Download - ASPHALT SOLIDIFICATION THEORY no 2 Asphalt Solidification Theory.pdfAsphalt Solidification Model Equilibrium Thermodynamics of Surfaces and Interfaces Phase Transformations and Colligative

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


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


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


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


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


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


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


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


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

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

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)


(Daltons)

Solubility Parameter((cal/mL) ½)

Viscosity(Pa*s)


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


(Dynes/cm2)

Density(g/mL)


(Daltons)


Viscosity(Pa*s)


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


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


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


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


AAA-1

AAG-1

Both of which exhibit Non-dramatic (unobservable) “bee” micro-structuring

r( )RrS cS

21=

?


(Dynes/cm2)

Density(g/mL)


(Daltons)


Viscosity(Pa*s)


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

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


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





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

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.


Film

Tem

pera

ture

, T°C

20

25

30

35

40

45


Film

Tem

pera

ture

, T°C

20

25

30

35

40

45

So Now, what’s all this stuff?

34°C


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

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

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

( )∞

−=

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


Film

Tem

pera

ture

, T°C

20

25

30

35

40

45


25°C


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


Film

Tem

pera

ture

, T°C

20

25

30

35

40

45


25°C


AAB-1-Neutrals

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





Inte

rfac

e Z-

axis

, nm

0

20

40

60

80

100

120

ε&γ−∇≥∇cD ! ∇Τ

TA

T

rn x

Jx

J ⎟⎠⎞

⎜⎝⎛

∂∂

−≥⎟⎠⎞

⎜⎝⎛

∂∂ γμ





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


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


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

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.



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.