The molecular model of PU used in this paper was proposed by Talapatra and Datta (2021), which is considered to be the typical PU molecular model (Wang et al., 2022). It is well known that PU is composed of both soft and hard segments. The hard segments are 4,4′-diphenylmethane diisocyanate (MDI) and butanediol (BDO), respectively. The soft segment is poly (trtramethylene) oxide (PTMO). The molecular models of MDI, BDO, PTMO and PU chains are illustrated in Figures 2a–d, respectively. It should be noted that the PU molecule has a degree of polymerisation of 10.

Materials Studio software was used to construct a molecular model of PU amorphous cells. The model contains 10 PU molecular chains, as shown in Figure 3.

In this study, SiO₂ and CaCO₃ were chosen to represent common granite aggregates and limestone aggregates, respectively. The crystal models of SiO₂ and CaCO₃ are shown in Table 1.

To create orthogonal aggregate layers, γ in the SiO₂ and CaCO₃ crystal models must be transformed to 90°. In this paper, the [0, 0, 1] crystal facets of the SiO₂ model and the [1, 0, 4] crystal facets of the CaCO₃ model were selected for the granite aggregate model and the limestone aggregate model. It is important to note that after the SiO₂ is cleaved, the model needs to be saturated by adding “H” or “-OH”. Finally, the aggregate layer model is obtained by expanding the cell. The construction process of the aggregate layer is illustrated in Figure 4.

The PU-aggregate interface model is created by superimposing a polyurethane model on top of an aggregate model. To counteract the effects of cyclicity, an additional vacuum layer of 50 Å was required above the PU-aggregate interface model. Depending on the actual application, the PU only interacts with the molecules on the surface of the aggregate and needs to immobilize the atoms on the bottom of the aggregate. The construction process of the PU-aggregate interface model is shown in Figure 5. In this study, the molecular dynamics simulation process was performed at 1,000 ps NVT. It should be noted that the temperatures simulated in this paper are 298 K, 318 K, and 338 K. The force field used is the COMPASS II force field.

The interaction energy (Eint) is the energy required to characterize the separation of two substances at an interface. A negative value of Eint indicates that the interaction between the two phases is attractive, whereas a positive value would represent a repulsive force. For intuitive comprehension, it should be noted that a larger absolute value of Eint signifies a stronger adhesive interaction between the PU and the aggregate surface, suggesting enhanced resistance to debonding. This parameter is closely related to the fracture and debonding characteristics of the two substances at the interface. In this work, Eint was used to evaluate the bonding characteristics between PU and aggregate surface. The formula for calculating Eint between PU and aggregate is shown in Equation 1 (Guo et al., 2023). The interaction energies of PU-SiO₂ aggregate and PU-CaCO₃ aggregate are shown in Figures 6, 7. E int = E A g g r e g a t e + E T P U − E A g g r e g a t e + T P U (1) where, Eint is the interaction energy between polyurethane and aggregate, E _Aggregate is the potential energy of the aggregate, E _PU is the potential energy of the polyurethane; E _Aggregate+PU is the potential energy at the interface of the polyurethane and the aggregate.

Figures 6a–c demonstrate the interaction energies of the PU-SiO₂ aggregate interface model at temperatures of 298 K, 318 K and 338 K, respectively. From Figure 6, it is found that the PU-SiO₂ aggregate interfacial interaction energy changes significantly with the increase of temperature. The PU-SiO₂ aggregate interfacial interaction energy is positively correlated with the temperature. In order to analyze the effect of temperature on the interfacial interaction energy of PU-SiO₂ aggregate, a steady-state interfacial model at 1,000 ps was chosen for the study. It is found that the interfacial interaction energies of PU-SiO₂ aggregate are −61.37 kcal/mol, −294.31 kcal/mol and −409.56 kcal/mol at 298 K, 318 K and 338 K, respectively. This suggests that the adhesion properties between the PU and the acidic aggregate have temperature sensitivity.

Figures 7a–c demonstrate the interaction energies of the PU-CaCO₃ aggregate interface model at temperatures of 298 K, 318 K and 338 K, respectively. To analyze the effect of temperature on the interfacial interaction energy of PU-CaCO₃ aggregate, a steady-state interfacial model at 1,000 ps was chosen for the study. The PU-CaCO₃ aggregate interfacial interaction energies were −772.73 kcal/mol, −692.58 kcal/mol and −788.75 kcal/mol at 298 K, 318 K and 338 K, respectively. It can be seen that temperature hardly affects the adhesion properties of the PU and the alkaline aggregate.

The interaction energy consists of chemical bonding energy and non-bonded forces. The non-bonding energy consists of van der Waals forces and electrostatic interactions (Yu et al., 2023). To explain the results of Section 3.1, non-bonded forces, van der Waals forces and electrostatic interactions were calculated in the last frame of different thermoplastic polyurethane-aggregate interface models selected in this paper, as shown in Table 2.

In Table 2, the non-bonded interaction energy, van der Waals force and electrostatic energy all increase significantly with increasing temperature. This indicates that the increase in temperature is beneficial to improve the interaction energy between the interface of PU and SiO₂. At 298 K, the van der Waals force in the PU-SiO₂ interface model is only 0.02 kcal/mol. This is due to the weaker molecular motion between PU and silica at lower temperatures, and the longer distance between the PU molecular model and the silica molecular model resulting in lower van der Waals forces and electrostatic energy. At 318 K and 338 K, the interaction between the PU-SiO₂ interface mainly originates from van der Waals forces. The increase in temperature favors an increase in the movement of the PU molecular chains and decreases the distance between the PU molecules and the SiO₂ molecules. And the distance between PU and CaCO₃ hardly changes, as shown in Figures 8, 9. The SiO₂ aggregate model has a highly polar “-OH” on its surface, while the PU molecules contain the polar functional group “-NH₂ and C=O”. As these polar functional groups can produce induced interactions and orientation interactions, the van der Waals forces and hydrogen bonding between PU and SiO₂ aggregate are increased. In addition, it was found that with the increase of temperature, the non-bonded energy, van der Waals force, and electrostatic energy of the PU-CaCO₃ interface model would hardly change from Table 2. This indicates that the adsorption properties of CaCO₃ interface on PU are relatively stable at different temperatures. This exceptional stability is fundamentally rooted in the strong chemical affinity between the PU molecules and the alkaline aggregate surface. Specifically, Ca²⁺ ions on the CaCO₃ surface can form stable coordination bonds with the carbonyl oxygen atoms and the nitrogen atoms in the amino groups of the PU chains. Unlike the temperature-sensitive physical adsorption seen in the SiO₂ system, these robust coordination interactions act as stable ‘chemical anchors’ that are less susceptible to thermal disturbances, thereby ensuring the consistent adhesion performance of PU-CaCO₃ across the studied temperature range.

To alleviate the effect of interfacial dimensions on the adhesion at the PU-aggregate interface (Yu et al., 2023), this paper utilizes the adhesion work (W _ta , as shown in Equation 2 to evaluate the adhesion performance between PU and aggregate (Guo et al., 2023). Figure 10 demonstrates the PU-SiO₂ interfacial adhesion work and PU-CaCO₃ interfacial adhesion work. W t a = E i n t A (2) where, A is the contact area between the PU and the aggregate.

Figure 10 presents the adhesion work of the PU-SiO₂ and PU-CaCO₃. The work of adhesion of PU-SiO₂ was 0.03266 kcal/Ų, 0.15663 kcal/Ų, and 0.21796 kcal/Ų at 298 K, 318 K, and 338 K, respectively. This phenomenon is attributed to the fact that the temperature enhances van der Waals forces, hydrogen bonding, and electrostatic energy between the PU and the SiO₂. The van der Waals forces between PU and SiO₂ play a dominant role for the adhesion work of PU and acidic aggregates. This van der Waals force mainly comes from the induced interaction and orientation interaction between “-NH₂” and “C=O” in PU and “-OH” on the surface of SiO₂ aggregate. The adhesion work of PU-CaCO₃ at 298 K, 318 K and 338 K were 0.44663 kcal/Ų, 0.40031 kcal/Ų and 0.45588 kcal/Ų. Unlike SiO₂, the adhesion work of PU-CaCO₃ is hardly affected by temperature. The adhesion work of PU-CaCO₃ is mainly derived from the electrostatic energy between PU and CaCO₃ (see Table 2).

The radial distribution function (RDF) can be used to predict the aggregation behavior of thermoplastic polyurethane molecules on aggregate surfaces (Jiao et al., 2024). To determine the effect of temperature on the aggregation characteristics of PU molecules on the aggregate surface, the RDF curves of PU-aggregate and PU-PU at 298 K, 318 K, and 338 K were analyzed. The results of the RDF calculations are shown in Figures 11, 12.

Figures 11a,b exhibit the RDF plots of PU-PU and PU-SiO₂ in the PU-SiO₂ aggregate interface model, respectively. At 298 K, 318 K, and 338 K, the values of the first RDF peak of PU-PU were 71.38, 39.16, and 38.16, respectively. This indicates that the PU-PU molecular interaction decreases with increasing temperature. As the temperature rises, the RDF peak of PU-SiO₂ shifts to the left and the peak gradually increases, as shown in Figure 11b. At 298 K, 318 K, and 338 K, the RDF peaks of PU-SiO₂ appeared at 60 Å, 46.71 Å, and 40.83 Å, respectively, as shown in Figure 11b. The RDF values were 1.27, 1.54, and 1.72. This suggests that the increase in temperature enhances the interaction between PU and SiO₂, causing PU to be tightly adsorbed on the surface of SiO₂, which in turn reduces the distance between PU and SiO₂ molecules. The results showed that the temperature promoted the adsorption of SiO₂ on PU molecules. Moreover, the temperature led to the redistribution of PU molecules on the surface of the SiO₂ aggregate, as shown in Figure 8.

Figures 12a,b exhibit the RDF plots of PU-PU and PU-CaCO₃ in the PU-CaCO₃ aggregate interface model, respectively. At 298 K, 318 K, and 338 K, the values of the first RDF peak of PU-PU were 35.42, 36.38, and 33.81, respectively. The RDF peaks of PU-CaCO₃ appeared at 39.77 Å, 38.23 Å and 37.59 Å. It was found that the peak values and peak positions of PU-PU and PU-CaCO₃ hardly changed at different temperatures. This suggests that the adsorption of CaCO₃ on PU molecules does not change depending on the temperature. In conclusion, the adsorption of SiO₂ on PU molecules is strongly temperature-dependent, whereas the adsorption of CaCO₃ on PU molecules is relatively stable.

Fractional free volume (FFV) is always used to characterize the permeability properties and migration properties of molecules. In this paper, FFV was employed to analyze the migration ability of PU molecules in the PU-SiO₂ aggregate interface model and the PU-CaCO₃ aggregate interface model at different temperatures. The formula for FFV is shown in Equation 3 (Ji et al., 2023). In this study, a probe with a radius of 1.1 Å was used to obtain the free volume distributions of the PU-SiO2 interfacial model and the PU-CaCO3 interfacial model. The selection of a 1.1 Å radius is based on its widespread use in molecular simulations to represent the kinetic radius of a helium atom, which is a standard probe for detecting ‘connective’ free volume that can be penetrated by small molecules in polymer systems. This parameter ensures that the calculated FFV accurately reflects the micro-migration space available within the PU-aggregate interface. The results are shown in Figures 13, 14. F F V = V f V f + V o × 100 % (3) where, FFV is the fraction of free volume, V _f is the free volume (FV), and V _o is the occupied volume.

It is clear from Figure 13 that the occupied volume distribution becomes tighter as the temperature increases. This indicates that elevated temperature favors the migration of PU molecules to the SiO₂ surface. The molecular spacing between the PU molecules and the SiO₂ surface was reduced. This is mainly attributed to the fact that the elevated temperature increases the thermal motion of the PU molecules, which overcomes the interfacial potential barrier between PU and SiO₂, allowing the PU molecules to migrate to the SiO₂ surface. Moreover, the van der Waals forces and hydrogen bonding between the PU molecules and the SiO₂ surface are enhanced at high temperatures, and these forces increase the driving force for the migration of PU molecules to the SiO₂ surface. In Figure 14, the free volume of the PU-CaCO₃ interface is almost unchanged, respectively. This indicates that the molecular migration of PU in the PU-CaCO₃ interface is hardly affected by temperature. This is because the interaction between PU-CaCO₃ is mainly dominated by electrostatic energy (see Table 2). In addition, Ca²⁺ on the surface of CaCO₃ can form stable coordination bonds with the carbonyl oxygen atoms in the PU molecules and the nitrogen atoms in the amino groups, respectively, which allows the PU molecules to be stably adsorbed on the CaCO₃ surface.

To quantitatively assess the effect of temperature on FFV, the free volume fraction at the interface of different types of polyurethane polymers was calculated in this study, the results are shown in Table 3.

From Table 3, The FFV of the PU-SiO₂ aggregate interface model was 69.8%, 69.5% and 69.3% at 298 K, 318 K and 338 K, respectively. This indicates that the FFV of the PU-SiO₂ aggregate interface model decreases gradually with the increase of temperature. This is due to the increase in temperature, which makes the PU molecules adsorb more closely to SiO₂. This reduces the molecular gap between the PU molecules and the SiO₂ aggregate surface (See Figure 13), which in turn leads to a decrease in the FFV in the PU-SiO₂ aggregate model. The FFV of the PU-CaCO₃ aggregate interface model was 72.76%, 72.79% and 72.73% at 298 K, 318 K and 338 K, respectively. It can be seen that the temperature has a negligible effect on the FFV in the PU-CaCO₃ aggregate interface. The adsorption of this surface PU with CaCO₃ is more stable.

Relative concentration distribution (RCD) can be used to reveal the interaction mechanisms between molecules in an interface (Tang et al., 2023). In this paper, the relative concentration distribution of PU molecules on the aggregate surface in the Z-direction is calculated, as shown in Figure 15. Figure 15a demonstrates the relative concentration distribution of PU on the SiO₂ surface. In Figure 15a, PU appears near 25 Å at 318K and 338K. At 298 K, PU appears near 35 Å. This suggests that increasing the temperature caused the PU molecules to move downward, increasing the adsorption of PU molecules on the SiO₂ surface and improving the adhesion properties at the PU-SiO₂ aggregate interface. Figure 15b demonstrates the relative concentration distribution of PU on the CaCO₃ surface. From the Figure 15b, it is found that PU molecules appear near 15 Å in all interfacial models. In addition, the relative concentration of PU molecules on the CaCO₃ surface hardly changes, resulting in little or no effect of temperature on the PU-CaCO₃ aggregate adhesion properties. In conclusion, the relative concentration distribution of PU on the aggregate surface directly affects the adhesion properties between PU and the aggregate. The closer the PU molecules appear to the aggregate, the easier the PU molecules interact with the aggregate, thus increasing the adhesion properties between the PU and the aggregate.