Evaluation of the compatibility between rubber and asphalt based on molecular dynamics simulation

Abstract

Using of rubber asphalt can both promote the recycling of waste tires and improve the performance of asphalt pavement. However, the segregation of rubber asphalt caused by the poor storage stability always appears during its application. Storage stability of asphalt and rubber is related to the compatibility and also influenced by rubber content. In this study, molecular models of different rubbers and chemical fractions of asphalt were built to perform the molecular dynamics simulation. The solubility parameter and binding energy between rubber and asphalt were obtained to evaluate the compatibility between rubber and asphalt as well as the influence of rubber content on compatibility. Results show that all three kinds of rubber are commendably compatible with asphalt, where the compatibility between asphalt and cis-polybutadiene rubber (BR) is the best, followed by styrene-butadiene rubber (SBR), and natural rubber (NR) is the worst. The optimum rubber contents for BR asphalt, SBR asphalt, and NR asphalt were determined as 15%, 15%, and 20%, respectively. In addition, the upper limits of rubber contents were found as between 25% and 30%, between 20% and 25%, and between 25% and 30%, respectively.

Keywords

rubber asphalt / compatibility / rubber content / molecular dynamics simulation

Introduction

Recycled-polymer modified asphalt has been extensively used in road construction, especially the recycled tire scrap rubber-modified asphalt [¹–⁵]. The rubber asphalt can improve properties and performance of asphalt mixtures, such as increasing skid resistance and durability, reducing rutting, mitigating the fatigue cracking, etc. [⁶–⁸]. However, the main problem during the application of rubber asphalt is poor storage stability which finally affects the service performance of the pavement [⁹,¹⁰]. Storage stability of rubber asphalt is mainly affected by processing technology, the type and the size of crumb rubber, density difference between rubber and asphalt phases, dynamic viscosity of asphalt matrix, etc. [¹¹–¹⁴]. In addition, storage stability is also related to the compatibility and interaction between asphalt and polymer [¹⁵]. Therefore, improving the compatibility between polymer and asphalt is an effective method to solve the poor storage stability of polymer modified asphalt. However, the source of rubber in rubber asphalt is complex and the compatibility and interaction between rubber and asphalt is influenced by properties of rubber and asphalt, temperature, rubber content, etc. [¹⁶,¹⁷]. It is difficult to investigate the mechanism of the compatibility and interaction between rubber and asphalt by macroscopic experiments.

To explore the mechanism of the interaction between matters from the source, molecular dynamics simulation method has been gradually applied to the research of materials [¹⁸,¹⁹], especially the research related to asphalt have sprung up [²⁰–²⁵]. Simulation for the compatibility of polymers is also prevalent, but the research focuses on the compatibility between polymers [²⁶–²⁸]. Overall, the simulation researches related to rubber and asphalt mainly focuses on asphalt, asphalt/aggregate interface, and properties of rubber [²⁹–³²], but the simulation research on rubber asphalt is rare [³³,³⁴].

The compatibility between rubber and asphalt is mainly achieved through the technological compatibility [³⁵]. The good compatibility of rubber asphalt means uniform distribution rather than complete dissolution. At this time, rubber powders are dispersed evenly in asphalt and rubber asphalt is in a state of micro-insolubilization but macro-stability [³⁶]. Currently, the compatibility between rubber and asphalt is mainly evaluated by tests instruments, such as scanning electronic microscope (SEM), fluorescence microscope [³⁷–⁴⁰]. However, these methods cannot evaluate the compatibility between rubber and asphalt quantitatively.

In this paper, three kinds of rubber (cis-polybutadiene rubber, styrene-butadiene rubber, and natural rubber) and asphalt binder were selected to build their molecular dynamics model based on Materials Studio software, where the modeling parameters of asphalt and rubber refer to existing research. Solubility parameter was used to evaluate the compatibility between three kinds of rubber and asphalt. Binding energy was used to analyze the influence of rubber content on compatibility.

Molecular modeling and evaluation indexes

Molecular modeling of asphalt binder

Asphalt binder is a complex mixture composited mainly by hydrocarbons and nonmetallic derivatives with different molecular weights [⁴¹–⁴³]. Therefore, it is very difficult to completely clarify the types and contents of asphalt fractions. Asphalt binder can be divided into different fractions by various separation technologies, where each fraction has similar polarities and molecular characteristics. Three-component analysis method and four-component analysis method are commonly used in experiments [⁴⁴,⁴⁵].

In the study of dynamics simulation, nuclear magnetic resonance (NMR) was applied by Storm and coworkers to asphalt fractions separated by the common alkane precipitation method. The conclusion was commonly used to select three different types of molecules as representative asphalt compositions, namely asphaltene, naphthene aromatic and saturate [⁴⁴,⁴⁵], which was the basis to build the molecular structure of asphalt binder. As shown in Fig. 1, the structure proposed by Artok et al. [⁴⁶] was adopted to present the molecular structure of asphaltene. Naphthene aromatic and saturate were represented by 1,7-dimethylnaphthalene (C₁₂H₂₂) and docosane (C₂₂H₄₆), respectively [⁴⁷,⁴⁸]. Many simulation researches were conducted based on these molecular structures of asphalt fractions and its reliability was also verified [²⁰,⁴⁹].

Molecular structure of asphalt binder could be built based on Materials Studio software 8.0 after the composition and structure of asphalt binder were determined. The molecular structures of asphaltene, naphthene aromatic and saturate were sketched in 3D Atomistic. Then the amorphous cell, a representative volume element of asphalt binder, was construct and the cell was under the conditions of periodic boundary, where the lattice type of amorphous cell was set to cubic, the molecular number and mass fraction for asphalt fractions were shown in Table 1 [⁵⁰], the temperatures were set to 298K or 453K and the density of asphalt binder was set to 0.873 g/cm³ [⁵¹]. The molecular structure of asphalt binder could be built based on these parameters, as shown in Fig. 2.

Molecular modeling of rubber

Rubber powder derived from waste tires has complex compositions, including carbon black and other additives besides rubber. The rubber compositions in waste tire mainly include cis-polybutadiene rubber (BR) styrene-butadiene rubber (SBR) and natural rubber (NR). In this study, these three compositions were used to represent rubber powder and to build an ideal structure of rubber asphalt, where the densities of NR, BR, and SBR are set to 0.913, 0.920, 0.932 g/cm³ [⁵²].

NR and BR are homopolymers polymerized by monomers. The repeating units for polymerization are shown in Fig. 3. The molecular chain structures can be built by specifying numbers of repeating units. The structures of NR and BR molecular chains are shown as examples in Fig. 4. The accurate molecular chains will be constructed according to the polymerization degrees, which will be shown in Sections 3.1 and 4.1.

SBR is a random copolymer formed by polymerization of styrene and butadiene monomer. Most of SBR is made by low-temperature emulsion polymerization, and the content of styrene in emulsion polymerized SBR accounts for 23.5%. The content of butadiene is shown in Table 2 [⁵²].

The repeating units of SBR monomer is shown in Fig. 5. The structure of SBR molecular chain is shown as example in Fig. 6 according to the proportion and the different structure contents (Table 2) of styrene and butadiene. The accurate molecular chain of SBR will be constructed as shown in Sections 3.1 and 4.1.

Molecular dynamics simulation and evaluation indexes

Molecular dynamics model of rubber asphalt can be built according to Sections 2.1 and 2.2, which will be shown in Sections 3.1 and 4.1 for different evaluation objectives. The evaluation indexes of the compatibility between rubber and asphalt were proposed in this section.

Solubility parameter

There are many methods can be used to evaluate the compatibility between asphalt and rubber, such as morphological method, glass transition temperature method, infrared method, electron microscopy method, cloud point method, reversed phase chromatography method, measurements of interaction parameter [³⁷,⁴⁰]. Solubility parameters is also a very important index to estimate of the degree of interaction between liquid molecules, and can be a good indication of solubility, particularly used to evaluate the compatibility between polymers [⁵³,⁵⁴]. Solubility parameter (d) proposed by Hildebrand first [⁵⁵], which can be calculated by square root of cohesive energy density. The formula for calculation is shown as follows.

(1)\delta =\sqrt{CED}=\sqrt{{\displaystyle \frac{\mathrm{\Delta }E}{V}}},

where \mathrm{\Delta }E is cohesive energy, V is volume, CED is cohesive energy density.

Solubility parameter represents the magnitude of intermolecular force of materials. According to the principle “like dissolves like”, the difference of solubility parameter will be smaller with the polarity of materials being closer, namely their compatibility will be better. It is generally accepted by that two polymer materials will tend to be mutually miscible on the condition of |Dd|<1.3–2.1 (J·cm⁻³)^1/2 if there are no strong polar groups or hydrogen bonds between the molecules [⁵⁶,⁵⁷]. Therefore, the solubility parameters of modifier and matrix asphalt can be used to evaluate their compatibility.

Binding energy

Binding energy is an important parameter to measure the interaction energy between components for a mixed system [⁵⁸]. It is can be also used to predict mixing capacity and compatibility of two materials in a mixed system. The binding energy is defined as the negative value of intermolecular interaction energy. The calculation formula of binding energy is shown as follows:

(2)E_{\mathrm{binding}}=-E_{\mathrm{inter}}=-\left(E_{\mathrm{total}}-E_{\mathrm{A}}-E_{\mathrm{B}}\right),

where E_{\mathrm{total}} is the total energy of the mixed system under equilibrium state, E_{\mathrm{A}} and E_{\mathrm{B}} are the total energy of two material under their respective equilibrium state.

The interaction will be stronger with the binding energy being larger, which indicates that the thermodynamic stability is higher, namely the compatibility between materials in the mixing system is better.

Evaluation of compatibility between rubber and asphalt

Molecular modeling for solubility parameter analysis

The molecular structure of asphalt binder for analyzing solubility parameters was the same as 2.1. The molecular structures of NR, BR, and SBR have been rebuilt. The minimum polymerization degrees of NB and BR were set to 20 and 15, respectively, on the basis of repeating unit structure of rubber [⁵⁹,⁶⁰], and the number of molecular chains were all set to 5. According to the mass fraction of SBR in Table 2, the molecular number ratio of styrene to butadiene was about 16:100, and the total molecular number of SBR was 116. Thus, the molecular number of styrene, trans-1,4-butadiene, cis-1,4-butadiene and 1,2- butadiene were 16, 76, 8, and 16, respectively. The number of molecular chain of SBR was set to 2.

The molecular structures of asphalt, NR, BR, and SBR for solubility parameter analysis are shown in Fig. 7.

The initial molecular conformation of asphalt binder and rubber built by construction did not represent the real rubber asphalt for its structure did not reach the lowest energy state. Therefore, geometry optimization with 10000 iterations in the Forcite-calculation module was conducted to the initial configuration in order to achieve energy minimization. The dynamic simulations were conducted with the optimized structures at the temperatures of 453K and 298K to simulate the compatibility between rubber and asphalt, where 453K represents the actual preparation temperature of rubber asphalt and 298K represents room temperature. NVT simulation of 500ps and NPT simulation of 1000ps were selected for dynamic process, and the pressure was set to 0.000101 GPa. To initiate the simulations, the lattice type of amorphous cell was set to cubic. COMPASS (Condensed-Phase Optimized Molecular Potentials for Atomistic Simulation Studies) force field was used because COMPASS is an optimized ab initio forcefield suitable for predicting the properties of common organic molecules, inorganic molecules and polymers under a wide range of pressures and temperatures [⁶¹]. The methods of temperature control and pressure control were Nose and Berendsen, respectively. Electrostatic forces and Van der Wals forces were calculated by Ewald and Atom based method, respectively. The cutoff distance of asphalt binder, NR, BR and SBR was set to 15.5 Å, 9.5 Å, 9.5 Å, and 12.5 Å, respectively.

Results analysis of the compatibility between rubber and asphalt

After the dynamic calculation, the stable configuration of last part of output trajectory file was selected as the basis to simulate the cohesive energy density. The solubility parameters can also be simulated and obtained directly by the Materials Studio. Thus, the solubility parameters between rubber and asphalt as well as their differences at 453K are shown in Table 3.

As can be seen in Table 3 that the differences of solubility parameters between three kinds of rubber and asphalt are all less than 1.3–2.1(J·cm⁻³)^1/2 at 453K, which shows that these three kinds of rubber are compatible with asphalt. Compared the differences of solubility parameters between rubber and asphalt, it can be seen that the difference between BR and asphalt is the smallest, followed by SBR, and NR is the greatest, which shows that the compatibility of BR and asphalt is the best, followed by SBR, and NR is the poorest relatively.

Repeating the simulation process above, it can be obtained that the solubility parameter of asphalt at 298K is 18.236 (J·cm⁻³)^1/2, which is consistent with the results of other researches [⁶²,⁶³]. The solubility parameter of NR obtained by molecular structure based on the minimum polymerization degree is 16.574 (J·cm⁻³)^1/2, which is similar to Ref. [⁶⁴]. The solubility parameters of BR and SBR are 18.024 and 17.210 (J·cm⁻³)^1/2, respectively. The solubility parameters between rubber and asphalt as well as their differences at 298K are shown in Table 4.

As can be seen in Table 4, the values of δ differ by less than 1.3–2.1 (J·cm⁻³)^1/2, indicating that the compatibility between rubber and asphalt is still good at 298K. The conclusion can be obtained that rubber asphalt can form a uniform system from preparation temperature to room temperature. More detail research about the influence of different temperatures on the compatibility between rubber and asphalt will be conducted afterwards.

As can be seen from Tables 3 and 4, the differences of solubility parameters between rubber and asphalt at 453K are less than that at 298K. It can be explained that the thermal motion of molecules is obviously affected by temperature. The thermal motion of molecules becomes more intense and the intermolecular force decreases with the increasing of temperature, which leads to lower cohesive energy and excellent compatibility of rubber and asphalt. Therefore, the compatibility between rubber and asphalt at high temperature is better than room temperature.

Influence of rubber content on compatibility

The compatibility between rubber and asphalt is related to many external factors besides its own factors. The solubility parameter is obtained based on the respective molecular structure of materials, which can evaluate the compatibility of materials itself and can be used to initially judge the compatibility of materials. Therefore, the solubility parameters cannot fully characterize the compatibility of rubber asphalt in the actual preparation as the content of rubber has a great influence on the compatibility. In this section, the influence of rubber content on the compatibility between rubber and asphalt was discussed.

Molecular modeling for binding energy analysis

Rubber contents were set to 5%, 10%, 15%, 20%, 25%, and 30%, respectively (the weight proportions of rubber to asphalt binder). The molecular number of rubber was calculated on the basis of asphalt binder weight and rubber contents. The asphalt molecular structure was just needed to simulate once for the fixed asphalt binder weight. Rubber asphalt molecular structure, rubber molecular structure and asphalt molecular structure were built to calculate the binding energy of rubber and asphalt under a certain rubber content. Taking the three kinds of rubber asphalt with rubber content of 10% as the example, the molecular structures of rubber and rubber asphalt are shown in Fig. 8.

Geometry optimization with 10000 iterations in the Forcite-calculation module was conducted to the initial configuration in order to achieve energy minimization. The dynamic simulations were carried out for these optimized structures at the temperature of 453K. The simulation parameters and process were the same as Section 3.1.

Influence of rubber contents on the compatibility between rubber and asphalt

The energy of each structure was extracted after the completion of dynamic simulation. The binding energy between rubber and asphalt under different rubber contents was calculated by Eq. (2). The binging energy of NR asphalt, BR asphalt, and SBR asphalt are shown in Tables 5, 6, and 7.

As can be seen from Tables 5, 6, and 7, the variation of energy for mixing system is directly related to the content of rubber. With the increasing of rubber content, the energy of rubber asphalt and rubber itself shows an increasing trend, but the binding energy between rubber and asphalt does not show a simple growth trend. The variation of binding energy between rubber and asphalt for three kinds of rubber asphalt with rubber content is shown in Fig. 9.

As can be seen from Fig. 9, binding energy between rubber and asphalt for three kinds of rubber asphalt shows a similar variation trend, namely binding energy increases first but decreases afterwards and finally turns into negative value with the increasing of rubber content, indicating that the compatibility between rubber and asphalt presents the same trend. The negative binding energy indicates that the compatibility between materials is poor, and the phase separation between materials occurs.

It can be seen that binding energy is positive and it increases with the increasing of rubber content when the rubber content is less than 15%. It indicates that three kinds of rubber and asphalt can be compatible well respectively and can form stable mixing system when rubber content is less than 15%. This is because rubber adsorbs light components of asphalt, and there are still adequate light components in asphalt dispersed phase to disperse the rubber and form homogeneous dispersed phase under this rubber content. Within this rubber content, binding energy of BR and asphalt is the largest, followed by BR, and NR is the smallest. The reason is that the compatibility between BR, SBR, NR and asphalt gets worse gradually.

The binding energy between rubber and asphalt reaches the maximum value when the rubber content is 15% for BR asphalt and SBR asphalt, which means the compatibility between rubber and asphalt is the best under this content. Under this condition, the adsorption of rubber to light components in asphalt is the strongest, and the content of light components in asphalt can still meet the requirement of rubber adsorption, but the mixing system reaches the saturation state. The binding energy between rubber and asphalt decreases sharply with the increasing of rubber content when the rubber content is greater than 15%. This is because that the content of light components in asphalt cannot meet the adsorption requirement of rubber, and rubber begins to compete for light components adsorbed in the near asphaltene range, which disrupts the optimal compatibility state of rubber asphalt and causes bad compatibility. Along with the further increase of rubber content, asphaltene is gradually separated from light components and clusters together, meanwhile, rubber clusters together as well. The binding energy starts to be negative when the rubber content exceeds limitation, then adsorption between rubber and asphalt disappears and the attractive force is replaced by the repulsive force. This indicates that the mixing system has become an inhomogeneous system with no stability, and the phase separation occurs. Therefore, the optimum rubber contents of BR asphalt and SBR asphalt are 15%. The upper limit rubber content of BR asphalt is between 25% and 30%, and the upper limit rubber content of SBR asphalt is between 20% and 25%.

As for NB asphalt, the optimum rubber content is 20% and the upper limit rubber content is between 25% and 30%.

Conclusions

1) Molecular dynamics model of rubber asphalt was built based on Materials Studio software. Solubility parameter and binding energy were used to evaluate the compatibility between rubber and asphalt and to analyze the influence of rubber content on compatibility, where binding energy was applied for the first time to evaluate the compatibility between rubber and asphalt.

2) The results of solubility parameter analysis show that three kinds of rubber are compatible with asphalt at 453K and 298K, where the compatibility of BR and asphalt is the best, followed by SBR, and NR is the poorest relatively. Rubber asphalt can form a stable system from preparation temperature to room temperature.

3) The results of binding energy analysis show that the optimum rubber contents for BR asphalt, SBR asphalt and NR asphalt were determined as 15%, 15%, and 20%, respectively. In addition, the upper limits of rubber contents were found as between 25% and 30%, between 20% and 25%, and between 25% and 30%, respectively. The infrared spectrometry was used to evaluate the storage stability of rubber asphalt in Ref. [⁶⁵]. The results showed that the optimum rubber content was 20%, the limited rubber content was 25%, which was consistent with this study, namely the study was reasonable in some extent.

This paper is a basic research to the compatibility between rubber and asphalt. The later study will continue to 1) obtain the rubber component types (BR, SBR, NR) and the proportions of components with different tire parts (tread, side wall, etc.) or even different tires (passenger car, trunk); 2) built the molecular dynamics model for different tire parts to obtain the proper dosage by using the evaluation indexes provided in this paper; 3) conduct the laboratory experiments like infrared spectrometry test, storage stability test, etc. to validate the results obtained by the simulation.

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