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ASPHALT SOLIDIFICATION THEORYTroy Pauli, Appy Beemer, and Julie Miller
43rd Petersen Asphalt Research Conference Pavement Performance Prediction SymposiumJune 21-23, 2005Laramie, WyomingModels Used to Predict Pavement Performance Compositional Models Session
ACKNOWLEDGEMENTS
FHWA for their Financial Support under Contract No. DTFH61-98-R-00093
NCHRP 9-37: Using Surface Energy Measurements to Select Materials for Asphalt Performance
ICAR-505: Surface Energy Measurements as Performance Indicatorsof Hot-Mix Asphalts (HMA) and Portland Cement Concrete (PCC) Performance
Towards a Unified Physico-ChemicalModel of Asphalt Binder
Asphalt Microstructure Model Introduction to micro-Emulsion Colloid MechanicsThe Onion Model and Colligative PropertiesEquilibrium Thermodynamics in micro-Emulsion Colloid MechanicsKinetics in micro-Emulsion Colloid Mechanics
Asphalt Solidification ModelEquilibrium Thermodynamics of Surfaces and InterfacesPhase Transformations and Colligative Propertiesnon-Equilibrium Thermodynamics of Surface micro-StructuringDissipative Structure TheoryApplication to Fracture Mechanics
Further Thoughts on Fatigue and Moisture Damage, Rutting, and Thermal Cracking
Asphalt Surface EnergyAnd Molecular Structure
Dependence of Surface EnergyOn Molecular Weight
And Molecular Structure
Some onions may have thick layers
While other onions will have thin layers
Number of Carbon Atoms in Molecule
0 20 40 60 80 100
Sur
face
Ene
rgy,
γ, e
rgs/
cm2
0
20
40
60
80
100
120
140 # of C vs alkanes predicted-alkanes
Surface Energy vs. #C-atoms (Homologous Series)
RCH3
n-Alkanes
Number of Carbon Atoms in Molecule
0 20 40 60 80 100
Sur
face
Ene
rgy,
γ, e
rgs/
cm2
0
20
40
60
80
100
120
140 # of C vs alkanes # of C vs aromatic chains predicted-alkanes predicted-aromatics
Aromatic Chains
Number of Carbon Atoms in Molecule
0 20 40 60 80 100
Sur
face
Ene
rgy,
γ, e
rgs/
cm2
0
20
40
60
80
100
120
140 # of C vs alkanes # of C vs aromatic chains # of C vs aromatic sheets predicted-alkanes predicted-aromatics
Aromatic Chains
Aromatic Sheets
Number of Carbon Atoms in Molecule
0 20 40 60 80 100
Sur
face
Ene
rgy,
γ, e
rgs/
cm2
0
20
40
60
80
100
120
140 # of C vs alkanes # of C vs alicyclic chains# of C vs aromatic chains # of C vs aromatic sheets predicted-alkanes predicted-aromatics predicted-cyclics
Aromatic Chains
Aromatic Sheets
Alicyclic Chains
Number of Carbon Atoms in Molecule
0 20 40 60 80 100
Sur
face
Ene
rgy,
γ, e
rgs/
cm2
0
20
40
60
80
100
120
140 # of C vs alkanes # of C vs alicyclic chains# of C vs aromatic chains # of C vs ketones # of C vs aromatic sheets predicted-alkanes predicted-aromatics predicted-cyclics # of C vs alicyclic sheets
Aromatic Chains
Aromatic Sheets
Alicyclic Chains
Alicyclic Sheets
Molecular Formula = C42 H65 N S2Formula Weight = 648.104Composition = C(77.83%) H(10.11%) N(2.16%) S(9.90%)Index of Refraction = 1.556 ± 0.02Surface Tension = 39.8 ± 3.0 dyne/cmDensity = 1.006 ± 0.06 g/cm3
AAD-1
Jennings, P.W. et al., SHRP-A-335, Strategic Highway Research Program, National Research Council, Washington, DC, 1993.
CH3
CH3
NHCH3
CH3
CH3
Molecular Formula = C85 H135 NFormula Weight = 1170.988Composition = C(87.18%) H(11.62%) N(1.20%)Index of Refraction = 1.561 ± 0.03Surface Tension = 44.3 ± 5.0 dyne/cmDensity = 0.98 ± 0.1 g/cm3 AAM-1
Number of Carbon Atoms in Molecule
0 20 40 60 80 100
Sur
face
Ene
rgy,
γ, e
rgs/
cm2
0
20
40
60
80
100
120
140 # of C vs alkanes # of C vs alicyclic chains# of C vs aromatic chains # of C vs ketones # of C vs aromatic sheets # of C vs asphalt AMS predicted-alkanes predicted-aromatics predicted-cyclics # of C vs alicyclic sheets
SHRP Asphalts
Number of Carbon Atoms in Molecule
0 20 40 60 80 100
Sur
face
Ene
rgy,
γ, e
rgs/
cm2
0
20
40
60
80
100
120
140 # of C vs alkanes # of C vs alicyclic chains# of C vs aromatic chains # of C vs ketones # of C vs aromatic sheets # of C vs asphalt AMS predicted-alkanes predicted-aromatics predicted-cyclics # of C vs alicyclic sheets# of C vs asphalt AFM
SHRP Asphalts
Number of Carbon Atoms in Molecule
0 20 40 60 80 100
Sur
face
Ene
rgy,
γ, e
rgs/
cm2
0
20
40
60
80
100
120
140 # of C vs alkanes # of C vs alicyclic chains# of C vs aromatic chains # of C vs ketones # of C vs aromatic sheets # of C vs asphalt AMS predicted-alkanes predicted-aromatics predicted-cyclics # of C vs alicyclic sheets# of C vs asphalt NMR # of C vs asphalt AFM
SHRP Asphalts
Number of Carbon Atoms in Molecule
0 20 40 60 80 100 120
Sur
face
Ene
rgy,
γ, e
rgs/
cm2
0
20
40
60
80
100
120
140 # of C vs alkanes # of C vs alicyclic chains# of C vs aromatic chains # of C vs ketones # of C vs aromatic sheets # of C vs asphalt AMS predicted-alkanes predicted-aromatics predicted-cyclics # of C vs alicyclic sheets# of C vs asphalt NMR # of C vs asphalt AFM # of C vs Col 20
Alicyclic Sheets
Number of Carbon Atoms in Molecule
0 20 40 60 80 100 120
Sur
face
Ene
rgy,
γ, e
rgs/
cm2
0
20
40
60
80
100
120
140 # of C vs alkanes # of C vs alicyclic chains# of C vs aromatic chains # of C vs ketones # of C vs aromatic sheets # of C vs asphalt AMS predicted-alkanes predicted-aromatics predicted-cyclics # of C vs alicyclic sheets# of C vs asphalt NMR # of C vs asphalt AFM # of C vs Col 20
Alicyclic Sheets
Number of Carbon Atoms in Molecule
0 20 40 60 80 100 120
Sur
face
Ene
rgy,
γ, e
rgs/
cm2
0
20
40
60
80
100
120
140 # of C vs alkanes # of C vs alicyclic chains# of C vs aromatic chains # of C vs ketones # of C vs aromatic sheets # of C vs asphalt AMS predicted-alkanes predicted-aromatics predicted-cyclics # of C vs alicyclic sheets# of C vs asphalt NMR # of C vs asphalt AFM # of C vs Col 20
Alicyclic Sheets
Physical Properties, Number Average Molecular Weight, Density, Refractive Index and Surface Tensions (AFM Measurement)Measured and Reported for Eight SHRP Asphalts
83.9, 5982.3, 6086.5, 7081.6, 5284.5, 6185.6, 5083.7, 6186.8, 87
46.3± 4.747.3± 0.744.0± 6.440.1± 4.348.3± 5.4
38.145.649.0
1.5651.5601.5351.5551.5601.5401.5301.530
1.0161.0241.0091.0231.0241.0181.0240.989
8508709707708707008701200
AAA-1AAB-1AAC-1AAD-1AAF-1AAG-1AAK-1AAM-1
%C a, # of
Carbons
Surface Tension γ,ergs/cm2
AFM
Index ofRefraction
n(RI)
Density b ρ,g/mL
Number AverageMolecular Weight
a Mn , DaSample
Solubility Parameters Calculated, Based on AFM, NMR and Asphalt Average MolecularStructure Surface Tension, Density and Molecular Weight
8.208.277.947.608.208.397.867.99
8.06 ± 0.26
8.138.197.807.768.267.698.067.90
7.97 ± 0.21
8.007.917.817.917.687.687.697.58
7.78 ± 0.158.23
8.18 b8.02
AAA-1AAB-1AAC-1AAD-1AAF-1AAG-1AAK-1AAM-1AVERAGEAlicyclic sheet (C42 H60)CyclohexaneMethylcyclohexane
δ, cal1/2/mL3/2 by γ(NMR) d
δ, cal1/2/mL3/2 by γ(AFM) c
δ, cal1/2/mL3/2 by γ(AMS) a
Solubility ParameterSample
( )
43.0
3/1/M1.4 ⎟⎟
⎠
⎞⎜⎜⎝
⎛
ργ
≈δ
Solubility Parameters Calculated, Based on AFM, NMR and Asphalt Average MolecularStructure Surface Tension, Density and Molecular Weight
8.208.277.947.608.208.397.867.99
8.06 ± 0.26
8.138.197.807.768.267.698.067.90
7.97 ± 0.21
8.007.917.817.917.687.687.697.58
7.78 ± 0.158.23
8.18 b8.02
AAA-1AAB-1AAC-1AAD-1AAF-1AAG-1AAK-1AAM-1AVERAGEAlicyclic sheet (C42 H60)CyclohexaneMethylcyclohexane
δ, cal1/2/mL3/2 by γ(NMR) d
δ, cal1/2/mL3/2 by γ(AFM) c
δ, cal1/2/mL3/2 by γ(AMS) a
Solubility ParameterSample
( )
43.0
3/1/M1.4 ⎟⎟
⎠
⎞⎜⎜⎝
⎛
ργ
≈δ
Solubility Parameters Calculated, Based on AFM, NMR and Asphalt Average MolecularStructure Surface Tension, Density and Molecular Weight
8.208.277.947.608.208.397.867.99
8.06 ± 0.26
8.138.197.807.768.267.698.067.90
7.97 ± 0.21
8.007.917.817.917.687.687.697.58
7.78 ± 0.158.23
8.18 b8.02
AAA-1AAB-1AAC-1AAD-1AAF-1AAG-1AAK-1AAM-1AVERAGEAlicyclic sheet (C42 H60)CyclohexaneMethylcyclohexane
δ, cal1/2/mL3/2 by γ(NMR) d
δ, cal1/2/mL3/2 by γ(AFM) c
δ, cal1/2/mL3/2 by γ(AMS) a
Solubility ParameterSample
( )
43.0
3/1/M1.4 ⎟⎟
⎠
⎞⎜⎜⎝
⎛
ργ
≈δ
P
SS
dTdGS ⎟⎟
⎠
⎞⎜⎜⎝
⎛=−
dTdS S γ
=−
SSS TSGH +=
Definition of Total Surface Entropy and Total Surface Enthalpy
Total surface entropy, SS, per surface area
Total surface enthalpy, HS, per surface area
P
SS
dTdGS ⎟⎟
⎠
⎞⎜⎜⎝
⎛=−
dTdS S γ
=−
SSS TSGH +=
Definition of Total Surface Entropy and Total Surface Enthalpy
Total surface entropy, SS, per surface area
Total surface enthalpy, HS, per surface area
VTroΔ
=SvapΔγ2
PVHvap +=Δ 2δ V
Gvap0 = Δ HvapΔ SvapTΔ= −
Thermodynamic Derivation of Gibbs Surface Free Energy
An Alternate View of the Regular Solution Model
TPTo
ro Δ+= )(2
2δγ !
r( )22
RTrT
Tn cbi −Δ
= γε
2εiS n
G =
TT
H bS
Δ= γ
r( )RrS cS
21=
Gibbs Surface or Interfacial Free Energy(defined by a point interaction energy)
Surface Enthalpy (related to change in surface tension per change in temperature
Surface Entropy
Energy Balance Expression Defining the Surface of an Ideal Liquid
Radius Ratio, κ = rc/<r>
0 20 40 60 80 100 120
Vap
or P
ress
ure,
Pva
p(29
3.15
K),
atm
0
200
400
600
800
AlcoholHC-AromaticAlkaneAminesHalohydrocarbonsEsters
r( )RrS cS
21=
Molar Radius, <r>,
0 2 4 6 8 10 12 14
Crit
ical
Rad
ius,
r o,
0
5
10
15
20
25
30
AlkanesCyclicsAromaticsAlcohols,WaterAsphaltsrc = 0.52587<r> + 0.45138, r ² = 0.9965
D
D
Molar Radius, <r>,
5 6 7 8 9 10 11 12 13
Crit
ical
Rad
ius,
r o,
0
5
10
15
20
25
30
35
n-pentane
n-hexane
C7-C12 C14, C16, C20, C24, & C40
8-SHRP Asphalts
Towards a Unified Physico-ChemicalModel of Asphalt Binder
Asphalt Microstructure Model Introduction to micro-Emulsion Colloid MechanicsThe Onion Model and Colligative PropertiesEquilibrium Thermodynamics in micro-Emulsion Colloid MechanicsKinetics in micro-Emulsion Colloid Mechanics
Asphalt Solidification ModelEquilibrium Thermodynamics of Surfaces and InterfacesPhase Transformations and Colligative Propertiesnon-Equilibrium Thermodynamics of Surface micro-StructuringDissipative Structure TheoryApplication to Fracture Mechanics
Further Thoughts on Fatigue and Moisture Damage, Rutting, and Thermal Cracking
Γ=Δ κT
21
112rrdV
drV +=Α∝=κ
SΔ=Γ
γ
Definition of Gibbs-Thomson Capillary Undercooling
Kurz, W., and D. J. Fisher (1998). Fundamentals of Solidification, 4th Ed., Trans Tech Publications, Inc., Switzerland, 12, 24, 99, and 205.
Undercooling in Metals Casting (Science of Solidification)
Curvature of Grain Boundary
Gibbs-Thomson Relationship
Asphalt
AAM-1 AAG-1 AAF-1 AAA-1 AAB-1 AAK-1 AAD-1
Perc
ent F
ract
ion
0
20
40
60
80
100
ASPHALTENES RESINS WAXES NEUTRALS-WAX
But what about the WAX ?!,
Asphalt
AAM-1 AAG-1 AAF-1 AAA-1 AAB-1 AAK-1 AAD-1
Perc
ent F
ract
ion
0
20
40
60
80
100
ASPHALTENES RESINS WAXES NEUTRALS-WAX
AsphaltSurface Tension
(Dynes/cm2)
Density(g/mL)
Number AverageMolecular Weight
(Daltons)
Solubility Parameter((cal/mL) ½)
Viscosity(Pa*s)
AAA-1AAB-1AAC-1AAD-1AAF-1AAG-1AAK-1AAM-1
32.426.232.425.833.632.232.534.0
0.8290.8740.6980.7440.8990.8480.8700.850
5906607505107005905901140
7.146.466.736.507.167.147.196.65
3615536020
48026146
1191
Some physical properties of IEC-Neutral Fractions of SHRP Core Asphalts
AsphaltSurface Tension
(Dynes/cm2)
Density(g/mL)
Number AverageMolecular Weight
(Daltons)
Solubility Parameter((cal/mL) ½)
Viscosity(Pa*s)
AAA-1AAB-1AAC-1AAD-1AAF-1AAG-1AAK-1AAM-1
32.426.232.425.833.632.232.534.0
0.8290.8740.6980.7440.8990.8480.8700.850
5906607505107005905901140
7.146.466.736.507.167.147.196.65
3615536020
48026146
1191
AsphaltSurface Tension
(Dynes/cm2)
Density(g/mL)
Number AverageMolecular Weight
(Daltons)
Solubility Parameter((cal/mL) ½)
Viscosity(Pa*s)
AAA-1AAB-1AAC-1AAD-1AAF-1AAG-1AAK-1AAM-1
32.426.232.425.833.632.232.534.0
0.8290.8740.6980.7440.8990.8480.8700.850
5906607505107005905901140
7.146.466.736.507.167.147.196.65
3615536020
48026146
1191
Temperature, T oC
20 30 40 50 60 70 80 90 100 110 120
Surfa
ce T
ensi
on, γ
, dyn
es/c
m
0
10
20
30
40
AAAAAB AACAAD AAF AAG AAKAAM <r2> = 0.94 +/- 0.03
Temperature, T oC
20 30 40 50 60 70 80 90 100 110 120
Surfa
ce T
ensi
on, γ
, dyn
es/c
m
0
10
20
30
40
AAAAAB AACAAD AAF AAG AAKAAM <r2> = 0.94 +/- 0.03
Temperature, T oC
20 30 40 50 60 70 80 90 100 110 120
Surfa
ce T
ensi
on, γ
, dyn
es/c
m
0
10
20
30
40
AAAAAB AACAAD AAF AAG AAKAAM <r2> = 0.94 +/- 0.03
Temperature, T oC
20 30 40 50 60 70 80 90 100 110 120
Surfa
ce T
ensi
on, γ
, dyn
es/c
m
0
10
20
30
40
AAAAAB AACAAD AAF AAG AAKAAM <r2> = 0.94 +/- 0.03
AAA-1
Temperature, T oC
20 30 40 50 60 70 80 90 100 110 120
Surfa
ce T
ensi
on, γ
, dyn
es/c
m
0
10
20
30
40
AAAAAB AACAAD AAF AAG AAKAAM <r2> = 0.94 +/- 0.03
AAA-1
AAG-1
Temperature, T oC
20 30 40 50 60 70 80 90 100 110 120
Surfa
ce T
ensi
on, γ
, dyn
es/c
m
0
10
20
30
40
AAAAAB AACAAD AAF AAG AAKAAM <r2> = 0.94 +/- 0.03
AAA-1
AAG-1
Both of which exhibit Non-dramatic (unobservable) “bee” micro-structuring
Temperature, T oC
20 30 40 50 60 70 80 90 100 110 120
Surfa
ce T
ensi
on, γ
, dyn
es/c
m
0
10
20
30
40
AAAAAB AACAAD AAF AAG AAKAAM <r2> = 0.94 +/- 0.03
AAA-1
AAG-1
Both of which exhibit Non-dramatic (unobservable) “bee” micro-structuring
r( )RrS cS
21=
?
AsphaltSurface Tension
(Dynes/cm2)
Density(g/mL)
Number AverageMolecular Weight
(Daltons)
Solubility Parameter((cal/mL) ½)
Viscosity(Pa*s)
AAA-1AAB-1AAC-1AAD-1AAF-1AAG-1AAK-1AAM-1
32.426.232.425.833.632.232.534.0
0.8290.8740.6980.7440.8990.8480.8700.850
5906607505107005905901140
7.146.466.736.507.167.147.196.65
3615536020
48026146
1191
Number Average Molecular Weight of Neutrals, Mn
0 200 400 600 800 1000 1200
Visc
osity
of I
EC N
eutra
ls, η
N, P
a*s
0
200
400
600
800
1000
1200
1400
AAG-1
AAF-1
AAD-1
SHRP Asphalt “n-Heptane Soluble” MalteneViscosity, η as a Function of 1/k
1/k(Abs*s) @ T=25°C and 50°C
0 200 400 600 800 1000
"n-H
epta
ne" M
alte
ne V
isco
sity
, η 0 @
25.
0°C
(Pa*
s)
0.0
2.0e+4
4.0e+4
6.0e+4
8.0e+4
1.0e+5
1.2e+5
AAG-1
AAF-1
1/k, Inverse rate constant @ 50°C
0 200 400 600 800 1000
Ln(η
n-he
ptan
e) @
60°C
0
20
40
60
80
100
120
140
160
AAG-1
AAF-1
25°C
AAB-1-Neat AAB-1-Maltenes
AAB-1-Neutrals
Towards a Unified Physico-ChemicalModel of Asphalt Binder
Asphalt Microstructure Model Introduction to micro-Emulsion Colloid MechanicsThe Onion Model and Colligative PropertiesEquilibrium Thermodynamics in micro-Emulsion Colloid MechanicsKinetics in micro-Emulsion Colloid Mechanics
Asphalt Solidification ModelEquilibrium Thermodynamics of Surfaces and InterfacesPhase Transformations and Colligative Propertiesnon-Equilibrium Thermodynamics of Surface micro-StructuringDissipative Structure TheoryApplication to Fracture Mechanics
Further Thoughts on Fatigue and Moisture Damage, Rutting, and Thermal Cracking
dAdnTdS
dVPdnTdSdVPdnTdS
dUdUdUdU
ii
iiii
γμ
μμϕϕ
ββββαααα
ϕβα
+++
−++−+=
++=
∑∑∑
Gibbs Equation Describing Interfacial Dynamics of a Binary System
U: Internal EnergyS: EntropyT: TemperatureP: Pressuren: Number of Molesμ: Chemical Potentialγ: Surface EnergyA: Surface Area
α-phase
β-phase
Point in Time0 2 4 6 8 10
Film
Tem
pera
ture
, T°C
20
25
30
35
40
45
Thin Asphalt Film Allowed to Relax for Several Months
Point in Time0 2 4 6 8 10
Film
Tem
pera
ture
, T°C
20
25
30
35
40
45
Point in Time0 2 4 6 8 10
Film
Tem
pera
ture
, T°C
20
25
30
35
40
45
Point in Time0 2 4 6 8 10
Film
Tem
pera
ture
, T°C
20
25
30
35
40
45
Point in Time0 2 4 6 8 10
Film
Tem
pera
ture
, T°C
20
25
30
35
40
45
Point in Time0 2 4 6 8 10
Film
Tem
pera
ture
, T°C
20
25
30
35
40
45
Point in Time0 2 4 6 8 10
Film
Tem
pera
ture
, T°C
20
25
30
35
40
45
Point in Time0 2 4 6 8 10
Film
Tem
pera
ture
, T°C
20
25
30
35
40
45
0111
1
2
2
1
1,
2
2,1,
21
1 ≥⎟⎟⎠
⎞⎜⎜⎝
⎛−+⎟⎟
⎠
⎞⎜⎜⎝
⎛−+⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
=
TTdtdA
TTdtdn
TTdtdU
dtdSS
rrr
prodprod
γγμμϕϕ
ϕϕ&
Definition of Rate of Entropy Production Between Two micro-States (ϕ -phase)
011
≥⎟⎠⎞
⎜⎝⎛
∂∂−
+⎟⎠⎞
⎜⎝⎛
∂∂−
==Φ ∑∑ ==
n
kT
kT
n
ii
i xJ
xJT γμσ
( ) ( ) 0≥∇−+∇−==Φ ∑∑ k=1i=1
nTxk
nixi JJT γμσ
Rate of Entropy Production DensityDefined in terms of Force Gradients
(Isothermal Condition)
(Vector Notation)
TA
T
rn x
Jx
J ⎟⎠⎞
⎜⎝⎛
∂∂
−≥⎟⎠⎞
⎜⎝⎛
∂∂ γμ
γ∇( ) ( )TxATrxn JJ μ −≥∇
Rate of Free Energy Production Defined in terms of Force Gradients
(Mass Transport Coupled to Stress Gradient)
Interface-plane Y-axis, μm0 1 2 3 4 5 6
Inte
rfac
e Z-
axis
, nm
0
20
40
60
80
100
120
ε&γ−∇≥∇cD ! ∇Τ
TA
T
rn x
Jx
J ⎟⎠⎞
⎜⎝⎛
∂∂
−≥⎟⎠⎞
⎜⎝⎛
∂∂ γμ
γ∇( ) ( )TxATrxn JJ μ −≥∇
Rate of Free Energy Production Defined in terms of Force Gradients
(Mass Transport Coupled to Stress Gradient)
Interface-plane Y-axis, μm0 1 2 3 4 5 6
Inte
rfac
e Z-
axis
, nm
0
20
40
60
80
100
120
γ∇
ε&γ−∇≥∇cD !
∇c
∇Τ
Morphological Stability Theory:Hill and Valley Model
∫∝ dSGS )(nγ
mc
m
ccc rrr
r )()()()()( 221
0nnnnn,
γγγγγ ++++= L
Herring, C., (1951). Some Theorems on the Free Energies of Crystal Surfaces. Physical Review, 82(1), 87-93.
x-axis
-6 -4 -2 0 2 4 6 8 10z-ax
is
-4
-2
0
2
4
ψ
θ T < T0
T > T0
T = T0
⊕ y-axis
Galatola, P., J. B. Fournier, and G. Durand, 1994.Spontaneous Undulation of Equilibrium Interfaces with Positive Surface Stiffness, Phys Rev. Lett. 73(16),
( )xxz ϖεsin)( =
Hill and Valley
ϖ( )yTSTCmTG mflleffeff εϖγ sin)( 2=ΔΔ−=Δ∝Δ
( )yTdS mf ϖεϖ sin2∝∫
Derivation of Effective Gibbs Free Energy of a Perturbed Interface
ϖ( )yTSTCmTG mflleffeff εϖγ sin)( 2=ΔΔ−=Δ∝Δ
( )yTdS mf ϖεϖ sin2∝∫
Derivation of Effective Gibbs Free Energy of a Perturbed Interface
Coupling Equations αα
TT ∑Δ=Δ
rCT TTTT Δ+Δ+Δ=Δ
mzT TTT −=Δ =ϕ
lt
lC CmT =Δ
)sin(2 yTT mr ϖεϖΓ=Δ
Tiller, W. A., , W., and D. J. Fisher (1991). The Science of Crystallization: Macroscopic Phenomena and Defect Generation, 4th Ed. Trans Tech Publications, Inc. Switzerland.
Point in Time0 2 4 6 8 10
Film
Tem
pera
ture
, T°C
20
25
30
35
40
45
Point in Time0 2 4 6 8 10
Film
Tem
pera
ture
, T°C
20
25
30
35
40
45
So Now, what’s all this stuff?
Point in Time0 2 4 6 8 10
Film
Tem
pera
ture
, T°C
20
25
30
35
40
45
So Now, what’s all this stuff?
Towards a Unified Physico-ChemicalModel of Asphalt Binder
Asphalt Microstructure Model Introduction to micro-Emulsion Colloid MechanicsThe Onion Model and Colligative PropertiesEquilibrium Thermodynamics in micro-Emulsion Colloid MechanicsKinetics in micro-Emulsion Colloid Mechanics
Asphalt Solidification ModelEquilibrium Thermodynamics of Surfaces and InterfacesPhase Transformations and Colligative Propertiesnon-Equilibrium Thermodynamics of Surface micro-StructuringDissipative Structure TheoryApplication to Fracture Mechanics
Further Thoughts on Fatigue and Moisture Damage, Rutting, and Thermal Cracking
34°C
AAB-1-Neat AAB-1-Maltenes
AAB-1-Neutrals
34°C
AAC-1-Neat AAC-1-Maltenes
AAC-1-Neutrals
34°C
AAK-1-Neat
AAK-1-Maltenes
AAK-1-Neutrals
AAK-1-Neutrals-Dewaxed
Marangoni convection: Shear stress balance at an interface “surface” between two fluid phases
zc
czT
Txu
xu
zxx
∂∂
∂∂
+∂∂
∂∂
=∂
∂−
∂∂
=∂∂ 2
221
21γγηηγ
∂∂∂∂∂∂
T
c2
ux2
ux1
γ2η1η
Flow velocity of fluid 1
Flow velocity of fluid 1
Viscosity of fluid 1
Viscosity of fluid 2
Interfacial surface tension
Temperature
Concentration of fluid 2
Tiller, W. A., 1991, The Science of Crystallization: Macroscopic Phenomena and Defect Generation, Cambridge University Press, Great Britain, New York, NY.
T∇
c∇
γ∇
ρ∇
μ∇
Material property gradients potentially induced by a thermal gradient
zc
czT
Txu
xu
zxx
∂∂
∂∂
+∂∂
∂∂
=∂
∂−
∂∂
=∂∂ 2
221
21γγηηγ
∂∂∂∂∂∂
z
x
T∇
c∇
γ∇
ρ∇
μ∇
Material property gradients potentially induced by a thermal gradient
zc
czT
Txu
xu
zxx
∂∂
∂∂
+∂∂
∂∂
=∂
∂−
∂∂
=∂∂ 2
221
21γγηηγ
∂∂∂∂∂∂
z
x
dzdTCh
NJh
NdzdT
dTd
V
MaqMa
ρ
ηαηγ2
2
−=
−=
Thermal diffusivity coefficient
The Marangoni number, NMa , quantifies the surface or interfacial “turbulence” resulting fromconcentration and surface tension gradients, ,
induced by a thermal gradient, , resulting in undulations
on the surface of a thin film composed of two fluids
c∇ γ∇
dzdT
AAK-1-G1
All images were collected at room temperature ~23°CFilm was spin cast on 11/18/2004
Film was kept under nitrogen purgeFilm thickness is 1553 nm
First thermal cycle: heated to 45°C and cooled to room tempSecond thermal cycle: heated to 50°C and cooled to room temp
Images collected 1 day after the last thermal cycle
x-Length, nm
0 500 1000 1500 2000
z-H
eigh
t, nm
0
10
20
30
40
50
60
70
x-Length, nm
200 300 400 500 600 700
z-H
eigh
t, nm
0
10
20
30
40
50
60
x-Length, nm
0 500 1000 1500 2000
z-H
eigh
t, nm
0
10
20
30
40
50
60
70
AAC-1-C5All images were collected at room temperature ~25°C
Film Thickness: 1098.5 nmFilm was spin cast on 11/18/2004
Film was kept under nitrogen purge1st thermal cycle: heated to 50°C in 3° steps, cooled in 10°steps2nd thermal cycle: heated to 35 in 2° steps, cooled to room temp
3rd thermal cycle: heated to 51°C in steps of 2°, cooled to RT4th thermal cycle: heated to 51°C, cooled to RT in 4° steps
Images were collected on the same day after the last thermal cycle
x-Length, nm
0 500 1000 1500 2000 2500
z-H
eigh
t, nm
8
10
12
14
16
18
20
22
24
26
28
x-Length, nm
0 500 1000 1500 2000 2500
z-H
eigh
t, nm
8
10
12
14
16
18
20
22
24
26
28
x-Length, nm
1000 1100 1200 1300 1400 1500
z-H
eigh
t, nm
8
10
12
14
16
18
20
22
24
26
28
x-Length, nm
0 500 1000 1500 2000 2500
z-H
eigh
t, nm
8
10
12
14
16
18
20
22
24
26
28
x-Length, nm
1600 1700 1800 1900 2000
z-H
eigh
t, nm
8
10
12
14
16
18
20
22
24
26
28
x-Length, nm
0 500 1000 1500 2000 2500
z-H
eigh
t, nm
8
10
12
14
16
18
20
22
24
26
28
x-Length, nm
2000 2050 2100 2150 2200 2250 2300
z-H
eigh
t, nm
8
10
12
14
16
18
20
22
24
26
28
x-Length, nm
0 500 1000 1500 2000 2500
z-H
eigh
t, nm
8
10
12
14
16
18
20
22
24
26
28
Terrace-Ledge-Kink (TLK) Crystallization kineticsTiller, W. A., 1991, The Science of Crystallization: Microscopic Interfacial Phenomena, Cambridge University Press, Great Britain, New York, NY.
ii GGG Δ−Δ=Δ ∞→∞
ii GGG Δ+Δ=Δ →∞∞
EKi GGG Δ+Δ=Δ
PDpdKi GGGGGGG Δ+Δ+Δ+Δ+Δ+Δ=Δ σγ
Total Free Energy Coupling during Crystallization
Kink step distanceLedge step distanceRate of kink formationRate of ledge formationRate of solidifying surfaceCritical nucleating kernals
kλ
lλ kυlυ
υa
'a
h
dRGRdRGGG E
πγδπ υ
υ
22 +=Δ+Δ=Δ
RG
VG γδ υ +=
ΔΔ
RG
VG
Vγδ +=
ΔΔ
=0
κγ
FE S
TTTΔ
−=−=Δ *
zdz
dGG f
ii δγ
δ ⎟⎟⎠
⎞⎜⎜⎝
⎛+Δ−=
max⎟⎟⎠
⎞⎜⎜⎝
⎛∝Δ
dxd
G fi
γ
llh υρυ =
lk
khaλλυυ 2
=
RTGLLL
Aeank /ˆ Δ−− = ν
( ) RTGGSS
KAeak /ˆ Δ+Δ−+ = ν
+− −= kkkkak '=υ
( ) ( ) *** ),(, dttTttDt i
t iqiq rrJ ∇−= ∫ ∞−
( ) ( ) *** ),(, dttCttDt i
t
jiC rrJ ∇−= ∫ ∞−
l,s-concentration fluxes
Given relaxation functions of concentration and thermal gradients in both i = l,s, l-liquidand crystal s-solid phases of a melt leads to
l,s-thermal fluxes
Galenko, P.K., D.A. Danilov, 2004, Linear morphological stability analysis of the solid-liquid interface in rapid solidification of a binary system. Phys. Rev. E, 69 051608.
GTm mCTTT ΚΓ+=−=Δ φφ
( )xxx
ωδωφφ sin1 22/3
2
2
−=⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛
∂∂
+=⎟⎟⎠
⎞⎜⎜⎝
⎛∂∂
=Κ−
( ) ( ) ( )xttxz ωδφ sin, =≡
λπω 2=
Undercoolings may then be defined as
where curvature is given as
An oscillating perturbed interface is then expressed as
give the frequency
( ) ( )xtbCCC ωδφ sin0 =−≡Δ
( ) ( )xtaTTT ωδφ sin0 =−≡Δ
where
and
Component Undercoolings may then be defined as
and
ssll
ssss
ssll
llll
aaaωω
υωωω
υωΚ+Κ
−Κ+
Κ+Κ−
Κ= // GG
υ
( )
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
≥
<
−
−−
−−
=
D
D
D
C
D
C
C
Dk
Db
υυ
υυ
υυυω
υυω
,0
,
/11
/1
22
22
G
υ
( )
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
≥
<
−
−−
−−
=
D
D
D
C
D
C
C
Dk
Db
υυ
υυ
υυυω
υυω
,0
,
/11
/1
22
22
G
⎪⎪⎩
⎪⎪⎨
⎧
≥=Δ=Κ+Κ+Γ
<=Δ−Δ+Δ+Δ=
−Κ+Κ+Γ
∑ DssslllGT
DCsl
CCssslllGT
T
TTTTm
υυξξω
υυξξξω
ζζ
φ
,0
,0
2
2
GG
GGG
Absolute stability is defined by
⎪⎪⎩
⎪⎪⎨
⎧
≥=Δ=Κ+Κ+Γ
<=Δ−Δ+Δ+Δ=
−Κ+Κ+Γ
∑ DssslllGT
DCsl
CCssslllGT
T
TTTTm
υυξξω
υυξξξω
ζζ
φ
,0
,0
2
2
GG
GGG
Absolute stability is defined by
( )∞
−=
Γ=Δ mC
kk
DT
CAGT
C 21υ
l
TAGT
T aT
υΓ=Δ
( )D
GTA k
mCkD υυ <Γ−
= ∞2
1
whereas marginal stability is defined by
( )∞
−=
Γ=Δ mC
kk
DT
CAGT
C 21υ
l
TAGT
T aT
υΓ=Δ
( )D
GTA k
mCkD υυ <Γ−
= ∞2
1
whereas marginal stability is defined by
These expressions represent solute partitioningin the material microstructure
( )∞
−=
Γ=Δ mC
kk
DT
CAGT
C 21υ
l
TAGT
T aT
υΓ=Δ
( )D
GTA k
mCkD υυ <Γ−
= ∞2
1
whereas marginal stability is defined by
These expressions represent solute partitioningin the material microstructure
( )∞
−=
Γ=Δ mC
kk
DT
CAGT
C 21υ
l
TAGT
T aT
υΓ=Δ
( )D
GTA k
mCkD υυ <Γ−
= ∞2
1
whereas marginal stability is defined by
These expressions represent solute partitioningin the material microstructure
Point in Time0 2 4 6 8 10
Film
Tem
pera
ture
, T°C
20
25
30
35
40
45
So Now, what’s all this stuff?
25°C
AAB-1-Neat AAB-1-Maltenes
AAB-1-Neutrals
Effect of adding resins to neutrals
Effect of adding asphaltenes to maltenes
( )∫∫=
=
=
=
⎟⎠⎞
⎜⎝⎛
∂∂
⎟⎠⎞
⎜⎝⎛
∂∂=
∂∂
⎥⎦⎤
⎢⎣⎡
∂−=
∂∂ lx
x
Ulx
x
UtotalX dxx
JtT
Tdx
xJ
tT
tS
02
0
11
tTC
xJ
VU
∂∂−=
∂∂
ρ
00
2
2≤⎟
⎠⎞
⎜⎝⎛
∂∂−=
∂∂ ∫
=
=
lx
x
VtotalX dxtT
TC
tS ρ
Total Entropy Production in a Dissipative Structure
i.e., through thermal dissipation
00
2
2≤⎟
⎠⎞
⎜⎝⎛
∂∂−=
∂∂ ∫
=
=
lx
x
VtotalX dxtT
TC
tS ρ
01
0
2
0
2
2≤⎟⎟
⎠
⎞⎜⎜⎝
⎛∂∂⎟
⎠⎞
⎜⎝⎛
∂∂−⎟
⎠⎞
⎜⎝⎛
∂∂−=
∂∂ ∫∫
=
=
=
=
lx
x n,T,Vr
rrlx
x
VtotalX dxctTdxt
TTC
tS
mμ
μρ
C 01
00
2
2≤
∂∂⎟
⎠⎞
⎜⎝⎛
∂∂+⎟
⎠⎞
⎜⎝⎛
∂∂−=
∂∂ ∫∫
=
=
llx
x
VtotalX dxxtT
dxtT
TtS ε&γρ
i.e., through thermal dissipation
i.e., bulk material dissipation
and, i.e., surface material dissipation
H( ) ( )( )
V
rrrrrr RTccccccTΔ
−−−−≤Δ
∗∗∗ 2lnln
εΔ⎟⎠⎞
⎜⎝⎛
∂∂≥Δ
xCTT
V
γρ
HH x( ) ( ) ( )( )
V
rrrrrr
V
RTccccccTTΔ
−−−+Δ⎟
⎠⎞
⎜⎝⎛
∂∂
Δ≥Δ
∗∗∗ 2lnlnεγ
The undercooling in the dissipative structure
Point in Time0 2 4 6 8 10
Film
Tem
pera
ture
, T°C
20
25
30
35
40
45
So Now, what’s all this stuff?
25°C
AAB-1-Neat AAB-1-Maltenes
AAB-1-Neutrals
Towards a Unified Physico-ChemicalModel of Asphalt Binder
Asphalt Microstructure Model Introduction to micro-Emulsion Colloid MechanicsThe Onion Model and Colligative PropertiesEquilibrium Thermodynamics in micro-Emulsion Colloid MechanicsKinetics in micro-Emulsion Colloid Mechanics
Asphalt Solidification ModelEquilibrium Thermodynamics of Surfaces and InterfacesPhase Transformations and Colligative Propertiesnon-Equilibrium Thermodynamics of Surface micro-StructuringDissipative Structure TheoryApplication to Fracture Mechanics
Further Thoughts on Fatigue and Moisture Damage, Rutting, and Thermal Cracking
n)m/(nc aaJ && ≅∝ +21
The visco-elastic J-dissipation energydefined in terms of the constant line zone stress, σc, the crack tip opening displacement, δ = 2y, and α, the wave velocity, or line zone length
Jc-critical dissipation energy
( )[ ] ταττ
τσ
δ α dxfKdd
tCt
cx )()(1 2
0/ ∫ −=
( )ττ
τατ d
tdxdftCKJ
t
⎟⎠⎞
⎜⎝⎛−= ∫ '
)('
0
20
CbGT c
ρ=Δ *
CktG
ktCberfciTT c
b πρρ =⎟
⎟⎠
⎞⎜⎜⎝
⎛−Δ=Δ
→ 1641*lim
22
0
Thermal Stability in Slow Crack GrowthThermal Hardening or Softening
Williams, J. C., Fracture Mechanics of Polymers, 1984. Ellis Horwood Limited, Chichester, England.
⎟⎟⎠
⎞⎜⎜⎝
⎛+Δ=
aaddK
KT
addT c
c &&& 211
⎟⎟⎠
⎞⎜⎜⎝
⎛−Δ
∝ 0
11TTR
Hnn
c eaK &
,
TA
T
rn x
Jx
J ⎟⎠⎞
⎜⎝⎛
∂∂
−≥⎟⎠⎞
⎜⎝⎛
∂∂ γμ
γ∇( ) ( )TxATrxn JJ μ −≥∇
Rate of Free Energy Production Defined in terms of Force Gradients
(Mass Transport Coupled to Stress Gradient)
Interface-plane Y-axis, μm0 1 2 3 4 5 6
Inte
rfac
e Z-
axis
, nm
0
20
40
60
80
100
120
ε&γ−∇≥∇cD ! ∇Τ
TA
T
rn x
Jx
J ⎟⎠⎞
⎜⎝⎛
∂∂
−≥⎟⎠⎞
⎜⎝⎛
∂∂ γμ
γ∇( ) ( )TxATrxn JJ μ −≥∇
Rate of Free Energy Production Defined in terms of Force Gradients
(Mass Transport Coupled to Stress Gradient)
Interface-plane Y-axis, μm0 1 2 3 4 5 6
Inte
rfac
e Z-
axis
, nm
0
20
40
60
80
100
120
γ∇
ε&γ−∇≥∇cD !
∇c
∇Τ
Thermal Stability in Slow Crack GrowthThermal Hardening or Softening
Williams, J. C., Fracture Mechanics of Polymers, 1984. Ellis Horwood Limited, Chichester, England.
aERTT
2o2∝ΔAsphalt Thermal Softening, or Hardening,
Modeled as a Colligative Property
ε&22
δo
o
rcDTT ∇=Δ
CktGc
πρ=
Molecular Reorganization due to temperature change, particle
diffusion and work of cohesion
Stain energy release rate perMaterial parameters
tCtCT c
VV
c
πκρκπρGG 11 ==Δ
H( ) ( ) ( )( )
( )221
2
'
lnln
TT
RTccccccxH
TCV
rrrrrr
Vc
λλκ
γκπρ
+≥
⎥⎦
⎤⎢⎣
⎡
Δ−−−
+Δ⎟⎠⎞
⎜⎝⎛
∂∂
Δ≥
∗∗∗
εG
( )( ) aKT
cRH
cVc &
242
2
'1 ∝≥
ΔΔ
κG
Critical Stress Intensity Factor
tCtCT c
VV
c
πκρκπρGG 11 ==Δ
H( ) ( ) ( )( )
( )221
2
'
lnln
TT
RTccccccxH
TCV
rrrrrr
Vc
λλκ
γκπρ
+≥
⎥⎦
⎤⎢⎣
⎡
Δ−−−
+Δ⎟⎠⎞
⎜⎝⎛
∂∂
Δ≥
∗∗∗
εG
( )( ) aKT
cRH
cVc &
242
2
'1 ∝≥
ΔΔ
κG
Critical Stress Intensity FactorCrack Propagation Rate
tCtCT c
VV
c
πκρκπρGG 11 ==Δ
H( ) ( ) ( )( )
( )221
2
'
lnln
TT
RTccccccxH
TCV
rrrrrr
Vc
λλκ
γκπρ
+≥
⎥⎦
⎤⎢⎣
⎡
Δ−−−
+Δ⎟⎠⎞
⎜⎝⎛
∂∂
Δ≥
∗∗∗
εG
( )( ) aKT
cRH
cVc &
242
2
'1 ∝≥
ΔΔ
κG
Critical Stress Intensity FactorCrack Propagation Rate
Material Dissipation Term
AAK-1-G6 097 Room Temp (25°C) 4/4/06
AAK-1-G6 104 Room Temp (25°C) 4/5/06
AAK-1-G6 108 Room Temp (25°C) 4/6/06
AAK-1-G6 109 Room Temp (25°C) 4/6/06
AAK-1-G6 112 Room Temp (25°C) 4/6/06
AAK-1-G6 120 Room Temp (25°C) 4/13/06
AAK-1-G6 122 Room Temp (23°C) 4/17/06
AAK-1-G6 123 Room Temp (23°C) 4/17/06
AAK-1-G6 126 Room Temp (23°C) 4/24/06
AAK-1-G6 132 Room Temp (22°C) 5/4/06
AAK-1-G6 133 Room Temp (22°C) 5/4/06
AAK-1-G6 135 Room Temp (22°C) 5/4/06
Towards a Unified Physico-ChemicalModel of Asphalt Binder
Asphalt Microstructure Model Introduction to micro-Emulsion Colloid MechanicsThe Onion Model and Colligative PropertiesEquilibrium Thermodynamics in micro-Emulsion Colloid MechanicsKinetics in micro-Emulsion Colloid Mechanics
Asphalt Solidification ModelEquilibrium Thermodynamics of Surfaces and InterfacesPhase Transformations and Colligative Propertiesnon-Equilibrium Thermodynamics of Surface micro-StructuringDissipative Structure TheoryApplication to Fracture Mechanics
Further Thoughts on Fatigue and Moisture Damage, Rutting, and Thermal Cracking
A Bottom-line Opinion?
Performance properties of asphalt at higher temperatures, like rutting, may be more influenced by the compositional properties of the asphaltenes, the asphaltenes coupling to resins, and the maltenes’viscosity
A Bottom-line Opinion?
Performance properties of asphalt at higher temperatures, like rutting, may be more influenced by the compositional properties of the asphaltenes, the asphaltenes coupling to resins, and the maltenes’viscosity
whereas
At lower temperatures, wax and neutral-fraction properties (compositional and physical) are more likely to affect pavement failure such as thermal cracking.
A Bottom-line Opinion?
Performance properties of asphalt at higher temperatures, like rutting, may be more influenced by the compositional properties of the asphaltenes, the asphaltenes coupling to resins, and the maltenes’viscosity
whereas
At lower temperatures, wax and neutral-fraction properties (compositional and physical) are more likely to affect pavement failure such as thermal cracking.
Finally, knowledge of synergy between wax, asphaltenes, and resins at midrange temperatures, especially at the surface, may help to explain pavement failure such as fatigue cracking and moisture damage, both of which are compounded by oxidative age-hardening.
top related