348 K

10 MPa

[EMIM]Ac

[BMIM]Ac

126

Internal pressure was found to decrease with temperature while increasing with pressure.

Figures VI.29 and 30 show internal pressures across a range of temperatures and pressures for

mixtures of 50 mass % IL with ethanol for [EMIM]Ac and [BMIM]Ac along with internal

pressures at 348 K for both ILs and all mixtures with ethanol. Internal pressure was found to be

higher for [EMIM]Ac than [BMIM]Ac, indication stronger attractive interactions in the pure

[EMIM]Ac system. As with the chloride anion containing ILs, this could be explained by

disruption of the cation – anion interaction by the alkyl functional groups. As the alkyl chain

increases from an ethyl to butyl group, the ability of the anion to associate with the cation

decreases, causing a decrease in melting point and density ([EMIM]Ac melts above 303 K while

[BMIM]Ac has a melting point below 253 K as seen in Table VI.1).

With regards to mixtures with ethanol, differing trends were seen between the two ILs.

For mixtures of [EMIM]Ac with ethanol, internal pressure increased with increasing mass % IL.

For mixtures of [BMIM]Ac with ethanol, internal pressure followed a trend similar to a third

order polynomial, going through a maximum at 50 mass % IL and a minimum at 75 mass % IL.

The comparison between both ILs on the effect of IL concentration on internal pressure at 348 K

and 10 MPa is shown in Figure VI.31.

As the acetate anion dissociates with increasing alkyl chain length, the effect of the

addition of a polar cosolvent on the derived thermodynamic properties of [BMIM]Ac changes.

Isothermal compressibility and internal pressure were found to have both a maximum (75 and 50

mass % IL respectively) and a minimum (50 and 75 mass % IL respectively) as the concentration

of [BMIM]Ac increased. As the interaction between the constituent ions weaken, the negatively

charged anion has a greater potential to interact with the ethanol cosolvent through hydrogen

bonding, potentially leading to the formation of short range order in the liquid phase.

127

Figure VI.29. Internal pressure versus pressure for 50% [EMIM]Ac + 50% ethanol (left) and

various concentrations of [EMIM]Ac + ethanol at 348 K (right).

Figure VI.30. Internal pressure versus pressure for 50% [BMIM]Ac + 50% ethanol (left) and

various concentrations of [BMIM]Ac + ethanol at 348 K (right).

300

320

340

360

380

400

420

440

460

480

500

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

50% [EMIM]Ac

250

300

350

400

450

500

550

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

[EMIM]Ac

348 K

ethanol

5%15%25%

50%

75%

IL

350

370

390

410

430

450

470

490

510

530

550

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

50% [BMIM]Ac

298K

323K

348K

373K

398K

300

320

340

360

380

400

420

440

460

480

500

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

[BMIM]Ac

348 K

IL

75%

50%

25%

14.9%

5%

ethanol

128

Figure VI.31. Internal pressure versus mass percent IL for mixtures of [EMIM]Ac and

[BMIM]Ac + ethanol at 348 K and 10 MPa.

VI.3.2.B Viscosity of [RMIM]Ac + Ethanol

Viscosity data were collected for both [EMIM]Ac and [BMIM]Ac and their mixtures

with ethanol, up to 10 mass % ethanol with [EMIM]Ac and up to 25 mass % ethanol with

[BMIM]Ac. The high pressure rotational viscometer has a lower limit of 3 cP. Due to the

significant effect of both temperature and ethanol addition on viscosity, the range of

concentrations studied in the current work was limited compared to the density measurements.

For the pure ILs, viscosity was fit to the free volume theory. The parameters for the free volume

theory for both ILs can be found in Table VI.12, along with RSME, % AAD, and % ℬ.

Viscosity was found to be very temperature dependent, with a viscosity drop of approximately

75 % when temperature was increased from 298 to 323 K. Additionally, Viscosity was found to

decrease with the addition of ethanol. Adding 10 mass % ethanol caused a decrease in viscosity

of approximately 40 % in [EMIM]Ac and 70 % in [BMIM]Ac. This significant difference in the

effect of ethanol on viscosity may be due to the stronger interaction between the cosolvent and

anion, leading to further dissociation between the anions and cations. Figures VI.32 and 33 show

the viscosity versus pressure of [EMIM]Ac and [BMIM]Ac across the full range of temperatures

250

300

350

400

450

500

550

0 20 40 60 80 100

Inte

rnal

Pre

ssu

re (

MP

a)

Mass % IL

348 K

10 MPa

[BMIM]Ac

[EMIM]Ac

129

studied and their mixtures with ethanol at 323 K. The full range of values for viscosity for both

ILs and their mixtures with ethanol can be found in Appendix E.

Table VI.12. Parameters for the free volume theory of viscosity.

[EMIM]Ac [BMIM]Ac

L (cm) X 105 2.2402 0.3535

α (MPa*cm6/g*mol) 1470000 1490000

B X 103 0.50737 0.7203

RSME (mPa s) 4.00 8.30

% AAD 13.2 13.9

% ℬ 8.47 12.1

Figure VI.32. Viscosity versus pressure for [EMIM]Ac from 298-373 K (left) and mixtures of

[EMIM]Ac with ethanol at 323 K and 500 rpm (right).

0

50

100

150

200

250

0 10 20 30 40 50

Vis

cosi

ty (

cP)

Pressure (MPa)

[EMIM]Ac

500 RPM298 K (200 RPM)

323 K

348 K373 K

0

10

20

30

40

50

60

0 10 20 30 40 50

Vis

cosi

ty (

cP)

Pressure (MPa)

[EMIM]Ac

323 K

500 rpmIL

95% IL

90% IL

130

Figure VI.33. Viscosity versus pressure for [BMIM]Ac from 298-373 K (left) and mixtures of

[BMIM]Ac with ethanol at 323 K and 500 rpm (right).

VI.3.3 Hildebrand Solubility Parameters of Ionic Liquids

With internal pressure calculated, Hildebrand solubility parameter was estimated using

equation III.21. Due to their negligible vapor pressure, the heat of vaporization of ILs cannot be

easily determined, rendering it difficult to calculate the solubility parameter. Figures VI.34 and

35 show solubility parameter versus pressure for mixtures of all six ILs with ethanol at 348 K.

As with internal pressure, solubility parameter was found to increase with pressure and decrease

with temperature. Looking at ILs with the chloride anion at temperatures of both 298 K and 323

K and a pressure of 10 MPa (Figure VI.36), solubility parameter was found to increase with

increasing IL concentration in mixtures of [EMIM]Cl with ethanol. This contrasts with

[PMIM]Cl, which follows a parabolic trend with a maximum at 50 mass % IL. [BMIM]Cl and

showed a maximum at 50 mass % IL and minimum at 75 mass % IL. [HMIM]Cl showed a

minimum at 75 mass % IL. For mixtures of [EMIM]Ac and ethanol, solubility parameter

decreased with increasing IL concentration, while mixtures of [BMIM]Ac with ethanol showed a

maximum at 50 mass % IL and a minimum at 75 mass % IL (Figure VI.37). Values of the

Hildebrand solubility parameter were calculated from the S-L EOS for [EMIM]Ac at ambient

pressure in the temperature range from 313 to 393 K and compared to literature values from Yoo

0

100

200

300

400

500

600

700

800

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

[BMIM]Ac

500 RPM298 K (50 RPM)

323 K (300 rpm)

348 K373 K

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

[BMIM]Ac

323 K

500 RPMIL (300 RPM)

5%

10%

25%

131

et al (Figure VI.36).20 These values were estimated through the use of a chromatographic

technique using mixtures of ILs with solvents with known solubility parameters. The estimates

from the S-L EOS were found to be on average 5 % lower than the those calculated using the

chromatographic technique. In addition, values of the Hildebrand solubility parameter at 298 K

and ambient pressures (0.1 MPa) were estimated using the S-L EOS. Based on these

extrapolated values, the solubility parameter overall decreases with increasing alkyl chain length

on the cation. Also, with the same cation, switching from the chloride anion to acetate causes a

drop in solubility parameter. Table VI.13 shows the extrapolated values for solubility parameter

at 298 K and 0.1 MPa.

132

Figure VI.34. Solubility parameter versus pressure for mixtures of [EMIM]Cl (top left),

[PMIM]Cl (top right), [BMIM]Cl (bottom left), and [HMIM]Cl (bottom right) with ethanol at

348 K.

15

16

17

18

19

20

21

22

23

24

25

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

[EMIM]Cl

348 K

ethanol

25%

50%

75%

IL

17

18

19

20

21

22

23

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

[PMIM]Cl

348 K

ethanol

IL

25%

50%

75%

17.5

18

18.5

19

19.5

20

20.5

21

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

[BMIM]Cl

348 K

ethanol

50%

25%

75%IL

17

17.5

18

18.5

19

19.5

20

20.5

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

[HMIM]Cl

348 K 25%

50%

IL

ethanol

75%

133

Figure VI.35. Solubility parameter versus pressure for mixtures of [EMIM]Ac (left) and

[BMIM]Ac (right) with ethanol at 348 K.

Figure VI.36. Solubility parameter versus mass % IL for mixtures of [EMIM]Cl, [PMIM]Cl,

[BMIM]Cl and [HMIM]Cl with ethanol at 298 K and (left) and 348 K and (right) and 10 MPa.

15

16

17

18

19

20

21

22

23

24

25

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

[EMIM]Ac

348 K

ethanol

5%

25%15%

50%

75%

IL

17

18

19

20

21

22

23

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

[BMIM]Ac

348 K

IL

75%

50%25%

14.9%

5%

ethanol

16

17

18

19

20

21

22

23

24

0 20 40 60 80 100

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Mass % IL

298 K

10 MPa

[PMIM]Cl

[BMIM]Cl

[HMIM]Cl

[EMIM]Cl

16

17

18

19

20

21

22

23

24

0 20 40 60 80 100

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Mass % IL

348 K

10 MPa

[PMIM]Cl

[BMIM]Cl

[HMIM]Cl

[EMIM]Cl

134

Figure VI.37. Solubility parameter versus mass % IL for mixtures of [EMIM]Ac and

[BMIM]Ac with ethanol at 298 K and (left) and 348 K and (right) and 10 MPa.

Figure VI.38. Solubility parameter versus temperature at ambient pressure as estimated in the

current work using the S-L EOS and estimated through chromatographic techniques in the

literature.20

17

18

19

20

21

22

23

24

25

0 20 40 60 80 100

Solu

bit

ilit

y P

ara

met

er (

MP

a0

.5)

Mass % IL

298 K

10 MPa

[BMIM]Ac

[EMIM]Ac

15

16

17

18

19

20

21

22

23

24

25

0 20 40 60 80 100

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Mass % IL

348 K

10 MPa

[BMIM]Ac

[EMIM]Ac

20

20.5

21

21.5

22

22.5

23

23.5

24

250 300 350 400 450

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Temperature (K)

[EMIM]Ac

0.1 MPa

Literature

Values

Current

Work

135

Table VI.13. Solubility parameters of ionic liquids at 298 K and 0.1 MPa.

Ionic Liquid Solubility Parameter (MPa0.5)

[EMIM]Cl 23.1

[PMIM]Cl 19.3

[BMIM]Cl 20.0

[HMIM]Cl 18.4

[EMIM]Ac 22.6

[BMIM]Ac 21.2

VI.4 Conclusions

Changing alkyl chain length on the cation not only effects the physical properties of the

pure ionic liquid, but the interaction of the IL with a polar cosolvent. Increasing alkyl chain

length caused further dissociation of the anion from the cation, allowing for hydrogen bonding

with to occur between the anion and ethanol. Additionally, the longer alkyl chain on the cation

could increase the interaction with the ethyl group of the added alcohol. Due to these

interactions, modifications to the mixing rules used in conjunction with the S-L EOS was

required. By making the binary interaction parameter concentration dependent, the root mean

squared deviation of the fits of the mixture data decreased by up to 64 %. For ILs with the

chloride anion, these changing IL + cosolvent interactions could also be seen in the effect of

ethanol on the derived thermodynamic properties, especially internal pressure. Internal pressure

increased with increasing IL concentration for mixtures with [EMIM]Cl. For [PMIM]Cl, this

trend changed to a parabolic effect, with a maximum at 50 mass %. Both [BMIM]Cl and

[HMIM]Cl showed both a maximum and minimum (maximum at 50 and 25 mass %

respectively, minimum at 75 mass %). These complex interactions and their effects on internal

pressure could also be seen in ILs with the acetate anion and their mixtures with ethanol.

The viscosity of ionic liquid was found to drastically decrease with ethanol concentration.

Adding 10 mass % ethanol to [EMIM]Ac resulted in a decrease in viscosity of 40 %, while a

similar addition of ethanol caused a drop of 70 % in [BMIM]Ac. Increasing the alkyl chain

136

length both increases the viscosity of the pure IL and increases the effect of cosolvent addition

on viscosity.

Hildebrand solubility parameter for the six ILs and their mixtures with ethanol were

estimated as a function of temperature, pressure, and IL concentrations. Estimates of the

solubility parameter for [EMIM]Ac was found to be within 5 % of literature values. In addition,

solubility parameter was found to decrease with increasing alkyl chain length and by changing

the anion from chloride to acetate. Additionally, these estimations followed the same trends as

internal pressure. Due to the existence of both minimum and maximums in solubility parameter

as concentration is adjusted, it may be possible to create specific solvent mixtures adequately

tuned to a particular process that neither pure ethanol or the pure IL could effectively handle.

VI.5 References

1. S.A. Forsyth, J.M. Pringle, D.R. MacFarlane, Ionic Liquids-An Overview, Aust. J. Chem.

57 (2004) 113-119.

2. W. Ye, X. Li, H. Zhu, X. Wang, S. Wang, H. Wang, T. Sun, Green fabrication of

cellulose/graphene composite in ionic liquid and its electrochemical and photothermal

properties, Chemical Engineering Journal, 299 (2016) 45-55.

3. V.S. Rao, T.V. Krishna, T.M. Mohan, P.M. Rao, Thermodynamic and volumetric

behavior of green solvent 1-butyl-3-methylimidazolium tetrafluoroborate with aniline

from T=(293.15 to 323.15) K at atmospheric pressure, The Journal of Chemical

Thermodynamics, 100 (2016) 165-176.

4. T. Vancov, A.S. Alston, T. Brown, S. McIntosh, Use of ionic liquids in converting

lignocellulosic materials to biofuels, Renewable Energy, 45 (2012) 1-6.

5. F. Endres, S.Z. El Abedin, Air and water stable ionic liquids in physical chemistry, Phys.

Chem. Chem. Phys. 8 (2006) 2101-2116.

6. M.E. Zakrzewska, E.B. Lukasik, R.B. Lukasik, Solubility of carbohydrates in ionic

liquids, Energy & Fuels, 24 (2010) 737-745.

7. P. Kubisa, Ionic liquids as solvents for polymerization processes – progress and challenges,

Progress In Polymer Science, 34 (2009) 1333-1347.

8. T. Ueki, M. Watanabe, Polymers in ionic liquids. Dawn of neoteric solvents and innovative

materials, Bulletin of the Chemical Society of Japan, 85 (2012) 33-50.

9. H.Q.N. Gunarante, R. Langrick, A.V. Puga, K.R. Seddon, K. Whiston, Production of

polyetheretherketone in ionic liquid media, Green Chemistry, 15 (2013) 1166-1172.

10. N. Byrne, A. Leblais, B. Fox, Preparation of polyacrylonitrile polymer composite

precursors for carbon fiber using ionic liquid co-solvent solutions, J. Materials Chemistry

A, 2 (2014) 3424-3429.

11. H. Wang, G. Gurau, R.D. Rogers, Ionic liquid processing of cellulose, Chemical Society

Reviews, 41 (2012) 1519-1537.

137

12. M.M. Hossain, L. Aldous, Ionic liquids for lignin processing: Dissolution, isolation and

conversion, Australian Journal of Chemistry, 65 (2012) 1465-1477.

13. M. Isik, H. Sardon, D. Mecerreyes, Ionic liquids and cellulose: Dissolution, chemical

modification and preparation of new cellulose materials, International J. Molecular

Science, 15 (2014) 11922-11940.

14. M.M. Alavianmehr, S.M. Hosseini, A.A. Mohsenipour, J. Moghadasi, Further property of

ionic liquids: Hildebrand solubility parameter from new molecular thermodynamic

model, Journal of Molecular Liquids, 218 (2016) 332-341.

15. S.H. Lee, S.B. Lee, The Hildebrand solubility parameters, cohesive energy densities and

internal energies of 1-alkyl-3-methylimidazolium-based room temperature ionic liquids,

Chem. Commun., (2005) 3469-3471.

16. D.R. MacFarlane, N. Tachikawa, M. Forsyth, J.M. Pringle, P.C. Howlett, G.D. Elliot,

J.H. Davis Jr., M. Watanabe, P. Simon, C.A. Angell, Energy applications of ionic liquids,

Energy Environ. Sci., 7 (2014) 232-250.

17. J.L. Allen, D.W. McOwen, S.A. Delp, E.T. Fox, J.S. Dickmann, S.D. Han, Z.B. Zhou,

T.R. Jow, W.A. Henderson, N-Alkyl-N-methylpyrrolidinium difluoro(oxalate)borate

ionic liquids: Physical/electrochemical properties and Al corrosion, Journal of Power

Sources, 237 (2013) 104-111.

18. J.S. Dickmann, J.C. Hassler, E. Kiran, Modeling of the volumetric properties and

estimation of the solubility parameters of ionic liquid plus ethanol mixtures with the

Sanchez-Lacombe and Simha-Somcynsky equations of state: [EMIM]Ac plus ethanol

and [EMIM]Cl plus ethanol mixtures, Journal of Supercritical Fluids, 98 (2015) 86-101.

19. Bio-Rad Laboratories, Inc. SpectraBase; SpectraBase Compound ID=FM76x1IROU9

http://spectrabase.com/compound/FM76x1IROU9 (accessed Mar 03, 2019).

20. B. Yoo, W. Afzal, J.M. Prausnitz, Solubility Parameters for Nine Ionic Liquids, Ind. Eng.

Chem. Res., 51 (2012) 9913–9917.

138

VII. Conclusions

In the present thesis, it has been shown that through both experimentation and modeling

approaches, a more holistic view allowing the examination of density, viscosity, and derived

thermodynamics simultaneously can be developed for complex fluid mixtures. A novel high

pressure rotational viscometer was built and validated, allowing for the collection of viscosity

data of base oils, oil and additive mixtures, and ionic liquids across a range of temperatures,

pressures, and shear rates while also allowing for the assessment of phase behavior. This high

pressure viscosity data was used in conjunction with density data to show that models could be

generated to look at both properties, along with the derived thermodynamic properties isothermal

compressibility, isobaric thermal expansion coefficient, and internal pressure. The Sanchez-

Lacombe equation of state was shown to accurately model density for a variety of mixtures

involving low molecular weight constituents. More specifically, this equation of state was

successfully used with base oils used in the formulation of automotive lubricants and, for the first

time, ionic liquids useful in the processing of biomass. Additionally, it was shown that the

Sanchez-Lacombe equation of state could be coupled with the free volume theory to model

viscosity, linking viscosity to density and the derived thermodynamic processes. For all

mixtures studied, the collection of high pressure density and viscosity data and subsequent

generation of holistic models allowed for the examination of how the composition of these

mixtures change their intermolecular interactions and, as a result, their volumetric properties and

viscosity.

In both lubricant and ionic liquid systems, the derived thermodynamic properties,

particularly isothermal compressibility and internal pressure, were found to be affected by

compositional effects. In the case of lubricants, the internal pressure was found to increase with

increasing cycloalkane concentration in base oils. Additionally, the addition of polymeric

additives caused changes in internal pressure that differed based in the functionality of polymer.

The addition of a small number of amine groups to the polymethacrylate base polymer added

more repulsive interactions, causing a subsequent drop in internal pressure in these mixtures

compared to the non-amine functionalized additive. The effect of cosolvent addition on ionic

liquids was found to change with cation modification. As the alkyl chain length increased on the

1-alkyl-3-methylimidazlium cation, the association with the anion further decreased. With the

139

greater opportunity for anion-cosolvent interactions, the overall trends for internal pressure

change from a near linear increase with increasing ionic liquid addition, to going through a

maximum, to even going through both a minimum and a maximum as fluid concentration

changes.

The ability to effectively model these trends creates opportunities for improving these

systems for their desired use cases. In the case of lubrication, understanding the effect of

composition on compressibility is useful in creating engine oils and automatic transmission

fluids that can effectively form films during the high pressure and high shear conditions they are

exposed to while in mechanical systems. In the case of ionic liquids, Hildebrand solubility

parameter can be estimated from these derived thermodynamic properties, allowing for the

tuning of these mixtures for task specific applications. Understanding the formation of short

range order between an ionic liquid with its cosolvent can lead to potentially better solvents than

either pure fluid, or cost savings as the amount on ionic liquid needed for a specialty process is

reduced. Additionally, the effectiveness of both lubricants and solvents requires knowledge of

the viscosity, showing the necessity of having a holistic understanding of all the properties of

these mixtures under high pressure conditions.

VII.1 Recommendations for Future Work

While the current study has looked at the volumetric properties, derived thermodynamic

properties, and viscosity of a number of complex mixtures and related them back to composition,

the research can be further expanded in the future. The following are some recommendations:

1. In addition to the work on determining the effect of viscosity index modifying polymers

on base oil properties carried out in the present study, other additives, in particular

dispersants, can be explored. Dispersants are known to form micellar structures in the

fluid phase. How the properties of oils are altered with respect to isothermal

compressibility, internal pressure, and viscosity in the presence of micelle forming

additives should be explored.

2. Data on volumetric properties and viscosity do not tell the whole story with regards to the

physical interactions between base oils and certain additives. In the case of the viscosity

index modifiers, there are still unanswered questions regarding how, for example, the

140

amine groups on polymethacrylate based additives effect both solvent – polymer and

polymer – polymer interactions. It would be useful to know what causes the significant

drop in internal pressure at the higher (~ 7 wt%) concentrations of polymer in the mixtures

with the amine containing polymer additive compared to the mixtures with the additive

that only contains alkyl group functionality. This drop appears to be due to an increase in

repulsive intermolecular interactions as these nitrogen containing groups are introduced to

a purely paraffinic fluid. However, this effect is not seen until high concentrations,

suggesting that short-range order between the polymer chains may form at these

conditions. In addition to the lubricants, the present findings suggest that short-range

order also forms in the case of the ionic liquid + ethanol mixtures. It may be possible to

further elucidate the formation of short – ranged structures in the bulk fluid using either

spectroscopy or light/x-ray scattering techniques. Of particular interest for this type of

study would be the use of Raman spectroscopy due to its previous use in the literature in

detecting the presence of aggregates in the bulk fluid phase of ternary mixtures at high

pressures.1

3. Ionic liquid structure has an impact on the interaction of the constituent ions with the

cosolvent. By varying alkyl chain length, the cation – anion interactions decrease, leading

to greater interactions with the cosolvent. In the current study, the 1-alkyl-3-

methylimidazolium cation was used. Further functionalization of the cation can be carried

out. Adding an additional alkyl group to the imidazolium cation can lead to further

dissociation of the anion. There is potential to further develop an understanding of the

solvent – anion interactions by studying 1-alkyl-2,3-dimethylimidazolium chloride ionic

liquids and their mixtures with ethanol. Adding further asymmetry to the cation should

have the effect of increasing solvent – anion interactions, allowing the further

confirmation and examination of the trends seen in the present thesis.

VII.2 References

1. N. Grimaldi, P.E. Rojas, S. Stehle, A. Cordoba, R. Schweins, S. Sala, S. Luelsdorf, D.

Pina, J. Veciana, J. Faraudo, A. Triolo, A.S. Braeuer, N. Ventosa, Pressure-Responsive,

Surfactant-Free CO2-Based Nanostructured Fluids, ACS Nano, 11 (2017) 10774-10784.

141

Appendix A: Publications Based on the Present Thesis

J.S. Dickmann, J.C. Hassler, E. Kiran, Modeling of the volumetric properties and estimation of

the solubility parameters of ionic liquid plus ethanol mixtures with the Sanchez-Lacombe and

Simha-Somcynsky equations of state: [EMIM]Ac plus ethanol and [EMIM]Cl plus ethanol

mixtures, Journal of Supercritical Fluids, 98 (2015) 86-101.

J.S. Dickmann, J.C. Hassler, E. Kiran, High Pressure Volumetric Properties and Viscosity of

Base Oils Used in Automotive Lubricants and Their Modeling, Industrial & Engineering

Chemistry Research, 57 (2018) 17266-17275.

142

Appendix B: Calibration and Verification of Density and Viscosity Measurements

In this section, the results of the verification and calibration of the experimental systems

have been reported.

Table B.1 shows the comparison of literature values to the results of a verification run

using ethanol in the variable-volume view-cell.

Figures B.1-B.12 show the collected torque values, both measured and corrected, for all

oil standards used in the calibration of the high pressure rotational viscometer. For a complete

list of these standards, see Table II.1.

This Appendix has been organized into three sections:

B.1 Verification Results of the Variable-Volume View-Cell for Density Determinations

B.2 Torque Values of Calibrations Standards ( N14, S60, RT50, RT 100) as Determined

with the High Pressure Rotational Viscometer

B.3 References

143

B.1 Verification Results of the Variable-Volume View-Cell for Density Determinations

Table B.1. Comparison of literature values with verification run for densities of ethanol in the

variable-volume view-cell.1

T (K) P (MPa) literature ρ (g/cm3) Average ρ (g/cm3) % Deviation

298 10 0.79398 0.78545 1.074

298 20 0.80179 0.79513 0.831

298 30 0.80896 0.80330 0.700

298 40 0.81562 0.81165 0.487

323 10 0.77347 0.76965 0.494

323 20 0.78237 0.77765 0.603

323 30 0.79046 0.78563 0.612

323 40 0.79788 0.79410 0.474

348 10 0.75137 0.74740 0.528

348 20 0.76167 0.75728 0.576

348 30 0.77087 0.76666 0.546

348 40 0.77922 0.77540 0.490

373 10 0.72705 0.72673 0.044

373 20 0.73918 0.73756 0.219

373 30 0.7498 0.74728 0.336

373 40 0.7593 0.75635 0.389

398 10 0.69993 0.70470 -0.681

398 20 0.71452 0.71738 -0.401

398 30 0.72697 0.72913 -0.298

398 40 0.73788 0.73975 -0.253

144

B.2 Torque Values of Calibrations Standards ( N14, S60, RT50, RT 100) as Determined with the

High Pressure Rotational Viscometer

Figure B.1. Torque versus time at 298 K for N14, both raw (left) and corrected (right) values.

Figure B.2. Torque versus time at 323 K for N14, both raw (left) and corrected (right) values.

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80

Torq

ue

(N m

)

Times (s)

N14

298 K

0.1 MPa

100 rpm

200 rpm

300 rpm

400 rpm

500 rpm

600 rpm

700 rpm

800 rpm

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80C

orr

ecte

d T

orq

ue

(N m

)

Times (s)

N14

298 K

0.1 MPa

100 rpm

200 rpm

300 rpm

400 rpm

500 rpm

600 rpm

700 rpm

800 rpm

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

0 20 40 60 80

Torq

ue

(N m

)

Time (s)

N14

323 K

0.1 MPa

800

700

600500

400

300

200

100

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

0 20 40 60 80

Corr

ecte

d T

orq

ue

(N m

)

Time (s)

N14

323 K

0.1 MPa

800

700

600

500

400300

200

100

145

Figure B.3. Torque versus time at 353 K for N14, both raw (left) and corrected (right) values.

Figure B.4. Torque versus time at 373 K for N14, both raw (left) and corrected (right) values.

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0 20 40 60 80

Torq

ue

(N m

)

Time (s)

N14

353 K

0.1 MPa

800

700

600500

400

300

200

100

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0 20 40 60 80

Corr

ecte

d T

orq

ue

(N m

)

Time (s)

N14

353 K

0.1 MPa

800

700

600

500

400300

200

100

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 20 40 60 80

Torq

ue

(N m

)

Time (s)

N14

373 K

0.1 MPa

100

200

300

400

500

600

700

800

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 20 40 60 80

Corr

ecte

d T

orq

ue

(N m

)

Time (s)

N14

373 K

0.1 MPa

100

200

300

400

500

600

700

800

146

Figure B.5. Torque versus time at 298 K for S60, both raw (left) and corrected (right) values.

Figure B.6. Torque versus time at 323 K for S60, both raw (left) and corrected (right) values.

0

0.004

0.008

0.012

0.016

0.02

0.024

0.028

0 20 40 60 80

Torq

ue

(N m

)

Time (s)

S60

298 K

0.1 MPa

300

250

200

150

100

50

0

0.004

0.008

0.012

0.016

0.02

0.024

0.028

0 20 40 60 80

Corr

ecte

d T

orq

ue

(N m

)

Time (s)

S60

298 K

0.1 MPa

250

150

300

200

50

100

0

0.004

0.008

0.012

0.016

0.02

0.024

0.028

0.032

0 20 40 60 80

Torq

ue

(N m

)

Time (s)

S60

323 K

0.1 MPa

800

700

600500

400

300

200

100

0

0.004

0.008

0.012

0.016

0.02

0.024

0.028

0.032

0 20 40 60 80

Corr

ecte

d T

orq

ue

(N m

)

Time (s)

S60

323 K

0.1 MPa

800

700

600

500

400300

200

100

147

Figure B.7. Torque versus time at 353 K for S60, both raw (left) and corrected (right) values.

Figure B.8. Torque versus time at 373 K for S60, both raw (left) and corrected (right) values.

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

0.024

0.026

0 20 40 60 80

Torq

ue

(N m

)

Time (s)

S60

353 K

0.1 MPa

800

700

600500

400

300

200

100

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

0.024

0.026

0 20 40 60 80

Corr

ecte

d T

orq

ue

(N m

)

Time (s)

S60

353 K

0.1 MPa

800

700

600

500

400300

200

100

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

0 20 40 60 80

Torq

ue

(N m

)

Time (s)

S60

373 K

0.1 MPa

800

700

600500

400

300

200

100

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0 20 40 60 80

Corr

ecte

d T

orq

ue

(N m

)

Time (s)

S60

373 K

0.1 MPa

800

700

600

500

400300

200

100

148

Figure B.9. Torque versus time at 298 K for RT50, both raw (left) and corrected (right) values.

Figure B.10. Torque versus time at 313 K for RT50, both raw (left) and corrected (right) values.

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80

Torq

ue

(N m

)

Time (s)

RT50

298 K

0.1 MPa

600

500

400

300

200

100

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80

Corr

ecte

d T

orq

ue

(N m

)

Time (s)

RT50

298 K

0.1 MPa

600

500

400

300

200

100

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80

Torq

ue

(N m

)

Time (s)

RT50

313 K

0.1 MPa800

700

600500

400

300

200

100

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80

Corr

ecte

d T

orq

ue

(N m

)

Time (s)

RT50

313 K

0.1 MPa

800

700

600

500

400

300

200

100

149

Figure B.11. Torque versus time at 298 K for RT100, both raw (left) and corrected (right)

values.

Figure B.12. Torque versus time at 313 K for RT100, both raw (left) and corrected (right)

values.

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80

Torq

ue

(N m

)

Time (s)

RT100

298 K

0.1 MPa

400

300

200

100

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80

Corr

ecte

d T

orq

ue

(N m

)

Time (s)

RT100

298 K

0.1 MPa

400

300

200

100

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80

Torq

ue

(N m

)

Time (s)

RT100

313 K

0.1 MPa

600

500

400

300

200

100

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80

Corr

ecte

d T

orq

ue

(N m

)

Time (s)

RT100

313 K

0.1 MPa

600

500

400

300

200

100

150

B.3 References

1. I.M. Abdulagatov, F.Sh. Aliyev, M.A. Talibov, J.T. Safarov, A.N. Shahverdiyev, E.P.

Hassel, High-pressure densities and derived volumetric properties (excess and partial

molar volumes, vapor-pressures) of binary methanol + ethanol mixtures, Thermochimica

Acta, 476 (2008) 51-62.

151

Appendix C: Density, Derived Thermodynamic Properties, and Viscosity of Base Oils

In this section, the full range of density, derived thermodynamic properties, and viscosity

for base oils IIA, IIIA, IIIB, PAO 4, and PAO 8 have been reported.

Figures C.1-C.5 show density, isothermal compressibility, isobaric thermal expansion

coefficient, and internal pressure of all five base oils from 10-40 MPa and 298-398 K.

Figures C.6-C.10 show viscosity versus pressure for all five base oils from 10-40 MPa

and 298-373 K.

Tables C.1-C.5 include select data for density as calculated from the Sanchez-Lacombe

equation of state, derived thermodynamic properties, and viscosity as calculated from the free

volume theory.

This Appendix has been organized into three sections:

C.1 PVT data and thermodynamic properties for IIA, IIIA, IIIB, PAO 4, and PAO 8

C.2 Viscosity data for IIA, IIIA, IIIB, PAO 4, and PAO 8

C.3 Select tabulated data for IIA, IIIA, IIIB, PAO 4, and PAO 8

152

C.1 PVT data and thermodynamic properties for IIA, IIIA, IIIB, PAO 4, and PAO 8

Figure C.1. PVT data and thermodynamic properties for IIA: Density (top left), isothermal

compressibility (top right), isobaric thermal expansion coefficient (bottom left), and internal

pressure (bottom right).

0.77

0.79

0.81

0.83

0.85

0.87

0.89

0.91

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

IIA298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

IIA

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

IIA

300

320

340

360

380

400

420

440

460

480

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

IIA

153

Figure C.2. PVT data and thermodynamic properties for IIIA: Density (top left), isothermal

compressibility (top right), isobaric thermal expansion coefficient (bottom left), and internal

pressure (bottom right).

0.73

0.75

0.77

0.79

0.81

0.83

0.85

0.87

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure, MPa

IIIA298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

IIIA

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

IIIA

300

320

340

360

380

400

420

440

460

480

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

IIIA

154

Figure C.3. PVT data and thermodynamic properties for IIIB: Density (top left), isothermal

compressibility (top right), isobaric thermal expansion coefficient (bottom left), and internal

pressure (bottom right).

0.73

0.75

0.77

0.79

0.81

0.83

0.85

0.87

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

IIIB298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

IIIB

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

IIIB

300

320

340

360

380

400

420

440

460

480

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

IIIB

155

Figure C.4. PVT data and thermodynamic properties for PAO 4: Density (top left), isothermal

compressibility (top right), isobaric thermal expansion coefficient (bottom left), and internal

pressure (bottom right).

0.73

0.75

0.77

0.79

0.81

0.83

0.85

0.87

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

PAO 4298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

PAO 4

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

PAO 4

290

310

330

350

370

390

410

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

PAO 4

156

Figure C.5. PVT data and thermodynamic properties for PAO 8: Density (top left), isothermal

compressibility (top right), isobaric thermal expansion coefficient (bottom left), and internal

pressure (bottom right).

0.75

0.77

0.79

0.81

0.83

0.85

0.87

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

PAO 8

298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

SS8

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

PAO 8

280

300

320

340

360

380

400

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

PAO 8

157

C.2 Viscosity data for IIA, IIIA, IIIB, PAO 4, and PAO 8

Figure C.6. Viscosity versus pressure for IIA at 500 rpm (left) and 323 K (right).

Figure C.7. Viscosity versus pressure for IIIA at 500 rpm (left) and 323 K (right).

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

IIA

500 RPM 298 K

323 K

348 K

373 K0

5

10

15

20

25

30

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)Pressure (MPa)

IIA

323 K

300-800 RPM

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

IIIA

500 RPM 298 K

323 K

348 K

373 K

0

2

4

6

8

10

12

14

16

18

20

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

IIIA

323 K

300-800 RPM

158

Figure C.8. Viscosity versus pressure for IIIB at 500 rpm (left) and 323 K (right).

Figure C.9. Viscosity versus pressure for PAO 4 at 500 rpm (left) and 323 K (right).

0

20

40

60

80

100

120

140

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

IIIB

500 RPM 298 K

(300 RPM)

323 K

348 K

373 K

0

10

20

30

40

50

60

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

IIIB

323 K

300-800 RPM

0

10

20

30

40

50

60

70

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

PAO 4

500 rpm298 K

323 K

348 K

373 K

0

5

10

15

20

25

30

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

PAO 4

323 K

300-800 RPM

159

Figure C.10. Viscosity versus pressure for PAO 8 at 500 rpm (left) and 323 K (right).

0

50

100

150

200

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

PAO 8

500 RPM298 K

(200 RPM)

348 K373 K

323 K

0

10

20

30

40

50

60

70

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

PAO 8

323 K

300-800 RPM

160

C.3 Select tabulated data for IIA, IIIA, IIIB, PAO 4, and PAO 8

Table C.1. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the

S-L EOS and free volume model for base oil IIA.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)

298 10 0.8773 0.0005165 0.0007563 426.3 47.86

298 15 0.8795 0.0004934 0.0007343 428.5 53.22

298 20 0.8816 0.0004720 0.0007135 430.5 59.09

298 25 0.8837 0.0004520 0.0006939 432.5 65.52

298 30 0.8856 0.0004333 0.0006753 434.4 72.55

298 35 0.8875 0.0004158 0.0006576 436.3 80.25

298 40 0.8893 0.0003994 0.0006407 438.1 88.65

323 10 0.8601 0.0006385 0.0008297 409.7 14.51

323 15 0.8627 0.0006080 0.0008043 412.3 16.08

323 20 0.8653 0.0005799 0.0007805 414.7 17.78

323 25 0.8678 0.0005539 0.0007581 417.1 19.63

323 30 0.8701 0.0005298 0.0007370 419.4 21.64

323 35 0.8724 0.0005073 0.0007171 421.5 23.83

323 40 0.8745 0.0004864 0.0006982 423.6 26.20

348 10 0.8416 0.0007800 0.0009018 392.4 5.33

348 15 0.8448 0.0007399 0.0008725 395.4 5.90

348 20 0.8479 0.0007032 0.0008452 398.2 6.50

348 25 0.8508 0.0006696 0.0008197 401.0 7.16

348 30 0.8536 0.0006387 0.0007958 403.6 7.87

348 35 0.8563 0.0006101 0.0007734 406.1 8.63

348 40 0.8588 0.0005836 0.0007522 408.6 9.46

373 10 0.8221 0.0009445 0.0009734 374.4 2.28

373 15 0.8259 0.0008919 0.0009394 377.9 2.51

373 20 0.8295 0.0008443 0.0009080 381.1 2.77

373 25 0.8329 0.0008010 0.0008790 384.3 3.04

373 30 0.8362 0.0007615 0.0008520 387.3 3.33

373 35 0.8393 0.0007253 0.0008268 390.2 3.65

373 40 0.8423 0.0006919 0.0008032 393.0 3.99

398 10 0.8017 0.0011365 0.0010451 356.0 -

398 15 0.8061 0.0010675 0.0010055 359.9 -

398 20 0.8103 0.0010057 0.0009695 363.7 -

398 25 0.8142 0.0009501 0.0009364 367.2 -

398 30 0.8180 0.0008999 0.0009059 370.6 -

398 35 0.8216 0.0008542 0.0008776 373.9 -

398 40 0.8250 0.0008124 0.0008513 377.0 -

161

Table C2. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the

S-L EOS and free volume model for base oil IIB.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)

298 10 0.8847 0.0005097 0.0007415 423.55 99.55

298 15 0.8869 0.0004869 0.0007199 425.66 107.44

298 20 0.8890 0.0004657 0.0006996 427.69 115.76

298 25 0.8910 0.0004459 0.0006803 429.65 124.53

298 30 0.8930 0.0004275 0.0006620 431.53 133.78

298 35 0.8948 0.0004102 0.0006447 433.34 143.52

298 40 0.8966 0.0003940 0.0006281 435.08 153.77

323 10 0.8676 0.0006290 0.0008128 407.40 26.16

323 15 0.8703 0.0005990 0.0007880 409.91 28.22

323 20 0.8729 0.0005714 0.0007648 412.31 30.39

323 25 0.8753 0.0005458 0.0007429 414.62 32.66

323 30 0.8776 0.0005221 0.0007222 416.84 35.05

323 35 0.8799 0.0005000 0.0007027 418.98 37.56

323 40 0.8820 0.0004794 0.0006842 421.03 40.18

348 10 0.8494 0.0007670 0.0008827 390.49 8.54

348 15 0.8526 0.0007277 0.0008541 393.42 9.22

348 20 0.8556 0.0006919 0.0008275 396.22 9.93

348 25 0.8585 0.0006589 0.0008026 398.90 10.67

348 30 0.8613 0.0006286 0.0007793 401.48 11.45

348 35 0.8640 0.0006005 0.0007574 403.95 12.26

348 40 0.8665 0.0005745 0.0007368 406.33 13.10

373 10 0.8302 0.0009268 0.0009517 372.99 3.30

373 15 0.8339 0.0008756 0.0009187 376.36 3.57

373 20 0.8375 0.0008291 0.0008882 379.58 3.84

373 25 0.8409 0.0007869 0.0008600 382.66 4.13

373 30 0.8441 0.0007482 0.0008337 385.61 4.43

373 35 0.8472 0.0007128 0.0008092 388.43 4.75

373 40 0.8502 0.0006802 0.0007862 391.15 5.07

398 10 0.8100 0.0011125 0.0010204 355.04 -

398 15 0.8143 0.0010455 0.0009822 358.89 -

398 20 0.8185 0.0009856 0.0009473 362.55 -

398 25 0.8224 0.0009316 0.0009153 366.04 -

398 30 0.8262 0.0008826 0.0008857 369.38 -

398 35 0.8297 0.0008381 0.0008583 372.57 -

398 40 0.8331 0.0007974 0.0008327 375.63 -

162

Table C.3. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the

S-L EOS and free volume model for base oil IIIA.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)

298 10 0.8365 0.0005734 0.0008003 405.91 26.37

298 15 0.8388 0.0005464 0.0007759 408.18 28.84

298 20 0.8411 0.0005213 0.0007529 410.37 31.50

298 25 0.8432 0.0004981 0.0007312 412.46 34.35

298 30 0.8453 0.0004765 0.0007108 414.48 37.41

298 35 0.8473 0.0004564 0.0006914 416.42 40.69

298 40 0.8492 0.0004376 0.0006730 418.28 44.22

323 10 0.8191 0.0007097 0.0008772 389.23 9.66

323 15 0.8220 0.0006737 0.0008488 391.93 10.54

323 20 0.8247 0.0006408 0.0008224 394.52 11.48

323 25 0.8273 0.0006105 0.0007976 396.99 12.49

323 30 0.8297 0.0005825 0.0007744 399.37 13.56

323 35 0.8321 0.0005566 0.0007525 401.65 14.71

323 40 0.8344 0.0005326 0.0007318 403.84 15.93

348 10 0.8006 0.0008685 0.0009529 371.82 4.15

348 15 0.8040 0.0008209 0.0009200 374.98 4.53

348 20 0.8072 0.0007778 0.0008895 377.99 4.92

348 25 0.8103 0.0007385 0.0008612 380.86 5.34

348 30 0.8132 0.0007024 0.0008349 383.61 5.79

348 35 0.8160 0.0006693 0.0008102 386.25 6.27

348 40 0.8187 0.0006388 0.0007871 388.79 6.77

373 10 0.7810 0.0010541 0.0010283 353.86 2.02

373 15 0.7850 0.0009913 0.0009899 357.49 2.20

373 20 0.7888 0.0009349 0.0009548 360.95 2.39

373 25 0.7924 0.0008840 0.0009225 364.25 2.59

373 30 0.7958 0.0008379 0.0008926 367.39 2.81

373 35 0.7991 0.0007958 0.0008649 370.41 3.04

373 40 0.8022 0.0007573 0.0008391 373.29 3.27

398 10 0.7605 0.0012718 0.0011040 335.49 -

398 15 0.7652 0.0011887 0.0010592 339.64 -

398 20 0.7696 0.0011152 0.0010187 343.57 -

398 25 0.7738 0.0010496 0.0009818 347.31 -

398 30 0.7777 0.0009906 0.0009480 350.87 -

398 35 0.7815 0.0009374 0.0009168 354.27 -

398 40 0.7851 0.0008891 0.0008880 357.51 -

163

Table C.4. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the

S-L EOS and free volume model for base oil IIIB.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)

298 10 0.8432 0.0005262 0.0007589 419.77 87.64

298 15 0.8453 0.0005025 0.0007367 421.93 97.08

298 20 0.8474 0.0004804 0.0007157 424.01 107.38

298 25 0.8494 0.0004598 0.0006959 426.01 118.60

298 30 0.8513 0.0004406 0.0006771 427.93 130.81

298 35 0.8532 0.0004227 0.0006593 429.78 144.11

298 40 0.8549 0.0004059 0.0006423 431.56 158.57

323 10 0.8266 0.0006494 0.0008311 403.40 26.60

323 15 0.8292 0.0006181 0.0008055 405.97 29.37

323 20 0.8317 0.0005892 0.0007816 408.43 32.37

323 25 0.8341 0.0005626 0.0007590 410.78 35.61

323 30 0.8364 0.0005379 0.0007378 413.05 39.12

323 35 0.8386 0.0005149 0.0007177 415.23 42.92

323 40 0.8407 0.0004935 0.0006987 417.33 47.02

348 10 0.8089 0.0007919 0.0009018 386.30 9.79

348 15 0.8120 0.0007508 0.0008722 389.29 10.78

348 20 0.8150 0.0007133 0.0008448 392.15 11.86

348 25 0.8178 0.0006790 0.0008192 394.89 13.01

348 30 0.8205 0.0006473 0.0007953 397.51 14.26

348 35 0.8231 0.0006182 0.0007728 400.04 15.59

348 40 0.8256 0.0005911 0.0007516 402.46 17.03

373 10 0.7901 0.0009571 0.0009715 368.62 4.18

373 15 0.7938 0.0009033 0.0009374 372.07 4.60

373 20 0.7973 0.0008548 0.0009060 375.35 5.05

373 25 0.8006 0.0008107 0.0008769 378.49 5.54

373 30 0.8038 0.0007704 0.0008499 381.49 6.06

373 35 0.8068 0.0007335 0.0008247 384.37 6.61

373 40 0.8097 0.0006996 0.0008011 387.13 7.20

398 10 0.7705 0.0011491 0.0010409 350.54 -

398 15 0.7748 0.0010788 0.0010015 354.46 -

398 20 0.7789 0.0010160 0.0009655 358.19 -

398 25 0.7827 0.0009596 0.0009325 361.75 -

398 30 0.7864 0.0009086 0.0009020 365.14 -

398 35 0.7899 0.0008622 0.0008739 368.39 -

398 40 0.7932 0.0008199 0.0008477 371.50 -

164

Table C.5. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the

S-L EOS and free volume model for base oil PAO 4.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)

298 10 0.8345 0.0006138 0.0007690 363.34 38.50

298 15 0.8370 0.0005820 0.0007432 365.52 41.76

298 20 0.8393 0.0005528 0.0007191 367.60 45.22

298 25 0.8416 0.0005260 0.0006964 369.58 48.89

298 30 0.8438 0.0005011 0.0006752 371.49 52.78

298 35 0.8458 0.0004781 0.0006551 373.31 56.91

298 40 0.8478 0.0004567 0.0006361 375.06 61.29

323 10 0.8178 0.0007573 0.0008417 349.00 15.14

323 15 0.8208 0.0007155 0.0008120 351.58 16.40

323 20 0.8237 0.0006774 0.0007845 354.03 17.72

323 25 0.8264 0.0006427 0.0007588 356.38 19.13

323 30 0.8290 0.0006107 0.0007348 358.62 20.61

323 35 0.8315 0.0005814 0.0007123 360.76 22.17

323 40 0.8339 0.0005542 0.0006911 362.81 23.81

348 10 0.8001 0.0009233 0.0009127 334.02 6.90

348 15 0.8037 0.0008685 0.0008785 337.02 7.47

348 20 0.8071 0.0008191 0.0008471 339.88 8.07

348 25 0.8103 0.0007744 0.0008180 342.60 8.70

348 30 0.8134 0.0007337 0.0007911 345.19 9.36

348 35 0.8163 0.0006965 0.0007659 347.66 10.05

348 40 0.8190 0.0006624 0.0007424 350.03 10.78

373 10 0.7813 0.0011158 0.0009828 318.56 3.52

373 15 0.7856 0.0010441 0.0009434 322.02 3.82

373 20 0.7896 0.0009803 0.0009074 325.29 4.12

373 25 0.7933 0.0009230 0.0008745 328.40 4.44

373 30 0.7969 0.0008714 0.0008442 331.36 4.78

373 35 0.8003 0.0008247 0.0008162 334.18 5.13

373 40 0.8035 0.0007820 0.0007902 336.87 5.49

398 10 0.7617 0.0013394 0.0010525 302.76 -

398 15 0.7667 0.0012457 0.0010069 306.69 -

398 20 0.7713 0.0011634 0.0009658 310.40 -

398 25 0.7756 0.0010905 0.0009286 313.92 -

398 30 0.7797 0.0010254 0.0008946 317.26 -

398 35 0.7836 0.0009669 0.0008634 320.43 -

398 40 0.7873 0.0009140 0.0008347 323.46 -

165

Table C.6. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the

S-L EOS and free volume model for base oil PAO 8.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)

298 10 0.8340 0.0006204 0.0007538 352.06 119.96

298 15 0.8366 0.0005875 0.0007278 354.19 131.98

298 20 0.8389 0.0005573 0.0007035 356.22 144.89

298 25 0.8412 0.0005295 0.0006808 358.16 158.75

298 30 0.8434 0.0005039 0.0006594 360.02 173.61

298 35 0.8455 0.0004801 0.0006393 361.79 189.54

298 40 0.8475 0.0004581 0.0006203 363.49 206.60

323 10 0.8177 0.0007649 0.0008251 338.43 35.56

323 15 0.8208 0.0007216 0.0007953 340.95 39.06

323 20 0.8237 0.0006824 0.0007676 343.35 42.81

323 25 0.8264 0.0006465 0.0007419 345.64 46.80

323 30 0.8290 0.0006137 0.0007179 347.83 51.06

323 35 0.8315 0.0005835 0.0006954 349.91 55.59

323 40 0.8339 0.0005557 0.0006742 351.91 60.43

348 10 0.8003 0.0009316 0.0008947 324.18 12.83

348 15 0.8040 0.0008751 0.0008604 327.13 14.09

348 20 0.8074 0.0008243 0.0008289 329.92 15.43

348 25 0.8106 0.0007784 0.0007998 332.57 16.85

348 30 0.8137 0.0007367 0.0007729 335.10 18.36

348 35 0.8166 0.0006986 0.0007478 337.51 19.96

348 40 0.8194 0.0006636 0.0007243 339.81 21.66

373 10 0.7820 0.0011245 0.0009631 309.47 5.40

373 15 0.7862 0.0010508 0.0009237 312.85 5.93

373 20 0.7902 0.0009854 0.0008878 316.05 6.49

373 25 0.7940 0.0009268 0.0008550 319.09 7.09

373 30 0.7976 0.0008740 0.0008248 321.97 7.71

373 35 0.8010 0.0008263 0.0007968 324.72 8.38

373 40 0.8042 0.0007828 0.0007709 327.34 9.08

398 10 0.7627 0.0013480 0.0010310 294.42 -

398 15 0.7677 0.0012521 0.0009855 298.27 -

398 20 0.7723 0.0011680 0.0009446 301.90 -

398 25 0.7767 0.0010935 0.0009076 305.33 -

398 30 0.7808 0.0010272 0.0008738 308.58 -

398 35 0.7847 0.0009676 0.0008429 311.67 -

398 40 0.7884 0.0009139 0.0008143 314.62 -

166

Appendix D: Density, Derived Thermodynamic Properties, and Viscosity of Mixtures of

Base Oils with Additives and Automatic Transmission Fluids

In this section, the full range of density, derived thermodynamic properties, and viscosity

for mixtures of PAO 4 with two methacrylate based polymeric additives and two automatic

transmission fluids have been reported.

Figures D.1-D.8 show density, isothermal compressibility, isobaric thermal expansion

coefficient, and internal pressure of mixtures of PAO 4 with both polymeric additives up to 7

mass percent from 10-40 MPa and 298-398 K.

Figures D.9-D.16 show viscosity versus pressure for all mixtures from 10-40 MPa and

298-373 K.

Figures D.17 and D.18 show density and the derived thermodynamic properties for both

ATFs.

Tables D.1-D.10 include select data for density as calculated from the Sanchez-Lacombe

equation of state, derived thermodynamic properties, and viscosity as calculated from the free

volume theory.

This Appendix has been organized into four sections:

D.1 Density and Derived Thermodynamic Properties of Mixtures of PAO4 + Viscosity

Index Modifiers

D.2 Viscosity of Mixtures of PAO 4 + Viscosity Index Modifiers

D.3 Density and Derived Thermodynamic Properties of ATFs

D.4 Select Tabulated Data for Mixtures of PAO 4 + Viscosity Index Modifiers and ATFs

167

D.1 Density and Derived Thermodynamic Properties of Mixtures of PAO4 + Viscosity Index

Modifiers

Figure D.1. PVT data and thermodynamic properties for a mixture of PAO 4 + 0.71 mass %

Polymer 1: Density (top left), isothermal compressibility (top right), isobaric thermal expansion

coefficient (bottom left), and internal pressure (bottom right).

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

0.71% Polymer 1

298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50κ

T(1

/MP

a)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

0.71% Polymer 1

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

0.71% Polymer 1

250

270

290

310

330

350

370

390

410

430

450

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

0.71% Polymer 1

168

Figure D.2. PVT data and thermodynamic properties for a mixture of PAO 4 + 1.42 mass %

Polymer 1: Density (top left), isothermal compressibility (top right), isobaric thermal expansion

coefficient (bottom left), and internal pressure (bottom right).

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

1.42% Polymer 1

298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

1.42% Polymer 1

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

1.42% Polymer 1

300

320

340

360

380

400

420

440

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

1.42% Polymer 1

169

Figure D.3. PVT data and thermodynamic properties for a mixture of PAO 4 + 2.85 mass %

Polymer 1: Density (top left), isothermal compressibility (top right), isobaric thermal expansion

coefficient (bottom left), and internal pressure (bottom right).

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

2.85% Polymer 1

298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

2.85% Polymer 1

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

2.85% Polymer 1

300

320

340

360

380

400

420

440

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

2.85% Polymer 1

170

Figure D.4. PVT data and thermodynamic properties for a mixture of PAO 4 + 7.12 mass %

Polymer 1: Density (top left), isothermal compressibility (top right), isobaric thermal expansion

coefficient (bottom left), and internal pressure (bottom right).

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

7.12% Polymer 1

298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K323 K

298 K

7.12% Polymer 1

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

7.12% Polymer 1

200

210

220

230

240

250

260

270

280

290

300

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

7.12% Polymer 1

171

Figure D.5. PVT data and thermodynamic properties for a mixture of PAO 4 + 0.70 mass %

Polymer 2: Density (top left), isothermal compressibility (top right), isobaric thermal expansion

coefficient (bottom left), and internal pressure (bottom right).

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

0.70% Polymer 2

298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

0.70% Polymer 2

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

0.0013

0.0014

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

0.70% Polymer 2

300

320

340

360

380

400

420

440

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

0.70% Polymer 2

172

Figure D.6. PVT data and thermodynamic properties for a mixture of PAO 4 + 1.40 mass %

Polymer 2: Density (top left), isothermal compressibility (top right), isobaric thermal expansion

coefficient (bottom left), and internal pressure (bottom right).

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

1.40% Polymer 2

298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

1.40% Polymer 2

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

1.40% Polymer 2

300

320

340

360

380

400

420

440

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

1.40% Polymer 2

173

Figure D.7. PVT data and thermodynamic properties for a mixture of PAO 4 + 2.80 mass %

Polymer 2: Density (top left), isothermal compressibility (top right), isobaric thermal expansion

coefficient (bottom left), and internal pressure (bottom right).

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

2.80% Polymer 2

298 K

323 K

348 K

373 K

398 K

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

2.80% Polymer 2

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

2.80% Polymer 2

300

320

340

360

380

400

420

440

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

2.80% Polymer 2

174

Figure D.8. PVT data and thermodynamic properties for a mixture of PAO 4 + 7.01 mass %

Polymer 2: Density (top left), isothermal compressibility (top right), isobaric thermal expansion

coefficient (bottom left), and internal pressure (bottom right).

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

7.01% Polymer 2

298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

7.01% Polymer 2

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

7.01% Polymer 2

250

270

290

310

330

350

370

390

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

7.01% Polymer 2

175

D.2 Viscosity of Mixtures of PAO 4 + Viscosity Index Modifiers

Figure D.9. Viscosity versus pressure for a mixture of PAO 4 + 0.71 mass % Polymer 1 at 500

rpm (left) and 323 K (right).

Figure D.10. Viscosity versus pressure for a mixture of PAO 4 + 1.42 mass % Polymer 1 at 500

rpm (left) and 323 K (right).

0

10

20

30

40

50

60

70

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

0.71% Polymer 1298 K

323 K

348 K

373 K

0

5

10

15

20

25

30

35

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)Pressure (MPa)

0.71% Polymer 1

300-800 rpm

0

10

20

30

40

50

60

70

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

1.42% Polymer 1298 K

323 K

348 K

373 K

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

1.42% Polymer

300-800 rpm

176

Figure D.11. Viscosity versus pressure for a mixture of PAO 4 + 2.85 mass % Polymer 1 at 500

rpm (left) and 323 K (right).

Figure D.12. Viscosity versus pressure for a mixture of PAO 4 + 7.12 mass % Polymer 1 at 500

rpm (left) and 323 K (right).

0

10

20

30

40

50

60

70

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

2.85% Polymer 1298 K

323 K

348 K

373 K

0

5

10

15

20

25

30

35

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

2.85% Polymer 1

300-800 rpm

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50

Vis

cosi

ty (

cP)

Pressure (MPa)

7.12% Polymer 1

298 K

323 K

348 K

373 K

0

5

10

15

20

25

30

35

40

45

0 10 20 30 40 50

Vis

cosi

ty (

cP)

Pressure (MPa)

7.12% Polymer 1

300-800 RPM

177

Figure D.13. Viscosity versus pressure for a mixture of PAO 4 + 0.70 mass % Polymer 2 at 500

rpm (left) and 323 K (right).

Figure D.14. Viscosity versus pressure for a mixture of PAO 4 + 1.40 mass % Polymer 2 at 500

rpm (left) and 323 K (right).

0

10

20

30

40

50

60

70

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

0.70% Polymer 2

298 K

323 K

348 K

373 K

0

5

10

15

20

25

30

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

0.70% Polymer 2

300-800 rpm

0

10

20

30

40

50

60

70

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

1.40% Polymer 2298 K

323 K

348 K

373 K

0

5

10

15

20

25

30

35

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

1.40% Polymer 2

300-800 rpm

178

Figure D.15. Viscosity versus pressure for a mixture of PAO 4 + 2.80 mass % Polymer 2 at 500

rpm (left) and 323 K (right).

Figure D.16. Viscosity versus pressure for a mixture of PAO 4 + 7.01 mass % Polymer 2 at 500

rpm (left) and 323 K (right).

0

10

20

30

40

50

60

70

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

2.80% Polymer 2298 K

323 K

348 K

373 K

0

5

10

15

20

25

30

35

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

2.80% Polymer 2

300-800 rpm

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

7.01% Polymer 2

298 K

323 K

348 K

373 K

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50

Vis

cosi

ty (

cP)

Pressure (MPa)

7.01% Polymer 2

300-800 rpm

179

D.3 Density and Derived Thermodynamic Properties of ATFs

Figure D.17. PVT data and thermodynamic properties for an experimental ATF: Density (top

left), isothermal compressibility (top right), isobaric thermal expansion coefficient (bottom left),

and internal pressure (bottom right).

0.77

0.79

0.81

0.83

0.85

0.87

0.89

0.91

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0 10 20 30 40 50κ

T(1

/MP

a)

Pressure (MPa)

298 K

323 K

348K

373K

398K

0.00075

0.0008

0.00085

0.0009

0.00095

0.001

250 300 350 400 450

Isob

ari

c E

xp

an

sivit

y (

1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

350

370

390

410

430

450

470

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

180

Figure D.18. PVT data and thermodynamic properties for a commercial ATF: Density (top

left), isothermal compressibility (top right), isobaric thermal expansion coefficient (bottom left),

and internal pressure (bottom right).

0.79

0.81

0.83

0.85

0.87

0.89

0.91

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

298 K

323 K

348 K

373 K

398

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

298 K

323 K

348K

373K

398K

0.0007

0.00075

0.0008

0.00085

0.0009

0.00095

250 300 350 400 450

Isob

ari

c E

xp

an

sivit

y (

1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

340

350

360

370

380

390

400

410

420

430

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

181

D.4 Select Tabulated Data for Mixtures of PAO 4 + Viscosity Index Modifiers and ATFs

Table D.1. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the

S-L EOS and free volume model for PAO 4 + 0.71 mass % Polymer 1.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)

298 10 0.81282 0.000636 0.000812 370.391 32.87341

298 15 0.815343 0.000604 0.000786 372.6943 35.82478

298 20 0.817747 0.000574 0.000761 374.8948 38.9718

298 25 0.820039 0.000546 0.000737 377 42.32589

298 30 0.82223 0.000521 0.000715 379.0166 45.89911

298 35 0.824324 0.000497 0.000694 380.9504 49.70417

298 40 0.826331 0.000475 0.000674 382.8068 53.75453

323 10 0.79572 0.000786 0.000888 354.9708 12.15951

323 15 0.798766 0.000743 0.000857 357.6936 13.23238

323 20 0.801659 0.000704 0.000828 360.2891 14.37013

323 25 0.804411 0.000668 0.000802 362.7673 15.5762

323 30 0.807034 0.000635 0.000777 365.1371 16.85416

323 35 0.809538 0.000605 0.000753 367.4064 18.20778

323 40 0.811932 0.000577 0.000731 369.5823 19.64102

348 10 0.777523 0.00096 0.000962 338.921 5.268102

348 15 0.78115 0.000903 0.000927 342.0906 5.730682

348 20 0.784583 0.000852 0.000894 345.1036 6.218834

348 25 0.787838 0.000805 0.000863 347.9735 6.7338

348 30 0.790933 0.000763 0.000835 350.7123 7.27687

348 35 0.793879 0.000725 0.000809 353.3303 7.849387

348 40 0.79669 0.000689 0.000784 355.8366 8.452754

373 10 0.758343 0.001162 0.001036 322.4063 2.57946

373 15 0.762617 0.001087 0.000994 326.0505 2.807398

373 20 0.766644 0.001021 0.000956 329.5032 3.04684

373 25 0.77045 0.000961 0.000922 332.7826 3.298312

373 30 0.774055 0.000907 0.00089 335.9045 3.562356

373 35 0.777479 0.000859 0.000861 338.8825 3.839533

373 40 0.780736 0.000814 0.000833 341.7281 4.130422

398 10 0.738284 0.001398 0.001109 305.5761 -

398 15 0.743277 0.0013 0.001061 309.7233 -

398 20 0.747959 0.001213 0.001017 313.6373 -

398 25 0.752364 0.001137 0.000978 317.3427 -

398 30 0.756523 0.001069 0.000942 320.8603 -

398 35 0.760459 0.001008 0.00091 324.2075 -

398 40 0.764193 0.000953 0.000879 327.3994 -

182

Table D.2. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the

S-L EOS and free volume model for PAO 4 + 1.42 mass % Polymer 1.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)

298 10 0.819331 0.00062622 0.000814 377.1491 36.04737

298 15 0.821834 0.00059468 0.000787 379.4576 39.26547

298 20 0.824221 0.00056567 0.000762 381.6648 42.69662

298 25 0.826499 0.00053891 0.000739 383.7778 46.35321

298 30 0.828678 0.00051415 0.000717 385.8033 50.24834

298 35 0.830762 0.00049116 0.000697 387.7469 54.39583

298 40 0.83276 0.00046977 0.000677 389.6139 58.81026

323 10 0.80207 0.00077347 0.000889 361.4261 13.1858

323 15 0.805093 0.00073171 0.000859 364.1552 14.34245

323 20 0.807966 0.00069366 0.000831 366.7587 15.56903

323 25 0.810701 0.00065884 0.000804 369.2464 16.8692

323 30 0.81331 0.00062687 0.000779 371.6269 18.24682

323 35 0.815802 0.0005974 0.000756 373.908 19.70594

323 40 0.818186 0.00057014 0.000734 376.0965 21.25079

348 10 0.783702 0.00094461 0.000964 345.0614 5.660301

348 15 0.787302 0.0008895 0.000928 348.2387 6.154336

348 20 0.790711 0.00083981 0.000896 351.2613 6.675699

348 25 0.793947 0.00079478 0.000866 354.1427 7.225707

348 30 0.797026 0.00075378 0.000838 356.8942 7.805735

348 35 0.799959 0.00071627 0.000812 359.5262 8.417214

348 40 0.802759 0.00068183 0.000788 362.0474 9.061636

373 10 0.764341 0.00114396 0.001037 328.223 2.750142

373 15 0.768583 0.00107136 0.000996 331.8765 2.991661

373 20 0.772584 0.0010067 0.000959 335.3407 3.245391

373 25 0.776368 0.00094871 0.000925 338.6337 3.511887

373 30 0.779956 0.00089641 0.000893 341.7708 3.791721

373 35 0.783365 0.00084897 0.000864 344.7651 4.085485

373 40 0.786611 0.00080575 0.000837 347.6283 4.393791

398 10 0.744092 0.00137675 0.001111 311.0631 -

398 15 0.749049 0.0012812 0.001063 315.2213 -

398 20 0.753702 0.00119724 0.00102 319.1491 -

398 25 0.758083 0.00112284 0.000981 322.8706 -

398 30 0.762222 0.00105643 0.000946 326.4059 -

398 35 0.766143 0.00099677 0.000914 329.7724 -

398 40 0.769865 0.00094286 0.000884 332.9846 -

183

Table D.3. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the

S-L EOS and free volume model for PAO 4 + 2.85 mass % Polymer 1.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)

298 10 0.819855 0.000627 0.000839 389.0425 36.31646

298 15 0.822365 0.000596 0.000813 391.4277 39.56122

298 20 0.82476 0.000568 0.000788 393.711 43.0226

298 25 0.827049 0.000541 0.000765 395.8994 46.71332

298 30 0.829239 0.000517 0.000743 397.9994 50.64679

298 35 0.831338 0.000494 0.000722 400.0167 54.83718

298 40 0.833352 0.000473 0.000702 401.9566 59.29944

323 10 0.802042 0.000775 0.000918 372.3206 13.1811

323 15 0.805073 0.000734 0.000887 375.1399 14.33889

323 20 0.807957 0.000697 0.000858 377.8324 15.56738

323 25 0.810706 0.000662 0.000831 380.408 16.87032

323 30 0.813331 0.000631 0.000806 382.8751 18.25164

323 35 0.815841 0.000602 0.000783 385.2416 19.71545

323 40 0.818244 0.000575 0.000761 387.5142 21.2661

348 10 0.783099 0.000948 0.000994 354.9411 5.620786

348 15 0.786712 0.000894 0.000959 358.2235 6.112384

348 20 0.790137 0.000845 0.000926 361.3495 6.631497

348 25 0.793392 0.0008 0.000895 364.3323 7.179466

348 30 0.79649 0.00076 0.000867 367.1835 7.757685

348 35 0.799445 0.000722 0.00084 369.9132 8.367608

348 40 0.802268 0.000688 0.000816 372.5305 9.010751

373 10 0.763144 0.001151 0.001071 337.0821 2.715188

373 15 0.767406 0.001078 0.001029 340.8575 2.954352

373 20 0.771429 0.001014 0.000991 344.4407 3.205774

373 25 0.775237 0.000957 0.000956 347.8499 3.470016

373 30 0.778851 0.000905 0.000924 351.1005 3.747656

373 35 0.782288 0.000857 0.000895 354.2059 4.039294

373 40 0.785563 0.000814 0.000867 357.1775 4.345549

398 10 0.742283 0.001388 0.001147 318.905 -

398 15 0.747269 0.001292 0.001098 323.2038 -

398 20 0.751953 0.001209 0.001054 327.2679 -

398 25 0.756367 0.001134 0.001015 331.1215 -

398 30 0.76054 0.001068 0.000979 334.7852 -

398 35 0.764495 0.001008 0.000945 338.2765 -

398 40 0.768253 0.000954 0.000915 341.6103 -

184

Table D.4. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the

S-L EOS and free volume model for PAO 4 + 7.12 mass % Polymer 1.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)

298 10 0.822226 0.000721 0.000672 267.9444 37.55771

298 15 0.825093 0.000672 0.000643 269.816 41.11807

298 20 0.827779 0.000629 0.000615 271.5757 44.89652

298 25 0.830301 0.000589 0.00059 273.2335 48.90472

298 30 0.832676 0.000554 0.000566 274.7984 53.15497

298 35 0.834914 0.000521 0.000544 276.278 57.66021

298 40 0.837029 0.000491 0.000524 277.6791 62.43408

323 10 0.807853 0.000887 0.000738 258.6586 14.19729

323 15 0.811315 0.000824 0.000704 260.8804 15.5272

323 20 0.81455 0.000768 0.000673 262.9651 16.93026

323 25 0.817582 0.000718 0.000645 264.926 18.41001

323 30 0.820429 0.000673 0.000619 266.7748 19.97013

323 35 0.82311 0.000632 0.000594 268.5212 21.61449

323 40 0.82564 0.000595 0.000572 270.174 23.34713

348 10 0.792447 0.001078 0.000802 248.8871 6.266918

348 15 0.796564 0.000997 0.000763 251.4804 6.853501

348 20 0.800399 0.000925 0.000728 253.9073 7.469044

348 25 0.803981 0.000862 0.000697 256.1854 8.114852

348 30 0.807339 0.000806 0.000668 258.3296 8.792274

348 35 0.810494 0.000755 0.000641 260.3524 9.502703

348 40 0.813465 0.000709 0.000616 262.2648 10.24759

373 10 0.776108 0.001296 0.000864 238.7301 3.119198

373 15 0.780947 0.001192 0.00082 241.7159 3.413765

373 20 0.785433 0.001102 0.000781 244.5013 3.721332

373 25 0.789611 0.001022 0.000746 247.1093 4.042473

373 30 0.793515 0.000952 0.000714 249.5589 4.377767

373 35 0.797175 0.00089 0.000684 251.866 4.727808

373 40 0.800614 0.000834 0.000657 254.0442 5.0932

398 10 0.75893 0.001547 0.000926 228.279 -

398 15 0.76456 0.001413 0.000876 231.6783 -

398 20 0.769755 0.001299 0.000832 234.8377 -

398 25 0.774574 0.0012 0.000792 237.787 -

398 30 0.779062 0.001113 0.000757 240.5504 -

398 35 0.783257 0.001037 0.000724 243.1479 -

398 40 0.78719 0.000969 0.000695 245.5964 -

185

Table D.5. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the

S-L EOS and free volume model for PAO 4 + 0.70 mass % Polymer 2.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)

298 10 0.818367 0.000619 0.000863 405.319 35.55873

298 15 0.820845 0.00059 0.000837 407.7765 38.71976

298 20 0.823213 0.000563 0.000812 410.1327 42.09336

298 25 0.825479 0.000538 0.000789 412.3945 45.69211

298 30 0.827652 0.000514 0.000767 414.5681 49.52932

298 35 0.829737 0.000492 0.000746 416.6592 53.61904

298 40 0.831739 0.000472 0.000727 418.6727 57.9761

323 10 0.800091 0.000767 0.000943 387.4177 12.85681

323 15 0.803084 0.000727 0.000913 390.3212 13.98001

323 20 0.805936 0.000691 0.000884 393.0984 15.17241

323 25 0.808659 0.000658 0.000857 395.759 16.4377

323 30 0.811262 0.000628 0.000833 398.3112 17.77978

323 35 0.813755 0.0006 0.000809 400.7627 19.20274

323 40 0.816144 0.000574 0.000787 403.12 20.71085

348 10 0.780675 0.000939 0.001022 368.8424 5.464581

348 15 0.784243 0.000886 0.000986 372.2221 5.939854

348 20 0.787632 0.000839 0.000953 375.4456 6.442013

348 25 0.790856 0.000796 0.000923 378.5259 6.972379

348 30 0.793931 0.000757 0.000895 381.4744 7.53233

348 35 0.796867 0.00072 0.000868 384.3011 8.123302

348 40 0.799675 0.000687 0.000843 387.0147 8.746796

373 10 0.760238 0.001141 0.0011 349.7837 2.632185

373 15 0.76445 0.001071 0.001059 353.6706 2.862757

373 20 0.768433 0.001009 0.001021 357.3653 3.105296

373 25 0.772209 0.000953 0.000986 360.8856 3.360356

373 30 0.775796 0.000902 0.000953 364.2466 3.628507

373 35 0.779212 0.000856 0.000924 367.4614 3.91034

373 40 0.782471 0.000814 0.000896 370.5417 4.206466

398 10 0.738889 0.001378 0.001179 330.4139 -

398 15 0.743821 0.001285 0.00113 334.8401 -

398 20 0.748461 0.001204 0.001086 339.0308 -

398 25 0.752841 0.001131 0.001046 343.0099 -

398 30 0.756986 0.001066 0.00101 346.7979 -

398 35 0.76092 0.001008 0.000976 350.4119 -

398 40 0.764663 0.000955 0.000945 353.867 -

186

Table D.6. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the

S-L EOS and free volume model for PAO 4 + 1.40 mass % Polymer 2.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)

298 10 0.812691 0.000609 0.000814 388.1513 32.81357

298 15 0.815109 0.000579 0.000788 390.4645 35.70653

298 20 0.817417 0.000552 0.000764 392.6787 38.79116

298 25 0.819623 0.000526 0.000742 394.8009 42.07869

298 30 0.821734 0.000503 0.00072 396.8373 45.581

298 35 0.823756 0.000481 0.0007 398.7935 49.31066

298 40 0.825697 0.00046 0.000681 400.6743 53.28089

323 10 0.79556 0.000753 0.00089 371.9596 12.13465

323 15 0.798479 0.000713 0.00086 374.6943 13.18409

323 20 0.801257 0.000677 0.000833 377.3063 14.29703

323 25 0.803906 0.000644 0.000807 379.8051 15.47684

323 30 0.806435 0.000613 0.000783 382.1988 16.72705

323 35 0.808854 0.000585 0.00076 384.495 18.05137

323 40 0.81117 0.000559 0.000738 386.7 19.45369

348 10 0.777329 0.000919 0.000964 355.1078 5.256254

348 15 0.780806 0.000867 0.00093 358.2917 5.707876

348 20 0.784104 0.00082 0.000898 361.3246 6.184511

348 25 0.787238 0.000777 0.000869 364.2193 6.687379

348 30 0.790224 0.000738 0.000841 366.9867 7.217747

348 35 0.793071 0.000702 0.000816 369.6365 7.776941

348 40 0.795792 0.000669 0.000792 372.1773 8.366342

373 10 0.758114 0.001113 0.001038 337.7687 2.573158

373 15 0.762212 0.001044 0.000998 341.4301 2.795314

373 20 0.766083 0.000983 0.000962 344.9067 3.028723

373 25 0.769749 0.000928 0.000928 348.2155 3.273901

373 30 0.773229 0.000878 0.000897 351.3713 3.531381

373 35 0.77654 0.000832 0.000869 354.3868 3.801713

373 40 0.779695 0.000791 0.000842 357.273 4.085468

398 10 0.738018 0.00134 0.001111 320.0988 -

398 15 0.742807 0.001249 0.001065 324.2665 -

398 20 0.747309 0.001169 0.001023 328.2091 -

398 25 0.751555 0.001098 0.000985 331.9494 -

398 30 0.755571 0.001035 0.00095 335.5068 -

398 35 0.75938 0.000978 0.000918 338.898 -

398 40 0.763001 0.000926 0.000889 342.1371 -

187

Table D.7. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the

S-L EOS and free volume model for PAO 4 + 2.80 mass % Polymer 2.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)

298 10 0.820019 0.000604 0.000796 383.0934 36.40073

298 15 0.822435 0.000574 0.000771 385.3541 39.60047

298 20 0.82474 0.000546 0.000747 387.5171 43.01048

298 25 0.826942 0.000521 0.000724 389.5891 46.64297

298 30 0.829048 0.000497 0.000703 391.5764 50.51085

298 35 0.831066 0.000475 0.000683 393.4843 54.62771

298 40 0.833 0.000455 0.000664 395.318 59.00795

323 10 0.803106 0.000745 0.000871 367.4541 13.36148

323 15 0.806023 0.000706 0.000841 370.1282 14.5136

323 20 0.808798 0.00067 0.000814 372.6811 15.73482

323 25 0.811443 0.000637 0.000789 375.1223 17.02879

323 30 0.813967 0.000606 0.000765 377.4598 18.39929

323 35 0.81638 0.000578 0.000742 379.701 19.85032

323 40 0.81869 0.000552 0.000721 381.8524 21.38607

348 10 0.785093 0.000909 0.000944 351.1554 5.75266

348 15 0.788567 0.000857 0.00091 354.2699 6.245392

348 20 0.791861 0.000811 0.000879 357.2355 6.765165

348 25 0.79499 0.000768 0.00085 360.0647 7.313281

348 30 0.79797 0.000729 0.000823 362.7685 7.891097

348 35 0.800811 0.000693 0.000798 365.3564 8.500026

348 40 0.803525 0.00066 0.000774 367.8369 9.141544

373 10 0.766093 0.0011 0.001016 334.3643 2.802136

373 15 0.770186 0.001032 0.000977 337.9466 3.043234

373 20 0.774051 0.000971 0.000941 341.347 3.296427

373 25 0.777711 0.000916 0.000908 344.5822 3.562263

373 30 0.781184 0.000867 0.000878 347.6668 3.841308

373 35 0.784487 0.000822 0.000849 350.6131 4.134146

373 40 0.787634 0.000781 0.000823 353.4322 4.441382

398 10 0.746208 0.001323 0.001088 317.2318 -

398 15 0.750989 0.001234 0.001042 321.3102 -

398 20 0.755483 0.001155 0.001001 325.1671 -

398 25 0.759721 0.001084 0.000964 328.8252 -

398 30 0.763729 0.001021 0.00093 332.3035 -

398 35 0.767528 0.000965 0.000898 335.6183 -

398 40 0.771139 0.000913 0.000869 338.7835 -

188

Table D.8. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the

S-L EOS and free volume model for PAO 4 + 7.01 mass % Polymer 2.

T (K) P (MPa) ρ (g/cm3) κT

(1/MPa)

βP (1/K) π (MPa) η (mPa s)

298 10 0.818058 0.000729 0.000833 330.8096 35.40306

298 15 0.820957 0.000687 0.000803 333.1588 38.78146

298 20 0.823704 0.000649 0.000774 335.3917 42.38607

298 25 0.82631 0.000615 0.000748 337.5178 46.22989

298 30 0.828788 0.000583 0.000723 339.5452 50.32662

298 35 0.831148 0.000554 0.0007 341.4812 54.69071

298 40 0.833397 0.000527 0.000678 343.3323 59.33741

323 10 0.800413 0.0009 0.000911 316.6931 12.90971

323 15 0.803912 0.000845 0.000875 319.4676 14.1282

323 20 0.807214 0.000796 0.000843 322.0981 15.42103

323 25 0.81034 0.000751 0.000813 324.5972 16.79207

323 30 0.813304 0.00071 0.000785 326.976 18.24533

323 35 0.81612 0.000673 0.000759 329.244 19.78506

323 40 0.818799 0.000639 0.000735 331.4098 21.41568

348 10 0.781656 0.0011 0.000986 302.024 5.527238

348 15 0.785821 0.001027 0.000945 305.2511 6.049505

348 20 0.789737 0.000962 0.000908 308.3011 6.600837

348 25 0.79343 0.000905 0.000874 311.1911 7.18262

348 30 0.796921 0.000852 0.000843 313.9357 7.796295

348 35 0.800229 0.000805 0.000814 316.5475 8.443359

348 40 0.80337 0.000762 0.000787 319.0376 9.125372

373 10 0.761906 0.001333 0.001061 286.9542 2.679491

373 15 0.766811 0.001237 0.001013 290.6614 2.93569

373 20 0.771402 0.001153 0.000971 294.1522 3.204859

373 25 0.775714 0.001078 0.000932 297.4495 3.487589

373 30 0.779775 0.001012 0.000897 300.5726 3.784483

373 35 0.783613 0.000953 0.000865 303.538 4.096163

373 40 0.787246 0.000899 0.000835 306.3596 4.423269

398 10 0.741271 0.001605 0.001136 271.6214 -

398 15 0.747 0.001478 0.00108 275.8366 -

398 20 0.752333 0.001369 0.001031 279.7886 -

398 25 0.757317 0.001274 0.000988 283.5081 -

398 30 0.761994 0.00119 0.000948 287.0204 -

398 35 0.766396 0.001116 0.000912 290.3469 -

398 40 0.770554 0.001049 0.000879 293.5053 -

189

Table D.9. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the Tait equation

for an experimental ATF.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa)

298 10 0.865318 0.000594 0.0009 441.4847

298 15 0.867854 0.000577 0.000884 441.6019

298 20 0.870325 0.000561 0.000869 441.6752

298 25 0.872736 0.000546 0.000855 441.706

298 30 0.875088 0.000531 0.000841 441.6955

298 35 0.877387 0.000518 0.000828 441.6448

298 40 0.879633 0.000505 0.000816 441.5553

323 10 0.845892 0.000681 0.000917 424.8183

323 15 0.848729 0.000659 0.000899 425.7044

323 20 0.851485 0.000638 0.000882 426.5349

323 25 0.854164 0.000619 0.000866 427.3118

323 30 0.85677 0.0006 0.000851 428.0368

323 35 0.859309 0.000583 0.000837 428.7117

323 40 0.861783 0.000567 0.000824 429.3381

348 10 0.82654 0.00078 0.000935 406.8522

348 15 0.82971 0.000751 0.000914 408.5746

348 20 0.832775 0.000724 0.000895 410.2272

348 25 0.835744 0.000699 0.000878 411.8128

348 30 0.838622 0.000676 0.000861 413.3338

348 35 0.841416 0.000655 0.000846 414.7926

348 40 0.844132 0.000634 0.000832 416.1914

373 10 0.807271 0.000892 0.000953 388.202

373 15 0.810804 0.000855 0.00093 390.8322

373 20 0.814204 0.00082 0.000909 393.3753

373 25 0.817484 0.000788 0.000889 395.8352

373 30 0.820652 0.000759 0.000871 398.2153

373 35 0.823716 0.000732 0.000855 400.5189

373 40 0.826684 0.000707 0.000839 402.7491

398 10 0.788092 0.001019 0.000971 369.3576

398 15 0.792018 0.00097 0.000946 372.9713

398 20 0.79578 0.000926 0.000922 376.477

398 25 0.799391 0.000886 0.000901 379.8801

398 30 0.802864 0.000849 0.000882 383.1854

398 35 0.806212 0.000816 0.000864 386.3974

398 40 0.809443 0.000785 0.000847 389.5202

190

Table D.10. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the Tait equation

for a commercial ATF.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa)

298 10 0.875381 0.000604 0.00085 409.1594

298 15 0.87799 0.000586 0.000834 408.8845

298 20 0.880531 0.00057 0.00082 408.5673

298 25 0.883009 0.000554 0.000806 408.2093

298 30 0.885427 0.00054 0.000793 407.8117

298 35 0.887788 0.000526 0.00078 407.3757

298 40 0.890095 0.000512 0.000769 406.9022

323 10 0.85682 0.000689 0.000865 395.5996

323 15 0.859727 0.000666 0.000847 396.0235

323 20 0.862548 0.000645 0.000831 396.3944

323 25 0.86529 0.000625 0.000816 396.7142

323 30 0.867957 0.000606 0.000801 396.9846

323 35 0.870553 0.000589 0.000788 397.2072

323 40 0.873084 0.000572 0.000775 397.3835

348 10 0.838331 0.000784 0.00088 380.6305

348 15 0.841563 0.000755 0.000861 381.8126

348 20 0.844688 0.000728 0.000843 382.9285

348 25 0.847713 0.000703 0.000826 383.9809

348 30 0.850647 0.000679 0.00081 384.9721

348 35 0.853494 0.000658 0.000795 385.9046

348 40 0.856261 0.000637 0.000781 386.7802

373 10 0.81992 0.000892 0.000896 364.8114

373 15 0.823505 0.000854 0.000874 366.8141

373 20 0.826958 0.00082 0.000854 368.7348

373 25 0.830288 0.000788 0.000836 370.5772

373 30 0.833504 0.000759 0.000819 372.3446

373 35 0.836615 0.000732 0.000803 374.04

373 40 0.839629 0.000707 0.000788 375.6664

398 10 0.801592 0.001013 0.000912 348.5938

398 15 0.805562 0.000964 0.000888 351.4831

398 20 0.809366 0.000921 0.000866 354.2714

398 25 0.813019 0.000881 0.000846 356.9638

398 30 0.816534 0.000845 0.000827 359.5649

398 35 0.819922 0.000812 0.00081 362.0787

398 40 0.823193 0.000781 0.000794 364.509

191

Appendix E: Density, Derived Thermodynamic Properties, and Viscosity of Ionic Liquids

and Their Mixtures with Ethanol

In this section, the full range of density, derived thermodynamic properties, and viscosity

for mixtures of PAO 4 with two methacrylate based polymeric additives and two automatic

transmission fluids have been reported.

Figures E.1-E.8 show densities of mixtures of ionic liquids with ethanol from 10-40 MPa

and 298-398 K.

Figures E.9-E.24 show the derived thermodynamic properties for all mixtures from 10-40

MPa and 298-398 K.

Figures D.25 and D.29 show viscosity values for mixtures of ionic liquids with ethanol

from 10-40 MPa and 298-373 K.

Tables E.1-E.28 include select data for density as calculated from the Sanchez-Lacombe

equation of state and derived thermodynamic properties.

This Appendix has been organized into four sections:

E.1 Density of Ionic Liquid + Ethanol Mixtures

E.2 Derived Thermodynamic Properties of Ionic Liquid + Ethanol Mixtures

E.3 Viscosities of Ionic Liquid + Ethanol Mixtures

E.4 Select Tabulated Data for Ionic Liquid + Ethanol Mixtures

192

E.1 Density of Ionic Liquid + Ethanol Mixtures

Figure E.1. Density data for 25 mass % IL + Ethanol: [EMIM]Cl (top left), [PMIM]Cl (top

right), [BMIM]Cl (bottom left), [HMIM]Cl (bottom right).

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

25% [EMIM]Cl

298 K

323 K

348 K

373 K

398 K

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

25% [PMIM]Cl298 K

323 K

348 K

373 K

398 K

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

25% [BMIM]Cl298K

323K

348K

373K

398K

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

25% [HMIM]Cl298 K

323 K

348 K

373 K

398 K

193

Figure E.2. Density data for 50 mass % IL + Ethanol: [EMIM]Cl (top left), [PMIM]Cl (top

right), [BMIM]Cl (bottom left), [HMIM]Cl (bottom right).

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

50% [EMIM]Cl

298 K

323 K

348 K

373 K

398 K

0.86

0.88

0.9

0.92

0.94

0.96

0.98

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

50% [PMIM]Cl298 K

323 K

348 K

373 K

398 K

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

50% [BMIM]Cl298K

323K

348K

373K

398K

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

50% [HMIM]Cl298 K

323 K

348 K

373 K

398 K

194

Figure E.3. Density data for 75 mass % IL + Ethanol: [EMIM]Cl (top left), [PMIM]Cl (top

right), [BMIM]Cl (bottom left), [HMIM]Cl (bottom right).

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

75% [EMIM]Cl

348 K

373 K

398 K

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

1.06

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

75% [PMIM]Cl298 K

323 K

348 K

373 K

398 K

0.9

0.92

0.94

0.96

0.98

1

1.02

1.04

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

75% [BMIM]Cl

298K

323K

348K

373K

398K

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

75% [HMIM]Cl 298 K

323 K

348 K

373 K

398 K

195

Figure E.4. Density data for 5 mass % IL + Ethanol: [EMIM]Ac (left) and [BMIM]Ac (right).

Figure E.5. Density data for 15 mass % IL + Ethanol: [EMIM]Ac (left) and [BMIM]Ac (right).

0.68

0.7

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

5% [EMIM][Ac]

298 K

323 K

348 K

373 K

398 K

0.7

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

5% [BMIM]Cl298K

323K

348K

373K

398K

0.7

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

15% [EMIM][Ac]

298 K

323 K

348 K

373 K

398 K

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

15% [BMIM]Ac298K

323K

348K

373K

398K

196

Figure E.6. Density data for 25 mass % IL + Ethanol: [EMIM]Ac (left) and [BMIM]Ac (right).

Figure E.7. Density data for 50 mass % IL + Ethanol: [EMIM]Ac (left) and [BMIM]Ac (right).

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

25% [EMIM][Ac]

298 K

323 K

348 K

373 K

398 K

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

25% [BMIM]Ac298K

323K

348K

373K

398K

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

50% [EMIM][Ac]

298 K

323 K

348 K

373 K

398 K

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

50% [BMIM]Ac298K

323K

348K

373K

398K

197

Figure E.8. Density data for 75 mass % IL + Ethanol: [EMIM]Ac (left) and [BMIM]Ac (right).

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

75% [EMIM][Ac]

298 K

323 K

348 K

373 K

398 K

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

1.04

0 10 20 30 40 50

Den

sity

(g/c

m3)

Pressure (MPa)

75% [BMIM]Ac

298K

323K

348K

373K

398K

198

E.2 Derived Thermodynamic Properties of Ionic Liquid + Ethanol Mixtures

Figure E.9. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 25 mass % [EMIM]Cl + ethanol.

0

0.0005

0.001

0.0015

0.002

0.0025

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K323 K

298 K

25% [EMIM]Cl

0.0007

0.0009

0.0011

0.0013

0.0015

0.0017

250 300 350 400 450

βP

(1/K

)Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

25% [EMIM]Cl

250

270

290

310

330

350

370

390

410

430

450

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

25% [EMIM]Cl

15

16

17

18

19

20

21

22

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

25% [EMIM]Cl

199

Figure E.10. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 75 mass % [EMIM]Cl + ethanol.

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

75% [EMIM]Cl

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

75% [EMIM]Cl

300

350

400

450

500

550

600

650

700

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

348 K373 K

398 K

75% [EMIM]Cl

15

16

17

18

19

20

21

22

23

24

25

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

348 K

373 K

398 K

75% [EMIM]Cl

200

Figure E.11. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 25 mass % [PMIM]Cl + ethanol.

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

25% [PMIM]Cl

298 K

323 K

348 K

373 K

398 K

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

250 300 350 400 450

βP

(1/K

)

Temperature (K)

25% [PMIM]Cl

10 MPa

20 MPa

30 MPa

40 MPa

350

370

390

410

430

450

470

490

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

25% [PMIM]Cl

298 K

323 K

348 K

373 K

398 K

17

17.5

18

18.5

19

19.5

20

20.5

21

21.5

22

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

25% [PMIM]Cl

298 K

323 K

348 K

373 K

398 K

201

Figure E.12. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 75 mass % [PMIM]Cl + ethanol.

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

75% [PMIM]Cl

298 K

323 K

348 K

373 K

398 K

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

250 300 350 400 450

βP

(1/K

)

Temperature (K)

75% [PMIM]Cl

10 MPa

20 MPa

30 MPa

40 MPa

350

370

390

410

430

450

470

490

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

75% [PMIM]Cl

298 K

323 K

348 K

373 K

398 K

19

19.5

20

20.5

21

21.5

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

75% [PMIM]Cl

298 K

323 K

348 K

373 K

398 K

202

Figure E.13. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 25 mass % [BMIM]Cl + ethanol.

0

0.0005

0.001

0.0015

0.002

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

348K

373K

398K

25% [BMIM]Cl

323 K

298 K

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

0.0013

0.0014

250 300 350 400 450

βP

(1/K

)

Pressure (MPa)

25% [BMIM]Cl 10 MPa

20 MPa

30 MPa

40 MPa

300

320

340

360

380

400

420

440

460

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

25% [BMIM]Cl

298K

323K

348K

373K

398K

17

18

19

20

21

22

23

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

25% [BMIM]Cl

298K

323K

348K

373K

398K

203

Figure E.14. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 75 mass % [BMIM]Cl + ethanol.

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

298K

323K

348K

373K

398K

75% [BMIM]Cl

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

250 300 350 400 450

Isob

ari

c E

xp

an

sivit

y (

1/K

)

Pressure (MPa)

75% [BMIM]Cl

10 MPa

20 MPa

30 MPa

40 MPa

320

340

360

380

400

420

440

460

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

75% [BMIM]Cl

298K

323K

348K

373K

398K

18

18.5

19

19.5

20

20.5

21

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

75% [BMIM]Cl

298K

323K

348K

373K

398K

204

Figure E.15. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 25 mass % [HMIM]Cl + ethanol.

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

25% [HMIM]Cl

298 K

323 K

348 K

373 K

398 K

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

0.0013

250 300 350 400 450

βP

(1/K

)

Temperature (K)

25% [HMIM]Cl10 MPa

20 MPa

30 MPa

40 MPa

320

340

360

380

400

420

440

460

480

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

25% [HMIM]Cl

298 K

323 K

348 K

373 K

398 K

18

18.5

19

19.5

20

20.5

21

21.5

22

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

25% [HMIM]Cl

298 K

323 K

348 K

373 K

398 K

205

Figure E.16. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 75 mass % [HMIM]Cl + ethanol.

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

75% [HMIM]Cl

298 K

323 K

348 K

373 K

398 K

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

250 300 350 400 450

βP

(1/K

)

Temperature (K)

75% [HMIM]Cl10 MPa

20 MPa

30 MPa

40 MPa

260

280

300

320

340

360

380

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

75% [HMIM]Cl

298 K

323 K

348 K

373 K

398 K

16

16.5

17

17.5

18

18.5

19

19.5

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

75% [HMIM]Cl

298 K

323 K

348 K

373 K

398 K

206

Figure E.17. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 5 mass % [EMIM]Ac + ethanol.

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

5% [EMIM][Ac]

0.0007

0.0009

0.0011

0.0013

0.0015

0.0017

0.0019

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

250

270

290

310

330

350

370

390

410

430

450

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

5% [EMIM][Ac]

15

16

17

18

19

20

21

22

23

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

5% [EMIM][Ac]

207

Figure E.18. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 15 mass % [EMIM]Ac + ethanol.

0

0.0005

0.001

0.0015

0.002

0.0025

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

15% [EMIM][Ac]

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

250

270

290

310

330

350

370

390

410

430

450

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

15% [EMIM][Ac]

15

16

17

18

19

20

21

22

23

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

15% [EMIM][Ac]

208

Figure E.19. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 25 mass % [EMIM]Ac + ethanol.

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

25% [EMIM][Ac]

0.0007

0.0009

0.0011

0.0013

0.0015

0.0017

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

25% [EMIM][Ac]

300

350

400

450

500

550

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K

323 K

348 K

373 K

398 K

25% [EMIM][Ac]

15

16

17

18

19

20

21

22

23

24

25

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

298 K323 K

348 K373 K

398 K

25% [EMIM][Ac]

209

Figure E.20. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 75 mass % [EMIM]Ac + ethanol.

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

398 K

373 K

348 K

323 K

298 K

75% [EMIM][Ac]

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

0.0013

0.0014

0.0015

250 300 350 400 450

βP

(1/K

)

Temperature (K)

10 MPa

20 MPa

30 MPa

40 MPa

300

350

400

450

500

550

600

650

700

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

298 K323 K348 K

373 K

398 K

75% [EMIM][Ac]

15

16

17

18

19

20

21

22

23

24

25

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

298 K323 K348 K

373 K

398 K

75% [EMIM][Ac]

210

Figure E.21. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 5 mass % [BMIM]Ac + ethanol.

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

298K

323K

348K

373K

398K

5% [BMIM]Ac

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

250 300 350 400 450

βP

(1/K

)

Pressure (MPa)

5% [BMIM]Ac 10 MPa

20 MPa

30 MPa

40 MPa

250

270

290

310

330

350

370

390

410

430

450

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

5% [BMIM]Ac

298K

323K

348K

373K

398K

15

16

17

18

19

20

21

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

5% [BMIM]Ac298K

323K

348K

373K

398K

211

Figure E.22. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 15 mass % [BMIM]Ac + ethanol.

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

298K

323K

348K

373K

398K

15% [BMIM]Ac

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

0.0013

0.0014

0.0015

250 300 350 400 450

βP

(1/K

)

Pressure (MPa)

15% [BMIM]Ac 10 MPa

20 MPa

30 MPa

40 MPa

270

290

310

330

350

370

390

410

430

450

470

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

15% [BMIM]Ac298K

323K

348K

373K

398K

16

17

18

19

20

21

22

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

15% [BMIM]Ac

298K

323K

348K

373K

398K

212

Figure E.23. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 25 mass % [BMIM]Ac + ethanol.

0

0.0005

0.001

0.0015

0.002

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

298K

323K

348K373K

398K

25% [BMIM]Ac

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

0.0013

250 300 350 400 450

βP

(1/K

)

Pressure (MPa)

25% [BMIM]Ac 10 MPa

20 MPa

30 MPa

40 MPa

340

360

380

400

420

440

460

480

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

25% [BMIM]Ac298K

323K

348K

373K

398K

17

18

19

20

21

22

23

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

25% [BMIM]Ac

298K

323K

348K

373K

398K

213

Figure E.24. Isothermal compressibility, isobaric thermal expansion coefficient, internal

pressure, and solubility parameter for a mixture of 75 mass % [BMIM]Ac + ethanol.

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 10 20 30 40 50

κT

(1/M

Pa)

Pressure (MPa)

298K

323K

348K

373K

398K

75% [BMIM]Ac

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

250 300 350 400 450

βP

(1/K

)

Temperature (K)

75% [BMIM]Ac10 MPa

20 MPa

30 MPa

40 MPa

350

370

390

410

430

450

470

490

510

530

550

0 10 20 30 40 50

Inte

rnal

Pre

ssu

re (

MP

a)

Pressure (MPa)

75% [BMIM]Ac

298K

323K

348K

373K

398K

17

18

19

20

21

22

23

0 10 20 30 40 50

Solu

bil

ity P

ara

met

er (

MP

a0

.5)

Pressure (MPa)

75% [BMIM]Ac

298K

323K348K

373K

398K

214

E.3 Viscosities of Ionic Liquid + Ethanol Mixtures

Figure E.25. Viscosity versus pressure for a mixture of 95 mass % [EMIM]Ac + ethanol at 500

rpm.

Figure E.26. Viscosity versus pressure for a mixture of 90 mass % [EMIM]Ac + ethanol at 500

rpm.

0

20

40

60

80

100

120

140

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

95% [EMIM]Ac

500 RPM

298 K (300 RPM)

323 K

348 K

373 K

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

90% [EMIM]Ac

500 RPM

298 K

323 K

348 K

298 K

215

Figure E.27. Viscosity versus pressure for a mixture of 95 mass % [BMIM]Ac + ethanol at 500

rpm.

Figure E.28. Viscosity versus pressure for a mixture of 90 mass % [BMIM]Ac + ethanol at 500

rpm.

0

50

100

150

200

250

300

350

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

95% [BMIM]Ac

500 RPM

298 K (150 RPM)

323 K

348 K373 K

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

90% [BMIM]Ac

500 RPM

298 K

323 K

348 K373 K

216

Figure E.29. Viscosity versus pressure for a mixture of 75 mass % [BMIM]Ac + ethanol at 500

rpm.

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50

Vis

cosi

ty (

mP

a s

)

Pressure (MPa)

75% [BMIM]Ac

500 RPM

298 K

323 K

348 K

217

E.4 Select Tabulated Data for Ionic Liquid + Ethanol Mixtures

Table E.1. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

[EMIM]Cl.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa)

348 10 1.068247 0.00053 0.000776 499.1067

348 15 1.071023 0.000508 0.000755 501.7042

348 20 1.073694 0.000488 0.000735 504.2091

348 25 1.076265 0.000469 0.000716 506.627

348 30 1.078743 0.000451 0.000699 508.9629

348 35 1.081134 0.000435 0.000682 511.2214

348 40 1.083442 0.000419 0.000666 513.4067

373 10 1.046798 0.000646 0.000847 479.2654

373 15 1.050109 0.000617 0.000823 482.3013

373 20 1.053284 0.000591 0.0008 485.2228

373 25 1.056335 0.000566 0.000779 488.0374

373 30 1.059268 0.000543 0.000759 490.7518

373 35 1.062093 0.000522 0.000739 493.3723

373 40 1.064814 0.000502 0.000721 495.9043

398 10 1.023921 0.000782 0.000921 458.5459

398 15 1.027835 0.000744 0.000892 462.0581

398 20 1.031577 0.00071 0.000866 465.429

398 25 1.035161 0.000678 0.000841 468.669

398 30 1.038599 0.000649 0.000818 471.7873

398 35 1.041901 0.000621 0.000796 474.7919

398 40 1.045077 0.000596 0.000775 477.6903

218

Table E.2. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

25 mass % [EMIM]Cl + ethanol.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa)

298 10 0.853326 0.00071521 0.000979 398.0595

298 15 0.856297 0.00067589 0.000943 400.8366

298 20 0.859118 0.00064011 0.00091 403.4817

298 25 0.861801 0.0006074 0.000878 406.0053

298 30 0.864356 0.00057737 0.000849 408.4167

298 35 0.866794 0.00054972 0.000822 410.7241

298 40 0.869124 0.00052417 0.000797 412.9347

323 10 0.83131 0.00092766 0.001114 377.7842

323 15 0.835054 0.00087075 0.001068 381.1946

323 20 0.838588 0.00081973 0.001026 384.4285

323 25 0.841934 0.00077372 0.000988 387.5021

323 30 0.845108 0.00073199 0.000953 390.4292

323 35 0.848125 0.00069398 0.00092 393.2217

323 40 0.850998 0.00065921 0.00089 395.8902

348 10 0.807011 0.00120016 0.001262 356.0223

348 15 0.811695 0.00111658 0.001204 360.167

348 20 0.816086 0.00104306 0.001151 364.0745

348 25 0.820217 0.00097786 0.001104 367.7696

348 30 0.824115 0.0009196 0.00106 371.2734

348 35 0.827803 0.00086722 0.001021 374.6036

348 40 0.8313 0.00081987 0.000984 377.7754

373 10 0.780329 0.00155726 0.001431 332.8696

373 15 0.786176 0.00143199 0.001355 337.8766

373 20 0.791607 0.00132444 0.001287 342.561

373 25 0.796677 0.00123101 0.001228 346.9624

373 30 0.801428 0.00114904 0.001174 351.1129

373 35 0.805896 0.0010765 0.001126 355.0393

373 40 0.810112 0.00101184 0.001082 358.7638

398 10 0.751084 0.00203808 0.00163 308.3863

398 15 0.758399 0.00184509 0.001527 314.4226

398 20 0.765112 0.00168454 0.001439 320.0133

398 25 0.771315 0.0015487 0.001363 325.2229

398 30 0.777078 0.00143216 0.001296 330.1017

398 35 0.78246 0.001331 0.001236 334.6902

398 40 0.787507 0.00124231 0.001183 339.0211

219

Table E.3. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

50 mass % [EMIM]Cl + ethanol.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa)

298 10 0.922728 0.000603 0.000885 427.5271

298 15 0.925443 0.000573 0.000856 430.0466

298 20 0.928033 0.000546 0.000828 432.4574

298 25 0.930509 0.00052 0.000803 434.7673

298 30 0.932877 0.000497 0.000779 436.9832

298 35 0.935145 0.000475 0.000756 439.1112

298 40 0.937321 0.000455 0.000734 441.1569

323 10 0.901282 0.000771 0.000998 407.8847

323 15 0.904667 0.000729 0.000962 410.9544

323 20 0.907884 0.000691 0.000928 413.882

323 25 0.910946 0.000656 0.000898 416.6789

323 30 0.913867 0.000624 0.000869 419.355

323 35 0.916656 0.000595 0.000842 421.9192

323 40 0.919325 0.000568 0.000817 424.3793

348 10 0.877776 0.00098 0.001118 386.8862

348 15 0.881956 0.000921 0.001074 390.5801

348 20 0.885908 0.000868 0.001033 394.0877

348 25 0.889652 0.00082 0.000995 397.4262

348 30 0.893208 0.000777 0.000961 400.6099

348 35 0.896593 0.000737 0.000929 403.6516

348 40 0.89982 0.000701 0.000899 406.5624

373 10 0.852193 0.001245 0.00125 364.6633

373 15 0.857327 0.00116 0.001194 369.0701

373 20 0.862147 0.001085 0.001143 373.2318

373 25 0.866688 0.001018 0.001098 377.1739

373 30 0.870979 0.000959 0.001056 380.9178

373 35 0.875044 0.000905 0.001018 384.4819

373 40 0.878904 0.000857 0.000983 387.8817

398 10 0.824471 0.001584 0.001399 341.3239

398 15 0.830763 0.00146 0.001326 346.5535

398 20 0.83662 0.001353 0.001263 351.4575

398 25 0.842098 0.00126 0.001206 356.075

398 30 0.847242 0.001178 0.001155 360.4382

398 35 0.852088 0.001105 0.00111 364.5735

398 40 0.856668 0.00104 0.001068 368.5033

220

Table E.4. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

75 mass % [EMIM]Cl + ethanol.

T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa)

348 10 0.962059 0.000766 0.000965 428.5136

348 15 0.965654 0.000727 0.000933 431.7221

348 20 0.96908 0.000691 0.000903 434.791

348 25 0.972351 0.000658 0.000875 437.7312

348 30 0.975479 0.000627 0.000848 440.5519

348 35 0.978474 0.000599 0.000824 443.2615

348 40 0.981346 0.000573 0.000801 445.8676

373 10 0.937957 0.000952 0.001066 407.3119

373 15 0.942305 0.000898 0.001026 411.0966

373 20 0.946429 0.000849 0.00099 414.7032

373 25 0.950351 0.000805 0.000957 418.147

373 30 0.954087 0.000765 0.000926 421.4414

373 35 0.957653 0.000728 0.000897 424.598

373 40 0.961063 0.000694 0.00087 427.627

398 10 0.912088 0.001182 0.001173 385.1539

398 15 0.917317 0.001107 0.001125 389.583

398 20 0.92225 0.00104 0.001081 393.7841

398 25 0.926916 0.00098 0.001041 397.7795

398 30 0.931343 0.000927 0.001005 401.588

398 35 0.935552 0.000878 0.000971 405.2259

398 40 0.939562 0.000834 0.00094 408.7073

221

Table E.5. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

[PMIM]Cl.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 1.103534 0.000372 0.000479 373.6855

298 15 1.105536 0.000353 0.000462 375.0424

298 20 1.10744 0.000336 0.000446 376.3356

298 25 1.109254 0.000319 0.000431 377.5692

298 30 1.110983 0.000304 0.000417 378.7473

298 35 1.112633 0.00029 0.000403 379.8731

298 40 1.114209 0.000276 0.000391 380.9499

323 10 1.089579 0.000465 0.000539 364.294

323 15 1.092048 0.000441 0.00052 365.947

323 20 1.094394 0.000418 0.000502 367.5211

323 25 1.096626 0.000397 0.000484 369.0217

323 30 1.098752 0.000378 0.000468 370.4539

323 35 1.100779 0.00036 0.000453 371.8222

323 40 1.102714 0.000343 0.000439 373.1307

348 10 1.074192 0.000572 0.000599 354.0777

348 15 1.077184 0.000541 0.000577 356.0529

348 20 1.080021 0.000512 0.000556 357.9311

348 25 1.082716 0.000485 0.000537 359.7196

348 30 1.08528 0.000461 0.000518 361.4249

348 35 1.087721 0.000438 0.000501 363.0529

348 40 1.090049 0.000417 0.000485 364.6088

373 10 1.05744 0.000696 0.000659 343.1203

373 15 1.061016 0.000655 0.000633 345.445

373 20 1.064399 0.000619 0.00061 347.6512

373 25 1.067605 0.000585 0.000588 349.7487

373 30 1.070649 0.000554 0.000567 351.7458

373 35 1.073543 0.000526 0.000548 353.6502

373 40 1.0763 0.0005 0.00053 355.4686

398 10 1.03938 0.000839 0.00072 331.5

398 15 1.043609 0.000787 0.00069 334.2033

398 20 1.047597 0.00074 0.000663 336.7625

398 25 1.051367 0.000698 0.000638 339.1905

398 30 1.054938 0.000659 0.000615 341.4983

398 35 1.058326 0.000624 0.000594 343.6955

398 40 1.061547 0.000592 0.000574 345.7908

222

Table E.6. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

25 mass % [PMIM]Cl + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.873888 0.000502 0.000739 428.7741

298 15 0.876029 0.000477 0.000714 430.8778

298 20 0.878073 0.000455 0.000691 432.8904

298 25 0.880026 0.000434 0.00067 434.8183

298 30 0.881894 0.000415 0.000649 436.6669

298 35 0.883684 0.000397 0.00063 438.4412

298 40 0.8854 0.00038 0.000612 440.1457

323 10 0.856837 0.000641 0.000838 412.205

323 15 0.859516 0.000608 0.000809 414.7867

323 20 0.862064 0.000577 0.000781 417.2501

323 25 0.864493 0.000549 0.000755 419.6043

323 30 0.86681 0.000523 0.000731 421.857

323 35 0.869025 0.000498 0.000708 424.0154

323 40 0.871144 0.000476 0.000687 426.0858

348 10 0.837965 0.000813 0.000944 394.2478

348 15 0.841279 0.000766 0.000908 397.3716

348 20 0.844417 0.000724 0.000874 400.3419

348 25 0.847396 0.000685 0.000843 403.1717

348 30 0.850229 0.00065 0.000814 405.8722

348 35 0.852929 0.000618 0.000788 408.4534

348 40 0.855505 0.000588 0.000763 410.9242

373 10 0.817252 0.001027 0.00106 374.9977

373 15 0.82132 0.000961 0.001014 378.7404

373 20 0.825152 0.000902 0.000973 382.2828

373 25 0.828772 0.00085 0.000935 385.6442

373 30 0.8322 0.000802 0.000901 388.841

373 35 0.835453 0.000759 0.000869 391.8873

373 40 0.838547 0.00072 0.000839 394.7955

398 10 0.794636 0.001297 0.001188 354.5303

398 15 0.799613 0.001203 0.00113 358.9856

398 20 0.804269 0.001121 0.001079 363.1779

398 25 0.808639 0.001048 0.001033 367.1359

398 30 0.812756 0.000984 0.000991 370.8838

398 35 0.816646 0.000927 0.000953 374.442

398 40 0.82033 0.000875 0.000918 377.8277

223

Table E.7. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

50 mass % [PMIM]Cl + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.950522 0.000359 0.000558 453.1684

298 15 0.952193 0.000343 0.000541 454.7629

298 20 0.953794 0.000329 0.000525 456.2933

298 25 0.955329 0.000315 0.00051 457.7633

298 30 0.956802 0.000302 0.000495 459.1764

298 35 0.958217 0.00029 0.000482 460.5357

298 40 0.959578 0.000278 0.000468 461.8445

323 10 0.936484 0.000454 0.000632 439.8814

323 15 0.938562 0.000433 0.000612 441.8357

323 20 0.940549 0.000413 0.000593 443.7088

323 25 0.942452 0.000395 0.000576 445.5059

323 30 0.944275 0.000378 0.000559 447.2317

323 35 0.946025 0.000362 0.000543 448.8904

323 40 0.947705 0.000347 0.000528 450.4861

348 10 0.920929 0.000566 0.000708 425.3906

348 15 0.923474 0.000538 0.000684 427.7443

348 20 0.925901 0.000512 0.000662 429.9957

348 25 0.92822 0.000488 0.000642 432.1521

348 30 0.930438 0.000466 0.000622 434.2198

348 35 0.932562 0.000446 0.000604 436.2047

348 40 0.934598 0.000427 0.000586 438.1118

373 10 0.903887 0.000699 0.000787 409.792

373 15 0.906967 0.000662 0.000759 412.5893

373 20 0.909895 0.000628 0.000733 415.2582

373 25 0.912685 0.000597 0.000709 417.8085

373 30 0.915347 0.000568 0.000686 420.2492

373 35 0.917891 0.000542 0.000665 422.5878

373 40 0.920324 0.000517 0.000645 424.8315

398 10 0.885367 0.000859 0.00087 393.1714

398 15 0.889065 0.000809 0.000837 396.4628

398 20 0.892568 0.000764 0.000806 399.5928

398 25 0.895893 0.000724 0.000777 402.5753

398 30 0.899055 0.000686 0.000751 405.4222

398 35 0.902068 0.000652 0.000726 408.1442

398 40 0.904943 0.000621 0.000703 410.7505

224

Table E.8. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

75 mass % [PMIM]Cl + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 1.026939 0.000316 0.000474 437.5741

298 15 1.028525 0.000302 0.00046 438.9269

298 20 1.030044 0.000289 0.000446 440.224

298 25 1.031499 0.000276 0.000432 441.4687

298 30 1.032894 0.000265 0.00042 442.6639

298 35 1.034233 0.000254 0.000408 443.8123

298 40 1.035519 0.000243 0.000396 444.9165

323 10 1.014044 0.000397 0.000537 426.6544

323 15 1.016011 0.000379 0.00052 428.3115

323 20 1.017893 0.000362 0.000504 429.899

323 25 1.019693 0.000346 0.000488 431.4213

323 30 1.021418 0.000331 0.000474 432.8823

323 35 1.023072 0.000317 0.00046 434.2855

323 40 1.02466 0.000304 0.000447 435.6343

348 10 0.99975 0.000491 0.000599 414.7111

348 15 1.002147 0.000467 0.00058 416.7021

348 20 1.004435 0.000445 0.000561 418.6069

348 25 1.006622 0.000425 0.000544 420.4313

348 30 1.008713 0.000406 0.000527 422.1805

348 35 1.010717 0.000388 0.000512 423.8592

348 40 1.012638 0.000372 0.000497 425.4717

373 10 0.984105 0.0006 0.000663 401.8328

373 15 0.986986 0.00057 0.00064 404.1893

373 20 0.98973 0.000541 0.000619 406.4397

373 25 0.992347 0.000515 0.000599 408.5915

373 30 0.994845 0.000491 0.00058 410.6518

373 35 0.997235 0.000469 0.000563 412.6268

373 40 0.999522 0.000448 0.000546 414.5218

398 10 0.967144 0.000728 0.000728 388.1013

398 15 0.970573 0.000688 0.000702 390.858

398 20 0.973828 0.000652 0.000677 393.4843

398 25 0.976925 0.000619 0.000654 395.9904

398 30 0.979875 0.000588 0.000633 398.3856

398 35 0.98269 0.00056 0.000613 400.6779

398 40 0.98538 0.000534 0.000594 402.8744

225

Table E.9. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

[BMIM]Cl.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 1.068676 0.000333 0.00046 402.1893

298 15 1.070414 0.000317 0.000445 403.4984

298 20 1.072074 0.000303 0.000431 404.7504

298 25 1.07366 0.000289 0.000418 405.9489

298 30 1.075177 0.000276 0.000405 407.097

298 35 1.076629 0.000264 0.000393 408.1977

298 40 1.078021 0.000253 0.000381 409.2536

323 10 1.055693 0.000415 0.000517 392.4761

323 15 1.057832 0.000395 0.0005 394.0686

323 20 1.059873 0.000376 0.000484 395.5907

323 25 1.061822 0.000359 0.000469 397.0469

323 30 1.063685 0.000343 0.000454 398.4415

323 35 1.065468 0.000327 0.000441 399.7781

323 40 1.067175 0.000313 0.000428 401.0602

348 10 1.041395 0.000509 0.000573 381.9173

348 15 1.043982 0.000483 0.000554 383.8169

348 20 1.046445 0.00046 0.000536 385.6304

348 25 1.048795 0.000438 0.000519 387.3637

348 30 1.051038 0.000417 0.000502 389.0223

348 35 1.053181 0.000398 0.000487 390.611

348 40 1.055233 0.00038 0.000472 392.1342

373 10 1.025853 0.000617 0.000629 370.6028

373 15 1.028937 0.000584 0.000607 372.8339

373 20 1.031867 0.000554 0.000587 374.9603

373 25 1.034656 0.000526 0.000567 376.9901

373 30 1.037315 0.000501 0.000549 378.93

373 35 1.039852 0.000477 0.000532 380.7864

373 40 1.042278 0.000455 0.000516 382.5648

398 10 1.009128 0.00074 0.000686 358.6168

398 15 1.012763 0.000699 0.00066 361.2049

398 20 1.016208 0.000661 0.000637 363.6667

398 25 1.01948 0.000626 0.000615 366.0123

398 30 1.022593 0.000594 0.000594 368.2508

398 35 1.025559 0.000565 0.000575 370.3901

398 40 1.028389 0.000538 0.000557 372.4372

226

Table E.10. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

25 mass % [BMIM]Cl + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.860406 0.000577 0.00081 408.2557

298 15 0.862828 0.000547 0.000782 410.5571

298 20 0.865133 0.00052 0.000755 412.7539

298 25 0.867331 0.000495 0.000731 414.8536

298 30 0.869429 0.000472 0.000707 416.8631

298 35 0.871435 0.00045 0.000685 418.7884

298 40 0.873354 0.00043 0.000665 420.635

323 10 0.842021 0.00074 0.000919 390.9947

323 15 0.845054 0.000699 0.000884 393.8163

323 20 0.847929 0.000661 0.000852 396.5011

323 25 0.850661 0.000626 0.000822 399.0601

323 30 0.853261 0.000595 0.000795 401.5032

323 35 0.85574 0.000566 0.000769 403.839

323 40 0.858105 0.000539 0.000744 406.0751

348 10 0.821712 0.000943 0.001036 372.3611

348 15 0.825471 0.000884 0.000993 375.7757

348 20 0.829017 0.000831 0.000953 379.011

348 25 0.83237 0.000784 0.000917 382.0835

348 30 0.835549 0.000741 0.000884 385.0074

348 35 0.838569 0.000702 0.000853 387.7952

348 40 0.841442 0.000667 0.000825 390.4575

373 10 0.799443 0.001198 0.001164 352.4522

373 15 0.804075 0.001114 0.00111 356.5479

373 20 0.808415 0.00104 0.001061 360.4074

373 25 0.812496 0.000975 0.001017 364.0555

373 30 0.816345 0.000917 0.000977 367.5132

373 35 0.819986 0.000864 0.00094 370.7982

373 40 0.823437 0.000817 0.000906 373.9258

398 10 0.775133 0.001527 0.001309 331.3425

398 15 0.780827 0.001404 0.001239 336.229

398 20 0.786119 0.001299 0.001178 340.8013

398 25 0.791058 0.001208 0.001123 345.0976

398 30 0.795688 0.001128 0.001074 349.1491

398 35 0.800043 0.001057 0.00103 352.9817

398 40 0.804153 0.000994 0.00099 356.6169

227

Table E.11. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

50 mass % [BMIM]Cl + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.923176 0.000477 0.000677 413.0553

298 15 0.925326 0.000454 0.000655 414.9811

298 20 0.927376 0.000432 0.000633 416.8227

298 25 0.929336 0.000412 0.000614 418.5856

298 30 0.931209 0.000394 0.000595 420.275

298 35 0.933003 0.000376 0.000577 421.8955

298 40 0.934721 0.00036 0.00056 423.4513

323 10 0.906703 0.000604 0.000764 398.4461

323 15 0.909373 0.000572 0.000737 400.7957

323 20 0.911912 0.000544 0.000712 403.0376

323 25 0.914333 0.000517 0.000689 405.1797

323 30 0.916642 0.000492 0.000667 407.2292

323 35 0.918849 0.00047 0.000646 409.1923

323 40 0.92096 0.000449 0.000626 411.0747

348 10 0.888564 0.000757 0.000854 382.6634

348 15 0.891835 0.000714 0.000821 385.4857

348 20 0.894936 0.000675 0.000792 388.1708

348 25 0.897881 0.00064 0.000764 390.73

348 30 0.900684 0.000607 0.000739 393.1731

348 35 0.903355 0.000578 0.000715 395.5087

348 40 0.905905 0.00055 0.000692 397.7447

373 10 0.868781 0.000942 0.000949 365.8134

373 15 0.872751 0.000883 0.00091 369.1644

373 20 0.876497 0.000831 0.000874 372.3407

373 25 0.880042 0.000784 0.000842 375.3583

373 30 0.883403 0.000741 0.000811 378.2309

373 35 0.886597 0.000703 0.000784 380.9705

373 40 0.889637 0.000667 0.000758 383.5876

398 10 0.84735 0.001168 0.001051 347.9889

398 15 0.85214 0.001088 0.001003 351.9342

398 20 0.856635 0.001017 0.00096 355.6563

398 25 0.860866 0.000955 0.000921 359.1784

398 30 0.864861 0.000898 0.000886 362.5196

398 35 0.868642 0.000848 0.000853 365.6966

398 40 0.87223 0.000802 0.000823 368.7235

228

Table E.12. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

75 mass % [BMIM]Cl + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.988827 0.000428 0.000589 400.7704

298 15 0.990891 0.000407 0.00057 402.4452

298 20 0.99286 0.000387 0.000551 404.0462

298 25 0.99474 0.00037 0.000534 405.578

298 30 0.996537 0.000353 0.000517 407.0451

298 35 0.998257 0.000337 0.000502 408.4514

298 40 0.999905 0.000323 0.000487 409.8007

323 10 0.97348 0.000537 0.000662 388.4271

323 15 0.976028 0.000509 0.000639 390.463

323 20 0.978453 0.000484 0.000618 392.406

323 25 0.980765 0.00046 0.000598 394.2627

323 30 0.982972 0.000439 0.000579 396.039

323 35 0.985081 0.000419 0.000561 397.7402

323 40 0.987099 0.0004 0.000544 399.3712

348 10 0.956622 0.000665 0.000736 375.0908

348 15 0.959719 0.000629 0.000709 377.5232

348 20 0.962659 0.000595 0.000684 379.8397

348 25 0.965455 0.000565 0.000661 382.0492

348 30 0.968118 0.000537 0.000639 384.1597

348 35 0.970658 0.000511 0.000619 386.1782

348 40 0.973084 0.000487 0.0006 388.1111

373 10 0.938306 0.000816 0.000811 360.865

373 15 0.942027 0.000768 0.00078 363.7328

373 20 0.945548 0.000725 0.000751 366.4564

373 25 0.948885 0.000685 0.000724 369.0479

373 30 0.952056 0.000649 0.000699 371.5182

373 35 0.955073 0.000617 0.000676 373.8767

373 40 0.957949 0.000586 0.000654 376.1316

398 10 0.918571 0.000995 0.00089 345.8443

398 15 0.923004 0.000932 0.000853 349.1908

398 20 0.927181 0.000875 0.000819 352.358

398 25 0.931126 0.000824 0.000788 355.3628

398 30 0.934861 0.000778 0.000759 358.2196

398 35 0.938405 0.000736 0.000732 360.9411

398 40 0.941775 0.000698 0.000708 363.5381

229

Table E.13. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

[HMIM]Cl.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 1.048114 0.000403 0.000478 342.9323

298 15 1.050172 0.000381 0.00046 344.28

298 20 1.052122 0.000361 0.000443 345.5601

298 25 1.053973 0.000342 0.000427 346.7772

298 30 1.055732 0.000325 0.000412 347.9356

298 35 1.057405 0.000309 0.000398 349.0394

298 40 1.058998 0.000294 0.000384 350.0919

323 10 1.034919 0.000502 0.000536 334.3522

323 15 1.037448 0.000474 0.000515 335.9879

323 20 1.039841 0.000448 0.000496 337.5402

323 25 1.042111 0.000424 0.000478 339.0152

323 30 1.044266 0.000402 0.000461 340.4186

323 35 1.046314 0.000382 0.000445 341.7553

323 40 1.048263 0.000363 0.00043 343.03

348 10 1.020424 0.000616 0.000593 325.0519

348 15 1.023476 0.000579 0.000569 326.9989

348 20 1.026359 0.000546 0.000548 328.844

348 25 1.029088 0.000516 0.000528 330.5954

348 30 1.031676 0.000489 0.000509 332.2603

348 35 1.034134 0.000463 0.000491 333.845

348 40 1.03647 0.00044 0.000474 335.3554

373 10 1.004702 0.000745 0.000649 315.1125

373 15 1.008334 0.000699 0.000623 317.3948

373 20 1.011757 0.000657 0.000598 319.5536

373 25 1.01499 0.00062 0.000576 321.5992

373 30 1.018051 0.000585 0.000555 323.5417

373 35 1.020952 0.000554 0.000535 325.3886

373 40 1.023708 0.000525 0.000517 327.1473

398 10 0.987816 0.000894 0.000707 304.6098

398 15 0.992092 0.000835 0.000676 307.2525

398 20 0.99611 0.000783 0.000648 309.7462

398 25 0.999895 0.000735 0.000623 312.1047

398 30 1.003469 0.000693 0.000599 314.34

398 35 1.006852 0.000654 0.000577 316.4625

398 40 1.010058 0.000618 0.000557 318.4813

230

Table E.14. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

25 mass % [HMIM]Cl + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.863198 0.000524 0.000751 417.098

298 15 0.865405 0.000498 0.000726 419.2337

298 20 0.86751 0.000474 0.000702 421.2749

298 25 0.869518 0.000452 0.000679 423.2282

298 30 0.871438 0.000431 0.000658 425.0993

298 35 0.873276 0.000412 0.000638 426.8936

298 40 0.875035 0.000394 0.000619 428.616

323 10 0.846091 0.000669 0.000851 400.7298

323 15 0.84885 0.000633 0.00082 403.3476

323 20 0.851472 0.0006 0.000792 405.8425

323 25 0.853966 0.00057 0.000765 408.2242

323 30 0.856345 0.000542 0.00074 410.501

323 35 0.858615 0.000517 0.000716 412.6804

323 40 0.860785 0.000493 0.000694 414.7691

348 10 0.827185 0.000848 0.000958 383.0212

348 15 0.830595 0.000798 0.00092 386.185

348 20 0.833819 0.000753 0.000885 389.1894

348 25 0.836876 0.000712 0.000853 392.0483

348 30 0.83978 0.000674 0.000823 394.7736

348 35 0.842543 0.00064 0.000795 397.376

348 40 0.845178 0.000609 0.00077 399.8648

373 10 0.806462 0.001071 0.001074 364.0697

373 15 0.810644 0.001 0.001026 367.8559

373 20 0.814578 0.000937 0.000984 371.4344

373 25 0.818288 0.000881 0.000945 374.8257

373 30 0.821797 0.000831 0.000909 378.0472

373 35 0.825123 0.000786 0.000876 381.1138

373 40 0.828283 0.000744 0.000846 384.0386

398 10 0.783865 0.001352 0.001202 343.9539

398 15 0.788979 0.001251 0.001143 348.4558

398 20 0.793752 0.001164 0.00109 352.6851

398 25 0.798227 0.001087 0.001042 356.6725

398 30 0.802435 0.001018 0.000999 360.4436

398 35 0.806406 0.000957 0.00096 364.0198

398 40 0.810163 0.000903 0.000924 367.4192

231

Table E.15. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

50 mass % [HMIM]Cl + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.914281 0.00052 0.000693 387.0189

298 15 0.916599 0.000493 0.000669 388.9843

298 20 0.918805 0.000468 0.000646 390.8584

298 25 0.920906 0.000445 0.000624 392.6478

298 30 0.922909 0.000424 0.000604 394.3582

298 35 0.924822 0.000404 0.000585 395.995

298 40 0.926651 0.000386 0.000567 397.5628

323 10 0.897592 0.000659 0.000781 373.019

323 15 0.90047 0.000622 0.000752 375.4144

323 20 0.903198 0.000589 0.000725 377.6933

323 25 0.905791 0.000558 0.0007 379.8646

323 30 0.908258 0.00053 0.000676 381.9366

323 35 0.910609 0.000504 0.000654 383.9165

323 40 0.912852 0.00048 0.000633 385.8105

348 10 0.879235 0.000825 0.000873 357.9178

348 15 0.88276 0.000776 0.000838 360.7929

348 20 0.886089 0.000731 0.000805 363.5194

348 25 0.889241 0.00069 0.000776 366.1102

348 30 0.892231 0.000653 0.000748 368.5767

348 35 0.895074 0.000619 0.000723 370.9287

348 40 0.89778 0.000588 0.000699 373.1749

373 10 0.859234 0.001028 0.000969 341.8186

373 15 0.863511 0.00096 0.000927 345.2299

373 20 0.867531 0.000899 0.000888 348.4519

373 25 0.871321 0.000845 0.000853 351.5031

373 30 0.874903 0.000797 0.000821 354.3993

373 35 0.878297 0.000753 0.000791 357.1539

373 40 0.881518 0.000713 0.000764 359.7787

398 10 0.837586 0.001276 0.001073 324.812

398 15 0.842745 0.001182 0.001021 328.8257

398 20 0.847565 0.001101 0.000975 332.5977

398 25 0.852085 0.001028 0.000933 336.1545

398 30 0.856338 0.000964 0.000895 339.5181

398 35 0.86035 0.000907 0.000861 342.7074

398 40 0.864146 0.000855 0.000829 345.7381

232

Table E.16. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

75 mass % [HMIM]Cl + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.963378 0.000612 0.000701 331.2972

298 15 0.966243 0.000576 0.000674 333.2712

298 20 0.968951 0.000543 0.000648 335.1415

298 25 0.971513 0.000513 0.000624 336.9164

298 30 0.973943 0.000486 0.000601 338.6035

298 35 0.976249 0.000461 0.00058 340.2091

298 40 0.978442 0.000437 0.00056 341.7392

323 10 0.945645 0.00077 0.000785 319.213

323 15 0.949177 0.000722 0.000752 321.602

323 20 0.952503 0.000678 0.000722 323.8599

323 25 0.955642 0.000639 0.000694 325.9982

323 30 0.958611 0.000603 0.000668 328.027

323 35 0.961424 0.00057 0.000644 329.9551

323 40 0.964094 0.00054 0.000621 331.7903

348 10 0.926277 0.000958 0.000871 306.2716

348 15 0.930571 0.000893 0.000832 309.1176

348 20 0.934598 0.000835 0.000796 311.7985

348 25 0.938385 0.000783 0.000764 314.3305

348 30 0.941955 0.000737 0.000734 316.7272

348 35 0.94533 0.000694 0.000706 319.0005

348 40 0.948525 0.000656 0.000681 321.1607

373 10 0.90533 0.001183 0.00096 292.5759

373 15 0.910498 0.001096 0.000913 295.9255

373 20 0.915319 0.001019 0.000871 299.0679

373 25 0.919834 0.000951 0.000834 302.0254

373 30 0.924075 0.00089 0.000799 304.8168

373 35 0.928069 0.000836 0.000768 307.4579

373 40 0.931842 0.000787 0.000739 309.9623

398 10 0.882839 0.001455 0.001054 278.2194

398 15 0.889014 0.001336 0.000998 282.1254

398 20 0.89474 0.001234 0.000948 285.7712

398 25 0.900073 0.001145 0.000904 289.188

398 30 0.90506 0.001067 0.000864 292.4016

398 35 0.90974 0.000997 0.000828 295.433

398 40 0.914144 0.000935 0.000795 298.3004

233

Table E.17. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

[EMIM]Ac.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 1.088334 0.000452 0.000795 514.3214

298 15 1.090747 0.000434 0.000775 516.6046

298 20 1.093073 0.000418 0.000756 518.8104

298 25 1.095317 0.000403 0.000738 520.943

298 30 1.097484 0.000388 0.00072 523.0064

298 35 1.099578 0.000374 0.000704 525.0041

298 40 1.101603 0.000362 0.000688 526.9396

323 10 1.065811 0.000564 0.000878 493.2547

323 15 1.068755 0.00054 0.000854 495.9835

323 20 1.071587 0.000518 0.000832 498.6148

323 25 1.074312 0.000498 0.000811 501.1544

323 30 1.076939 0.000479 0.000791 503.6078

323 35 1.079472 0.000461 0.000772 505.9799

323 40 1.081918 0.000444 0.000754 508.2751

348 10 1.041581 0.000696 0.000962 471.0821

348 15 1.045127 0.000664 0.000934 474.2956

348 20 1.048528 0.000635 0.000908 477.3866

348 25 1.051792 0.000608 0.000883 480.3636

348 30 1.054929 0.000583 0.00086 483.2339

348 35 1.057949 0.00056 0.000839 486.0042

348 40 1.060858 0.000538 0.000818 488.6806

373 10 1.015752 0.000853 0.001047 448.0086

373 15 1.019984 0.000811 0.001014 451.749

373 20 1.024026 0.000772 0.000984 455.3364

373 25 1.027893 0.000736 0.000955 458.7823

373 30 1.0316 0.000704 0.000928 462.0969

373 35 1.035157 0.000674 0.000903 465.2893

373 40 1.038576 0.000646 0.00088 468.3676

398 10 0.988417 0.001041 0.001136 424.2199

398 15 0.99343 0.000984 0.001096 428.5341

398 20 0.998198 0.000932 0.00106 432.657

398 25 1.002742 0.000885 0.001027 436.6049

398 30 1.007081 0.000843 0.000996 440.3918

398 35 1.011232 0.000803 0.000967 444.0301

398 40 1.01521 0.000768 0.00094 447.5306

234

Table E.18. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for 5

mass % [EMIM]Ac + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.804804 0.000803 0.00105 379.9313

298 15 0.807943 0.000755 0.001008 382.9009

298 20 0.810912 0.000712 0.00097 385.7199

298 25 0.813726 0.000674 0.000934 388.4012

298 30 0.816398 0.000638 0.000902 390.956

298 35 0.81894 0.000606 0.000871 393.3943

298 40 0.821362 0.000576 0.000842 395.7249

323 10 0.782484 0.001052 0.001202 359.1497

323 15 0.78647 0.000982 0.001149 362.8183

323 20 0.790216 0.00092 0.0011 366.2823

323 25 0.793746 0.000864 0.001056 369.5619

323 30 0.797081 0.000814 0.001015 372.6744

323 35 0.800241 0.000769 0.000978 375.6346

323 40 0.80324 0.000728 0.000943 378.4554

348 10 0.757717 0.00138 0.001375 336.774

348 15 0.762755 0.001274 0.001304 341.267

348 20 0.767448 0.001182 0.001241 345.4793

348 25 0.771838 0.001102 0.001185 349.4432

348 30 0.77596 0.001031 0.001135 353.1858

348 35 0.779843 0.000967 0.001089 356.7294

348 40 0.783511 0.000911 0.001047 360.093

373 10 0.730327 0.001822 0.001577 312.8664

373 15 0.736697 0.001657 0.001481 318.3483

373 20 0.742564 0.001519 0.001399 323.4388

373 25 0.748 0.001401 0.001327 328.1915

373 30 0.753062 0.001299 0.001263 332.649

373 35 0.757798 0.00121 0.001206 336.8459

373 40 0.762244 0.001132 0.001155 340.8104

398 10 0.700017 0.00244 0.001823 287.4366

398 15 0.708123 0.002175 0.00169 294.1321

398 20 0.715473 0.001962 0.001579 300.2694

398 25 0.722198 0.001785 0.001485 305.9403

398 30 0.728395 0.001637 0.001403 311.2139

398 35 0.734142 0.00151 0.001332 316.1442

398 40 0.739499 0.0014 0.001269 320.7741

235

Table E.19. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

15 mass % [EMIM]Ac + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.830447 0.000728 0.000994 396.9745

298 15 0.833391 0.000688 0.000957 399.7935

298 20 0.836183 0.000651 0.000923 402.4776

298 25 0.838839 0.000618 0.000891 405.0375

298 30 0.841367 0.000587 0.000861 407.4829

298 35 0.843778 0.000558 0.000834 409.8221

298 40 0.846082 0.000532 0.000808 412.0627

323 10 0.808682 0.000947 0.001132 376.4381

323 15 0.812396 0.000888 0.001085 379.9044

323 20 0.815901 0.000835 0.001043 383.1897

323 25 0.819217 0.000788 0.001003 386.3106

323 30 0.822361 0.000745 0.000967 389.2814

323 35 0.825348 0.000706 0.000934 392.1147

323 40 0.828192 0.00067 0.000902 394.8213

348 10 0.784632 0.001228 0.001286 354.3814

348 15 0.78929 0.001141 0.001225 358.6011

348 20 0.793653 0.001065 0.001171 362.5762

348 25 0.797753 0.000998 0.001122 366.3329

348 30 0.80162 0.000938 0.001077 369.893

348 35 0.805277 0.000884 0.001037 373.2749

348 40 0.808742 0.000835 0.000999 376.4947

373 10 0.758185 0.001599 0.001462 330.8941

373 15 0.764015 0.001468 0.001382 336.0024

373 20 0.769424 0.001356 0.001312 340.7765

373 25 0.774467 0.001259 0.00125 345.258

373 30 0.779188 0.001174 0.001194 349.4808

373 35 0.783626 0.001099 0.001145 353.4727

373 40 0.78781 0.001032 0.001099 357.2572

398 10 0.729139 0.002103 0.00167 306.0268

398 15 0.736459 0.001899 0.001562 312.2024

398 20 0.743164 0.001731 0.001469 317.913

398 25 0.74935 0.001589 0.00139 323.2273

398 30 0.755091 0.001467 0.00132 328.1988

398 35 0.760446 0.001362 0.001259 332.87

398 40 0.765461 0.00127 0.001204 337.2757

236

Table E.20. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

25 mass % [EMIM]Ac + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.855787 0.000678 0.000957 410.8726

298 15 0.858614 0.000642 0.000923 413.5914

298 20 0.861303 0.000609 0.000892 416.1859

298 25 0.863865 0.000579 0.000862 418.6656

298 30 0.86631 0.000552 0.000835 421.039

298 35 0.868647 0.000526 0.000809 423.3133

298 40 0.870883 0.000502 0.000785 425.4955

323 10 0.834234 0.000875 0.001085 390.4375

323 15 0.837784 0.000824 0.001043 393.7672

323 20 0.841144 0.000778 0.001004 396.9317

323 25 0.844331 0.000736 0.000968 399.9456

323 30 0.847361 0.000698 0.000935 402.8211

323 35 0.850246 0.000663 0.000904 405.5692

323 40 0.852999 0.000631 0.000875 408.1996

348 10 0.810509 0.001127 0.001225 368.5459

348 15 0.814932 0.001052 0.001171 372.5791

348 20 0.819092 0.000986 0.001123 376.3919

348 25 0.823015 0.000927 0.001079 380.0064

348 30 0.826726 0.000874 0.001038 383.4413

348 35 0.830245 0.000826 0.001001 386.7126

348 40 0.833589 0.000783 0.000967 389.834

373 10 0.784542 0.001452 0.001383 345.3087

373 15 0.790035 0.001342 0.001313 350.1609

373 20 0.795157 0.001246 0.001252 354.7164

373 25 0.799955 0.001162 0.001196 359.0095

373 30 0.804464 0.001088 0.001147 363.0688

373 35 0.808717 0.001022 0.001102 366.9178

373 40 0.812739 0.000963 0.00106 370.5766

398 10 0.756831 0.001868 0.001557 321.7948

398 15 0.7639 0.001696 0.001462 328.0519

398 20 0.7704 0.001553 0.00138 333.8683

398 25 0.776431 0.00143 0.001309 339.337

398 30 0.782032 0.001325 0.001247 344.4566

398 35 0.787263 0.001233 0.001191 349.2788

398 40 0.792165 0.001153 0.001141 353.8292

237

Table E.21. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

50 mass % [EMIM]Ac + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.920358 0.000612 0.000915 435.3855

298 15 0.923109 0.000582 0.000885 437.9922

298 20 0.925736 0.000555 0.000858 440.4893

298 25 0.92825 0.00053 0.000832 442.8843

298 30 0.930657 0.000506 0.000807 445.1842

298 35 0.932965 0.000485 0.000785 447.3951

298 40 0.93518 0.000464 0.000763 449.5226

323 10 0.898298 0.000781 0.001027 414.7645

323 15 0.901718 0.000739 0.000991 417.9285

323 20 0.904971 0.000702 0.000958 420.9495

323 25 0.908071 0.000667 0.000927 423.8385

323 30 0.911031 0.000635 0.000898 426.6057

323 35 0.91386 0.000606 0.000871 429.2597

323 40 0.916569 0.000579 0.000845 431.8085

348 10 0.874227 0.000991 0.001147 392.8342

348 15 0.878438 0.000932 0.001102 396.6275

348 20 0.882422 0.000879 0.001062 400.2337

348 25 0.886202 0.000831 0.001024 403.6696

348 30 0.889795 0.000788 0.000989 406.9498

348 35 0.893218 0.000748 0.000957 410.0869

348 40 0.896485 0.000712 0.000927 413.0918

373 10 0.848148 0.001255 0.001278 369.7462

373 15 0.853303 0.001171 0.001222 374.2544

373 20 0.858148 0.001096 0.001171 378.517

373 25 0.862719 0.00103 0.001125 382.5594

373 30 0.867041 0.000971 0.001084 386.4029

373 35 0.871141 0.000917 0.001045 390.0656

373 40 0.875038 0.000869 0.00101 393.5631

398 10 0.820021 0.001593 0.001423 345.6292

398 15 0.826317 0.00147 0.001351 350.9568

398 20 0.832186 0.001364 0.001288 355.9598

398 25 0.837681 0.001271 0.001232 360.6768

398 30 0.842847 0.00119 0.001181 365.1394

398 35 0.84772 0.001118 0.001135 369.3738

398 40 0.85233 0.001053 0.001094 373.4021

238

Table E.22. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

75 mass % [EMIM]Ac + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.993053 0.000566 0.00089 458.3899

298 15 0.995804 0.000541 0.000864 460.933

298 20 0.99844 0.000517 0.000839 463.3768

298 25 1.00097 0.000495 0.000816 465.7278

298 30 1.0034 0.000475 0.000794 467.9918

298 35 1.005737 0.000456 0.000773 470.1741

298 40 1.007986 0.000438 0.000753 472.2794

323 10 0.96999 0.000715 0.000991 437.3455

323 15 0.973378 0.00068 0.000959 440.4063

323 20 0.976614 0.000648 0.000929 443.3395

323 25 0.97971 0.000618 0.000902 446.1543

323 30 0.982675 0.000591 0.000876 448.8591

323 35 0.985519 0.000565 0.000852 451.4611

323 40 0.988251 0.000542 0.000829 453.967

348 10 0.945036 0.000897 0.001095 415.133

348 15 0.949165 0.000848 0.001057 418.768

348 20 0.95309 0.000804 0.001021 422.2391

348 25 0.956831 0.000764 0.000989 425.5599

348 30 0.960402 0.000727 0.000958 428.742

348 35 0.963816 0.000693 0.00093 431.7958

348 40 0.967086 0.000662 0.000903 434.7304

373 10 0.918253 0.001119 0.001206 391.9362

373 15 0.923246 0.001051 0.001159 396.2099

373 20 0.927968 0.000991 0.001116 400.2733

373 25 0.932446 0.000936 0.001077 404.1457

373 30 0.936703 0.000887 0.001041 407.844

373 35 0.940758 0.000842 0.001007 411.3826

373 40 0.944628 0.000801 0.000976 414.7743

398 10 0.889674 0.001396 0.001325 367.9192

398 15 0.895685 0.0013 0.001267 372.9071

398 20 0.901332 0.001216 0.001215 377.6238

398 25 0.906656 0.001141 0.001168 382.0981

398 30 0.911691 0.001075 0.001125 386.3539

398 35 0.916466 0.001016 0.001085 390.4117

398 40 0.921005 0.000962 0.001049 394.289

239

Table E.23. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

[BMIM]Ac.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 1.055047 0.000445 0.000693 454.3626

298 15 1.057344 0.000426 0.000673 456.3435

298 20 1.05955 0.000408 0.000655 458.2494

298 25 1.06167 0.000392 0.000637 460.0848

298 30 1.063709 0.000376 0.000621 461.8537

298 35 1.065672 0.000362 0.000605 463.5598

298 40 1.067563 0.000348 0.00059 465.2065

323 10 1.035976 0.000552 0.000766 438.0853

323 15 1.038776 0.000528 0.000744 440.4565

323 20 1.041459 0.000504 0.000723 442.7343

323 25 1.044032 0.000483 0.000703 444.9246

323 30 1.046502 0.000463 0.000684 447.0329

323 35 1.048877 0.000444 0.000666 449.0641

323 40 1.051162 0.000427 0.000648 451.0227

348 10 1.015386 0.000678 0.00084 420.8441

348 15 1.01875 0.000645 0.000813 423.6374

348 20 1.021964 0.000615 0.000789 426.3149

348 25 1.02504 0.000587 0.000766 428.8847

348 30 1.027987 0.000561 0.000744 431.3542

348 35 1.030814 0.000537 0.000724 433.73

348 40 1.033529 0.000515 0.000705 436.0179

373 10 0.993379 0.000825 0.000913 402.7994

373 15 0.997377 0.000782 0.000883 406.0484

373 20 1.001185 0.000743 0.000854 409.1545

373 25 1.004817 0.000707 0.000828 412.1289

373 30 1.008288 0.000673 0.000803 414.9813

373 35 1.011611 0.000643 0.00078 417.7205

373 40 1.014795 0.000615 0.000759 420.3543

398 10 0.970043 0.000998 0.000989 384.0975

398 15 0.974756 0.000941 0.000953 387.8385

398 20 0.979226 0.00089 0.00092 391.4037

398 25 0.983476 0.000843 0.000889 394.8082

398 30 0.987524 0.000801 0.000861 398.0653

398 35 0.991388 0.000762 0.000835 401.1864

398 40 0.995082 0.000726 0.000811 404.1816

240

Table E.24. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for 5

mass % [BMIM]Ac + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.80975 0.000723 0.000978 392.9433

298 15 0.8126 0.000683 0.000941 395.7137

298 20 0.815301 0.000646 0.000906 398.3492

298 25 0.817867 0.000612 0.000874 400.8607

298 30 0.820309 0.000581 0.000845 403.2579

298 35 0.822636 0.000553 0.000817 405.5492

298 40 0.824857 0.000526 0.000791 407.7422

323 10 0.788836 0.000943 0.001118 372.9074

323 15 0.792443 0.000884 0.00107 376.3261

323 20 0.795844 0.00083 0.001027 379.5632

323 25 0.799059 0.000783 0.000988 382.6355

323 30 0.802104 0.00074 0.000951 385.5576

323 35 0.804995 0.0007 0.000918 388.3421

323 40 0.807745 0.000664 0.000887 391

348 10 0.765633 0.001227 0.001274 351.2926

348 15 0.770172 0.001139 0.001213 355.4701

348 20 0.774418 0.001062 0.001158 359.4011

348 25 0.778406 0.000994 0.001108 363.1122

348 30 0.782163 0.000933 0.001064 366.6258

348 35 0.785713 0.000879 0.001023 369.9605

348 40 0.789074 0.00083 0.000985 373.1327

373 10 0.740004 0.001604 0.001455 328.1681

373 15 0.745708 0.001471 0.001373 333.2468

373 20 0.750993 0.001357 0.001302 337.9865

373 25 0.755914 0.001258 0.001239 342.4303

373 30 0.760516 0.001172 0.001183 346.6128

373 35 0.764837 0.001096 0.001133 350.5626

373 40 0.768907 0.001028 0.001087 354.3035

398 10 0.711718 0.002121 0.001671 303.5592

398 15 0.718915 0.001911 0.001559 309.7296

398 20 0.725494 0.001738 0.001465 315.4248

398 25 0.731554 0.001593 0.001384 320.7164

398 30 0.737171 0.001469 0.001313 325.6597

398 35 0.742403 0.001362 0.00125 330.2987

398 40 0.747298 0.001269 0.001194 334.669

241

Table E.25. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

15 mass % [BMIM]Ac + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.840878 0.000569 0.000837 428.9056

298 15 0.843211 0.00054 0.000809 431.2896

298 20 0.845437 0.000514 0.000783 433.5693

298 25 0.847562 0.00049 0.000758 435.752

298 30 0.849595 0.000468 0.000735 437.8444

298 35 0.851541 0.000447 0.000713 439.8524

298 40 0.853406 0.000428 0.000692 441.7813

323 10 0.822293 0.000732 0.000952 410.1567

323 15 0.825223 0.000692 0.000917 413.0849

323 20 0.828006 0.000655 0.000885 415.8757

323 25 0.830654 0.000622 0.000855 418.54

323 30 0.833179 0.000592 0.000827 421.0876

323 35 0.835588 0.000564 0.0008 423.5269

323 40 0.837892 0.000538 0.000776 425.8655

348 10 0.801738 0.000936 0.001075 389.9068

348 15 0.805382 0.000879 0.001032 393.459

348 20 0.808824 0.000828 0.000992 396.8298

348 25 0.812085 0.000782 0.000955 400.0356

348 30 0.81518 0.00074 0.000921 403.0907

348 35 0.818124 0.000702 0.00089 406.0074

348 40 0.820929 0.000667 0.000861 408.7964

373 10 0.779156 0.001196 0.001213 368.2516

373 15 0.783665 0.001114 0.001157 372.526

373 20 0.787895 0.001041 0.001107 376.559

373 25 0.791878 0.000977 0.001062 380.376

373 30 0.79564 0.000919 0.001021 383.9981

373 35 0.799201 0.000868 0.000983 387.4433

373 40 0.802581 0.000821 0.000948 390.7271

398 10 0.752154 0.001587 0.001409 343.1703

398 15 0.757875 0.001459 0.001332 348.4106

398 20 0.763188 0.001348 0.001265 353.313

398 25 0.768147 0.001252 0.001205 357.9194

398 30 0.772795 0.001169 0.001152 362.2637

398 35 0.777167 0.001094 0.001104 366.3737

398 40 0.781291 0.001028 0.00106 370.2732

242

Table E.26. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

25 mass % [BMIM]Ac + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.868371 0.000487 0.000756 452.9301

298 15 0.870437 0.000464 0.000732 455.0879

298 20 0.872414 0.000443 0.00071 457.1574

298 25 0.874308 0.000424 0.000689 459.1444

298 30 0.876124 0.000406 0.000669 461.0539

298 35 0.877868 0.000389 0.00065 462.8907

298 40 0.879543 0.000373 0.000632 464.659

323 10 0.851058 0.000621 0.000856 435.0497

323 15 0.853639 0.00059 0.000827 437.6921

323 20 0.8561 0.000562 0.000801 440.2199

323 25 0.858452 0.000536 0.000775 442.6414

323 30 0.860701 0.000511 0.000752 444.9638

323 35 0.862855 0.000489 0.00073 447.1937

323 40 0.86492 0.000468 0.000709 449.3372

348 10 0.831946 0.000787 0.000962 415.7291

348 15 0.835133 0.000743 0.000927 418.9203

348 20 0.83816 0.000704 0.000895 421.9626

348 25 0.841041 0.000669 0.000864 424.8681

348 30 0.843787 0.000636 0.000836 427.6474

348 35 0.846409 0.000606 0.00081 430.3099

348 40 0.848917 0.000578 0.000785 432.8637

373 10 0.811019 0.000992 0.001078 395.0775

373 15 0.814927 0.000932 0.001034 398.8938

373 20 0.818618 0.000877 0.000994 402.516

373 25 0.822115 0.000828 0.000957 405.9621

373 30 0.825435 0.000784 0.000924 409.2473

373 35 0.828593 0.000744 0.000892 412.385

373 40 0.831603 0.000707 0.000863 415.3868

398 10 0.788226 0.001252 0.001205 373.183

398 15 0.793001 0.001166 0.00115 377.7177

398 20 0.797481 0.00109 0.0011 381.9976

398 25 0.801699 0.001022 0.001056 386.0496

398 30 0.805683 0.000962 0.001015 389.8962

398 35 0.809456 0.000908 0.000978 393.5566

398 40 0.813038 0.000859 0.000943 397.0472

243

Table E.27. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

50 mass % [BMIM]Ac + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.926811 0.000438 0.000701 466.8361

298 15 0.928798 0.000419 0.00068 468.84

298 20 0.930704 0.000401 0.000661 470.7663

298 25 0.932535 0.000385 0.000642 472.6194

298 30 0.934293 0.000369 0.000625 474.4038

298 35 0.935985 0.000355 0.000608 476.1233

298 40 0.937613 0.000341 0.000592 477.7815

323 10 0.909727 0.000554 0.000788 449.7843

323 15 0.912189 0.000528 0.000764 452.2222

323 20 0.914545 0.000504 0.000741 454.5608

323 25 0.916802 0.000482 0.000719 456.8066

323 30 0.918966 0.000461 0.000698 458.9657

323 35 0.921043 0.000442 0.000679 461.0434

323 40 0.92304 0.000424 0.000661 463.0447

348 10 0.89098 0.000693 0.000878 431.4375

348 15 0.893991 0.000658 0.000849 434.3585

348 20 0.896862 0.000626 0.000822 437.153

348 25 0.899605 0.000596 0.000796 439.8303

348 30 0.902228 0.000569 0.000772 442.3988

348 35 0.90474 0.000544 0.00075 444.8659

348 40 0.907149 0.00052 0.000728 447.2382

373 10 0.870599 0.000861 0.000974 411.9254

373 15 0.874249 0.000813 0.000938 415.3858

373 20 0.877714 0.00077 0.000905 418.6849

373 25 0.881011 0.00073 0.000875 421.8363

373 30 0.884154 0.000695 0.000847 424.8514

373 35 0.887155 0.000661 0.000821 427.7407

373 40 0.890025 0.000631 0.000796 430.5133

398 10 0.848591 0.001067 0.001076 391.3622

398 15 0.852987 0.001001 0.001032 395.4276

398 20 0.85714 0.000942 0.000993 399.2871

398 25 0.861073 0.00089 0.000957 402.9598

398 30 0.864807 0.000842 0.000923 406.4624

398 35 0.86836 0.000799 0.000893 409.8091

398 40 0.871747 0.000759 0.000864 413.0124

244

Table E.28. Density, isothermal compressibility, isobaric thermal expansion coefficient, and

internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for

75 mass % [BMIM]Ac + ethanol.

T (K) P

(MPa)

ρ

(g/cm3)

κT

(1/MPa)

βP (1/K) π (MPa)

298 10 0.981295 0.000486 0.000741 444.0145

298 15 0.98363 0.000465 0.000719 446.1304

298 20 0.985868 0.000444 0.000698 448.1621

298 25 0.988013 0.000425 0.000678 450.1149

298 30 0.990073 0.000408 0.00066 451.9935

298 35 0.992052 0.000391 0.000642 453.8025

298 40 0.993956 0.000376 0.000625 455.5457

323 10 0.962257 0.000611 0.000826 426.953

323 15 0.965129 0.000581 0.0008 429.5051

323 20 0.967872 0.000554 0.000776 431.9505

323 25 0.970497 0.000529 0.000753 434.2965

323 30 0.973011 0.000506 0.000731 436.5497

323 35 0.975423 0.000484 0.00071 438.7162

323 40 0.977738 0.000464 0.000691 440.8014

348 10 0.941559 0.000759 0.000914 408.7832

348 15 0.945045 0.000719 0.000882 411.8153

348 20 0.948363 0.000683 0.000853 414.7126

348 25 0.951528 0.00065 0.000827 417.4854

348 30 0.954552 0.000619 0.000801 420.143

348 35 0.957445 0.000591 0.000778 422.6934

348 40 0.960216 0.000565 0.000755 425.144

373 10 0.919266 0.000937 0.001004 389.6551

373 15 0.923457 0.000883 0.000967 393.2159

373 20 0.92743 0.000835 0.000932 396.6068

373 25 0.931205 0.000791 0.000901 399.8423

373 30 0.9348 0.000751 0.000871 402.9352

373 35 0.938229 0.000714 0.000844 405.8964

373 40 0.941505 0.000681 0.000819 408.736

398 10 0.895422 0.001152 0.001099 369.7037

398 15 0.900428 0.001079 0.001054 373.8488

398 20 0.905149 0.001014 0.001013 377.7794

398 25 0.909615 0.000956 0.000976 381.5162

398 30 0.91385 0.000903 0.000942 385.077

398 35 0.917875 0.000856 0.00091 388.4768

398 40 0.921709 0.000812 0.000881 391.7288