ASPHALT SOLIDIFICATION THEORY

Transcription

1 ASPHAL SOLIDIFICAION HEORY roy Pauli, Appy Beemer, and Julie Miller 43 rd Petersen Asphalt Research Conference Pavement Performance Prediction Symposium June 1-3, 005 Laramie, Wyoming Models Used to Predict Pavement Performance Compositional Models Session

2 ACKNOWLEDGEMENS FHWA for their Financial Support under Contract No. DFH61-98-R NCHRP 9-37: Using Surface Energy Measurements to Select Materials for Asphalt Performance ICAR-505: Surface Energy Measurements as Performance Indicators of Hot-Mix Asphalts (HMA) and Portland Cement Concrete (PCC) Performance

3 owards a Unified Physico-Chemical Model of Asphalt Binder Asphalt Microstructure Model Introduction to micro-emulsion Colloid Mechanics he Onion Model and Colligative Properties Equilibrium hermodynamics in micro-emulsion Colloid Mechanics Kinetics in micro-emulsion Colloid Mechanics Asphalt Solidification Model Equilibrium hermodynamics of Surfaces and Interfaces Phase ransformations and Colligative Properties non-equilibrium hermodynamics of Surface micro-structuring Dissipative Structure heory Application to Fracture Mechanics Further houghts on Fatigue and Moisture Damage, Rutting, and hermal Cracking

4 Asphalt Surface Energy And Molecular Structure Dependence of Surface Energy On Molecular Weight And Molecular Structure

5 Some onions may have thick layers While other onions will have thin layers

6 Surface Energy vs. #C-atoms (Homologous Series) 140 # of C vs alkanes predicted-alkanes 10 Surface Energy, γ, ergs/cm n-alkanes R CH Number of Carbon Atoms in Molecule

7 Surface Energy, γ, ergs/cm # of C vs alkanes # of C vs aromatic chains predicted-alkanes predicted-aromatics Aromatic Chains Number of Carbon Atoms in Molecule

8 Aromatic Sheets Surface Energy, γ, ergs/cm # of C vs alkanes # of C vs aromatic chains # of C vs aromatic sheets predicted-alkanes predicted-aromatics Aromatic Chains Number of Carbon Atoms in Molecule

9 Alicyclic Chains Surface Energy, γ, ergs/cm # 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 Sheets Number of Carbon Atoms in Molecule Aromatic Chains

10 Alicyclic Chains Alicyclic Sheets Surface Energy, γ, ergs/cm # 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 Sheets Number of Carbon Atoms in Molecule Aromatic Chains

11 Molecular Formula = C4 H65 N S Formula Weight = Composition = C(77.83%) H(10.11%) N(.16%) S(9.90%) Index of Refraction = ± 0.0 Surface ension = 39.8 ± 3.0 dyne/cm Density = ± 0.06 g/cm 3 AAD-1 CH3 H3C Molecular Formula = C85 H135 N Formula Weight = Composition = C(87.18%) H(11.6%) N(1.0%) Index of Refraction = ± 0.03 Surface ension = 44.3 ± 5.0 dyne/cm Density = 0.98 ± 0.1 g/cm 3 AAM-1 H3C NH CH3 CH3 Jennings, P.W. et al., SHRP-A-335, Strategic Highway Research Program, National Research Council, Washington, DC, 1993.

12 Surface Energy, γ, ergs/cm # 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

13 Surface Energy, γ, ergs/cm # 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

14 Surface Energy, γ, ergs/cm # 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

15 Surface Energy, γ, ergs/cm Alicyclic Sheets # 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 Number of Carbon Atoms in Molecule

16 Surface Energy, γ, ergs/cm Alicyclic Sheets # 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 Number of Carbon Atoms in Molecule

17 Surface Energy, γ, ergs/cm Alicyclic Sheets # 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 Number of Carbon Atoms in Molecule

18 Physical Properties, Number Average Molecular Weight, Density, Refractive Index and Surface ensions (AFM Measurement) Measured and Reported for Eight SHRP Asphalts Sample Number Average Molecular Weight a M n, Da Density b ρ, g/ml Index of Refraction n(ri) Surface ension γ, ergs/cm AFM %C a, # of Carbons AAA-1 AAB-1 AAC-1 AAD-1 AAF-1 AAG-1 AAK-1 AAM ± ± ± ± ± , , , , , , , , 87

19 Solubility Parameters Calculated, Based on AFM, NMR and Asphalt Average Molecular Structure Surface ension, Density and Molecular Weight δ γ 4.1 1/ 3 ( M / ) ρ 0.43 Sample δ, cal 1/ /ml 3/ by γ(ams) a Solubility Parameter δ, cal 1/ /ml 3/ by γ(afm) c δ, cal 1/ /ml 3/ by γ(nmr) d AAA-1 AAB-1 AAC-1 AAD-1 AAF-1 AAG-1 AAK-1 AAM-1 AVERAGE Alicyclic sheet (C 4 H 60 ) Cyclohexane Methylcyclohexane ± b ± ± 0.6

20 Solubility Parameters Calculated, Based on AFM, NMR and Asphalt Average Molecular Structure Surface ension, Density and Molecular Weight δ γ 4.1 1/ 3 ( M / ) ρ 0.43 Sample δ, cal 1/ /ml 3/ by γ(ams) a Solubility Parameter δ, cal 1/ /ml 3/ by γ(afm) c δ, cal 1/ /ml 3/ by γ(nmr) d AAA-1 AAB-1 AAC-1 AAD-1 AAF-1 AAG-1 AAK-1 AAM-1 AVERAGE Alicyclic sheet (C 4 H 60 ) Cyclohexane Methylcyclohexane ± b ± ± 0.6

21 Solubility Parameters Calculated, Based on AFM, NMR and Asphalt Average Molecular Structure Surface ension, Density and Molecular Weight δ γ 4.1 1/ 3 ( M / ) ρ 0.43 Sample δ, cal 1/ /ml 3/ by γ(ams) a Solubility Parameter δ, cal 1/ /ml 3/ by γ(afm) c δ, cal 1/ /ml 3/ by γ(nmr) d AAA-1 AAB-1 AAC-1 AAD-1 AAF-1 AAG-1 AAK-1 AAM-1 AVERAGE Alicyclic sheet (C 4 H 60 ) Cyclohexane Methylcyclohexane ± b ± ± 0.6

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27 Definition of otal Surface Entropy and otal Surface Enthalpy S S = dg d S P otal surface entropy, S S, per surface area S S = dγ d S S H = G + S S otal surface enthalpy, H S, per surface area

28 Definition of otal Surface Entropy and otal Surface Enthalpy S S = dg d S P otal surface entropy, S S, per surface area S S = dγ d S S H = G + S S otal surface enthalpy, H S, per surface area

29 hermodynamic Derivation of Gibbs Surface Free Energy An Alternate View of the Regular Solution Model H vap = δ V + PV Δ γ V Δ S vap = r o Δ G vap 0 = Δ = Δ H vap Δ S vap r o! γ = ( δ + P ) Δ o

30 Energy Balance Expression Defining the Surface of an Ideal Liquid n ε i b = γ Δ ( ) r c r R S n i ε G = Gibbs Surface or Interfacial Free Energy (defined by a point interaction energy) H S = γ Δ b Surface Enthalpy (related to change in surface tension per change in temperature S S = 1 ( r r )R c Surface Entropy

31 Vapor Pressure, P vap (93.15 K), atm S Alcohol HC-Aromatic Alkane Amines Halohydrocarbons Esters S = 1 ( r r )R c Radius Ratio, κ = r c /<r>

32 30 D Critical Radius, r o, Alkanes Cyclics Aromatics Alcohols, Water Asphalts rc = <r> , r ² = Molar Radius, <r>, D

33 35 30 n-pentane Critical Radius, r o, n-hexane C 7 -C 1 C 14, C 16, C 0, C 4, & C 40 8-SHRP Asphalts Molar Radius, <r>,

34 owards a Unified Physico-Chemical Model of Asphalt Binder Asphalt Microstructure Model Introduction to micro-emulsion Colloid Mechanics he Onion Model and Colligative Properties Equilibrium hermodynamics in micro-emulsion Colloid Mechanics Kinetics in micro-emulsion Colloid Mechanics Asphalt Solidification Model Equilibrium hermodynamics of Surfaces and Interfaces Phase ransformations and Colligative Properties non-equilibrium hermodynamics of Surface micro-structuring Dissipative Structure heory Application to Fracture Mechanics Further houghts on Fatigue and Moisture Damage, Rutting, and hermal Cracking

35 Definition of Gibbs-homson Capillary Undercooling Kurz, W., and D. J. Fisher (1998). Fundamentals of Solidification, 4th Ed., rans ech Publications, Inc., Switzerland, 1, 4, 99, and 05. Undercooling in Metals Casting (Science of Solidification) Δ = κγ Curvature of Grain Boundary κ = V r dα dv = 1 r r Gibbs-homson Relationship Γ = γ ΔS

36 But what about the WAX?!, ASPHALENES RESINS WAXES NEURALS-WAX Percent Fraction AAM-1 AAG-1 AAF-1 AAA-1 AAB-1 AAK-1 AAD-1 Asphalt

37 ASPHALENES RESINS WAXES NEURALS-WAX Percent Fraction AAM-1 AAG-1 AAF-1 AAA-1 AAB-1 AAK-1 AAD-1 Asphalt

38 Some physical properties of IEC-Neutral Fractions of SHRP Core Asphalts Asphalt Surface ension (Dynes/cm ) Density (g/ml) Number Average Molecular Weight (Daltons) Solubility Parameter ((cal/ml) ½ ) Viscosity (Pa*s) AAA-1 AAB-1 AAC-1 AAD-1 AAF-1 AAG-1 AAK-1 AAM

39 Asphalt Surface ension (Dynes/cm ) Density (g/ml) Number Average Molecular Weight (Daltons) Solubility Parameter ((cal/ml) ½ ) Viscosity (Pa*s) AAA-1 AAB-1 AAC-1 AAD-1 AAF-1 AAG-1 AAK-1 AAM

40 Asphalt Surface ension (Dynes/cm ) Density (g/ml) Number Average Molecular Weight (Daltons) Solubility Parameter ((cal/ml) ½ ) Viscosity (Pa*s) AAA-1 AAB-1 AAC-1 AAD-1 AAF-1 AAG-1 AAK-1 AAM

41 40 Surface ension, γ, dynes/cm AAA AAB AAC AAD AAF AAG AAK AAM <r > = / emperature, o C

42 40 Surface ension, γ, dynes/cm AAA AAB AAC AAD AAF AAG AAK AAM <r > = / emperature, o C

43 40 Surface ension, γ, dynes/cm AAA AAB AAC AAD AAF AAG AAK AAM <r > = / emperature, o C

44 40 AAA-1 Surface ension, γ, dynes/cm AAA AAB AAC AAD AAF AAG AAK AAM <r > = / emperature, o C

45 40 AAA-1 AAG-1 Surface ension, γ, dynes/cm AAA AAB AAC AAD AAF AAG AAK AAM <r > = / emperature, o C

46 Both of which exhibit Non-dramatic (unobservable) bee micro-structuring 40 AAA-1 AAG-1 Surface ension, γ, dynes/cm AAA AAB AAC AAD AAF AAG AAK AAM <r > = / emperature, o C

47 Both of which exhibit Non-dramatic (unobservable) bee micro-structuring 40 AAA-1 AAG-1 Surface ension, γ, dynes/cm AAA AAB AAC AAD AAF AAG AAK AAM <r > = / S S =? 1 ( rc r )R emperature, o C

48 Asphalt Surface ension (Dynes/cm ) Density (g/ml) Number Average Molecular Weight (Daltons) Solubility Parameter ((cal/ml) ½ ) Viscosity (Pa*s) AAA-1 AAB-1 AAC-1 AAD-1 AAF-1 AAG-1 AAK-1 AAM

49 1400 Viscosity of IEC Neutrals, η N, Pa*s AAF AAG-1 00 AAD Number Average Molecular Weight of Neutrals, M n

50 SHRP Asphalt n-heptane Soluble Maltene Viscosity, η as a Function of 1/k 1.e+5 "n-heptane" Maltene Viscosity, η 5.0 C(Pa*s) 1.0e+5 AAG-1 8.0e+4 6.0e+4 4.0e+4 AAF-1.0e =5 C and 50 C

51 Ln(η n-heptane C AAG-1 AAF /k, Inverse rate 50 C

52 5 C AAB-1-Neat AAB-1-Maltenes AAB-1-Neutrals

53 owards a Unified Physico-Chemical Model of Asphalt Binder Asphalt Microstructure Model Introduction to micro-emulsion Colloid Mechanics he Onion Model and Colligative Properties Equilibrium hermodynamics in micro-emulsion Colloid Mechanics Kinetics in micro-emulsion Colloid Mechanics Asphalt Solidification Model Equilibrium hermodynamics of Surfaces and Interfaces Phase ransformations and Colligative Properties non-equilibrium hermodynamics of Surface micro-structuring Dissipative Structure heory Application to Fracture Mechanics Further houghts on Fatigue and Moisture Damage, Rutting, and hermal Cracking

54 Gibbs Equation Describing Interfacial Dynamics of a Binary System du = = ds + ds du α ϕ + + α + du μ dn i μ dn i β α i ϕ i + du P ϕ α + γda dv α + ds β + μ dn i β i P β dv β U: Internal Energy S: Entropy : emperature P: Pressure n: Number of Moles μ: Chemical Potential γ: Surface Energy A: Surface Area α-phase β-phase

55 Film emperature, C Point in ime hin Asphalt Film Allowed to Relax for Several Months

56 Point in ime Film emperature, C

57 Point in ime Film emperature, C

58 Point in ime Film emperature, C

59 Point in ime Film emperature, C

60 Point in ime Film emperature, C

61 Point in ime Film emperature, C

62 Point in ime Film emperature, C

63 Definition of Rate of Entropy Production Between wo micro-states (ϕ -phase) & ϕ prod S = du dt ϕ prod ds = dt ϕ ϕ 1,1,,1 dnr μr μr da γ γ1 dt 1 + dt 1 0

64 = = Φ = = n k k n i i i x J x J γ μ σ ( ) ( ) 0 + = = Φ k=1 i=1 n x k n i x J i J γ μ σ Rate of Entropy Production Density Defined in terms of Force Gradients (Isothermal Condition) (Vector Notation)

65 Rate of Free Energy Production Defined in terms of Force Gradients (Mass ransport Coupled to Stress Gradient) J n μr x J A γ x J ( ) ( γ) n x μ r J A x c γ ε& Interface Z-axis, nm ! 40 D 0 Τ Interface-plane Y-axis, μm

66 Rate of Free Energy Production Defined in terms of Force Gradients (Mass ransport Coupled to Stress Gradient) J n μr x J A γ x J ( ) ( γ) n x μ r J A x! D c γ ε& Interface Z-axis, nm c γ Τ Interface-plane Y-axis, μm

67 Morphological Stability heory: Hill and Valley Model Herring, C., (1951). Some heorems on the Free Energies of Crystal Surfaces. Physical Review, 8(1), G S γ (n) ds γ ( n) γ ( n) γ n, = γ n L+ 1 ( rc ) 0( ) rc rc γ ( n) m m rc

68 Hill and Valley Galatola, P., J. B. Fournier, and G. Durand, 1994.Spontaneous Undulation of Equilibrium Interfaces with Positive Surface Stiffness, Phys Rev. Lett. 73(16), 4 z( x) = ( ) εsin ϖx θ < 0 z-axis ψ = 0 - x-axis > 0-4 y-axis

69 Derivation of Effective Gibbs Free Energy of a Perturbed Interface ΔG eff ( Δ = m C Δ ) ΔS = γ ϖ ε sin( ϖy) eff l l f m ds f m ϖ ε sin( ϖy)

70 Derivation of Effective Gibbs Free Energy of a Perturbed Interface ΔG eff ( Δ = m C Δ ) ΔS = γ ϖ ε sin( ϖy) eff l l f m ds f m ϖ ε sin( ϖy)

71 Coupling Equations Δ = Δ α α iller, W. A.,, W., and D. J. Fisher (1991). he Science of Crystallization: Macroscopic Phenomena and Defect Generation, 4th Ed. rans ech Publications, Inc. Switzerland. Δ = Δ + Δ C + Δ r Δ = z =ϕ m Δ = m C C l t l Δ r = m Γεϖ sin( ϖy)

72 Point in ime Film emperature, C

73 Film emperature, C Point in ime So Now, what s all this stuff?

74 Film emperature, C Point in ime So Now, what s all this stuff?

75 owards a Unified Physico-Chemical Model of Asphalt Binder Asphalt Microstructure Model Introduction to micro-emulsion Colloid Mechanics he Onion Model and Colligative Properties Equilibrium hermodynamics in micro-emulsion Colloid Mechanics Kinetics in micro-emulsion Colloid Mechanics Asphalt Solidification Model Equilibrium hermodynamics of Surfaces and Interfaces Phase ransformations and Colligative Properties non-equilibrium hermodynamics of Surface micro-structuring Dissipative Structure heory Application to Fracture Mechanics Further houghts on Fatigue and Moisture Damage, Rutting, and hermal Cracking

76 34 C AAB-1-Neat AAB-1-Maltenes AAB-1-Neutrals

77 34 C AAC-1-Neat AAC-1-Maltenes AAC-1-Neutrals

78 34 C AAK-1-Neat AAK-1-Maltenes AAK-1-Neutrals AAK-1-Neutrals- Dewaxed

79 Marangoni convection: Shear stress balance at an interface surface between two fluid phases iller, W. A., 1991, he Science of Crystallization: Macroscopic Phenomena and Defect Generation, Cambridge University Press, Great Britain, New York, NY. γ ux ux γ γ c 1 = η η = + 1 z x x z c z u x1 u x η 1 η γ c Flow velocity of fluid 1 Flow velocity of fluid 1 Viscosity of fluid 1 Viscosity of fluid Interfacial surface tension emperature Concentration of fluid

80 c γ ρ μ Material property gradients potentially induced by a thermal gradient z c c z x u x u z x x + = = 1 1 γ γ η η γ z x

81 c γ ρ μ Material property gradients potentially induced by a thermal gradient z c c z x u x u z x x + = = 1 1 γ γ η η γ z x

82 he Marangoni number, N Ma, quantifies the surface or interfacial turbulence resulting from concentration and surface tension gradients, c, γ induced by a thermal gradient, d dz, resulting in undulations on the surface of a thin film composed of two fluids dγ d d dz = αηn h Ma = J η q N Ma d h ρcv dz hermal diffusivity coefficient

83 AAK-1-G1 All images were collected at room temperature ~3 C Film was spin cast on 11/18/004 Film was kept under nitrogen purge Film thickness is 1553 nm First thermal cycle: heated to 45 C and cooled to room temp Second thermal cycle: heated to 50 C and cooled to room temp Images collected 1 day after the last thermal cycle

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88 z-height, nm x-length, nm

89 z-height, nm x-length, nm z-height, nm x-length, nm

90 AAC-1-C5 All images were collected at room temperature ~5 C Film hickness: nm Film was spin cast on 11/18/004 Film was kept under nitrogen purge 1 st thermal cycle: heated to 50 C in 3 steps, cooled in 10 steps nd thermal cycle: heated to 35 in steps, cooled to room temp 3 rd thermal cycle: heated to 51 C in steps of, cooled to R 4 th thermal cycle: heated to 51 C, cooled to R in 4 steps Images were collected on the same day after the last thermal cycle

91 8 6 4 z-height, nm x-length, nm

92 8 6 4 z-height, nm x-length, nm

93 8 6 4 z-height, nm x-length, nm z-height, nm x-length, nm

94 8 6 4 z-height, nm x-length, nm z-height, nm x-length, nm

95 8 6 4 z-height, nm x-length, nm z-height, nm x-length, nm

96 errace-ledge-kink (LK) Crystallization kinetics iller, W. A., 1991, he Science of Crystallization: Microscopic Interfacial Phenomena, Cambridge University Press, Great Britain, New York, NY.

97 otal Free Energy Coupling during Crystallization ΔG ΔG ΔG = ΔG Δ i G i i ΔG i = ΔG = ΔG = ΔG + Δ i G i K K + ΔG + ΔG E γ + ΔG σ + ΔG d + ΔG p + ΔG PD

98 Kink step distance Ledge step distance Rate of kink formation Rate of ledge formation Rate of solidifying surface Critical nucleating kernals

99 a' λ k a υ λl h υk υ l

100 dr G RdR G G G E πγ δ π υ υ = + + Δ = Δ Δ R G V G γ = δ υ + Δ Δ R G V G V γ = δ + Δ Δ 0 = κ γ F E S Δ = = Δ * z dz d G G f i i δ γ δ + Δ = max Δ dx d G f i γ

101 l l h υ ρ υ = l k k ha λ λ υ υ = R G L L L A e a n k / ˆ Δ = ν ( ) R G G S S K A e a k / ˆ Δ + Δ + = ν + = k k k k a k ' = υ

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109 Given relaxation functions of concentration and thermal gradients in both i = l,s, l-liquid and crystal s-solid phases of a melt leads to Galenko, P.K., D.A. Danilov, 004, Linear morphological stability analysis of the solidliquid interface in rapid solidification of a binary system. Phys. Rev. E, J q i t i * * * ( ) ( ) r, t = Dq t t i ( t, r) dt l,s-thermal fluxes J C i t * * * ( ) ( ) r, t = D j t t C i ( t, r) dt l,s-concentration fluxes

110 Undercoolings may then be defined as Δ = φ φ Κ = = x m = mc 1+ z φ + φ x φ ΚΓ G where curvature is given as 3 / = δω sin ( x t) δ() t sin( ωx), = ( ωx) An oscillating perturbed interface is then expressed as give the frequency ω = π λ

111 () ( ) x t b C C C ω δ φ sin 0 = Δ () ( ) x t a ω δ φ sin 0 = Δ where and Component Undercoolings may then be defined as and s s l l s s s s s s l l l l l l a a a ω ω υ ω ω ω υ ω + Κ Κ + Κ + Κ Κ = Κ / / G G υ ( ) < = D D D C D C C D k D b υ υ υ υ υ υ υ ω υ υ ω 0,, / 1 1 / 1 G

112 υ ( ) < = D D D C D C C D k D b υ υ υ υ υ υ υ ω υ υ ω 0,, / 1 1 / 1 G

113 = Δ = + Κ + Κ Γ < = Δ +Δ + Δ = Δ + Κ + Κ Γ D s s s l l l G D C s l C C s s s l l l G m υ υ ξ ξ ω υ υ ξ ξ ξ ω ζ ζ φ 0, 0, G G G G G Absolute stability is defined by

114 = Δ = + Κ + Κ Γ < = Δ +Δ + Δ = Δ + Κ + Κ Γ D s s s l l l G D C s l C C s s s l l l G m υ υ ξ ξ ω υ υ ξ ξ ξ ω ζ ζ φ 0, 0, G G G G G Absolute stability is defined by

115 whereas marginal stability is defined by Δ Γ υ D ( ) C G A k = = C k 1 mc Δ = Γ G a υ l A ( ) D k 1 mc υ = < υ A Γ k G D

116 whereas marginal stability is defined by Δ Γ υ D ( ) C G A k = = C k 1 mc Δ = Γ G a υ l A ( ) D k 1 mc υ = < υ A Γ k G D hese expressions represent solute partitioning in the material microstructure

117 whereas marginal stability is defined by Δ Γ υ D ( ) C G A k = = C k 1 mc Δ = Γ G a υ l A ( ) D k 1 mc υ = < υ A Γ k G D hese expressions represent solute partitioning in the material microstructure

118 whereas marginal stability is defined by Δ Γ υ D ( ) C G A k = = C k 1 mc Δ = Γ G a υ l A ( ) D k 1 mc υ = < υ A Γ k G D hese expressions represent solute partitioning in the material microstructure

119 Film emperature, C Point in ime So Now, what s all this stuff?

120 5 C AAB-1-Neat AAB-1-Maltenes AAB-1-Neutrals

121 Effect of adding resins to neutrals

122 Effect of adding asphaltenes to maltenes

123 ( ) = = = = = = l x x U l x x U total X dx x J t dx x J t t S t C x J V U = ρ 0 0 = = = l x x V total X dx t C t S ρ otal Entropy Production in a Dissipative Structure i.e., through thermal dissipation

124 0 0 = = = l x x V total X dx t C t S ρ = = = = = l x x n V,, r r r l x x V total X dx c t dx t C t S m μ μ ρ C = = = l l x x V total X dx x t dx t t S ε& γ ρ i.e., through thermal dissipation i.e., bulk material dissipation and, i.e., surface material dissipation

125 H ( ) ( ) ( ) V r r r r r r R c c c c c c Δ Δ ln ln Δε Δ x C V γ ρ H H x ( ) ( ) ( ) ( ) V r r r r r r V R c c c c c c Δ + Δ Δ Δ ln ln ε γ he undercooling in the dissipative structure

126 Film emperature, C Point in ime So Now, what s all this stuff?

127 5 C AAB-1-Neat AAB-1-Maltenes AAB-1-Neutrals

128 owards a Unified Physico-Chemical Model of Asphalt Binder Asphalt Microstructure Model Introduction to micro-emulsion Colloid Mechanics he Onion Model and Colligative Properties Equilibrium hermodynamics in micro-emulsion Colloid Mechanics Kinetics in micro-emulsion Colloid Mechanics Asphalt Solidification Model Equilibrium hermodynamics of Surfaces and Interfaces Phase ransformations and Colligative Properties non-equilibrium hermodynamics of Surface micro-structuring Dissipative Structure heory Application to Fracture Mechanics Further houghts on Fatigue and Moisture Damage, Rutting, and hermal Cracking

129 he visco-elastic J-dissipation energy defined in terms of the constant line zone stress, σ c, the crack tip opening displacement, δ = y, and α, the wave velocity, or line zone length t d δ α = 1 x C( t τ ) / ) α d σ dτ c 0 [ K ( τ f( x )] τ J t' ( ) df x α τ = K C t 0 ( τ ) dτ dτ t' 0 J c a& n /( 1+m ) a& n J c -critical dissipation energy

130 hermal Stability in Slow Crack Growth hermal Hardening or Softening Williams, J. C., Fracture Mechanics of Polymers, Ellis Horwood Limited, Chichester, England. K c nδh 1 1 R n 0 a& e d 1 dkc 1 = Δ + da& Kc da& a& Δ = b C ρ limδ * i erfc b kt = G c πρckt, Δ * = Gc ρcb

131 Rate of Free Energy Production Defined in terms of Force Gradients (Mass ransport Coupled to Stress Gradient) J n μr x J A γ x J ( ) ( γ) n x μ r J A x c γ ε& Interface Z-axis, nm ! 40 D 0 Τ Interface-plane Y-axis, μm

132 Rate of Free Energy Production Defined in terms of Force Gradients (Mass ransport Coupled to Stress Gradient) J n μr x J A γ x J ( ) ( γ) n x μ r J A x! D c γ ε& Interface Z-axis, nm c γ Τ Interface-plane Y-axis, μm

133 hermal Stability in Slow Crack Growth hermal Hardening or Softening Williams, J. C., Fracture Mechanics of Polymers, Ellis Horwood Limited, Chichester, England. Asphalt hermal Softening, or Hardening, Modeled as a Colligative Property Δ R E a o Δ = o D c roδ ε& = G c πρckt Molecular Reorganization due to temperature change, particle diffusion and work of cohesion Stain energy release rate per Material parameters

134 t C t C c V V c πκ ρ κ πρ G G 1 1 = = Δ H ( ) ( ) ( ) ( ) ( ) 1 ' ln ln R c c c c c c x H C V r r r r r r V c λ λ κ γ κ πρ + Δ + Δ Δ ε G ( ) ( ) a K c R H c V c & 4 ' 1 Δ Δ κ G Critical Stress Intensity Factor

135 t C t C c V V c πκ ρ κ πρ G G 1 1 = = Δ H ( ) ( ) ( ) ( ) ( ) 1 ' ln ln R c c c c c c x H C V r r r r r r V c λ λ κ γ κ πρ + Δ + Δ Δ ε G ( ) ( ) a K c R H c V c & 4 ' 1 Δ Δ κ G Critical Stress Intensity Factor Crack Propagation Rate

136 t C t C c V V c πκ ρ κ πρ G G 1 1 = = Δ H ( ) ( ) ( ) ( ) ( ) 1 ' ln ln R c c c c c c x H C V r r r r r r V c λ λ κ γ κ πρ + Δ + Δ Δ ε G ( ) ( ) a K c R H c V c & 4 ' 1 Δ Δ κ G Critical Stress Intensity Factor Crack Propagation Rate Material Dissipation erm

137 AAK-1-G6 097 Room emp (5 C) 4/4/06

138 AAK-1-G6 104 Room emp (5 C) 4/5/06

139 AAK-1-G6 108 Room emp (5 C) 4/6/06

140 AAK-1-G6 109 Room emp (5 C) 4/6/06

141 AAK-1-G6 11 Room emp (5 C) 4/6/06

142 AAK-1-G6 10 Room emp (5 C) 4/13/06

143 AAK-1-G6 1 Room emp (3 C) 4/17/06

144 AAK-1-G6 13 Room emp (3 C) 4/17/06

145 AAK-1-G6 16 Room emp (3 C) 4/4/06

146 AAK-1-G6 13 Room emp ( C) 5/4/06

147 AAK-1-G6 133 Room emp ( C) 5/4/06

148 AAK-1-G6 135 Room emp ( C) 5/4/06

149 owards a Unified Physico-Chemical Model of Asphalt Binder Asphalt Microstructure Model Introduction to micro-emulsion Colloid Mechanics he Onion Model and Colligative Properties Equilibrium hermodynamics in micro-emulsion Colloid Mechanics Kinetics in micro-emulsion Colloid Mechanics Asphalt Solidification Model Equilibrium hermodynamics of Surfaces and Interfaces Phase ransformations and Colligative Properties non-equilibrium hermodynamics of Surface micro-structuring Dissipative Structure heory Application to Fracture Mechanics Further houghts on Fatigue and Moisture Damage, Rutting, and hermal Cracking

150 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

151 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.

152 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.

153