Molecular dynamics simulation of temperature-affected microstructural characteristics of graphene/bitumen interfacial composites

HUANG Lixin, ZHOU Kun, HUANG Jun, YE Taizhi

School of Civil Engineering and Architecture, Guangxi University, Key Laboratory of Engineering Disaster Prevention and Structural Safety, Ministry of Education, Guangxi University

Abstract: The influence of temperature on the microstructure characteristics of graphene/bitumen interface was studied by molecular dynamics simulation method. The 4-component model of bitumen was selected for molecular dynamics simulation, and a reasonable bitumen glass transition temperature was obtained. Graphene was then added to build a graphene/asphalt composite composite model and molecular dynamics simulation. On this basis, based on the relative concentration of composite slices, the van der Waals gap and dense interval of the interface interval are defined. According to the relative concentration curve of the composite, the van der Waals gap thickness was calculated, and then the curve of the cumulative concentration of asphalt matrix and the first derivative was obtained by statistical method, and the dense interval thickness was calculated. Under various temperature conditions, the thickness of the van der Waals gap and the dense interval of the interface interval of graphene/asphalt composites was obtained by molecular dynamics simulation. The results show that temperature has little effect on the thickness of the dense interval and has a greater influence on the thickness of the van der Waals gap. And before the glass transition temperature, the Vander-Waals gap thickness fluctuates with the increase of temperature, and after the glass transition temperature, the Vander-Waals gap thickness gradually increases with the increase of temperature.

Keywords: graphene modified bitumen; molecular dynamics simulation; Van der Waals gap; dense interval; temperature influences;

Fund: National Natural Science Foundation of China, project number 11262002;

Bitumen is mainly a by-product from crude oil distillation and is a highly complex material containing 105~106 different molecules [1]. In recent years, nanomaterials have often been added to modify bitumen to obtain bitumen mixtures with better performance and more stability [2,3]. Bitumen nanocomposites are weak links at the interface of two materials, and the microstructure characteristics of the interface have a significant impact on the mechanical properties and failure strength of the composites [4]. Therefore, the interfacial microstructure characteristics are the focus of studying the mechanical properties of composites.

Literature [5,6,7] Scanning electron microscopy, X-ray and atomic force microscopy were used to directly observe the microscopic interface of asphalt composites to obtain the interface failure mechanism of composite materials. The test is time-consuming, laborious, and microscopic does not make it easy to understand the mechanism of action of bitumen and other components. Molecular Dynamics (MD) modeling is one of the effective ways to study these microscopic mechanisms. Xu et al. [8] used the MD method to predict the physical properties such as density and solubility parameters of bitumen, and analyzed the composition of the adhesion work, and concluded that van der Waals (vdW) force plays a key role in the adhesion performance of asphalt binders. Ramezani et al. [9] concluded from MD simulations that the vdW force makes a major contribution to the bonding performance in the carbon nanotube-modified asphalt interface. Therefore, the vdW force has a significant effect on the interfacial mechanical properties of the composite.

As a heat-sensitive material, changes in ambient temperature can leave the asphalt surface layer in an unsteady and inhomogeneous state [10]. Studying the mechanical properties of bitumen at variable temperatures is a current hot spot. Zhou et al. [11] measured the thermodynamic properties such as glass transition temperature of carbon nanotube-modified bitumen and graphene modified asphalt (GMA) through experiments, and then compared with the MD simulation results, the calculated temperature value was in good agreement with the test results. The simulation shows that the Young's modulus and shear modulus of the modified bitumen will gradually decrease with the increase of temperature. Liu et al. [12] analyzed the mechanical properties of static dynamic loading of asphalt mixture at different temperatures, and the results showed that the increase of temperature would reduce the mechanical properties of asphalt. Ouyang et al. [13] established a mathematical model to describe the compressive strength and Young's modulus of bitumen at different temperatures. However, this method has obvious limitations because the glass transition temperature cannot exist in the operating temperature range of the model. Zhu et al. [14] studied the effects of silica on the thermodynamic and mechanical properties of modified bitumen, and the results showed that the glass transition temperature of modified bitumen decreased with the increase of silica incorporation, and the mechanical properties gradually increased with the increase of filler. However, the microscopic mechanism of the effect of temperature on mechanical properties is not further explained in the literature.

In summary, the interfacial microstructural characteristics of asphalt composites are of great significance for the study of the mechanical properties of composites, while the influence of temperature on the interfacial microstructural characteristics is poorly studied. In this paper, a 4-component model of asphalt was selected, graphene was added to asphalt as a reinforcing material, and the software Material Studio 2017 (MS) was used for molecular dynamics simulation, first the glass transition temperature of bitumen was calculated and compared with the experimental value, and then the relative concentration curve of graphene/bitumen composite material was obtained by slicing method, the gap thickness of vdW was obtained, and finally the dense interval thickness was obtained by statistical method. The changes of vdW gap and dense interval at different temperatures were studied.

1 Molecular dynamics simulation theory

The basic method of MD simulation is to treat the simulated substance as a collective, and then solve the classical mechanical equations of motion of the collective system numerically, and count the structural characteristics and properties of the system [15]. Generally, there are several statistical systems, including microregular ensembles (NVE ensembles), regular ensembles (NVT ensembles), isothermal-isobaric ensembles (NPT ensembles), isenthalpy-isobaric ensembles (NPH ensembles), and generalized ensembles [16]. The NVT ensemble used in this paper refers to a thermodynamic system in which the number of particles N, volume V, and temperature T are the same, and the temperature in the unit cell is constant and the total energy changes. The internal system of the NPT ensemble has a constant pressure, but the volume changes, and is often used in simulations to compress the volume of the unit cell to achieve the density of the real material.

In the kinetic simulation of GMA, the Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) is used. This force field is used to describe bonding and non-bonding interactions and has been validated to fit experimental data very accurately for polymers, inorganic small molecules, and most organics [17]. The force field can be expressed as:

Ebonded=Eb+Eθ+Et+Eo+Eb,b′+Eb,θ+Eθ,θ′+Eb,t+Eθ,t+Eθ,t,θ′ (1)

Enon-bonded=EvdW+Ecoul (2)

Etotal=Ebonded+Enon-bonded (3)

Formula: Eb is the key expansion potential; Eθ is the bending potential of the bond angle; Et is the dihedral twist potential; EO is the potential energy of off-surface bending; The cross-coupling terms include the telescopic-flexile coupling potential Eb,b′, the telescopic-bending coupling potential Eb,θ, the bending-bending coupling potential Eθ,θ′, the telescopic-torsional coupling potential Eb,t, the bending-torsion coupling potential Eθ,t,θ′; Non-bonded interactions include vdW interaction potential EvdW and electrostatic interaction potential Ecoul.

Model building uses Amorphous Cell (AC), MD's Forcite module for operation and calculation. The vdW interaction adopts the atom-based summation method, and the electrostatic interaction uses the Ewald summation method, and the truncation radius is 1.55 nm. Except for the GMA model relaxation, Nose thermostats and Berendsen thermostats were used to maintain the target temperature and pressure, respectively. All simulations were performed at a time step of 1 fs at a pressure of 1 atmosphere.

2 Model building

2.1 Asphalt model establishment

The Strategic Highway Research Program (SHRP) of the United States divides bitumen into four components, including asphaltene, polar aromatic hydrocarbon, naphthenic aromatic hydrocarbon, and saturated hydrocarbon, according to solubility [18,19]. Derek et al. [20] proposed a 4-component model on this basis. This model is selected because it can well simulate asphalt in real conditions, and their molecular weight and molecular area are basically the same, which is easy to calculate. The individual molecular structure of the model is shown in Figure 1, and the relevant parameters of the model are shown in Table 1.

Figure 1 Molecular structure of asphalt 4-component model Download the original figure

Table 1 Asphalt 4-component model parameters EXPORTED TO EXCEL

Component	Name of the molecule	chemical formula	Molecular weight g/mol Molecular weight g/mol	Number of molecules, number of molecules
Asphaltene	Asphaltene-phenol	C42H54O	574.89	3
Asphaltene-pyrrole	C66H81N	888.38	2
Asphaltene-thiophene	C51H62S	707.11	3
Saturated hydrocarbons	Squalane	C30H62	422.82	4
Hophane	C35H62	482.88	4
naphthene Aromatic hydrocarbons	PHPN	C35H44	464.73	11
DOCHN	C30H46	406.69	13
polarity Aromatic hydrocarbons	Quinolinohopane	C40H59N	553.91	4
Thioisorenieratane	C40H60S	572.97	4
Trimethylbenzeneoxane	C29H50	414.71	5
Pyridinohopane	C36H57N	503.85	4
Benzobisbenzothiophene	C18H10S2	290.39	15

After the asphalt components are selected, the asphalt unit cells need to be established, and the specific steps are as follows.

(1) 12 molecules of bitumen were established in MS, and then geometric optimization and energy minimization were performed on each molecule separately.

(2) Construction of AC model of asphalt molecules. To prevent the molecular chains from entangled with each other, the above molecular distribution must be completely randomized, and the three-dimensional periodic model of asphalt must be constructed at an initial density of 0.1 g/cm3 in the AC module. The established bitumen initial unit cell size is 8.05 nm× 8.05 nm× 8.05 nm. Then the unit cell is optimized geometrically, with 10 000 iterations and the highest accuracy.

(3) Annealing operation of asphalt molecular AC model. Since the AC module adopts the Monte Carlo method, all molecules are completely randomly distributed, so the resulting model has extremely high energy, which is not conducive to subsequent calculations, and it is necessary to anneal. When annealing, the temperature range is 300 K~800 K, the accuracy is the highest, 50 iterations are performed, and the molecular optimization is carried out again during the iteration process. After completion, the lowest energy frame among the 50 configurations is selected for subsequent operations.

(4) After annealing operation, in order to make the asphalt system enter a more balanced state from the initial state at the target temperature and realize the pre-equilibrium of the system, the model performs NVT relaxation at 500 ps, and then performs NPT comprehensive relaxation at 500 ps. The relaxation process is shown in Figure 2. With increasing time, the unit cell size of the 3D periodic model of asphalt decreases, and the density gradually increases to the true density. At a temperature of 298 K and a pressure of 1 atmosphere (p=1 atm), the asphalt model after relaxation is shown in Figure 3. The relaxation size was 3.752 nm× 3.752 nm× 3.752 nm, and the density was stable at 0.99g/cm3, which was not much different from the 1.03 g/cm3 measured in SHRP test [19], and the results were satisfactory.

Figure 2 Density change under NPT relaxation Download the original figure

2.2 Establishment of graphene model

When building the graphene model, take the periodic graphene three-dimensional model that comes with MS. Since the unit cell size of the graphene sheet needs to be similar to the unit cell size of the asphalt model in the subsequent operation to build the composite interface model, it is necessary to establish a superunit cell on the basis of a single graphene. The graphene superunit cell plane size is 3.935 nm × 3.834 nm, as shown in Figure 4.

Figure 3 Asphalt unit cell model Download the original figure

Figure 4 Graphene superunit cell model Download the original figure

2.3 Establishment of composite material model

When the interface was built, in order to make the graphene remain within the unit cell range after the relaxation of the phylogeny, two graphene pieces were placed in the study to stabilize. In order to prevent the underlying graphene from affecting the asphalt and causing incorrect results, the coordinates of the underlying graphene need to be fixed. After the interface model is built, it is necessary to optimize the geometry of the interface construction model and relax the NVT system to make the energy pre-stable. Finally, the NPT series relaxation of 500 ps is carried out, Nose is selected for the thermostat, Souza-Martins is selected for the thermostat, and the pressure in the y direction is set to 1 atmosphere (p=1 atm), and the rest of the directions are all set to 0. The equilibrated unit cell is shown in Figure 5.

3 Results and analysis

3.1 Bitumen glass transition temperature

As an amorphous substance, there is a large amount of colloids in the dispersion of bitumen, resulting in the existence of a special temperature, that is, the glass transition temperature Tg. The glass transition temperature Tg has a great influence on the mechanical properties of asphalt. Below this temperature, bitumen is in a glass state, and its constitutive relationship is linear; Above this temperature, bitumen is in a highly elastic state, exhibiting viscoelastic properties. For a material such as bitumen, whose physical properties change with temperature, the glass transition temperature needs to be analyzed.

Figure 5 Graphene-modified asphalt model Download the original figure

In MS, a script was written to calculate the glass transition temperature Tg of the asphalt model, the temperature range was taken between 188.15 K~368.15 K, and the temperature interval was calculated at 20 K, and the corresponding asphalt density at 10 temperatures was simulated, and the results were shown in Table 2. According to the data in Table 2, the asphalt temperature ~ density scatter plot is plotted, as shown in Figure 6. As can be seen from Figure 6, the density of bitumen decreases with increasing temperature, and the slope of the temperature~density curve has a significantly variable interval. The glass transition temperature can be understood as the temperature at the intersection of two linear regression lines on the temperature~density curve. Therefore, first visually measure the data points and roughly estimate where the two regression lines intersect. Then, taking this position as the demarcation, the data points are divided into left and right parts, that is, divided into two intervals: 188 K~248 K and 268 K~368 K. The regression analysis of the two parts of the data points was carried out by the least squares method respectively, and two regression straight line equations were obtained, namely:

D=-9.5×10-5T+1.047 (188≤T≤248) (4)

D=-4.7×10-4T+1.146 (268≤T≤368) (5)

Where: T represents temperature; D represents density.

TABLE 2 ASPHALT DENSITY AT DIFFERENT TEMPERATURES EXPORTED TO EXCEL

Temperature/K	188.15	208.15	228.15	248.15	268.15	288.15	308.15	328.15	348.15	368.15
Density/(g·cm-3)	1.028	1.028	1.027	1.022	1.018	1.011	1.002	0.993	0.984	0.970

Figure 6 Bitumen temperature ~ density scatter distribution Download the original figure

Solving the equation together yields a point of (263.76, 1.021 9), so the bitumen glass transition temperature Tg is 263.76 K.

The comparison of bitumen glass transition temperature and literature results obtained in this paper is listed in Table 3. It can be seen that the measurement methods are different, and the Tg obtained by each literature varies greatly. However, since Tg belongs to a temperature range, the result of Tg=263.76 K obtained in this paper is reasonable, which proves that the adopted model can be used for further simulation calculation.

Table 3 Comparison of asphalt glass transition temperature results Export to EXCEL

Results of this article	Literature results
method	Tg/K	method	Tg/K
Molecular dynamics	263.76	Test[21]	248.55
Molecular Dynamics[22]	298.15
Test[23]	223～303
Molecular dynamics[11]	250
Molecular dynamics[14]	278.66

3.2 Van der Waals gap and dense interval

The vdW gap is a vacuum band between graphene and asphalt matrix materials created by the combined action of vdW and electrostatic forces. With the increase of the operating distance, the vdW force will generate an attraction potential, which acts on the asphalt matrix, resulting in an increase in density in the action area. This area of action is the dense interval. Since the system used is microscopic, it is more accurate to discuss the interfacial interval properties of composites using relative concentrations. First divide the unit cells into N boxes in equal terms, then the relative concentration expression is:

cR=cic¯ (0<i≤N)         (6)cR=cic¯ (0<i≤Ν)         (6)

Formula: cR is Relative Concentration; ci is the atomic concentration in the ith box; c ̄c ̄ is the average concentration of atoms within the unit cell.

CI and C ̄c ̄ are calculated by the following equation:

ci=niVi (0<i≤N) (7)ci=niVi (0<i≤Ν) (7)

c ̄=ntotalVtotal (8)c ̄=ntotalVtotal (8)

where ni is the total number of atoms in the i-th box; Vi is the ith box volume; ntotal is the total number of atoms in the unit cell; Vtotal is the unit cell volume.

The molecular dynamics model of graphene/bitumen composites at a temperature of 208.15 K at one atmosphere (p=101 325 Pa) is used as an example to illustrate the relative concentration calculation. For the coordinate system shown in Figure 7, the model geometry is 3.857 nm× 4.539 nm× 3.766 nm. Divide the model equally into 300 boxes along the y-axis, each with a thickness of 0.015 13 nm. As the y-axis coordinates increase, the boxes are numbered from smallest to largest. According to Equation (6) ~ Equation (8), the relative concentration of each box atom is calculated, and then the relative concentration curve of the composite material is obtained, as shown in Figure 8. In Figure 8, the two peaks of the curve before point A (yA=0.624 nm) are graphene sheets, and the asphalt concentration increases from point B (yB=0.749 nm), and the distance between points A and B is the gap thickness of vdW. Due to the great attraction of graphene to the matrix, the concentration of bitumen increases sharply, and the third peak C point (yC=0.848 nm) appears, and then the fluctuation changes tend to be stable. Point D, where the smooth start, is the end point of the dense interval.

Figure 7 Equal portions Download the original image

In order to determine the thickness of the dense interval, the coordinates of the D point at the end of the dense interval are required, so the change of asphalt matrix concentration with the y coordinate is analyzed separately. Select the matrix portion of the composite concentration curve in Figure 8 for magnification, as shown in Figure 9(a). The amplitude of the obtained magnification curve is too large, and the visual method is not conducive to accurate processing of the dense interval. In order to reduce the fluctuation, this study modified the asphalt matrix concentration curve with reference to the statistical method [24]. First, the average cumulative concentration treatment is carried out, and the calculation formula is:

Figure 8 Composite concentration curve Download the original figure

ca(s)=1N1∑i=bscica(s)=1Ν1∑i=bsci(b<s) (9)

Formula: ci is the concentration of the i-th box; b is the box number at point B; s is the box number at a point outside point B; N1 is the total number of boxes in the statistical sample [b,s], which indicates the upper limit of the statistical sample.

Figure 9 Relative concentration and cumulative concentration of bitumen Download the original figure

After treatment, the cumulative concentration curve is obtained, as shown in Figure 9(b). It can be observed that the cumulative concentration curve of asphalt in Figure 9(b) still fluctuates significantly, and it is still not convenient to determine the coordinates of point D. Therefore, on the basis of the cumulative concentration, the introduction of the standard deviation function can better observe the change of its curve. Accumulated Standard Deviation (ASD) is defined as:

ASD(s)=1N1∑i=bs(ci−c¯ave)2−−−−−−−−−−−−−−−√         (10)ASD(s)=1Ν1∑i=bs(ci-c¯ave)2         (10)

where c ̄avec ̄ave is the average of the matrix concentration, as shown in Equation (11).

c¯ave=∑i=b300ci300−b+1         (11)c¯ave=∑i=b300ci300-b+1         (11)

Find the first derivative of the ASD curve, i.e. d(ASD)dyd(ASD)dy. Figure 10 is a graph of ASD and its first derivatives. As can be seen from Figure 10, the ASD curve of asphalt matrix first decreases rapidly and then tends to plateau. However, it is not easy to see the position of the point that begins to flatten through the ASD curve, and on the d(ASD)dy(ASD)dy curve, the point with the slope of the curve is 0 as the end point D of the dense interval.

Figure 10 Cumulative standard deviation and its first derivative Download the original figure

As can be seen from Figure 7, the gap thickness tvdW and the dense interval thickness tDense are respectively:

tvdW=yB−yAtDense=yD−yB (12)tvdW=yB-yAtDense=yD-yB (12)

Where: yA, yB, and yD are the ordinate values of points A, B, and D, respectively.

The same method was used to analyze the vdW gap and dense interval thickness of nine different temperatures between 208.15 K~328.15 K, and the results were shown in Table 4. As can be seen from Table 4, tDense stabilized around 0.6 nm at nine different temperatures. When T=208.15 K and T=238.15 K, that is, the temperature is low, the gap thickness of vdW basically does not change, because the intermolecular structure and spatial position of bitumen with lower temperature are in an extremely stable state. When the temperature T slowly increases to the glass transition temperature of 263.76 K, tvdW will gradually decrease, and reach a minimum value of 0.090 nm at the glass transition temperature (T=263.76 K). Then, tvdW gradually increases with the increase of temperature, and when the temperature T=328.15 K, tvdW reaches a maximum value of 0.198 nm. In summary, the temperature change has little effect on the dense interval, but has a greater effect on the vdW gap thickness, and the vdW gap thickness is minimized at the glass transition temperature Tg. After the temperature is higher than the glass transition temperature Tg, the gap thickness of vdW increases with the increase of temperature.

TABLE 4 INTERFACE PARAMETERS AT DIFFERENT TEMPERATURES EXPORT TO EXCEL

Temperature/K	yA/nm	yB/nm	yD/nm	tvdW/nm	tDense/nm
208.15	0.624	0.749	1.341	0.125	0.592
238.15	0.606	0.732	1.334	0.126	0.602
253.15	0.579	0.687	1.317	0.108	0.575
263.76	0.579	0.669	1.361	0.090	0.692
268.15	0.580	0.696	1.343	0.116	0.647
283.15	0.580	0.733	1.335	0.153	0.602
298.15	0.580	0.741	1.298	0.161	0.557
313.15	0.580	0.732	1.370	0.152	0.638
328.15	0.553	0.751	1.345	0.198	0.593

4 Conclusion

(1) The 4-component model of asphalt was selected and the molecular dynamics simulation was carried out using Material Studio 2017 software, and the density of bitumen at 298 K and 1 atmosphere was 0.99 g/cm3, which was consistent with the experimental value of 1.03 g/cm3 in the literature.

(2) In the temperature range of 188.15 K~368.15 K, molecular dynamics simulation calculations were carried out at 20 K temperature intervals to obtain the corresponding asphalt density at 10 temperatures. Then, the linear regression method was used to obtain the glass transition temperature of asphalt of 263.76 K. Comparison with the results of the literature shows that the glass transition temperature is within a reasonable range.

(3) Graphene was added to the asphalt model, and the composite material model was jointly constructed and molecular dynamics simulation was carried out, and the results showed that there was not only a van der Waals gap in the interface interval, but also a dense interval in the asphalt matrix due to the action of van der Waals force and electrostatic force.

(4) Under various temperature conditions, the thickness of the interfacial interval of graphene/asphalt composites was calculated by molecular dynamics simulation. The results show that temperature has little effect on the thickness of the dense interval and greater influence on the thickness of the van der Waals gap. Before the glass transition temperature, the Vander-Waals gap thickness fluctuation decreases with the increase of temperature; After the glass transition temperature, the van der Waals gap thickness increases roughly gradually as the temperature increases. And when the temperature before the glass transition temperature is low (T=208.15 K and T=238.15 K), the gap thickness of van der Waals is basically unchanged, the interface interval is in a stable state, and the thickness of the interface interval basically does not change. However, after the glass transition temperature, the temperature increase will increase the van der Waals gap thickness in the interface interval significantly, resulting in an increase in the thickness of the interface interval. Therefore, in the study of the mechanical properties of graphene/asphalt composites, the influence of temperature needs to be considered.

bibliography

[1] Wiehe I A,Liang K S.Asphaltenes,resins,and other petroleum macromolecules [J]. Fluid Phase Equilibria,1996,117(1996):201-210.

[2] ZHANG Qisen, XIAO Xin. Review of constitutive model and microstructure of asphalt and asphalt mixture[J].China Journal of Highway and Transport,2016,29(5):26-33.)

[3] Du H,Pang S D.Enhancement of barrier properties of cement mortar with graphene nanoplatelet [J]. Cement and Concrete Research,2015,76(2015):10-19.

[4] Zhu X Y,Yang Z X,et al. Modulus prediction of asphalt concrete with imperfect bonding between aggregate-asphalt mastic [J]. Composites Part B:Engineering,2011,42(6):1404-1411.

[5] Poulikakos L D,Partl M N.Investigation of porous asphalt microstructure using optical and electron microscopy [J]. J Microsc,2010,240(2):145-154.

[6] Bhasin A,Izadi A,BEDGAKER S.Three dimensional distribution of the mastic in asphalt composites [J]. Construction and Building Materials,2011,25(10):4079-4087.

[7] Dong Z,Liu Z,et al. Nanostructure characterization of asphalt-aggregate interface through molecular dynamics simulation and atomic force microscopy [J]. Fuel,2017,189:155-163.

[8] Xu G,Wang H.Molecular dynamics study of interfacial mechanical behavior between asphalt binder and mineral aggregate [J]. Construction and Building Materials,2016,121:246-254.

[9] Ramezani M G,Rickgauer J.Understanding the adhesion properties of carbon nanotube,asphalt binder,and mineral aggregates at the nanoscale:a molecular dynamics study [J]. Petroleum Science and Technology,2019,38(1):28-35.

[10] ZHENG Jianlong, QIAN Guoping, YING Ronghua. Experimental determination of thermal viscoelastic constitutive relationship of asphalt mixture and its mechanical application[J].Engineering Mechanics,2008,25(1):34-41.)

[11] Zhou X,Zhang X,et al. Evaluation of thermo-mechanical properties of graphene/carbon-nanotubes modified asphalt with molecular simulation [J]. Molecular Simulation,2017,43(4):312-319.

[12] Yongliang L,Xiangming K,et al. Static and Dynamic Mechanical Properties of Cement-Asphalt Composites [J]. Journal of Materials in Civil Engineering,2013,25(10):1489-1497.

[13] Ouyang J,Zhao J,Tan Y.Modeling Mechanical Properties of Cement Asphalt Emulsion Mortar with Different Asphalt to Cement Ratios and Temperatures [J]. Journal of Materials in Civil Engineering,2018,30(10):1-10.

[14] Zhu X,Du Z,et al. Effect of filler on thermodynamic and mechanical behaviour of asphalt mastic:a MD simulation study [J]. International Journal of Pavement Engineering,2018,21(10):1248-1262.

[15] Yan Liuming, Zhu Suhua. Theory and practice of molecular dynamics simulation[M].Beijing:Science Press,2013:1-6.)

[16] Bandyopadhyay A,Valavala P K,et al. Molecular modeling of crosslinked epoxy polymers:The effect of crosslink density on thermomechanical properties [J]. Polymer,2011,52(11):2445-2452.

[17] Sun H.COMPASS:An ab Initio Force-Field Optimized for Condensed-Phase Applications Overview with Details on Alkane and Benzene Compounds [J]. The Journal of Physical Chemistry B,1998,102:7338-7364.

[18] Robertson Re B J.Fundamental Properties of Asphalts and Modified Asphalts,Volume 1 Interpretive Report [M]. Federal Highway Administration.2001.

[19] Jones D R.SHRP Materials Reference Libary:Asphalt Cements:A Concise Data Compilation [M]//Council Strategic Highway Research Program National Research.National Research Council,Washington,DC.1993.

[20] Li D D,Greenfield M L.Chemical compositions of improved model asphalt systems for molecular simulations [J]. Fuel,2014,115(1):347-356.

[21] Broome D C.Asphalt:Science and Technology [J]. Nature,1964,202(4934):739-740.

[22] Zhang L,Greenfield M L.Analyzing Properties of Model Asphalts Using Molecular Simulation [J]. Energy & Fuels,2007,21(3):1712-1716.

[23] Tabatabaee H A,Velasquez R,Bahia H U.Predicting low temperature physical hardening in asphalt binders [J]. Construction and Building Materials,2012,34:162-169.

[24] Alizadeh Sahraei A,Mokarizadeh A H,et al. Insights into interphase thickness characterization for graphene/epoxy nanocomposites:a molecular dynamics simulation [J]. Phys Chem Chem Phys,2019,21(36):19890-19903.

Disclaimer: We respect originality and focus on sharing. Some of the content comes from the Internet, the copyright belongs to the original author, only for learning reference, prohibited for commercial use, such as inadvertently infringing the intellectual property rights of which media, company, enterprise or individual, etc., please contact to delete, and this headline push content only represents the author's views, and the headline operator has nothing to do with it, the authenticity of the content please readers identify by themselves, this headline number does not assume any responsibility.