Transient Interfacial Phenomena in MisciblePolymer Systems

(TIPMPS)

John A. Pojman

University of Southern Mississippi

Vitaly Volpert

Université Lyon I

Hermann Wilke

Institute of Crystal Growth,

Berlin

A flight project in the Microgravity Materials Science Program

2002 Microgravity Materials Science MeetingJune 25, 2002

2

What is the question to beanswered?

Can gradients of composition and temperature inmiscible polymer/monomer systems create

stresses that cause convection?

3

Why?The objective of TIPMPS is to confirm Korteweg’smodel that stresses could be induced in miscible fluidsby concentration gradients, causing phenomena thatwould appear to be the same as with immiscible fluids.The existence of this phenomenon in miscible fluidswill open up a new area of study for materials science.

Many polymer processes involving miscible monomerand polymer systems could be affected by fluid flowand so this work could help understand misciblepolymer processing, not only in microgravity, but alsoon earth.

4

How

An interface between two miscible fluids will be becreated by photopolymerization, which allows thecreation of precise and accurate concentration gradientsbetween polymer and monomer.

Optical techniques will be used to measure therefractive index variation caused by the resultanttemperature and concentration fields.

5

Impact

Demonstrating the existence of this phenomenon inmiscible fluids will open up a new area of study formaterials science.

“If gradients of composition and temperature in misciblepolymer/monomer systems create stresses that causeconvection then it would strongly suggest that stress-inducedflows could occur in many applications with miscible materials.The results of this investigation could then have potentialimplications in polymer blending (phase separation), colloidalformation, fiber spinning, polymerization kinetics, membraneformation and polymer processing in space.”SCR Panel, December 2000.

6

Science Objectives

• Determine if convection can be induced byvariation of the width of a miscible interface

• Determine if convection can be induced byvariation of temperature along a miscibleinterface

• Determine if convection can be induced byvariation of conversion along a miscibleinterface

7

Surface-Tension-InducedConvection

convection caused by gradients in surface(interfacial) tension between immisciblefluids, resulting from gradients inconcentration and/or temperature

high temperature low temperature

fluid 1

fluid 2

interface

8

Consider a Miscible “Interface”

x

y

“interface” = ∂C/∂y

C = volume fraction of A

fluid A

fluid B

9

Can the analogous process occurwith miscible fluids?

high temperature low temperature

fluid 1

fluid 2

10

Korteweg (1901)• treated liquid/vapor interface as a

continuum

• used Navier-Stokes equations plus tensordepending on density derivatives

• for miscible liquid, diffusion is slow enoughthat “a provisional equilibrium” could exist(everything in equilibrium except diffusion)– i.e., no buoyancy

• fluids would act like immiscible fluids

11

Korteweg Stress• mechanical interpretation (“tension”)

k has units of N

σ has units of N m–1

yx

Change in a concentration gradient along the interface causes a volume force

pN − pT = kdcdx

2

= kdc

dx

2

dx∫

FV

= ky

cx

2

12

Hypothesis: Effective InterfacialTension

= k(∆C)2

C

δ

k is the same parameter in the Korteweg model

(Derived by Zeldovich in 1949)

13

Theory of Cahn and Hilliard

= k ∇2∫ C(r)dralso called the surface tension (N m–1)

square gradient contribution to surface free energy (J m–2)

Cahn, J. W.; Hilliard, J. E. "Free Energy of a Nonuniform System. I. Interfacial Free

Energy,"J. Chem. Phys. 1958, 28, 258-267.

k > 0

Thermodynamic approach

g = g0 + k ∇C∫2

Square gradient theory

PN − PT = kdcdx

2

Cahn-Hilliard Theory ofDiffuse Interfaces (1958)

Convection: experiment and theory

Korteweg Stress

Effective Interfacial Tension

= k ∇C∫spinning drop tensiometry

f = f0 + k

1901

Mechanics Thermodynamics

Cahn-Hilliard Theory ofPhase Separation

Nonuniform Materials

PTPNk

simulation

material properties 14

Zeldovich Theory(1949)

van der Waals

1893

15

Why is this important?• answer a 100 year-old question of Korteweg

• stress-induced flows could occur in manyapplications with miscible materials

• link mechanical theory of Korteweg tothermodynamic theory of Cahn & Hilliard

• test theories of polymer-solvent interactions

16

How?

• photopolymerization of dodecyl acrylate

• masks to create concentration gradients

• measure fluid flow by PIV or PTV

• use change in fluorescence of pyrene tomeasure viscosity

17

Photopolymerization can be usedto rapidly prepare

polymer/monomer interfaces

We have anexcellent modelto predictreaction ratesand conversion

0

50

100

150

200

0 10 20 30 40 50 60

Temperature - model / CConversion - model / %Temperature - exp / C

Tem

pera

ture

(˚C

) or

% c

onve

rsio

n

Time (s)

+

Experimental conversion after 10 seconds exposure

18

Schematic

UV

laser sheet illumination

videocamera

mask

no reaction

reaction1 cm

6 cm

100 W Hg arc lamp

filter (330 - 400 nm)

19

20

Variable gradient

21

Why Microgravity?

• buoyancy-drivenconvection destroyspolymer/monomertransition

2.25 cm

1 g

(Polymer)UV exposure region

22

Simulations

• add Korteweg stress terms in Navier-Stokesequations

• validate by comparison to steady-statecalculations with standard interface model

• spinning drop tensiometry to obtain k

• theoretical estimates of k

• predict expected fluid flows and optimizeexperimental conditions

23

Model of Korteweg Stresses inMiscible Fluids

T

t+ v∇T = ∆T

Ct

+ v∇ = D∆C

vt

+ v∇( )v = − 1 ∇p + ∆v +1

K11

x1

+ K12

x2

K21

x1

+ K22

x2

div v = 0

K11 = kCx2

2

K12 = K21 = −kx1

C

x2

K22 = kC

x1

2

where k is system specific,

Navier-Stokes equations + Korteweg terms

24

Essential Problem: Estimation ofSquare Gradient Parameter “k”

• using spinning drop tensiometry

• use thermodynamics (work of B. Nauman)

25

Spinning Drop Technique

• Bernard Vonnegut, brother of novelist KurtVonnegut, proposed technique in 1942

Vonnegut, B. "Rotating Bubble Method for theDetermination of Surface and InterfacialTensions,"Rev. Sci. Instrum. 1942, 13, 6-9.

ω = 3,600rpm

1 cm

= ∆ 2r3

4

26

Image of drop

1 mm

27

Evidence for Existence of EIT

0

0.1

0.2

0.3

0.4

0.5

0 100 200 300 400 500

EIT (mN/m) 2000 RPMEIT (mN/m) 3000 RPMEIT (mN/m) 4000 RPMEIT (mN/m) 5000 RPMEIT (mN/m) 6000 RPMEIT (mN/m) 7000 RPMEIT (mN/m) 7900 RPM

EIT

(m

N m

–1)

Time (sec)

drop relaxes rapidly and reaches a quasi-steady value

28

Estimation of k from SDT

• estimates from SDT: k = 10–8 N– k = EIT * δ– k = 10-4 Nm–1 * 10–4 m

• Temperature dependence– ∂k/∂T = -10–9 N/k

– results are suspect because increased Tincreases diffusion of drop

29

Balsara & Nauman: Polymer-Solvent Systems

k =Rgyr

2 RT

6Vmolar

Χ +3

1− C

X = the Flory-Huggins interaction parameter for apolymer and a good solvent, 0.45.

Balsara, N.P. and Nauman, E.B., "The Entropy of Inhomogeneous Polymer-SolventSystems", J. Poly. Sci.: Part B, Poly. Phys., 26, 1077-1086 (1988)

k = 5 x 10–8 N at 373 K

Rgyr = radius of gyration of polymer = 9 x 10–16 m2

Vmolar = molar volume of solvent

30

Simulations

• Effect of variable transition zone, δ• Effect of temperature gradient along

transition zone

• Effect of conversion gradient alongtransition zone

31

We validated the model bycomparing to “true interface

model”

• Interfacial tension calculated using Cahn-Hilliard formula:

• same flow pattern

• Korteweg stress model exceeds the flowvelocity by 20% for a true interface

= k(∆C)2

32

Variation in δ

Korteweg Interface

33

Simulation of Time-DependentFlow

• we used pressure-velocity formulation

• adaptive grid simulations

• temperature- and concentration-dependentviscosity

• temperature-dependent mass diffusivity

• range of values for k

34

Concentration-DependentViscosity: µ = µ0eλc

1

10

100

1000

0 0.2 0.4 0.6 0.8 1

λ = 1λ = 2λ = 3λ = 4λ = 5

Rel

ativ

e V

isco

sity

Conversion

λ = 5 gives apolymer thatis 120 X moreviscous thanthe monomer

35

Variable transition zone, δ, 0.2 to 5 mm

k = 2 x 10–9 N

polymer

monomer

36

streamlines

37

Maximum Displacement Dependenceon k

1=0.2mm; 2=5mm; k1 *106, N =0; 0, Pa*s =0.006;

C =3; T =0; d0*106, kg/(m*s) =0.1; d 1*106, kg/(m*s) =0.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 100 200 300 400 500 600 700 800

seconds

k0 = 1e-7, Nk0 = 1e-8, Nk0 = 2e-9, N

38

Dependence on variation in δIsothermal case with variable transition zone:

k0 *106, N =0.01; k 1 *106, N =0; 0, Pa*s =0.006;

C =3; T =0; d0*106, kg/(m*s) =0.1; d 1*106, kg/(m*s) =0.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 100 200 300 400 500 600 700 800

seconds

epsilon1=0.2mm, epsilon2=5mm

epsilon1=0.2mm, epsilon2=2mm

epsilon1=0.2mm, epsilon2=1mm

39

Effect of Temperature Gradient

Temperature is scaled so T= 1 corresponds to ∆T = 50K.

Simulations with different k(T) -does it increase or decreasewith T?

Simulations with temperature-dependent diffusioncoefficient

40

viscosity 10X monomer (0.01 Pa s)

k0 = 1.3 x 10–7 N

k1 = 0.7 x 10–7 N

41

side heating,δ = 0.9 mm

polymer = 10 cm2 s–1

monomer = 10 cm2 s–1

T0T0 + 50K

Two vortices are observed

42

side heating,δ = 0.9 mm,µ(c) =0 .01 Pa s * e5 c

polymer = 12 cm2 s–1

monomer = 0.1 cm2 s–1

asymmetric vortices are observed with variable viscosity model

43

effect of temperature-dependentD

• k independent of T

• D increases 4 times across cell

• higher T means larger δ• effect is larger than k depending on T even

with viscosity 100 times larger

44

significant flow

T0T1 T0 T1

45

mm =1; k0 *106, N =1.3; k 1*106, N =0; 0, Pa*s =0.1;

C =5; T =0; d0*106, kg/(m*s) =10; d 1*106, kg/(m*s) =40.

0

0.2

0.4

0.6

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

seconds

46

Effect of Conversion Gradient

• T also varies because polymer conversionand temperature are coupled through heatrelease of polymerization

• T affects k

• T affects D

47

9.4

C =1 C =0

monomer

k = 10–8 N

T = 150 ˚C

T = 25 ˚C

polymer viscosityindependent of T

48

with D(T)

C =1 C =0

monomer

k = 10–8 N

T = 150 ˚C

T = 25 ˚C

D=1.2 x 10-5 cm2 s-1 D=1 x 10-6

cm2 s-1

49

Limitations of Model

• two-dimensional

• does not include chemical reaction

• neglects temperature difference betweenpolymer and monomer– polymer will cool by conduction to monomer

and heat loss from reactor

50

Conclusions

• Modeling predicts that the three TIPMPSexperiments will produce observable fluidflows and measurable distortions in theconcentration fields.

• TIPMPS will be a first of its kindinvestigation that should establish a newfield of microgravity materials science.

51

Quo Vademus?

• refine estimations of “k” using spinningdrop tensiometry

• completely characterize the dependence ofall parameters on T, C and molecular weight

• prepare 3D model that includes chemistry

• include volume changes

52

Acknowledgments

• Support for this project was provided byNASA’s Microgravity Materials ScienceProgram (NAG8-973).

• Yuri Chekanov for work onphotopolymerization

• Nick Bessonov for numerical simulations