1. Introduction

2. Materials

2.1. Asphalt material

The structure of the asphalt’s internal component is complicated, and it contains a variety of elements (e.g., C, H, O, N, S). In earlier periods, it was divided into three, four and six components through experiments [13,14,15,16]. Zhang et al. adopted three-way representative molecules for the construction of micro-models to analyse their related performance. Li et al. divided the asphalt molecule into 12 molecules with the AAA-1 model, representing the molecule of each component [17,18,19,20,21]. Twelve molecular representative models were selected to build matrix asphalt [22,23], and the component distribution ratio of each asphalt molecular model was obtained to obtain the asphalt molecular model.

Steps of asphalt model construction[24]:

(1) Random agency is used to build a distributed module amorphous cell. The construction command is selected to build a model. In a periodic architecture, each representative molecule is filled in, a model system of each representative is built, and a density of 0.1 g/cm³ is set.

(2) The forcite dynamic analysis module is adopted, geometric optimisation is used, the unstable molecular bonds of the molecules in the system are regulated, and the energy is optimised to achieve a stable system.

(3) Annealing settings are set to relax the molecular structure. The setting temperature is 300 to 500 K, and the cycle repeatedly relaxes to eliminate the adverse structure.

(4) At a temperature of 443.13 K (170 °C) temperature, the NPT ensemble and 1 standard atmospheric pressure are set, and 100 ps dynamics are optimised, the asphalt system model is made and compressed.

(5) On the basis of the NVT system with 100 ps dynamics optimisation, a stable architecture is obtained.

Through this operation process, the structure of each asphalt molecular is obtained. Further details are shown below.

Table 1. Details of the components of the matrix asphalt.

Table 1. Details of the components of the matrix asphalt.

component	molecular fame	molecular	molecular weight	number of atoms	number of molecules
saturation	Sa-A	C30H62	422.8	92	4
	Sa-B	C35H62	482.9	97	4
fragrance	Ar-A	C35H44	464.7	79	11
	Ar-B	C30H46	406.7	76	13
glue	Co-A	C40H59N	553.9	100	4
	Co-B	C40H60S	573.0	101	4
	Co-C	C18H10S2	290.4	30	15
	Co-D	C36H57N	503.9	94	4
	Co-E	C29H78O	414.7	80	5
asphaltence	As-A	C42H54O	574.9	97	3
	As-B	C66H81N	888.4	148	3
	As-C	C51H62S	7071	114	2

Figure 1. Asphalt structure diagram, 12 molecular diagram.

Figure 1. Asphalt structure diagram, 12 molecular diagram.

3. Method

3.1. Modified asphalt performance analysis

3.1.1. Free volume theory

Due to the space volume of asphalt materials due to its own material, part of the model volume occupied by the asphalt molecule’s own molecular structure, in order to occupy the volume; some are the free space in the asphalt molecular structure, so that it has space liquidity in a certain environment, which is both free volume essence. In the space system of asphalt, the higher the proportion of its free volume, the stronger the possibility of the molecular movement route of the components. This article explores the free volume score in the asphalt material system. Materials Studio software is used to build the asphalt molecular model. The molecule of the atom volume and surface tool calculation system occupies the volume and freedom volume (Eq.3) to obtain the free volume score of the asphalt material system. Given that the van der Waals radius of the water molecule is 1.45 Å , to further explore the performance of asphalt materials, the probe radius is set to 0 Å and 1.45 Å to analyse the stability and water damage resistance of the asphalt material.

Figure 3. Freedom volume calculation model diagram of asphalt material.

Figure 3. Freedom volume calculation model diagram of asphalt material.

Table 2. Freedom volume of asphalt materials calculated data table (ų).

Table 2. Freedom volume of asphalt materials calculated data table (ų).

species	content	probe radius 0 Å			proportion	probe radius 1.45 Å			proportion
asphalt	0%	33107.86	19897.88	53005.74	0.37	44750.65	8255.09	53005.74	0.15
rubbe asphalt	18%	40605.17	23478.83	64084.00	0.36	54461.06	9622.94	64084.00	0.12
	20%	42201.74	23728.64	65930.38	0.36	58346.86	7583.52	65930.38	0.12
	22%	43391.79	24384.97	67776.76	0.35	59373.05	8403.71	67776.76	0.12
	24%	44535.79	25087.34	69623.13	0.35	60267.79	9355.34	69623.13	0.13
	26%	45735.50	25734.00	71469.5	0.35	61553.00	9916.51	71469.51	0.14
sbs asphalt	4%	34622.97	20730.97	55353.94	0.37	47640.93	8407.22	56048.15	0.15
	6%	35344.28	20980.96	56325.24	0.37	48303.15	8022.08	56325.23	0.14
	8%	36089.70	21612.45	57702.15	0.37	49259.07	8443.08	57702.15	0.15
	10%	37130.95	22031.50	59162.45	0.37	50315.52	8846.93	59162.45	0.15
	12%	37569.33	22481.02	60050.35	0.37	50862.32	9188.03	60050.35	0.15

Through software calculation, the free volume data of asphalt materials (Table 2) is obtained. According to the data in the table, the free volume proportion of the basic asphalt material is higher than the modified asphalt system, showing that the asphalt material itself can trigger spatial movement performance. The stability and water damage resistance of modified asphalt material system are lower than those of corresponding modified asphalt. In the rubber modified asphalt material, the corresponding free volume proportion under different measurement conditions is lower than that of the matrix asphalt material, indicating that the rubber modified agent can modify the stability and damage performance of the asphalt material itself. When the amount of rubber modifiers is 22%, its free volume proportion is the lowest, corresponding to the most impact of improving asphalt material performance. In SBS modified asphalt materials, the free volume proportion of asphalt materials under different measuring volumes is lower than that of the matrix asphalt material. The SBS modified agent can effectively improve the stability of the matrix asphalt material and resist water damage performance. When the SBS modified agent is 6%, the free volume proportion of the SBS modified asphalt is lower than that of other doping.

Compared with different modified asphalt materials, the free volume proportion of rubber modified asphalt materials is lower than the SBS modified asphalt material. The structure of the structure enhances the spatiality of the asphalt material. The free volume after the modification of the matrix asphalt is occupied, enhancing its spatial stability.

3.1.2. Radial Distribution Function

The radial distribution function is an analysis method of the material structure of the material structure, in which the local spatial distribution is calculated. The radial distribution function is the probability of another atom near a specified atom[24]. The expression is:

$$g(r)=4\pi r^2\rho dr$$

(1)

In the formula, r is the atomic spacing and the quantity density of the atom. g (r) is the probability of other atoms specified at distance r of the atom. This can reflect the arrangement and interaction of molecules and atoms in the system. The peak position of the radial distribution function can determine the type of interaction, and the size of the interaction force can be inferred from the height of the peak.

To analyse the distribution of molecular agglomeration in the group in the asphalt material model, this article uses a radial distribution function to explore the position of its component molecular space. In the radial distribution function curve of Figure 3, on matrix asphalt material, the first peak value point is r = 1.1 Å, g (r) = 9.16, indicating that the asphaltene group with the most central position in the asphalt molecular model is higher than that of other groups. The distribution situation is as follows: r = 1.36 Å, g (r) = 1.66. The glue group is close to the asphalt group, and its molecular aggregation value is lower than that of asphalt quality. The component molecular energy is made more uniform, facilitating its closer proximity to the large number of benzene structures of asphalt components and therefore to the asphalt group points in the space. R = 1.53 Å, g (r) = 1.96 is the aromatic grouping. It is in the third layer of the gathering position, and its aggregation is higher than that of the glue group. It is lower than the agglomeration of the asphalt group. A large number of C-C long chains are at the edge of the asphalt space system, giving it a better space movement.

For the SBS modified agent asphalt material, the 4% SBS doping makes the aggregation of each component in the asphalt material higher than that of the matrix asphalt material and other SBS doped matrix asphalt materials, thereby improving the space gathering situation at the same space position. For the original peak value, the ratio is asphalt quality:glue:aroma division:saturation division = 2.1:1.81:2.11:3.54. The SBS modified agent mixed up makes the g (r) value higher, making the asphalt material more compact. This can effectively improve the ability of asphalt materials to resist the external environment.

For rubber modified asphalt materials, the use of 20% rubber modifiers mixes the amount of components in each component in the asphalt material compared with the matrix asphalt material and other rubber modifiers. The space agglomeration is increased to asphalt quality:gel quality:aroma division:saturation division = 1.44:1.06:1.48:2.20. The rubber modified agent results in higher g (r) values ​​and improves the performance of matrix asphalt materials.

In the modified asphalt material, 4% SBS modifiers have a greater impact on the performance of matrix asphalt materials than 20% rubber modifiers.

Figure 3. Modified asphalt radial distribution function.

Figure 3. Modified asphalt radial distribution function.

3.1.3. Diffusion coefficient

Einstein proposed the theory of the average number of the distance between the distance between the particle random movement.

$$\langle r^2\rangle =6Dt+C$$

(2)

where $\langle r^2\rangle$the average displacement, D is the diffusion coefficient, and C is the constant. MSD is the average displacement of the model system, which represents the distance between the random particles in the asphalt molecule at the initial position of the particles at time t:

$$MS{D}_{\left(\Delta t\right)}=\langle {\left[r\left(t-\Delta t\right)-r\left(t\right)\right]}^2\rangle$$

(3)

The formula of the diffusion coefficient is:

$$D=\frac{1}{6t}\underset{t\to \infty }{\lim }\frac{dMSD}{d\Delta t}$$

(4)

The molecular dynamic analysis asphalt material model is used, and the mean square displacement analysis task is set to set up a constructor in the Forcite module. The 300 ps simulation steps are calculated to get the MSD curve graph of each model (Figure 4).

On the basis of the average orientation data curve and the calculation formula, the asphalt material in different modified asphalt materials in Table 3 is at the asphalt material diffusion coefficient under the temperature condition of 298.13 K. The MSD curve in Figure 4 indicates that the motion diffusion coefficient of modified asphalt materials under different amounts of SBS modified agents can be obtained. When the SBS modified asphalt is 6%, the motion performance of the asphalt material reaches the highest value, and its diffusion coefficient value is 8.46 × 10⁻⁹ m²/s. In different rubber modified asphalt materials, the motion diffusion coefficient of the modified asphalt material is 24%NR ﹥ 26%NR ﹥ 22%NR ﹥ 18%NR ﹥ 20%NR, of which the SBS modified asphalt is doped at 24%. and the movement performance of asphalt materials reaches the highest value when the SBS modified asphalt content is 24%, and its diffusion coefficient value is 8.46 × 10⁻⁹ m²/s. The diffusion coefficient values of different asphalt material molecular models are calculated, and comparison and analysis show that the motion diffusion performance of the asphalt material is lower than that of the modified asphalt material. These findings promote asphalt materials to have higher potential energy and stimulate the movement mechanism of touching asphalt materials in the external environment, enabling the effective storage of energy for motorsport.

4. Conclusion

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