Viscosity, relaxation time, and dynamics within a model asphalt of larger molecules.

Viscosity, relaxation time, and dynamics within a model asphalt of larger molecules Derek D. Li and Michael L. Greenfield Citation: The Journal of Chemical Physics 140, 034507 (2014); doi: 10.1063/1.4848736 View online: http://dx.doi.org/10.1063/1.4848736 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Rotational relaxation times of individual compounds within simulations of molecular asphalt models J. Chem. Phys. 132, 184502 (2010); 10.1063/1.3416913 Relaxation time, diffusion, and viscosity analysis of model asphalt systems using molecular simulation J. Chem. Phys. 127, 194502 (2007); 10.1063/1.2799189 Model linear metallocene-catalyzed polyolefins: Melt rheological behavior and molecular dynamics J. Rheol. 47, 1505 (2003); 10.1122/1.1621422 Diffusion of plasticizer in elastomer probed by rheological analysis J. Rheol. 46, 629 (2002); 10.1122/1.1470521 Modeling self-assembling of proteins: Assembled structures, relaxation dynamics, and phase coexistence J. Chem. Phys. 110, 2195 (1999); 10.1063/1.477831

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THE JOURNAL OF CHEMICAL PHYSICS 140, 034507 (2014)

Viscosity, relaxation time, and dynamics within a model asphalt of larger molecules Derek D. Lia) and Michael L. Greenfieldb) Department of Chemical Engineering, University of Rhode Island, Kingston, Rhode Island 02881, USA

(Received 30 September 2013; accepted 2 December 2013; published online 21 January 2014) The dynamics properties of a new “next generation” model asphalt system that represents SHRP AAA-1 asphalt using larger molecules than past models is studied using molecular simulation. The system contains 72 molecules distributed over 12 molecule types that range from nonpolar branched alkanes to polar resins and asphaltenes. Molecular weights range from 290 to 890 g/mol. All-atom molecular dynamics simulations conducted at six temperatures from 298.15 to 533.15 K provide a wealth of correlation data. The modified Kohlrausch-Williams-Watts equation was regressed to reorientation time correlation functions and extrapolated to calculate average rotational relaxation times for individual molecules. The rotational relaxation rate of molecules decreased significantly with increasing size and decreasing temperature. Translational self-diffusion coefficients followed an Arrhenius dependence. Similar activation energies of ∼42 kJ/mol were found for all 12 molecules in the model system, while diffusion prefactors spanned an order of magnitude. Viscosities calculated directly at 533.15 K and estimated at lower temperatures using the Debye-Stokes-Einstein relationship were consistent with experimental data for asphalts. The product of diffusion coefficient and rotational relaxation time showed only small changes with temperature above 358.15 K, indicating rotation and translation that couple self-consistently with viscosity. At lower temperatures, rotation slowed more than diffusion. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4848736] I. INTRODUCTION

Multicomponent condensed-phase systems such as asphalt are highly complex and possess rich thermodynamic phase diagrams.1 Their dynamic properties are difficult to obtain through an analytic model and differ from single components due to a compositional distribution of relaxation times. Simulations of model multicomponent systems can provide knowledge of how different molecules contribute to overall dynamics, response, and functionality. Efforts to improve the understanding of molecular motions using computational models for condensed phase systems like asphalt have been conducted in our group.2, 3 In this work, we present the dynamics properties and behaviors of individual molecules within a revised computational composition model4 of asphalt system AAA-1 of the Strategic Highway Research Program (SHRP). Compared to our prior AAA-1 model,5 the molecule sizes are larger and the asphaltene choices include modifications6 to newer proposed asphaltene structures7 that are consistent with reviews of current asphaltene science.8 Asphalt is widely used as a binder for road pavement construction and comes mainly from crude oil distillation.9 It has been well established that the rheological properties of the asphalt cement binder affect pavement performance.9 The viscosity and the dynamics properties of asphalts are closely associated to mechanical property objectives that include resistance to permanent deformation (related to rutting), fatigue

a) Present address: Cabot Corporation, Billerica, Massachusetts 01821, USA. b) Electronic mail: [email protected]

0021-9606/2014/140(3)/034507/10/$30.00

resistance (related to stress or strain), resistance to low temperature cracking, and durability.9 The chemical compositions of asphalts are made up of tens of thousands to millions of different organic compounds.10 The compositions and molecular structures of asphalts are known to affect their rheological and mechanical properties and thus have a direct, significant role on asphalt road performance.11–14 The functionality of molecules in asphalts can be classified into asphaltenes, polar aromatics, naphthene aromatics, and saturates. In broader terms, the aromatics and saturates may be grouped as resins and maltene (oil). Asphaltenes are the most complex, largest size with high polarity and biggest contribution to asphalt viscosity. Maltenes are less viscous and polar than asphaltenes. The viscosity and polarity of resins are in between maltenes and asphaltenes. Recent oilfield studies15 have shown that asphaltenes can assemble within crude oil into nanoaggregates of ∼2 nm diameter, and nanoaggregates can then assemble into clusters of ∼5 nm. These large effective sizes, compared to the size of a single molecule, contribute to the impacts of asphaltenes on viscosity. From a microstructure point of view, the different chemistries in asphalt have a significant effect on its viscosity, rheological properties, and complex modulus. External forces can cause disturbances to asphalt systems after which molecules return to their original state at different relaxation times. Our study corresponds to small forces such that this relaxation is equivalent to the response to spontaneous fluctuations. The rotational relaxation time is related to the orientation of molecules, which locally are dynamically fast and their correlations are almost completely lost in the long term. Molecular systems relax faster at higher temperatures in part because there is more volume accessible for

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TABLE I. Molecules in model asphalt AAA-1. Molecule Squalane Hopane perhydrophenanthrene-naphthalene dioctylcyclohexane-naphthalene Quinolinohopane Thioisorenieratane Trimethylbenzeneoxane Pyridinohopane Benzobisbenzothiophene Asphaltene-phenol Asphaltene-pyrrole Asphaltene-thiophene

Label

MW (g/mol)

Rings (aromatic)

(aliphatic)

Squ Hop PHPN

422.9 483.0 464.8

0 0 3

0 5 3

6 CH3 6 CH3 , 1 i-C8 1 C1 , 1 C2 , 1 C3 ,

DOCHN

406.8

2

1

2 n-C8

QHop TIR TMBO PHop BbBT APhen APyrr AThio

554.0 573.1 414.8 530.9 290.4 575.0 888.5 707.2

2 3 1 1 5 4 8 7

5 0 1 5 0 2 3 2

7 CH3 , 1 C5 10 CH3 4 CH3 , 1 C13 –(CH3 )3 7 CH3 , 1 C5 None 5 of C2 to i-C5 6 of C2 to i-C9 2 CH3 , 3 of C2 to C7

relaxations. Such orientation rates have been analyzed previously for other condensed-phase model asphalts.2, 3, 16 At lower temperatures, asphalts become viscoelastic. These phenomena have been explored previously in a model asphalt.16 Viscoelastic interpretations of the stress dynamics for the systems in this work are explored in another paper.17 Aspects of asphaltene structure and properties have been simulated by several groups, as recently reviewed.18 Structure elucidations have proposed molecular architectures for asphaltenes.19–22 Quantum mechanics calculations have suggested ranges of 7–10 fused rings per asphaltene23, 24 and have recently compared island and archipelago architectures.25 Earlier molecular mechanics26 and dynamics27, 28 simulations of asphaltene aggregation under vacuum were followed by more detailed simulations of asphaltene density29 and of asphaltene packing in solution.30, 31 Our group proposed combinations of compounds to represent asphalt or bitumen systems. Initial work focused on ternary systems.32 A system with a larger number of more polar molecules was proposed next;5 its molecules were later found to be too small.3 A new set of yet larger molecules was proposed recently.4, 33 Hansen et al.16 have proposed a four-component united-atom system that contains molecules intermediate in size between those in our earlier and more recent works. Numerous comparisons to that work are made below. Many researchers have used molecular dynamics (MD) simulation to model the viscosity of both simple and complex chemical systems. The present work was influenced by viscosity calculations for short n-alkanes using equilibrium MD simulation with Green-Kubo and Einstein methods applied to atomic and molecular stresses.34 Subsequent studies35, 36 have used MD to study the viscosity of simple liquid systems of ndecane and n-hexadecane. Our group was the first to simulate asphalt viscosity.2, 3 Green-Kubo and Einstein methods were used to calculate the viscosity at high temperature of asphalt systems,2, 3 while a scaling relationship37, 38 derived from the Debye-Stokes-Einstein equation was used to estimate the viscosity at low temperatures. Hansen et al.16 analyzed stress correlation function convergence at 452 and 603 K, finding more equilibrated results at the higher temperature. In this work, the methods we used previously are applied to obtain

Branches

the viscosity of a revised AAA-1 model asphalt system4 at different temperatures. In addition, dynamic properties such as rotational relaxation times, diffusion coefficients, and diffusion activation energies are calculated to compare contributions to relaxations by different molecules. The outcome is a comparison of how different size molecules participate in the overall relaxation process.

II. METHODS A. Model asphalt and simulation details

This work explores a 12-component system that was proposed4 as a model representation for the AAA-1 asphalt of the Strategic Highway Research Program.11 Its components, their molecular weights, and the number of rings are listed in Table I. Asphaltenes are from Mullins7 with slight modifications to alleviate side chain “pentane effect” overlaps.6 The sizes of these molecules are consistent with two-step laser desorption studies,39 which decreased the impacts of experimental artifacts on measured asphaltene molecular weight distribution. Saturates are branched or naphthenic, consistent with characterizations40 that find relatively few linear alkanes in a bitumen; this contrasts with our choosing n-C22 in prior models. Naphthene aromatics are taken from asphalt literature.41, 42 Polar aromatics were identified in geochemical studies.43–47 These molecules are larger than those proposed in our prior model asphalts.5, 32 They are also larger than the molecules proposed in a recent four component united-atom model bitumen of Hansen et al.16 The resins are similar in size but different in structure from those used by Murgich et al.26 The model system for AAA-1 contains 72 molecules: 8 saturates, 24 naphthene aromatics, 32 polar aromatics, and 8 asphaltenes.4 The corresponding mass percentages are 11.2% saturates, 39.7% naphthene aromatics, 31.9% polar aromatics, and 17.2% asphaltenes; values listed elsewhere4 have been renormalized to match the 95.9% total that is listed48 for the experimental system. Two of three asphaltene types are larger in molecular weight than the other compounds, with most polar aromatics being about 20%–40% smaller, as shown in


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(a)

J. Chem. Phys. 140, 034507 (2014)

(b)

FIG. 1. Atoms used for unit vectors in (a) asphaltene-phenol and (b) asphaltene-pyrrole.

Table I. The only outlier in mass or composition is benzobisbenzothiophene (BbBT), a polar aromatic sulfur resin. It has a molar mass of only 290 g/mol and comprises 15 of the 72 molecules. So many BbBT were used to bring the aromatic sulfur mass fraction closer toward the experimental value of 5.5 mass % known for this asphalt.48 Full details that describe this model and the choices that guided its development are available elsewhere.4, 33 Asphaltenes exist as independent entities in the model. The number of asphaltene molecules (8) is comparable to the number proposed to be in a single asphaltene nanoaggregate (6–10).8, 15 Larger system sizes would be required to track dynamics of an equilibrated nanoaggregate or a loose cluster of nanoaggregates. Molecular dynamics simulations were conducted using the Lammps2001 software.49–51 In-house modifications enabled calculating a symmetrical, traceless stress tensor using the molecular virial,52 rather than the more typical atomic virial. Time steps from 0.1 to 1.0 fs were used at different stages of the MD simulation. The initial runs were performed with 0.1 fs for 300 000 time steps with constant volume and temperature (NVT), using velocity rescaling. Next, constant pressure and temperature (NPT) conditions with the NoséHoover method53, 54 were applied with a 0.5 fs time step until the system reached an equilibrium state of stable volume and energy fluctuations. Once the system reached equilibrium, simulations at NVT conditions using the Nosé-Hoover method were conducted for a duration of 4.0–6.3 ns with a 1.0 fs time step. Earlier work in our group2 found good energy conservation for this time step. The OPLS force field55–57 was employed, with additional parameters determined as detailed in our prior work.4, 6 B. Correlation function

Molecular movements occur in MD simulations and lead to changes in molecular orientations. Time correlation functions are useful for analyzing the dynamic correlation of the molecules from MD simulations and extracting relaxation times. The lth order orientation time correlation function Cl (t)

for a molecule is expressed as58 C l (t) = Pl (u(t) · u(0)),

(1)

where u is a unit vector and Pl (x) is the lth degree Legendre polynomial. For l = 1, P1 (x) = x; for l=2, P2 (x) = 12 (3x 2 − 1); and for l=3, P3 (x) = 12 (5x 3 − 3x). At long times, the correlation functions decay from 1 to 0. At t = 0, this correlation can be related to u(0) · u(0) = 1, P (1) = 1 while at long t, u(t) · u(0) equals a distribution of values with averages cos θ = 0, cos 2 θ = 1/3, and cos 3 θ = 0. Among time correlation functions, P1 corresponds to the spectral band shapes measured in infrared absorption,58 P2 is related to NMR and Raman scattering experiments,58–60 and P3 is related to the polarized Raman spectra.61 Unit vectors for analyzing local dynamics were chosen for each molecule on the basis of molecular structure and possible local motions.2 For squalane and hopane, we chose the start and the end carbon atoms to form a unit vector because the end-to-end vector shows the longest relaxation time for long chain molecules.62 For aromatic and nonsymmetric molecules like asphaltene-phenol and asphaltenepyrrole, tumbling motions that accompany shear flow require fused aromatic rings to change their geometry relative to the flow direction, as noted in earlier work.2 We picked 4 atoms from two fused aromatic rings to form two unit vectors, as shown in Fig. 1. A unit normal vector uˆ = v/|v| was formed by the cross product of the two unit vectors, v=

(x4 − x3 ) (x2 − x1 ) × . |(x2 − x1 )| |(x4 − x3 )|

(2)

The asphaltene motion can be divided into independent motions about three principal axes, each with its own rate,59 and these rates in experiments on real asphaltenes have been found to be similar.63 For perhydrophenanthrene-naphthalene (PHPN), dioctylcyclohexane-naphthalene (DOCHN), pyridinohopane, and quinolinohopane, we analyzed relaxation time using both the end-to-end vector (atoms 3 and 5) and the normal vector (atoms 1, 2, 3, 4). Examples of the atoms used for squalane and DOCHN are shown in Fig. 2.


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C. Viscosity

(a)

To calculate the viscosity η of model asphalt systems from MD simulation, we used the Green-Kubo and Einstein methods ∞ V st st η= Pab (0)Pab (t) dt, (6) 10k B T a,b 0

(b)

V d η = lim t→∞ dt 20k B T

FIG. 2. Atoms used for unit vectors in (a) squalane and (b) dioctylcyclohexane-naphthalene.

The correlation functions were regressed to a modified Kohlrausch-Williams-Watts (mKWW) function,64, 65 PmKW W (t) = α exp(−t/τ0 ) + (1 − α) exp(−(t/τKW W )β ). (3) τ 0 and τKW W in the mKWW function are characteristic times. τ 0 relates to an initial exponential decay of molecule orientation correlations, while τKW W relates to a slow stretched exponential decay. The terms α and (1−α) determine the balance between initial and stretched exponential decay contributions. The term β determines the width of stretched exponential decay. In prior NVT simulations at constant composition, these parameters showed consistent relationships with temperature.2 Then rotational relaxation times were obtained by integrating the time correlation functions58 as ∞ τc,l =

∞ C (t)dt ≈ l

0

PmKW W (t)dt 0

1 = ατ0 + (1 − α)τKW W β

1 , β

(4)

where is the gamma function. The different orders of the characteristic decay time are related by the Debye rule58 as τl l+2 = τl+1 l

(5)

with the assumption that reorientation occurs as the result of a succession of small, uncorrelated steps.58 Using the Debye rule, we can determine the rotational relaxation time τ r from the mKWW relaxation time τ c . The rotational relaxation times determined from the 1st, 2nd, and 3rd order Legendre polynomials are τ r = τ c,1 , τ r = 3τ c,2 , and τ r = 6τ c,3 , respectively. Relaxation times τ r span a wide range. Thus, an average rotational relaxation time is calculated using the geometric mean of mKWW fits τ r to correlation functions of three different Legendre polynomial orders l. This extends beyond our prior works2, 3 that considered only P3 (t) when determining relaxation times.

2 (Aab (t)) ) ,

(7)

a,b

that incorporate the symmetric traceless pressure tensor, Pab st , as done earlier by others.34, 36, 66 In Eqs. (6) and (7), V is the system volume, kB is the Boltzmann constant, T is the t temperature, and Aab (t) = 0 Pab st (t1 )dt1 quantifies stress accumulation (essentially a “mean-squared displacement” of stress). The matrix Pab st is obtained by averaging the instantaneous off-diagonal stress components and subtracting the pressure from the diagonal components.34 Prior studies in the literature34–36 found that integrations out to 100 times greater than the relaxation time were required to achieve accurate direct viscosity estimates. The Debye-Stokes-Einstein (DSE) theory can be used to relate molecular reorientation relaxation time and viscosity for temperatures above the glass transition temperature range.37, 38 Prior works in our group32 estimated glass transition temperatures of ternary model asphalt systems of approximately 298 K over MD time scales; differential scanning calorimetry experiments over longer time scales indicate lower temperature ranges for the glass transition in asphalts.67 The Debye-Stokes-Einstein relationship is expressed as59 υp η τr = K , (8) kB T where υ p is the volume of the rotating molecule, K is a prefactor that depends on the hydrodynamic boundary condition (stick or slip) and the molecule shape. For symmetric molecules, K is 1.59 For an asymmetric molecule like an asphaltene, K can be determined by experiment. In this work, we assume K can be treated as a temperature-independent constant, and we do not explore the question of stick-vs.-slip further. In addition, the temperature dependence of singlemolecule volume at temperatures above the glass transition is neglected. Under these assumptions for Eq. (8), the τ r and ratio of η/T should scale similarly as a function of temperature. D. Diffusion coefficient

Diffusion analyzes the translational motion of particles at different temperatures. The diffusion coefficient D for each molecule type was calculated using the center of mass displacement (Einstein relation).68 Mean-squared displacement was averaged over the d = 3 Cartesian coordinates, over all molecules of each type, and over all time origins. The StokesEinstein relationship anticipates scaling37 D = K

kB T Rp η

(9)


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1

1 APhen TMBO BbBT

0.8

0.1

P3

P3

0.6

0.4 0.01 0.2

0

0.001 0

200

400

600

800

0

1000

2000

1000

Time (ps)

between diffusion coefficient and viscosity, where Rp is a particle radius and K is a prefactor analogous to K in Eq. (8). The product τ r D becomes independent of temperature if viscosity couples simultaneously to rotation and translation.38 III. RESULTS A. Correlation functions and rotational relaxation times

The rotational relaxation time of a molecule depends on its molecular size. Finding the molecule with the longest relaxation time is required for viscosity estimation at low temperatures. The relaxation time of each molecule type was analyzed using MD simulation results of temperatures from 298.15 to 533.15 K. The mKWW function was fit to the correlation functions to obtain parameters α, β, τ 0 , and τKW W . As an example, Fig. 3 shows the P3 correlation functions for asphaltene-phenol, trimethylbenzene-oxane, and benzobisbenzothiophene at 400.15 K. Asphaltenephenol, the largest of the three molecules, has the slowest decay rate and the longest relaxation time with τ c,3 = 24.9 ns. Large extrapolations were used to determine the relaxation time of asphaltene-phenol due to its slow decay rate. Benzobisbenzothiophene is the smallest molecule in the model asphalt system, and it has the shortest relaxation time of the three molecules with τ c,3 = 0.43 ns. The relaxation rate of benzobisbenzothiophene is more than 50 times faster than asphaltene-phenol at 400.15 K. These results show that the molecular size has a direct influence on the relaxation time, and smaller size structures have much shorter relaxation times. Temperature has a large influence on molecular relaxation time and on overall physical properties of asphalts. A comparison of the P3 correlations as a function of temperature using benzobisbenzothiophene is shown in Fig. 4. At 298.15 K, the correlation function has a much slower decay rate compared to higher temperatures. As temperature increases, the correlation functions decay much faster toward zero. For comparison, the relaxation times

4000

FIG. 4. The correlation function for benzobisbenzothiophene at 298.15, 333.15, 358.15, 400.15, 443.15, 533.15 K. Lines indicate mKWW fits.

τ c,3 of benzobisbenzothiophene at 298.15 and 443.15 K are 195.5 and 0.18 ns, respectively. These P3 relaxation times at 298.15 and 443.15 K convert to rotational relaxation times τ r of 1173 and 1.08 ns. These results show that temperature strongly influences the relaxation rate. Scatter at P3 < 0.05 illustrates the difficulty of converging the correlation function at longer times. The rotational relaxation times for various molecules in the system at temperatures from 298.15 to 533.15 K are shown in Fig. 5. Relaxation times for most molecules are listed in the supplementary material.77 These results show overall effects of molecular size and temperature. The rotational relaxation times τ r are much shorter at higher temperatures for all molecules, and they increase as the temperature decreases. The rotational relaxation times increase by more than would be predicted by an Arrhenius dependence (straight line in Fig. 5), in agreement with results found previously for the larger molecules in simpler multicomponent model asphalt systems.2, 3 Molecular structure largely affects the rotational relaxation time. The smallest molecule, benzobisbenzothiophene, has the shortest relaxation time. Asphaltenepyrrole, the largest molecule, has the longest relaxation time. 15 APyrr 12

log τr(ps)

FIG. 3. The correlation function P3 for asphaltene-phenol, trimethylbenzene-oxane, and benzobisbenzothiophene at 400.15 K. Lines indicate mKWW fits.

3000

Time (ps)

AThio APhen DOCHN QHop

9

BbBT 6

3

0 1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4

1000/T (1/K) FIG. 5. Rotational relaxation times for different molecules.


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2 -1

log D (cm s )

-5

BbBT DOCHN Squ

-6

QHop BbBT DOCHN Squ

-7

PHop AThio

QHop PHop

-8

AThio APyrr -9 2

2.2

2.4

2.6

2.8

3

2 -1

log D (cm s )

-5

3.2

TMBO TIR Hop

-6

PHPN APhen APyrr

BbBT TMBO TIR Hop

-7

-8

PHPN APhen APyrr

-9 1.8

2

2.2

2.4

2.6

2.8

3

3.2

-1

1000/T (K ) FIG. 6. Diffusion coefficients vs. temperature. Lines indicate Arrhenius fits.

Cui et al.35, 69 previously found that rotational relaxation times increased as molecular size increased. B. Molecular diffusion

The molecular size and temperature also affect the translational diffusion rate. Fig. 6 shows an Arrhenius plot of diffusion coefficients over temperatures ranging from 298.15 to 533.15 K. Lines represent Arrhenius fits done independently for each compound. Diffusion is much faster at higher temperatures. Larger molecules diffuse slower than smaller molecules in the model asphalt system. For comparison, the diffusion coefficients of benzobisbenzothiophene and asphaltene-pyrrole differ by about an order of magnitude at each temperature. The diffusion coefficients at all but 533.15 K are below the average self-diffusion coefficient ∼2 × 10−6 cm2 /s measured by neutron scattering for molecules in a bitumen.70 The diffusion coefficients follow Arrhenius behavior within some scatter. The Arrhenius equation D = D0 exp (−Ea /RT) relates the diffusion coefficient and activation energy Ea as a function of temperature, where D0 is the diffusion prefactor. Figures 7 and 8 show the diffusion coefficient prefactor and diffusion activation energy as functions of molecular weight. The prefactor decreased with molecular weight, and a linear trend approximates this dependence. The outliers below

FIG. 7. Diffusion coefficient prefactor as a function of molecular weight.

the line are squalane, hopane, pyridinohopane, and thioisorenieratane. The activation energies show little dependence on molecular weight. The dashed line shows their average value of just under 42 kJ/mol. The same four compounds are outliers at lower activation energy. The prefactors for these compounds would have been less negative and their activation energies larger if their diffusion rates at 298.15 K were predicted to be slower. The product of diffusion coefficient and rotational relaxation time describes how temperature simultaneously affects translational and rotational motions.38 Based on DebyeStokes-Einstein relationships, τ r and D have direct and inverse relationships with viscosity. The product of τ r and D should be constant if translation and rotation equally reflect viscosity. The products of diffusion coefficients and rotational relaxation times as a function of temperature in Fig. 9 show a similar pattern to the rotational relaxation as a function of temperature in Fig. 5. The values of τ r D increase with inverse temperature and molecular size. The increase with decreasing temperature is particularly notable at temperatures below 358.15 K. This suggests that molecular rotations control the viscosity more than diffusion. The τ r D products of the asphaltenes are higher than those of most other molecules; products for asphaltene-pyrrole are higher by orders of magnitude

46 44

Ea (kJ/mol)

1.8

42 40 38 36 200

300

400

500

600

700

800

900

Molecular Weight FIG. 8. Activation energy as a function of molecular weight.


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9

10

8

Asphaltene-pyrrole

7

Asphaltene-thiophene

6

Asphaltene-phenol

5

Quinolinohopane

4

DOCHN Benzobisbenzothiophene

10 10

2

τr D (nm )

10 10 10

3

10

2

10

1

10

0

10

-1

10 10

-2

1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4

from a smooth temperature dependence for β values is more of a consequence of signal-to-noise ratio than of underlying physics; it reflects the challenge of regressing noisy long-time rotation correlation results to a simple P(t) function. In our analysis, the values of α and τKW W also vary with temperature. The values of τKW W have similar trends as the relaxation time, being lower at higher temperatures and increasing with molecular size. The values of α ranged from approximately zero to 0.235. In most cases, as the temperature increased α also increased, indicating a larger contribution from a fast exponential relaxation. For most of the molecules, α decreased with smaller size. We have the least idea on the behavior of τ 0 because relaxations were not carefully examined at its short time scale (t < 1 ps).

1000/T (1/K) FIG. 9. Product of relaxation time and diffusion for various molecules.

than for benzobisbenzothiophene due to the larger molecular size of an asphaltene. C. mKWW parameters

Figure 10 shows the temperature dependence of the averaged β parameters from the mKWW function. The β parameters fit to the three correlation functions (P1 , P2 , P3 ) are averaged arithmetically. A β value close to 1 corresponds to a narrow distribution of relaxation times, while decreasing β corresponds to an increasingly broad distribution. As temperature decreases, β also decreases for each molecule type. These results suggest no distinct trend in β as a function of molecular size. At 333.15 and 358.15 K, the values of β for thio-isorenieratane are slightly lower than asphaltene-pyrrole. However, at 400.15 and 443.15 K, the values of β for asphaltene-pyrrole are much lower than thio-isorenieratane. Similarly, this behavior is observed for squalane and asphaltene-thiophene at different temperatures. The difference between β parameters for molecules at lower temperatures are much smaller than at higher temperatures (400.15 K, 443.15 K). We hypothesize that this discrepancy

D. Viscosity

Model asphalt viscosity at 533.15 K was calculated using the Green-Kubo and the Einstein methods as a function of integration time as shown in Fig. 11. The viscosity estimates are read from the plateau of the integrated function. The viscosity estimates for AAA-1 at 533.15 K are approximately 2.2 cP, as shown with the horizontal line drawn in Fig. 11. The Green-Kubo method has a better plateau and contains less noise compared to the Einstein method. The divergence of the two methods from each other after approximately 850 ps indicates the impact of noise in the stress correlation function. The temperature was increased compared to 443.15 K in our prior work2, 3, 5 to reduce the relaxation time, which enables obtaining viscosity estimates at shorter integration times. The viscosity and rotational relaxation time determined at the highest temperature can be used to estimate the viscosity at lower temperatures from the DSE relationship (Eq. (8)). The rotational relaxation time of asphaltene-pyrrole was used to estimate the viscosity using the DSE relationship because it has the longest relaxation time. We assumed that the molecular volume and system-dependent numerical prefactor have qualitatively negligible temperature dependences compared with other terms in the DSE equation. The viscosity estimates 4

1

3.5 APyrr

0.6

β

QHop TIR

0.4

3

Viscosity (cP)

AThio APhen Squ

0.8

Green-Kubo

2.5 2 1.5 1

Einstein

0.5

0.2

0 0

0 1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4

-1

1000/T (K ) FIG. 10. The β parameter from the mKWW function for various molecules.

500

1000

1500

2000

2500

3000

Integration Time (ps) FIG. 11. Viscosity comparison between the Green-Kubo and the Einstein methods for revised model AAA-1 at 533.15 K. The horizontal dashed line is the viscosity estimate.


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10 Model AAA-1 (this work) Prior Model AAA- 1 Ternary asph1 model Ternary asph2 model Expt AAA-1 (SHRP) B, 300-400 C, 85-100 PG 64-22 70/100 Hansen et al

8

log (η , Pa-s)

6 4 2 0 -2 -4 1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4

1000/T (1/K) FIG. 12. Viscosity comparison of new model AAA-1 asphalt, old model AAA-1 asphalt,3 ternary model systems,2 experimental results for SHRP AAA-1 asphalt,48, 71 experimental results for a range of penetration-graded asphalts (curves B and C),72 a performance-graded 64–22 asphalt,73 and experimental (70/100) and high-pressure model results from Hansen et al.16

for AAA-1 are shown in Fig. 12. The viscosity decreases as temperature increases, and it shows a non-Arrhenius shape typical of a “fragile” liquid: log(η) increases faster than linearly as 1/T increases. The viscosity has a similar trend to the rotational relaxation times as a function of temperature in Fig. 5 because the DSE equation is based on rotational relaxation time. Further interpretations of model asphalt viscosity using frequency analysis are available in a related paper.17

IV. DISCUSSION

Rotational relaxation times have been measured by Groenzin and Mullins63, 74 for asphaltenes and maltenes at 19 ◦ C in toluene solution of viscosity 0.59 cP. They found relaxation times of 0.15–1.1 ns for asphaltenes and 0.1–0.95 ns for maltenes from a Kuwaiti crude oil. Results for asphaltenes from different crude oil sources differed by factors of 1.5–2.74 The model asphalt system here reaches a viscosity of 2.2 cP at 533.15 K. Rotational relaxation times at 533.15 K span from 0.1 to 1 ns for the different components in the model asphalt. This is satisfactory agreement with the measured relaxation times at a comparable condensed-phase viscosity. The longer rotation time for asphaltenes compared to maltenes is also consistent with these experimental data. Figure 12 compares several viscosity results. Open symbols indicate experimental results from the literature. Squares are a performance-graded (PG) 64–22 asphalt studied by Zhai and Salomon.73 SHRP AAA-1 asphalt reaches high and low temperature PG specifications at 58 and –28 ◦ C48 and thus is expected to have a lower viscosity. Circles show the range measured for a number of asphalts by Khong et al.72 These asphalts had been characterized using the older “penetration” scale and are included to show a range of possible temperature dependences. Diamonds at 298.15 and 333.15 K indicate the zero shear viscosity reported for AAA-1 asphalt.48, 71 Leftpointing triangles indicate measurements for a paving grade 70/100 bitumen reported by Hansen et al.;16 their model re-

sult for a 4-component united atom bitumen at high pressure is also shown (×). The model asphalt viscosities obtained in this work (filled circles) through the direct calculation at 533.15 K and DSE scaling to lower temperatures show a temperature dependence that falls among the experimental results at moderate temperatures and are higher at the lowest temperatures. The viscosity reported for a PG 64-22 asphalt shows larger changes with temperature than the new model AAA1 asphalt, though the viscosities are of comparable orders of magnitude. The 298.15 K prediction is higher than the experimental value for AAA-1. Zero-shear viscosity is expected to depend on composition, including asphaltene content. Unfortunately, the sources of experimental data in Fig. 12 do not provide much composition information. Polystyrene-equivalent molecular weights of Mn = 835 and 875, Mw = 1160 and 1210 were reported for the B/300-400 and C/85-100 asphalts, respectively.72 The exact source of the PG 64-22 asphalt is not stated;73 it likely has 14%–16% asphaltenes. The experimental section for the 70/100 asphalt16 is quite brief and mentions no composition information. The experimental AAA-1 system contains 16.2% asphaltene, 37.3% polar aromatics, 31.8% naphthene aromatics, and 10.6% saturates;48 4.1% remains unspecified in the literature source. The experimental system has an equivalent molecular weight of 790 g/mol in toluene. The current4 and former5 model AAA-1 contain 17.2% and 18.2% asphaltenes, respectively, or 16.5% and 17.5% if the experimental normalization to 95.9% is applied. Further comparisons of experimental and model AAA-1 composition are described elsewhere.4 Zhai and Salomon73 show that glass transition varied between –50 and –20 ◦ C without a clear dependence on asphaltene content for 15 different binders. The larger molecules in the current work have led to a new model asphalt that shows improvement over the prior model AAA-1 asphalt5 (filled squares) when compared to experimental data for various asphalts. The smaller molecules in that system (1–2 rings per resin molecule, shorter or nonexistent side chains) led to rotation rates that slowed too little as temperature decreased, suggesting a comparably smaller rise in viscosity that is smaller than the change in any of the systems studied experimentally. The low-temperature viscosity predictions here are larger in magnitude than those in our prior ternary asphalt models.32 Their temperature dependences are similar. The predicted viscosities are smaller than the results of Hansen et al.16 for their four component united-atom model bitumen. Hansen et al.16 calculated 13 cP as the low frequency limit of complex viscosity at 603 K and 2500 MPa. This higher viscosity at a higher temperature is likely a consequence of the very high pressure in that NVT simulation16 (∼104 times higher than ambient pressure). Figure 9 shows that most molecules in the system express a similar temperature dependence of the τ c D product. Likewise, the activation energy for diffusion is similar among all 12 molecules, despite differences in their size. These results suggest that dynamics of the individual molecules express collective behavior of the entire system. While smaller molecules rotate and diffuse more quickly by virtue of their smaller size, the extent that those behaviors change with


034507-9


temperature depends on the overall rates at which all the molecules move. This collective behavior establishes a framework for chemo-mechanical effects. Systems that differ in composition, such as different SARA ratios, or different sizes or shapes for molecules within an asphalt solubility class, will combine their dynamics in composition-dependent ways to obtain the collective temperature dependence. Indeed, recent works in petroleum physics seek to establish the contribution of different molecules toward the overall physical and mechanical behavior and underlying relaxation times.75, 76 Further interpretations of intramolecular correlations and their implications are the subject of continuing work.

V. CONCLUSIONS

Analyzing the dynamics of individual molecules within molecular dynamics simulations of a revised AAA-1 model asphalt system4 enable contributions from different molecule types to be inferred. Self-diffusion coefficients, calculated using center of mass displacement within the multicomponent system, followed Arrhenius behavior. The activation energy was found to be similar for all molecule sizes; different rates originated in the diffusion prefactor. Rotational relaxation times were obtained by regressing the mKWW equation to orientation correlation functions and then extrapolating to long times. Rotational relaxation times increased with bigger molecular size and lower temperature. Asphaltene-pyrrole had the longest rotational relaxation time and slowest diffusion rate, while benzobisbenzothiophene had the shortest rotational relaxation time and fastest diffusion rate at all temperatures. Rotation and diffusion coupled similarly to viscosity at temperatures above 358.15 K. Rotation slowed more than diffusion at lower temperatures. The viscosity was calculated at 533.15 K using the Green-Kubo and Einstein methods, and viscosities at lower temperatures were estimated by the Debye-Stokes-Einstein equation using rotational relaxation time. The viscosity of this new model asphalt follows trends of experimental data for some real asphalts. Also, the viscosity predicted for this new model asphalt is larger and closer to experimental results compared to that for our previous model of AAA-1 asphalt. Results from this “next generation” of model asphalt that contains larger molecules are expected to be useful for future studies that relate microstructure to macrostructure behaviors.

ACKNOWLEDGMENTS

This material is based upon work supported by the Federal Highway Administration under Agreement No. DTFH6107-H-0009. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the view of the Federal Highway Administration. The New England University Transportation Center is acknowledged for a Graduate Transportation Fellowship to D. Li.

J. Chem. Phys. 140, 034507 (2014) 1 D.

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