2.1 Construction of CWTB modified asphalt model
In this study, natural rubber was selected as a representative of CWTB. However, natural rubber is a polymer made of cis-1,4-isoprene as monomer polymerization, and its molecular weight varies with the degree of polymerization, and the computational cost of MD simulation is proportional to the molecular weight of the system [11, 20]. Therefore, the molecular model of natural rubber needs to be selected. The method used in this study is to calculate the solubility parameter of natural rubber with different polymerization degrees and take the sudden change in the slope of the solubility parameter curve as the model needed for the simulation [21]. The solubility parameter can be calculated by the following equation.
![](data:image/png;base64,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)
where, δ = solubility parameter, CED = cohesion energy density, Ecoh = cohesion energy, and V = system volume.
Amorphous cells of natural rubber with different degrees of polymerization were constructed in Materials Studio (MS), they were all geometrically optimized in 500000 steps, and finally the solubility parameters were calculated for different systems. The above processes were performed in the Forcite package of the MS software. The solubility parameters of different natural rubbers are shown in Fig. 1, it can be found that the solubility parameters first increase and then basically equilibrate as the degree of polymerization increases, and the critical point polymerization degree is 12. Therefore, the natural rubber used in this study was with a polymerization degree of 12.
The asphalt model was constructed using the assembly method, as it better reflects the complexity of asphalt. The model was used as proposed in the literature [22], which used 12 molecules to represent the four components of asphalt, and the ball-and-stick model of asphalt molecules is shown in Fig. 2. The virgin asphalt sample used in this study was GS-90, and based on the results of the determination of its four-component content (ASTM D4124-09), the number of various asphalt molecules was calculated so that the model four-component content was consistent with the experimental value, and finally the asphalt model could be constructed in the MS software. The number of molecules of the asphalt model in this study, the four-component content of the model and the samples are shown in Fig. 3. It can be found that the various component contents of the asphalt samples are highly consistent with those in the molecular model, which proves the correctness of the asphalt model.
The molecular model of CWTB-modified asphalt was further constructed, and the rationality of the native asphalt model was fully validated in previous studies [21]. The asphalt models used in this study are shown in Fig. 4. It must be mentioned that the content of natural rubber in the CWTB modified asphalt model is 5%. A geometric optimization with a step number of 500000 was performed for each asphalt model with the aim of getting the system to the energy minimum state for subsequent dynamic simulations. The dynamic simulation in this study has two stages, the first stage is 50ps in duration and the system synthesis used is NVT, with the aim of eliminating the high forces present in the system. The second stage is 200ps in duration and the system synthesis used is NPT, which aims to balance the mechanical forces in the system.
In this study, the MD simulation temperature was set to 298.13 K and the pressure was set to 1 atm, so as to simulate the system variation of modified asphalt at room temperature and pressure. quality was adopted as Ultra-fine, which is to ensure the accuracy of MD simulation. The energy deviation is set to 40,000 kcal/mol to control the energy change of the simulation. velocities and forces are included for the kinetic simulation trajectory, which is to facilitate our analysis of the various properties of the system.
During the simulation, Nose was used for Thermostat, Berendsen was used for Barostat, Decay constant was set to 0.1ps, Time step was set to 1fs, Number of steps was set to 200000, Frame output every was set to 5000 steps, Electrostatic was calculated by Ewald method, and van der Waals was calculated by Atom based method. In addition, COMPASSII force field was used throughout the simulation, which is more accurate compared to COMPASS force field.
The changes of energy, amorphous cell edge length, density and temperature of the CWTB modified asphalt system during the MD simulation are shown in Fig. 5. It can be clearly seen that the energy and temperature of the CWTB modified asphalt system have reached the equilibrium after 15ps. And after 25ps, the system edge length and density also tend to equilibrium, which means that the system has reached the kinetic equilibrium state at this time, and the microscopic quantities of the system can be calculated.
The indicator used in this study to characterize the stability of the interaction is the binding energy, which is currently one of the most commonly used and most effective microscopic characterization quantities. There are many definitions of binding energy, but the most accepted one is the amount of energy or work required to separate two systems. The binding energy can be used to quantify the strength of the bond between two substances. For modified asphalt systems, the state of the bond between the modifier and the asphalt has a direct effect on the performance. The binding energy can be calculated by the following equation.
![](data:image/png;base64,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)
where Ebond = bonding energy, Elrc = long range correction, Ecoulomb = electrostatic energy, EedW = vdW energy and Enon-bond = non-bonding energy.
2.2 Materials and experiment
The asphalt used in this study was GS-90 provided by Sinopec, whose base properties are shown in Table 1. CWTB of 30 mesh was prepared from waste tires of Henan Huihua Waste Tire Recycling and Treatment Co. Since the CWTB are very hard and have a high melting point, the CWTB cannot be modified to be directly ground into powder and added into the base asphalt. In this study, the CWTB were cracked first, and the amine cracking agent was used, and the rubber powder was made at the end. The various properties of the prepared CWTB are shown in Table 2, and its particle size distribution is shown in Fig. 6. The rubber powder obtained from the cracking was mixed with the base asphalt in a high-speed shear in a certain ratio and sheared at 185°C for 3 hours at a speed of 5000 rpm, with the aim of allowing the rubber powder to fully interact with the base asphalt to obtain a stable CWTB modified asphalt.
Table 1. Basic properties of GS-90
Project
|
GS-90
|
After RTOF
|
Testing standards
|
Penetration
|
25 °C [0.1mm]
|
91.0
|
65.5
|
ASTM D5
|
Softening point
|
TR&B [°C]
|
48.3
|
91.1
|
ASTM D36
|
Density
|
25 °C [g/cm3]
|
1.030
|
1.121
|
ASTM D70
|
Ductility
|
15 °C [cm]
|
105.2
|
76.2
|
ASTM D113
|
Table 2. Basic properties of CWTB
Water [%]
|
Rubber hydrocarbon [%]
|
Ash [%]
|
Acetone extracts [%]
|
Natural rubber [%]
|
Density [g/cm3]
|
Carbon black [%]
|
0.7
|
49
|
3
|
4
|
37
|
1.20
|
6
|
In this study, FTIR tests, SEM tests, fluorescence microscopy tests and DMA were performed successively on virgin and CWTB modified asphalts with the aim of exploring the multi-scale modification mechanism of CWTB modified asphalt in combination with MD simulations. The SEM uses the TM3030PLUSTM. FTIR by Bruker Spectroscopy, Germany, model VERTEX 70TM. The model number of fluorescence microscope is BSM-600ETM, the optical magnification is 40X-2000X, provided by Shanghai BIMU Instruments Co. And the DSR model is Bohlin GeminiTM by Xi’an Minx Testing Equipment Co., Ltd. and the test standard is AASHTO T 315. The technical route of this study is shown in Fig. 6.