Cross-scale Correlation of Macro-micro Evaluation Indexes for Asphalt Binder

YU Tengjiang, ZHANG Haitao＊, SUN Xiaowen, LI Ming, WANG Haomin

(1. College of Civil Engineering, Northeast Forestry University, Harbin 150040, China; 2. Safety Production Technology Center of Heilongjiang Province, Harbin 150040, China; 3. School of Civil Engineering & Architecture, Chongqing Jiaotong University, Chongqing 400074,China)

Abstract: In order to further study the reliability of macro evaluation indexes, molecular dynamics (MD)was applied to the evaluation of asphalt binder. Micro evaluation indexes (potential energy, surface free energy,solubility parameter and diffusion coefficient) of asphalt binder in different service phases (virgin, modified,aged and rejuvenated) were simulated. Combined with the variation characteristics of asphalt binder macro evaluation indexes (permeability, ductility, viscosity and softening point) in different service phases, the crossscale correlation of macro-micro evaluation indexes was explored. The results show that the macro and micro evaluation indexes of asphalt binder have different characteristics in different service phases. The essence of the variation in the properties of asphalt binders is the difference in micro composition. In addition, there is a certain correlation between macro and micro evaluation indexes, which can be described by the gray relation theory.The cross-scale correlation of macro-micro evaluation indexes can provide a certain theoretical basis for the development of asphalt binder.

Key words: asphalt binder; macro-micro indexes; cross-scale correlation; different service phases;molecular dynamics

1 Introduction

Asphalt binder is one of the most widely used materials in road engineering, and its non-renewable feature is the focus of many scholars[1-3]. At present,modification and rejuvenation are considered as the main means to alleviate and prolong the service life of asphalt binder. The essence of modification is to delay the aging process, and the purpose of rejuvenation is to restore the performance of asphalt after aging[4]. The macro evaluation indexes of rejuvenated asphalt can be recovered, but the continuity of its performance cannot meet the expectation[5]. So, the macro evaluation indexes of asphalt binder have some shortcomings.Meanwhile, the service performance can be revealed by the micro evaluation indexes from the micro scale, but there is a scale difference between the macro and micro[6]. Therefore, it is very important to study the crossscale correlation of macro-micro evaluation indexes to further understand the performance of asphalt binder.

To improve the macro evaluation index, different types of modifiers (polymers, resins, plastics, nano-silica and so on) were applied to asphalt binder[7,8]. Among them, styrene-butadiene-styrene block copolymer (SBS)modifier can significantly improve the macro evaluation indexes of asphalt binder, which has been confirmed by the studies[9]. For example, Qian studied the performance of waste rubber/SBS modified asphalt and established relevant evaluation indexes[10]; Dong made an in-depth study on various properties of SBS modified asphalt and found the relationship between modification effect and SBS particle size[11]. Although the evaluation indexes of asphalt binder have been greatly improved by the modification, it is still under the influence of aging. In order to rejuvenate the aged asphalt,the research of rejuvenation technology has become a key problem[12,13]. For example, Noorvand explored the rejuvenation mechanism of crumb rubber modified asphalt; Matolia analyzed the influence of aging and rejuvenation on the chemical composition of asphalt binder and so on[14,15]. However, the performance of rejuvenated asphalt binder cannot reach the durability described by macro evaluation indexes.

The application of molecular simulation technology in asphalt binder makes it easier to obtain micro evaluation indexes[16,17]. For example, Guo used molecular simulation to evaluate the compatibility between rubber and asphalt binder; Sun evaluated the diffusivity of different rejuvenators and aged asphalt binder at micro level; Zhang evaluated the effect of aging on asphalt binder at multiple scales[18-20]. Because of the scale difference between micro evaluation indexes and macro evaluation indexes, micro evaluation index cannot be directly used in the evaluation of macro performance.

In conclusion, the service performance of asphalt binder can be measured by macro evaluation indexes,but the accuracy of evaluation indexes cannot be guaranteed, especially for rejuvenated asphalt. Although the micro evaluation indexes can reveal the service performance mechanism of asphalt binder from the nanometer scale, there is scale difference between the micro evaluation indexes and the macro evaluation indexes.Therefore, we studied the change characteristics of macro and micro evaluation indexes of asphalt binder in different service phases, and the correlation of macro-micro evaluation indexes were explored.

2 Materials and macro evaluation indexes

2.1 Materials

According to the asphalt commonly used in Heilongjiang Province, virgin asphalt (90#) was selected as the material in the study. The technical indexes of asphalt binder are shown in Table 1[21].

Research shows that styrene-butadiene-styrene block copolymer (SBS) has a good effect on improving the performance of asphalt binder[22]. Its principal component is thermoplastic rubber elastomer material. Asphalt rejuvenator has the characteristics of low viscosity, diffusion asphaltene, increasing oil content,improving and adjusting asphalt structure. By adding rejuvenator, various indexes of waste asphalt can be recovered[23]. The performance indexes of the asphalt rejuvenator and SBS modifier are shown in Table 2.

2.2 Asphalt binders in different service phases

To clearly explore and compare the performance changes of asphalt binder in different service phases,the following scheme was designed. The macro test plan was carried out according to the following steps:

(1) The macro evaluation indexes of virgin asphalt(90#) were tested and labeled as VA;

(2) The VA was modified with SBS modifier to obtain SBS modified asphalt (4%), which was labeled as MA-SBS;

(3) Laboratory aging (20 h and 163 ℃) was applied to MA-SBS, and the aged SBS modified asphalt was obtained, which was labeled as AA-SBS;

(4) The rejuvenator was added to AA-SBS to obtain the rejuvenated aged SBS modified asphalt (6%),which was labeled as RA-SBS.

Modification, aging and rejuvenation of asphalt binder were integrated into the use cycle, forming acycle of asphalt binder utilization. Therefore, the performance of different service phases directly affects the utilization efficiency of asphalt binder.

Table 1 Technical indexes of virgin asphalt

Table 2 Parameters of regenerating agent and SBS modifier

Table 3 Macro evaluation indexes of asphalt binders

2.3 Macro evaluation indexes of asphalt binder in different service phases

The engineering practice has proved that the macro evaluation indexes (penetration, ductility, viscosity and softening point) can reflect the performance of asphalt binder[24,25]. Therefore, macro evaluation indexes of asphalt binder in different service phases were measured, and the results are shown in Table 3.

It can be seen from Table 3 that the macro evaluation indexes of asphalt binder in different service phases have different characteristics. After the modification (SBS), in addition to a small decrease in penetration, other evaluation indexes were increased, especially the viscosity. It shows that the SBS modified asphalt becomes more viscous and the low temperature performance was strengthened. However, after the aging of MA-SBS, all evaluation indexes decrease, among which, the viscosity and ductility have a great decline.It shows that aging will lead to the change of asphalt binder properties. After the rejuvenation, the values of the ductility and penetration were worth to be restored,but in general, they cannot reach the MA-SBS.

In conclusion, the macro evaluation indexes (ductility, viscosity and softening point) of MA-SBS are all higher than other service phases. Although the AA-SBS has not reached the MA-SBS, it is still better than the VA. In the whole macro evaluation index, viscosity and ductility have a larger range of changes.

3 Analysis of micro evaluation indexes in different service phases

3.1 Micro models of asphalt binder

Molecular simulation (MS) based on molecular dynamics theory can combine computer technology with physical and chemical theory to intuitively describe the structure and behavior characteristics of material molecules[26]. Molecular simulation is based on periodic boundary conditions and molecular force field.The physical problem with spatiotemporal periodicity is reduced to a unit problem, and the global properties are expressed by partial properties. The force field can calculate the interactions between atoms, including intramolecular bonding interactions and intermolecular van der Waals’ interaction[27]. Therefore, molecular simulation applied to asphalt binder can further study and explore the service mechanism of asphalt binder from the micro-scale.

In order to reflect the influence of modifier molecules and rejuvenator molecules on the performanceof asphalt binder, the average molecular method was selected in the study. Virgin asphalt molecule, aged asphalt molecule, SBS modifier molecule and rejuvenator molecule were selected as the basic units to constitute asphalt micro model (as shown in Fig.1)[28,29]. The detailed number of different molecules in different service phases is shown in Table 4[30].

Table 4 Components of micro models in different service phases

Fig.1 Micro models of asphalt binder in different service phases

According to the number of different molecules in Table 4, micro models of asphalt binder in different service phases were established (as shown in Fig.1).The simulation parameters were NPT (constant-pressure, constant-temperature) for ensemble, COMPSS(Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies) for force field, and the running time was 100 ps. After quenching simulation,the micro models finally reaches a stable state and conforms to the description of macro asphalt binder[31].

3.2 Micro evaluation indexes of asphalt binder in different service phases

3.2.1 Potential energy and surface free energy

Molecular potential energy is the energy generated by the interaction of molecules with respect to their relative positions. In general, the molecules are in relative equilibrium[32]. When it is less than the equilibrium position, it shows repulsive force, and when it is greater than the equilibrium position, it shows gravitational force. Thus, when the intermolecular distance is equal to the equilibrium distance, the molecular potential energy is the minimum (as shown in Fig.2).

Fig.2 Molecular potential energy

The potential energy of the steady-state micro models was calculated, and the results are shown in Table 5. On the basis of the micro model of asphalt binder, the surface free energy can be further calculated. The surface free energy refers to the intermolecular force on the surface of a material, which is defined as the work required to produce a unit of new surface under vacuum[33]. In the study, the surface free energy can be calculated by calculating the energy difference between the asphalt model with and without surfaces[34].The calculation formula is shown in Eq.(1), and the results are shown in Table 5.

where,γSurfacerepresents the surface free energy,E1is the potential energy of the asphalt model with surface,E2is the potential energy of the asphalt model without surface,Ais the new surface area.

As can be seen from Table 5, theE2is greatly different, but the difference values are regular. The higher the potential energy, the less stable. The surface free energy has the maximum value after modification,which is related to the properties of asphalt binder.

3.2.2 Cohesion energy density and solubility parameter

Cohesive energy density (CED) is defined as the intermolecular forces per unit volume of the polymer[35]. The cohesive energy density of the micro models can be calculated by software. The solubility parameter is the square root of the cohesive energy density. The solubility parameters can be used to study the molecular adsorption properties of asphalt systems and to evaluate the stability of colloids. The solubility parameters of asphalt are expressed by van der Waals force and electrostatic force, as shown in Eq.(2), and the calculation results are shown in Table 6.

where,δis the solubility parameter,CEDrepresents the cohesive energy density,δvdwis the contribution of van der Waals forces to solubility,δeleis the contribution of electrostatic forces to solubility.

It can be seen from Table 6 that the cohesion energy density and solubility parameters of different service phases are different. The aging effect increases thenumber of oxygen atoms in the micro model, which is more obvious in the rejuvenated asphalt. The increase of solubility parameter can reflect the stronger interaction between molecules inside the asphalt binder. At the same time, the larger the solubility parameter, the weaker the diffusion ability and the weaker the flow ability.

Table 5 Potential energy and surface free energy

Table 6 Cohesive energy density and solubility parameter

3.2.3 Mean square displacement and diffusion coefficient

In the process of molecular motion, diffusion coefficient is regarded as the most intuitive data to study diffusion[36]. In theory, the molecules in the system are in constant motion at all times (Brownian motion), and the square of the average molecular motion is proportional to time. When using molecular simulation to calculate the diffusion coefficient, the most commonly used is to use Einstein equation calculation, namely mean square displacement (MSD) curve. The calculation process of MSD and diffusion coefficient is shown in Eqs.(3)-(5).

where,ri(0) andri(t) represent the position of the center of mass ofiat time0and timet,Dis the diffusion coefficient of the particles,Nis the number of molecules that are diffusing through the system, andais the linear slope ofMSD.

Fig.3 Different service phases of MSD

SinceNis constant, the diffusion coefficientDis proportional to the linear slopea. When the linear relationship between theMSDand time is good, it can be calculated by Eq.(5). The relationship ofMSDwith time was obtained as shown in Fig.3, and the relationship betweenMSDand time was linearly fitted, as shown in Table 7.

Table 7 Calculation of fitting formula and diffusion coefficient

As can be seen from Table 7 and Fig.3, the diffusion coefficients (D) of asphalt models in different phases are different. The diffusion coefficient of MASBS reduced obviously, which indicated that the asphalt binder had weaker fluidity. The decrease of diffusion coefficient after aging indicates the decrease of fluidity, which is consistent with the macro cognition.The diffusion coefficient of AA-SBS and RA-SBS has a large value, which indicates that the AA-SBS and RA-SBS have strong diffusion energy and high diffusion ability at the interface of different materials.

3.3 Analysis of micro evaluation indexes in different service phases

By calculating the micro models of asphalt binder,different micro evaluation indexes were obtained. The results are summarized as shown in Table 8.

It can be clearly seen from Table 8 that the micro evaluation indexes of different service phases are different. Among them, the variation range of solubility parameter is small, compared with other micro evaluation indexes. The surface free energy of MASBS increases greatly, while diffusion coefficients and potential energy decrease. This indicates that the stability of asphalt binder is strengthened. The aging and rejuvenation effects gradually increase the diffusion coefficients, which indicates that the stability of rejuvenated asphalt is still unfavorable from the perspective of diffusion coefficient.

Table 8 Micro evaluation indexes of asphalt binders

4 Correlation of macro-micro evaluation indexes for asphalt binder

4.1 Comparative analysis of macro-micro evaluation indexes

Although the micro and macro evaluation indexes are of different scales, they are all evaluation indexes of the same asphalt binder. And both have their own advantages, macro evaluation indexes are easily accessible and understood, while micro evaluation indexes can reveal deeper mechanisms. Comparison of macro and micro evaluation indexes is shown in Fig.4.

It can be clearly seen from Fig.4 that the viscosity, ductility and surface free energy fluctuate positively after modification, while the penetration and diffusion coefficient fluctuate negatively. After aging, the macro evaluation index decreases, while the diffusion coefficient of micro evaluation index increases. In addition,the rejuvenation increased penetration, ductility, surface free energy and diffusion coefficient, but decreased potential energy and viscosity.

In summary, the ductility and surface free energy have the same positive trend, while the viscosity and diffusion coefficient have the opposite trend. The changes of softening point and solubility parameter were stable in different service phases.

4.2 Cross-scale correlation of macro-micro evaluation indexes

Fig.4 Evaluation indexes in different service phases: (a) Macro evaluation indexes; (b) Micro evaluation indexes

The correlation of macro-micro evaluation indexes of asphalt binder can be evaluated by using gray relation theory. If the variation of two factors is consistent, the degree of correlation between them will be higher[37]. The calculation formula of relative relation grade is shown in Eqs.(6)-(9), and the calculation results are shown in Table 9.

where,γ0irepresents the grey correlation coefficient,andxi0’(n) represents the zeroing image of the initial value ofx(n).

From the calculation results of Table 9, it can be seen that there is a certain correlation between macro evaluation indexes and micro evaluation indexes.Among the macro evaluation indexes, there are high correlations between penetration and potential energy,between ductility and surface free energy, between viscosity and surface free energy, and between soft-ening point and potential energy. In terms of the close connection between micro evaluation index and macro evaluation index: potential energy＞diffusion coefficient＞surface free energy＞solubility parameter. In addition, the correlation between the continuance and the micro evaluation index is the weakest, while the correlation between the solubility parameter and the macro evaluation index is the weakest.

Table 9 Grey correlation coefficient of macro-micro evaluation indexes

To sum up, by integrating the description of macro and micro indexes of asphalt binder in different service phases and exploring the correlation, it is helpful to infer the microstructure of the macro evaluation indexes and provide the micro mechanism in the improvement process of asphalt binder. It is helpful for the development and improvement of asphalt binder to establish a unified correlation between micro and macro.

5 Conclusions

a) Asphalt binder was studied in different service phases (virgin, modified, aged and regenerated), which makes the research have continuity and comparability.The macro evaluation indexes (ductility, viscosity and softening point) of MA-SBS were all higher than other phases. In the whole macro evaluation indexes, viscosity and ductility have a large range of variations.

b) The potential energy and diffusion coefficient are greatly influenced by different service phases. Ductility and surface free energy have the same positive trend, while viscosity and diffusion coefficient have the opposite trend. The softening point and solubility parameters changed stably in different service phases.

c) The modification, aging and rejuvenation have great influence on the ductility and viscosity. The potential energy and solubility parameter are very similar to the change of penetration and softening point. In terms of the close connection for macro-micro evaluation indexes: potential energy＞diffusion coefficient＞-surface free energy＞solubility parameter.

d) The correlation of macro-micro evaluation indexes was studied and the cross-scale correlation of macro-micro evaluation indexes for asphalt binder was established. The correlations of different scale evaluation indexes enrich the significance of asphalt binder evaluation indexes and provide a deeper theoretical basis for the development.