Glass Transition and Molecular Mobility in StyreneâButadiene

Subscriber access provided by University of Pennsylvania Libraries

Article

Glass Transition and Molecular Mobility in Styrene-Butadiene Rubber Modified Asphalt Fardin Khabaz, and Rajesh Khare J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b06191 • Publication Date (Web): 09 Oct 2015 Downloaded from http://pubs.acs.org on October 12, 2015

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Glass Transition and Molecular Mobility in Styrene-Butadiene Rubber Modified Asphalt

Fardin Khabaz and Rajesh Khare* Department of Chemical Engineering Texas Tech University, Box 43121 Lubbock, TX 79409-3121 United States

*

Corresponding author email: [email protected] Tel.: (806) 834-0449

1 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Asphalt, a soft matter consisting of more than thousand chemical species is of vital importance for the transportation infrastructure, yet poses significant challenges for microscopic theory and modeling approaches due to its multicomponent nature. Polymeric additives can potentially enhance the thermo-mechanical properties of asphalt thus helping reduce the road repair costs; rational design of such systems requires knowledge of the molecular structure and dynamics of these systems. We have used molecular dynamics (MD) simulations to investigate the volumetric, structural and dynamic properties of the neat asphalt as well as styrene-butadiene rubber (SBR) modified asphalt systems. The volume-temperature behavior of the asphalt systems exhibited a glass transition phenomenon, akin to that observed in experiments. The glass transition temperature, room temperature density, and the coefficient of volume thermal expansion of the neat asphalt systems so evaluated were in agreement with experimental data when the effect of the high cooling rate used in simulations is accounted for. While the volumetric properties of SBR modified asphalt were found to be insensitive to the presence of the SBR additive, the addition of SBR led to an increase in the aggregation of asphaltene molecules. Furthermore, addition of SBR caused a reduction in the mobility of the constituent molecules of asphalt; the reduction being more significant for the larger constituent molecules. Similar to other glass forming liquids, the reciprocal of the diffusion coefficient of the selected molecules was observed to follow the VogelFulcher-Tammann (VFT) behavior as a function of temperature. These results suggest the potential for using polymeric additives for enhancing the dynamic mechanical properties of asphalt without affecting its volumetric properties. Keywords: Glass transition, Diffusion coefficient, VFT behavior, Styrene-butadiene rubber, Asphalt


Page 2 of 37

Page 3 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.

Introduction Asphalt is widely used as construction material for road surfaces. Sensitivity of asphalt

thermo-physical properties to weather changes, especially temperature changes, leads to the need for road repair work. The physical properties of asphalt can be enhanced by inclusion of additives such as styrene-butadiene rubber (SBR). Rational design of such polymer modified asphalt necessitates detailed molecular level understanding of the chemical interactions in the additive modified asphalt and their effect on the structure and properties of the system. Such knowledge can be obtained from microscopic theory and simulations, however, the multicomponent nature of asphalt makes this a difficult task. Physically, asphalt is a complex soft material that has a high viscosity at elevated temperatures and exhibits glassy behavior at low temperatures.1 The volumetric and rheological properties of asphalt that are important in the pavement industry have been investigated in several experimental studies.2-7 In particular, the glass transition temperature (Tg) was found to be in the range of 243 K - 258 K for several asphalt systems,3 and multiple Tg’s were also found in some cases.2, 8 In order to enhance the mechanical properties of asphalt, different types of polymers such as styrene-butadiene-styrene (SBS) triblock copolymer,4, 9 poly(ethyl methyl acrylate)4 and styrene-butadiene rubber (SBR),6, 7 are added to asphalt, the typical mass fraction of the polymer being smaller than 8-10%.1 From the chemical point of view, asphalt is a mixture of a very large number of hydrocarbon molecules and its composition can be divided into four major groups based on its chemistry and solubility in different solvents: (1) asphaltenes (2) saturates (3) polar aromatics and (4) naphthene aromatics.1, 10, 11 Given the extremely large number of chemical species present in



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

asphalt as well as the dependence of its composition on the crude source, exact determination of molecular composition of asphalt is a difficult task. Few simulation studies in the literature have dealt with the composition of the asphalt using the all-atom12-14 or the united-atom15 models. The initial studies included three,13 four15 or six14 constituent models for asphalt. More recently, Li and Greenfield10 proposed a twelve-component model for AAA-1, AAK-1 and AAM-1 asphalts in which larger molecules were considered compared to the prior studies. Volumetric properties of different asphalt systems have previously been studied using molecular simulations.10, 13, 14 The emphasis of these studies was on capturing the density of the asphalt models. Addition of a 50-mer of polystyrene was found to cause a small increase in the density of the system.14 Among these studies, the simulations with the older three component model13 exhibited a glass transition, whereas the simulations with the newer six14 and the twelve component10 models did not exhibit a clear glass transition in the volume-temperature behavior reported in these studies. Existence of different types of molecules in the asphalt structure leads to complex dynamic behavior in the system. Specifically, the temperature dependence of the diffusivities of the constituent molecules has been studied in the literature.12, 14, 15 Recent simulation work12 with the twelve component asphalt model indicated that the diffusion coefficient of the asphalt constituents follows an Arrhenius temperature dependence. Furthermore, the diffusivities of the asphaltene molecules determined from the all atom simulations of the twelve component model12 were about 5 to 8 times larger than those determined from the united atom simulations of the four component model.15


Page 4 of 37

Page 5 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The motivation for this work is twofold: At the fundamental level, a detailed understanding of the effect of polymer additives on the glass transition of asphalt will be useful for predicting the thermo-mechanical behavior of polymer modified asphalt.

Furthermore, establishment of a

quantitative functional relationship for the temperature dependence of diffusivities of asphalt components will allow for the development of approaches such as time-temperature-superposition for describing the dynamic and mechanical properties of asphalt over a range of temperatures and time scales. At the practical level, such detailed molecular scale knowledge of the effect of polymer additives on the thermo-mechanical properties of asphalt will in the long run, enable design of new asphalt systems with longer service life without the need for frequent repairs. In this study, the molecular models of two types of neat asphalt systems were built and the structures were validated by calculating their volumetric properties. We show that simulated asphalt systems exhibit glass transition phenomenon, similar to that observed in experiments. Modified asphalt systems were prepared by inclusion of SBR chain to reinforce the asphalt structure. The possible aggregation of the asphaltene molecules and the effect of the additive polymer on the local structure as well as the dynamics of molecules in asphalt was also studied. The temperature dependence of the diffusion coefficient of the constituent molecules was evaluated and it was shown to follow the VFT behavior. The rest of the paper is organized as follows. We begin by describing the details of the simulation systems and the methods used in this work. The results for the volumetric, structural and dynamic properties of the system are described next. We close the paper with a brief summary of our findings and conclusions.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2.

Simulation Systems and Methods

2.1.

Asphalt systems: Model and Simulation Details For modeling asphalt in this study, we have used the twelve component model of Li and

Greenfield10 which comprises the four major types of the constituent molecules (asphaltenes, polar aromatics, naphthene aromatics and saturates). Two types of asphalt systems were studied: AAA1 and AAM-1,10 further details of the system size are given in Table 1. We used general AMBER force field (GAFF)16, 17 to represent the molecular interactions in the systems. The partial charges of the system were calculated using the AM1-bcc method.18, 19 The cut-off distance of interactions used in the simulations was 9 Å and the Lennard-Jones and electrostatic interactions beyond that distance were handled by applying the tail correction and the particle-particle particle-mesh (PPPM) algorithms, respectively.20 The temperature and pressure of the systems were controlled by using Nosé-Hoover thermostat and barostat.21, 22 To prepare the model structures, all the molecules in a given stoichiometric ratio10 were initially placed in a large cubic box and then the simulation box was compressed by applying an isotropic pressure of 100 atm. After reducing the box size, the systems were relaxed under conditions of constant number of molecules, pressure and temperature (NPT) at T = 600 K and P = 1 atm for a duration of 2 ns. Five replicas were built for each type of asphalt. All molecular dynamics simulations were performed using the LAMMPS package23 with a timestep of 1 fs. 2.2.

SBR containing asphalt The additive modified systems consisted of a random copolymer (chain length = 375 and

343 for the modified AAA-1 and AAM-1 systems, respectively) of styrene-butadiene (SBR) with a mass fraction of 6.5%. These chain length values are expected to be much longer than the 6 ACS Paragon Plus Environment

Page 6 of 37

Page 7 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


entanglement length of the SBR copolymer in the melt state, thus allowing us to study the system behavior in the long chain limit. For preparing the model, the styrene and butadiene monomers (mole ratio of styrene to butadiene = 0.3) were added to the initial mixture of the asphalt components. The reaction between styrene and butadiene molecules was performed by utilizing the simulated annealing polymerization technique24, 25 which allows for finding the shortest path between the potential reacting pairs of atoms. New bonds were then created between the reacting atom pairs so identified and these bonds were relaxed by applying a stepwise harmonic restraint to reduce the bond length and increase the harmonic constant to the actual value.26 Constant NVT and NPT simulations were performed for a duration of 0.1 ns at each iteration of bond length and harmonic constant. Finally systems were relaxed for a duration of 2 ns at T = 600 K. Snapshot of the simulation box containing the SBR modified asphalt system is shown in Figure 1.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1. Simulation box of AAA-1-SBR system: Asphalt constituents (cyan color) and SBR chain (red color) are shown.


Page 8 of 37

Page 9 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1. Details of the simulated systems Approximate corresponding

Mass fraction of

System

Number of atoms commercial asphalt

Polymer

AAA-1

Canadian/Lloydminster

66864

0.0

AAM-1

USA/West Texas Intermediate

68346

0.0

AAA-1-SBR

-

60736

0.065

AAM-1-SBR

-

57742

0.065

2.

Results and Discussion

2.1.

Volumetric properties The prepared structures were initially heated up to a temperature T = 600 K, and were

subjected to stepwise quenching at a rate of 5 K/ns (temperature was reduced in steps of 20 K per each 4 ns) in order to cool the systems down to a low temperature of 80 K. The specific volume of the systems was determined by averaging its values over the second half of the 4 ns long run at each temperature. The specific volume as a function of temperature is shown for AAA-1 and AAM-1 asphalt structures in Figure 2a.

The Tg was determined by finding the point of

intersection of the fitted lines in the rubbery and the glassy regions on this specific volumetemperature plot. The Tg of the AAA-1 and AAM-1 asphalt systems is reported in literature to be 248.56 K and 252.06 K respectively,27 while our results show Tg values of 350.0 ± 6.9 K and 348.3 ± 7.7 K respectively for these systems (the uncertainties in the Tg values were evaluated using the bootstrap method).28

This difference between the Tg values obtained from the

simulations and those obtained from the experiments is routinely observed in molecular 9 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 37

simulations of polymers,29, 30 and is due to the very high cooling rate that is used in the molecular simulations compared to experiments. Indeed, it is well known in polymer literature that higher cooling rates lead to a higher value of the Tg .31 The amount of the expected shift in Tg ( Tg ) resulting from the higher cooling rate can be calculated using the William-Landel-Ferry (WLF) equation as follows 31,29, 30

log10

qexp qsim

 log10

 g, sim C1 (Tg ,shifted  Tg ,exp ) tsim  log10  texp  g,exp C2  Tg , shifted  Tg ,exp

(1)

where q and t are the cooling rate and timescale, respectively. Tg , shifted is the shifted value of the Tg while C1 and C2 are the constants of the WLF equation. Using the values of constants C1  19

and

C2  92 K that have been reported for asphalt in the literature,32 we get

Tg  Tg ,shifted  Tg ,exp  113.1 K. If this expected shift value is added to the experimental Tg values,

the resulting shifted Tg values are within 10-15 K of the simulated Tg values (see Table 2). The values of the Tg for SBR-modified systems (Figure 2b) are also shown in Table 2. Within statistical uncertainties, the neat and the modified asphalt systems have the same Tg . At a temperature of 300 K, the density of our AAA-1 asphalt model system is 0.997 g/cm3, which is in a very good agreement with the density value of about 1 g/cm3 that was reported by Li and Greenfield10 for the same asphalt system. We note that the simulated density value is lower than the experimentally reported value of the asphalt density which is in the range of 1.01 – 1.04 g/cm3 for various asphalt systems (see Table 2).1 The origin of this lower density value is the shift in the simulated Tg value; specifically, a glass formed at a higher temperature will have a higher specific volume and hence a lower density than the glass formed at a lower temperature.


Table

Page 11 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2 also indicates that within statistical uncertainties, there is no density difference between AAM1 asphalt and SBR modified AAM-1, while there is very small (~0.5%) reduction in density of the AAA-1 asphalt on addition of the polymer. However, we do not believe that contemporary atomistic simulations are accurate enough to decipher such small density differences with the nm scale models, and hence we do not consider this difference as a definitive indicator of a decrease in density of the system. The temperature dependence of the volume can be quantified by the coefficient of volume thermal expansion (CVTE) which is defined as:  

1  V    , where V and T are the specific V  T  P

volume and temperature of the system at constant pressure conditions. The value of CVTE was calculated from the volumetric data using numerical differentiation. As seen in Figure 3a, the values of α of AAA-1 and AAM1 asphalts show two distinct plateau-like regions or regions of slow change: these high (T > 420 K) and low (T < 180 K) temperature regions correspond to the rubbery and the glassy states respectively. The intermediate temperature range of 180 K < T < 420 K that shows a large drop in the CVTE value, corresponds to the glass transition. This glass transition region in simulations is much broader than that observed in experiments, the observation can be attributed to the very high cooling rate that is used in the simulations.33 We note that a similar broad transition region for CVTE has also been observed in simulations of glass transition in polymeric systems.34 The α values of AAA-1 and AAM1 systems in the glassy state from simulations are 2.04×10-4 K

-1

and 2.06×10-4 K-1; these are in good agreement with the

experimental values of 3.5×10-4 K -1 and 3.6×10-4 K-1 for the AAA-1 and AAM-1 asphalt systems, respectively.35 As seen in Figure 3b, the temperature dependence of the CVTE for AAA-1-SBR and AAM-1-SBR systems is very similar to that for the neat asphalt systems. A comparison of the CVTE values in Table 2 indicates that the addition of SBR to asphalt leads to a small reduction of 11 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 37

5-10% in the value of CVTE, this can be attributed to the long chain nature of SBR which leads to a larger resistance to volume change than that from the smaller constituent molecules of asphalt. We note that an approximately 25% reduction in the value of CVTE of asphalt at a temperature close to 300 K was also observed by Zhang and Greenfield14 on addition of polystyrene. In summary, addition of the SBR chain to asphalt does not cause a measurable change in its density or the Tg, and causes only a small change in its CVTE. In what follows, we report the structural and dynamic properties of neat asphalt systems and the effect of addition of SBR on these properties. These studies are performed only for the AAA-1 system.

Table 2. Summary of the volumetric properties of asphalt from simulations and experiments. Numbers in the parenthesis show the uncertainties in the values. ρ (g/cm3) at T = 300 K

Tg (K)

α ×104(1/K)-glassy

AAA-1 (Sim.)

0.997(0.0006)

350.0 (6.9)

2.04(0.02)

AAA-1 (Exp.)

1.01-1.041

248.5627+113.1*

3.535

AAA-1-SBR (Sim.)

0.992(0.0002)

354.7 (7.2)

1.86(0.01)

AAM1 (Sim.)

0.970(0.0010)

348.3 (7.7)

2.06(0.05)

AAM1 (Exp.)

1.01-1.041

252.0627+113.1*

3.635

0.969(0.0018)

352.9 (6.8)

1.97(0.04)

System

AAM1-SBR (Sim.)

*Expected shift to be added to the experimental Tg value to account for the difference in cooling rates between experiments and simulation (see text).


Page 13 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2a. Volume-temperature data for AAA-1(red circle) and AAM-1 (blue diamond). Error bars are of the size of the symbols.

Figure 2b.

Volume-temperature data for AAA-1-SBR (red circle) and AAM-1-SBR (blue

diamond). Error bars are of the size of the symbols. 13 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 37

Figure 3a. Coefficient of volume thermal expansion for AAA-1 and AAM-1 structures. Symbols have the same meaning as in Figure 2a. Error bars are of the size of the symbols.

Figure 3b. Coefficient of volume thermal expansion for AAA-1-SBR and AAM-1-SBR structures. Symbols have the same meaning as in Figure 2b. Error bars are of the size of the symbols.


Page 15 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2. Structural properties The aggregation of the asphaltene molecules in asphalt has been reported in prior MD simulation studies.14, 36 We are interested in studying the effect of the SBR additive on asphaltene aggregation. For this purpose, the molecular structure in the system was characterized by determining the radial distribution function (RDF), which gives the normalized probability of occurrence of a molecule or an atom at a given distance 𝑟 from another molecule or atom. The RDFs were calculated from a constant NPT simulation run of duration 1 ns at each temperature of interest. In particular, the structural arrangement of asphaltene molecules in AAA-1 asphalt was studied by determining the RDFs of the oxygen atoms (O-O) of asphaltene-phenol, the nitrogen atoms (NN) of asphaltene-pyrrole and sulfur (S-S) atoms of asphaltene-thiophene, at a temperature of T = 333 K (Figure 4). The RDF for the asphaltene-phenol shows a strong first peak (peak height greater than 6) indicating a tendency for strong aggregation of the asphaltene-phenol molecules. A weaker tendency for aggregation is also exhibited by the asphaltene-pyrrole molecules (height of the first peak greater than 4), while the third type of asphaltene molecules do not exhibit aggregation in the system. We attribute these observations to the stronger electrostatic interactions experienced by the oxygen (in asphaltene-phenol) and nitrogen (in asphaltene-pyrrole) atoms of these asphaltenes due to the higher partial charge that is present on these atoms. A snapshot of the simulation box at T = 333 K is shown in Figure 5, which illustrates the strong aggregation of asphaltene molecules. At short distance 𝑟, Lemarchand et al.36 had reported a large uncertainty in the RDF between asphaltene molecules with other molecules; similarly, we also find that at the small values of 𝑟 (𝑟 < 10 Å), the uncertainty in the RDF is very large (around 80 % of the value



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 37

of RDF) for the AAA-1 system. This can be attributed to the smaller overall mole fraction of each type of asphaltene molecule in the whole system.

Figure 4. RDFs of O-O atoms of asphaltene-phenol (black color solid line), N-N atoms of asphaltene-pyrrole (red color dot dash line), and S-S atoms of asphaltene-thiophene (green color dashed line) at a temperature T = 333 K in the AAA-1 system. Inset: RDF of O-N atoms (black color solid line), O-S atoms (red color dot dash line) and N-S atoms (green color dashed line) in the same system.


Page 17 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 5. Simulation box of AAA-1 at T = 408 K showing aggregation of asphaltene-phenol molecules (purple color) in the system.

The effect of the addition of the SBR chain on the aggregation of the asphaltene molecules can be seen in the RDFs shown in Figure 6. The heights of the first peaks for the asphaltenephenol and the asphaltene-pyrrole molecules have increased to about 25 and 8, respectively. These observations indicate that the presence of the SBR additive significantly enhances the aggregation tendency of these two types of asphaltene molecules. On the other hand, the third type of asphaltene molecules - asphaltene-thiophene - continue to be in the dispersed state in this system as well. In addition, the uncertainty in the RDF values is much smaller than that in the RDF for the neat system and is about 20% of the value of the RDF at the first peak. The interactions between the SBR chain and the various constituents of the asphalt system can be further probed 17 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

by studying the RDFs between the four different types of constituent molecules and the SBR chain. For this purpose, the RDF was calculated at T = 333 K by considering only the heavy atoms (Figure 7). As can be seen, the RDFs for all systems had a value smaller than unity up to separation of 15 Å, indicating unfavorable interactions between the SBR chain and the asphalt components. Furthermore, the RDF between the SBR chain and the asphaltene molecules had the smallest value, further indicating that the interactions between SBR and asphaltene are least favorable. A consequence of this is the higher tendency for aggregation of the asphaltene molecules as seen in Figure 6.

Figure 6. RDFs in the AAA-1-SBR system at T = 333 K. Lines have the same meaning as those in Figure 4.


Page 18 of 37

Page 19 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 7. RDF between SBR-asphaltene (black circle), SBR-polar aromatics (red diamond), SBR-saturates (green square) and SBR-naphthenes (blue cross) molecules at T = 333 K.

Figure 8. RDF of O-O atoms of asphaltene-phenol at T = 333 K (red circle) and T = 440 K (black circle) in AAA-1-SBR system.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 37

The effect of temperature on the aggregation behavior of asphaltene-phenol was also studied by comparing the structural properties at T = 408 K and T = 333 K (Figure 8). As seen, the asphaltene-phenol molecules continue to be aggregated at the higher temperature, however, the tendency for aggregation reduces significantly with an increase in the temperature, as seen from the decrease in the height of the first peak from about 25 to 11.

3. Dynamic properties The dynamics of asphalt constituent molecules has implications on its rheological properties, which in turn, are important for the end-use application. We thus determined the mobility of different molecules in the asphalt model structures by tracking the mean-squared displacement (MSD) of their center of mass in both the AAA-1 and SBR modified AAA-1 systems. The translational mobility of molecules was tracked over a range of temperatures from 400 K to 600 K (this range ensures that the systems are always above the glass transition temperature). A constant NPT MD simulation was carried out at each of the selected temperatures and the atomic coordinates were tracked at time intervals of 40 ps. One chemical species from each constituent category was selected for monitoring its mobility as a function of temperature. Specifically, asphaltene phenol, quinolinohopane, perhydrophenanthrene and squalane were selected from the asphaltene, polar aromatics, naphthene aromatics and saturates constituent groups respectively. Figure 9 shows a plot of MSD as a function of time for asphaltene phenol, quinolinohopane, perhydrophenanthrene (PHPN) and squalane at temperature T = 520 K in the AAA-1 system. The molecular mobility is correlated with the molecule size as seen from that asphaltene-phenol shows the slowest dynamics due to its highest molecular weight among these four molecules while squalane exhibits the fastest dynamics in the system due to its lowest 20 ACS Paragon Plus Environment

Page 21 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


molecular weight.

MSD of quinolinohopane as a function of simulation time at different

temperatures is shown in Figure 10. As expected, the mobility of the quinolinohopane molecule increases with an increase in the temperature, as seen from the magnitude of the MSD. Quinolinohopane begins to show diffusive behavior (slope = 1 on log scale) at a time of 0.1 ns at the temperature of 560 K, whereas the onset of diffusive behavior is delayed at the two lower temperatures. The MD simulations were run for a long enough time (100 ns below 500 K, shorter duration above 500 K) to ensure that the molecule showed “true diffusive” behavior in each case. As an aside, we note that at these temperatures, the MD run times are also longer than the expected rotational relaxation times12 of all asphalt component molecules with the possible exception of asphaltene-phenol and asphaltene-pyrrole at temperatures closer to the lower end of our temperature range of interest i.e. 400 K. We only focus on the translational diffusivities in this work; we do not expect a strong coupling between the rotational and translational diffusivities of these molecules. The diffusivity of the molecules can be calculated from the slope of the MSD vs. time plot and applying the Einstein relation D  lim

r 2  t 

t 

6t

where

r 2  t 

is the mean-squared

displacement of the center of mass of each molecule. For the asphaltene-phenol molecule at a temperature of T = 443 K, we obtain a diffusivity value of 2.01 (0.18) 107 cm2/s. This value is 7 in good agreement with the asphaltene diffusivity value of ~ 10 cm2/s that was reported by

Hansen et al.15 using a four-component united-atom model of asphalt. On the other hand, our 7 2 value is about 4.5 times smaller than the value of 9.2 10 cm / s reported by Li and Greenfield12

for asphaltene-phenol using the same asphalt model but that was simulated using the OPLS force



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

field.37-39 This difference in the diffusivity values increases with a decrease in temperature (for example, at T = 400 K, the values differ by a factor of about 10).

Figure 9. Time dependence of the MSD of asphaltene phenol (black circle), quinolinohopane (red diamond), PHPN (green square) and squalane (blue cross) at temperature T = 520 K in the AAA-1 system. A line with slope = 1.0 (signifying diffusive behavior) is also shown as a guide to the eye.


Page 22 of 37

Page 23 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 10. MSD of quinolinohopane as a function of time at different temperatures. Results are shown for the following temperatures: 560 K (black circle), 480 K (red diamond), and 420 K (green square). A line with slope = 1.0 (signifying diffusive behavior) is also shown as a guide to the eye.

The addition of the SBR chain to the AAA-1 system significantly reduces the translational mobility of the larger component molecules of asphalt (e.g. asphaltene phenol) whereas the effect is not as prominent for the smaller molecules like squalane. Indeed, as seen from Figure 11, the MSD of the quinolinohopane molecule in the AAA-1-SBR system is about half of its value in the AAA-1 system at a temperature of T = 400 K. Other larger component molecules show similar 23 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

behavior (not shown here). This result suggests that the dynamics of the larger molecules in the asphalt system is strongly coupled to the dynamics of the polymer chain. Similar behavior was also reported by Zhang and Greenfield14 where the addition of a polystyrene oligomer was found to reduce mobility of all component molecules in the system.

Figure 11. Comparison of the MSD of quinolinohopane molecules in the AAA-1 (black circle) and AAA-1-SBR (red circle) systems. A line with slope = 1.0 (signifying diffusive behavior) is also shown as a guide to the eye.

The effect of temperature on the diffusion coefficient of the selected molecules is shown in Figure 12. As expected, diffusivities increase with an increase in the temperature. However, the curvature in the semi-log plot suggests that the temperature dependence of the diffusivity is not Arrhenius. The temperature dependence of the viscosity (η) of glass forming liquids is often 24 ACS Paragon Plus Environment

Page 24 of 37

Page 25 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


fit by the Vogel-Fulcher-Tammann-Hess (VFTH) equation or commonly known as VFT equation

 A  as follows:   0 exp   , where  is the viscosity, and  0 , A and T0 are the constants of  T  T0  the VFT equation.40 The equation is widely used for quantifying the viscosity of the glass forming liquids in the range of Tg to Tg  100 C . Recognizing the inverse relationship (i.e.  ~

1 ), the D

VFT equation can be written to capture the temperature dependence of the diffusivity:

 A   BT0  1 1 1 1  exp   exp   , which can also be written as  , where parameter 𝐵 D D0 D D0  T  T0   T  T0  was evaluated from the fit to the simulation data. Recently, such an expression was used to model the temperature dependence of the diffusivity of supercooled water.41 The behavior of the reciprocal of diffusion coefficient as a function of the inverse temperature (i.e. Arrhenius plot) is shown in Figure 13a for the selected component molecules of the AAA-1 system. The figure also shows VFT equation fits for each molecule. As seen, the VFT equation provides an excellent quantitative description of the temperature dependence of the diffusivity values; the resulting parameters are listed in Table 3. The values of the constants of the VFT equation for all four molecules are the same within the statistical uncertainties. Furthermore, the VFT equation fits to the diffusivity values of the same molecules in the SBR modified asphalt systems are shown in Figure 13b. Once again, VFT equation provides an



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

excellent description of the diffusivity values for the SBR-modified asphalt systems as well and the corresponding fitted parameters are shown in Table 3.

Figure 12. Diffusion coefficient for asphaltene-phenol (black circle), quinolinohopane (red diamond), PHPN (green square) and squalane (blue cross) as a function of inverse of T in AAA-1 system. Error bars are of the same size as the symbols.


Page 26 of 37

Page 27 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 13a.

Reciprocal of diffusion coefficient for asphaltene-phenol (black circle),

quinolinohopane (red diamond), PHPN (green square) and squalane (blue cross) as a function of inverse of T in AAA-1 system. Error bars are of the same size as the symbols. The dotted lines show the VFT fits.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 13b.

Page 28 of 37

Reciprocal of the diffusion coefficient for asphaltene-phenol (black circle),

quinolinohopane (red diamond), PHPN (green square) and squalane (blue cross) as a function of inverse of T in AAA-1-SBR system. Error bars are of the same size as the symbols. The dotted lines show the VFT fits.


Page 29 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3. Results from the VFT equation fit to the diffusion data for the neat and SBR modified asphalt systems. The average uncertainties in values of parameters D0, B and T0 are 2%, 5% and 5% respectively.

Component

log  1   D0  Neat Modified

B

Neat

T0 Modified

Neat

Modified

Asphaltene-phenol

3.62

3.34

4.9

6.6

260.8

247.5

Quinolinohopane

3.34

3.39

6.0

5.8

247.1

255.5

PHPN

3.39

3.67

5.8

4.4

246.7

270.1

Squalane

3.61

2.73

4.4

14.2

261.4

167.2

3.

Summary and Conclusions We have used MD simulations to study the volumetric, structural and dynamic properties

of neat asphalt model structures and the effect of addition of a polymeric additive, SBR on these properties. We carried out a detailed simulation investigation of the glass transition process of asphalt including quantitative comparison with experimental data. Furthermore, we quantified the temperature dependence of the diffusivity of the component molecules of asphalt. The volumetric properties studied here, especially, glass transition and CVTE, have a large impact on the mechanical properties as well as thermal stress management behavior of asphalt, properties that are vital for its application as the road surface material. This work demonstrates that molecular simulations can be used as part of a toolkit for designing asphalt systems for given weather conditions.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 37

Our simulations indicate that the volumetric properties of asphalt determined by using the twelve component model proposed by Li and Greenfield10 are in good agreement with the literature experimental data. Specifically, the glass transition temperature and the density values of the asphalt determined by simulations are in good quantitative agreement with experimental data after accounting for the effect of high cooling rates used in simulations. Simulations also allow for a detailed investigation of the temperature dependence of the molecular mobility in the asphalt system. Our results indicate that the temperature dependence of the molecule diffusivity follows VFT behavior that is characteristic of glass forming liquids. Simulation results show that addition of the SBR modifier to asphalt does not alter its Tg and the density, and causes only a small change in its CVTE. However, addition of SBR causes a large reduction in the mobility of the asphalt component molecules. Furthermore, aggregation of the asphaltene molecules is enhanced by the addition of the SBR modifier. These differences in the molecular dynamics as well as the molecular structure of the system are expected to impact its viscosity and viscoelasticity, properties that are of importance for the end use application of asphalt. Our current work is focused on the simulation investigation of the rheological properties of the system and the underlying molecular mechanisms, the effect of addition of SBR on the asphalt rheological properties is also being studied.

Acknowledgments The authors thank Sanjaya Senadheera and Tharanga Dissanayaka for many insightful discussions on the topic of asphalt physical properties. The authors also gratefully acknowledge support for this project from Southern Plains Transportation Center (SPTC) award SPTC14.1-64. Further 30 ACS Paragon Plus Environment

Page 31 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


support for the project was provided by matching funds from the TechMRT TxDOT research projects. The SPTC is a University Transportation Center sponsored by the Office of the Assistant Secretary for Research & Technology, U.S. Department of Transportation (USDOT).



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

References 1.

Lesueur, D., The Colloidal Structure of Bitumen: Consequences on the Rheology and on

the Mechanisms of Bitumen Modification. Adv. Colloid Interface Sci. 2009, 145 (1–2), 42-82. 2.

Claudy, P. M., Létoffé, J. M., Martin, D. and Planche, J. P., Thermal Behavior of Asphalt

Cements. Thermochim. Acta 1998, 324 (1–2), 203-213. 3.

Planche, J. P., Claudy, P. M., Létoffé, J. M. and Martin, D., Using Thermal Analysis

Methods to Better Understand Asphalt Rheology. Thermochim. Acta 1998, 324 (1–2), 223-227. 4.

Zhai, H., Salomon, D. and Trb, in Bituminous Binders 2005 (Transportation Research

Board Natl Research Council, Washington, 2005), pp. 44-51. 5.

Kamiya, S., Tasaka, S., Zhang, X., Dong, D. and Inagaki, N., Compatibilizer Role of

Styrene-Butadiene-Styrene Triblock Copolymer in Asphalt. Polym J 2001, 33 (3), 209-213. 6.

Qinqin, Z., Weiyu, F., Tiezhu, W. and Guozhi, N., presented at the Electric Technology

and Civil Engineering (ICETCE), 2011 International Conference on, 2011 (unpublished). 7.

Zhang, F. and Yu, J., The Research for High-Performance Sbr Compound Modified

Asphalt. Constr Build Mater 2010, 24 (3), 410-418. 8.

Masson, J. F., Polomark, G. and Collins, P., Glass Transitions and Amorphous Phases in

Sbs–Bitumen Blends. Thermochim. Acta 2005, 436 (1–2), 96-100. 9.

Kamiya, S., Tasaka, S., Zhang, X. M., Dong, D. W. and Inagaki, N., Compatibilizer Role

of Styrene-Butadiene-Styrene Triblock Copolymer in Asphalt. Polym. J. 2001, 33 (3), 209-213. 10.

Li, D. D. and Greenfield, M. L., Chemical Compositions of Improved Model Asphalt

Systems for Molecular Simulations. Fuel 2014, 115 (0), 347-356. 11.

Robertson, R. E., Petersen, J. C., Branthaver, J. F., Harnsberger, P. M., Dorrence, S. M.,

McKay, J. F., Turner, T. F., Pauli, A. T., Huang, S.-C., Huh, J.-D., Tauer, J. E., Thomas, K. P., 32 ACS Paragon Plus Environment

Page 32 of 37

Page 33 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Netzel, D. A., Miknis, F. P. and Williams, T., Fundamental Properties of Asphalts and Modified Asphalts, Volume I: Interpretive Report. Report No. FHWA-RD-99-212, 2001. 12.

Li, D. D. and Greenfield, M. L., Viscosity, Relaxation Time, and Dynamics within a

Model Asphalt of Larger Molecules. J. Chem. Phys. 2014, 140 (3), 034507. 13.

Zhang, L. and Greenfield, M. L., Analyzing Properties of Model Asphalts Using

Molecular Simulation. Energy Fuels 2007, 21 (3), 1712-1716. 14.

Zhang, L. and Greenfield, M. L., Effects of Polymer Modification on Properties and

Microstructure of Model Asphalt Systems. Energy Fuels 2008, 22 (5), 3363-3375. 15.

Hansen, J. S., Lemarchand, C. A., Nielsen, E., Dyre, J. C. and Schrøder, T., Four-

Component United-Atom Model of Bitumen. J. Chem. Phys. 2013, 138 (9), 094508. 16.

Wang, J., Wang, W., Kollman, P. A. and Case, D. A., Automatic Atom Type and Bond

Type Perception in Molecular Mechanical Calculations. J. Mol. Graphics Modell. 2006, 25 (2), 247-260. 17.

Wang, J., Wolf, R. M., Caldwell, J. W., Kollman, P. A. and Case, D. A., Development

and Testing of a General Amber Force Field. J. Comput. Chem. 2004, 25 (9), 1157-1174. 18.

Jakalian, A., Bush, B. L., Jack, D. B. and Bayly, C. I., Fast, Efficient Generation of High-

Quality Atomic Charges. Am1-Bcc Model: I. Method. J. Comput. Chem. 2000, 21 (2), 132-146. 19.

Jakalian, A., Jack, D. B. and Bayly, C. I., Fast, Efficient Generation of High-Quality

Atomic Charges. Am1-Bcc Model: Ii. Parameterization and Validation. J. Comput. Chem. 2002, 23 (16), 1623-1641. 20.

Hockney. R . W and W, E. J., in Computer Simulation Using Particles (Taylor & Francis

1988, 1988), pp. 267–304.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

21.

Page 34 of 37

Parrinello, M. and Rahman, A., Polymorphic Transitions in Single Crystals: A New

Molecular Dynamics Method. J. Appl. Phys. 1981, 52 (12), 7182-7190. 22.

Shinoda, W., Shiga, M. and Mikami, M., Rapid Estimation of Elastic Constants by

Molecular Dynamics Simulation under Constant Stress. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69 (13), 134103. 23.

Plimpton, S., Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput.

Phys. 1995, 117 (1), 1-19. 24.

Khare, R., Paulaitis, M. E. and Lustig, S. R., Generation of Glass Structures for

Molecular Simulations of Polymers Containing Large Monomer Units: Application to Polystyrene. Macromolecules 1993, 26 (26), 7203-7209. 25.

Lin, P.-H. and Khare, R., Molecular Simulation of Cross-Linked Epoxy and Epoxy−Poss

Nanocomposite. Macromolecules 2009, 42 (12), 4319-4327. 26.

Khare, K. S. and Khare, R., Directed Diffusion Approach for Preparing Atomistic Models

of Crosslinked Epoxy for Use in Molecular Simulations. Macromol. Theory Simul. 2012, 21 (5), 322-327. 27.

Usmani, A., Asphalt Science and Technology. ( CRC Press, New York, 1997).

28.

Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P., Numerical

Recipes: The Art of Scientific Computing, 3 ed. (Cambridge University Press, New York, 2007). 29.

Soldera, A. and Metatla, N., Glass Transition of Polymers: Atomistic Simulation Versus

Experiments. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2006, 74 (6), 061803. 30.

Soni, N. J., Lin, P.-H. and Khare, R., Effect of Cross-Linker Length on the Thermal and

Volumetric Properties of Cross-Linked Epoxy Networks: A Molecular Simulation Study. Polymer 2012, 53 (4), 1015-1019.


Page 35 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


31.

Ferry, J. D., Viscoelastic Properties of Polymers, 3 ed. (Wiley, New York, 1980).

32.

Petersen, J. C., Robertson, J. F., Branthaver, J. F., Harnsberger, P. M., Duvall, J. J., Kim,

S. S., Anderson, D. A., Christiansen, D. W. and Bahia, H. U., Binder Characterization and Evaluation Volume 1. 1994. 33.

Schmelzer, J. W. P. and Tropin, T. V., Dependence of the Width of the Glass Transition

Interval on Cooling and Heating Rates. J. Chem. Phys. 2013, 138 (3), 034507. 34.

Sirk, T. W., Khare, K. S., Karim, M., Lenhart, J. L., Andzelm, J. W., McKenna, G. B.

and Khare, R., High Strain Rate Mechanical Properties of a Cross-Linked Epoxy across the Glass Transition. Polymer 2013, 54 (26), 7048-7057. 35.

Anderson, D. A., Christiansen, D. W., Bahia, H. U., Dongre, R., Sharma, M. G., Antle, C.

E. and Button, J., Binder Characterization and Evaluation Volume 3: Physical Characterization. 1994. 36.

Lemarchand, C. A., Schrøder, T. B., Dyre, J. C. and Hansen, J. S., Cooee Bitumen. Ii.

Stability of Linear Asphaltene Nanoaggregates. J. Chem. Phys. 2014, 141 (14), 144308. 37.

Jorgensen, W. L., Maxwell, D. S. and Tirado-Rives, J., Development and Testing of the

Opls All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996, 118 (45), 11225-11236. 38.

Jorgensen, W. L. and McDonald, N. A., Development of an All-Atom Force Field for

Heterocycles. Properties of Liquid Pyridine and Diazenes. J. Mol. Struct.: THEOCHEM 1998, 424 (1–2), 145-155. 39.

McDonald, N. A. and Jorgensen, W. L., Development of an All-Atom Force Field for

Heterocycles. Properties of Liquid Pyrrole, Furan, Diazoles, and Oxazoles. J. Phys. Chem. B 1998, 102 (41), 8049-8059.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

40.

Larson, R. G., The Structure and Rhelology of Complex Fluids. (Oxford University Press,

New York, 1999). 41.

Chen, S.-H., Mallamace, F., Mou, C.-Y., Broccio, M., Corsaro, C., Faraone, A. and Liu,

L., The Violation of the Stokes–Einstein Relation in Supercooled Water. Proc. Natl. Acad. Sci. U. S. A. 2006, 103 (35), 12974-12978.


Page 36 of 37

Page 37 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


For Table of Contents (TOC) Use Only Glass Transition and Molecular Mobility in Styrene-Butadiene Rubber Modified Asphalt Fardin Khabaz and Rajesh Khare


Glass Transition and Molecular Mobility in StyreneâButadiene

Recommend Documents

Glass Transition and Molecular Mobility in StyreneâButadiene