Effects of High Temperature on the Interfacial Mechanical Properties of Rubber and Calcium Silicate Hydrate: Nanoscale Insights

Abstract

Currently, the partial substitution of mineral aggregates with rubber particles in the preparation of rubber concrete (RC) is an effective method for recycling waste rubber materials. However, the mechanism of interfacial interactions in RC at high temperatures is not well understood. This study aims to explore the effect of high temperature on intermolecular interactions at the RC interface and its relationship with macroscopic mechanical properties. Molecular dynamics (MD) simulation technology was employed to construct an RC interface model. The temperature is controlled at room temperature (300 K), medium low temperature (320 K, 340 K, 360 K), and high temperature (500 K, 700 K). The interface model was analyzed from multiple dimensions such as binding energy, turning radius, and interface structure. The results show that the higher the temperature, the more easily water molecules aggregate at the interface of the two phases. As the temperature increases, the proportion of water molecules at the interface increases from 6% to 16%. Since rubber and water molecules cannot form hydrogen bonds, the formation of chemical bonds at the interface between the two phases is affected, leading to a decrease in RC binding energy. The interface bonding energy decreases by 12.6% at a temperature of 700 K. In addition, the radius of gyration of rubber is proportional to temperature. As the temperature increases, the average radius of gyration increases from 5.8 Å to 6.15 Å, and the numerical fluctuation amplitude is greater, resulting in a relatively loose and unstable rubber structure. Furthermore, the bonding strength in RC mainly comes from non-hydrogen bond interactions, and high temperatures cause an increase in bond length while reducing the strength and stability of chemical bonds. Finally, high temperatures increase the atomic movement speed in natural rubber (NR). As the temperature increases, the diffusion coefficients of H_NR and C_NR increase from 0.08 and 0.04 to 1.835 and 1.473, respectively, preventing good connections between atoms at the interface. The study provides nanoscale insights for optimizing RC.

1. Introduction

With the advancement of science and technology and the rapid development of industry, the number of automobiles has been increasing yearly, leading to a rise in the production of waste tires, posing a potential threat to the global environment. Therefore, addressing the disposal of waste tires in an environmentally friendly manner has become a pressing issue [1,2]. Currently, incorporating waste rubber into concrete to form composite materials has been widely applied in the construction industry [3,4]. This method helps mitigate the environmental harm caused by a large volume of waste rubber materials. Leveraging the high elastic modulus of rubber and its ability to form a three-dimensional network structure within the concrete, it can effectively absorb external impact energy and reduce crack formation and propagation. Consequently, rubber concrete exhibits better toughness, crack resistance, and impact resistance compared to ordinary concrete [5]. Additionally, there have been attempts to apply rubber concrete in various engineering fields, including buildings, roads, and bridges [6,7]. However, in high-temperature environments, rubber tends to soften and decompose, leading to molecular chain breakage and poor high-temperature resistance [8], which in turn reduces the durability of the structure.

In recent years, researchers have focused on the mechanical properties of rubber concrete at high temperatures, particularly on the strength and stiffness of components. Mahmoud et al. [9] studied the mechanical properties of rubber-reinforced concrete columns at room temperature and high temperatures, finding an inverse relationship between temperature and the residual failure load of the columns. Yan et al. [10] conducted axial compression tests on square steel tube rubber concrete columns after high temperatures, showing that high temperatures reduce the ultimate load and stiffness of the columns. Furthermore, researchers have focused on the micro and macro mechanical properties of RC structures at high temperatures, primarily on crack size and tensile-compressive strength. Su et al. [11] studied the performance of rubber concrete at high temperatures, indicating various degrees of loss in both static and dynamic compressive strength of the material under high temperatures. Gupta et al. [12] compared the mass loss and compressive strength changes of ordinary concrete and rubber fiber concrete at high temperatures. Yang et al. [13] investigated the compressive strength, stress–strain characteristics, and other properties of rubber concrete at high temperatures. The results showed that as the temperature increased, surface cracks widened, and compressive strength decreased. Mousavimehr et al. [14] studied the mechanical properties of rubber concrete after thermal exposure, indicating significant degradation in mechanical properties as temperature increased. Yong et al. [2] studied the microstructure and impact resistance of crumb rubber concrete (CRC) after high temperatures, finding that high temperatures increased large pore structures in the concrete, while the addition of rubber particles enhanced high-temperature impact resistance. Fadiel et al. [8] investigated the mechanical properties of rubber concrete at different temperature levels, demonstrating that high temperatures lead to increased cracking, weight loss, and reduced compressive strength, with tensile strength being more sensitive to temperature than compressive strength. Previous studies [2,14] have extensively investigated the macroscopic physical and mechanical properties as well as durability at high temperatures, but the nanoscale mechanism of the interaction between rubber and cement interfaces at high temperatures has not been mentioned.

Molecular dynamics (MD) simulation technology provides a means to observe atomic interactions at the nanoscale. MD can provide information on the interaction modes between atoms at the two-phase interface, the state of chemical bond connections, and system stability, explaining the mechanisms affecting the macroscopic mechanical properties of materials from a nanoscale perspective [15]. Through MD studies, the macroscopic mechanical properties of composite materials can be understood in advance, providing insights for designing new materials and improving existing ones. Currently, most studies using MD simulation technology focus on the interfacial mechanical properties of modified concrete [16,17,18]. For example, Feng et al. [16,17] analyzed the multiscale modification of recycled concrete using silane coupling agents, polyvinyl alcohol (PVA) fibers, and ethylene-vinyl acetate (EVA) copolymers, showing that the overall performance of recycled concrete was improved under the synergistic effect of the modifiers. Huang et al. [18] studied modified carbon fibers (CF) as reinforcement materials for concrete, which avoided the corrosion problems associated with steel fibers. Additionally, research on rubber concrete mainly focuses on the mechanical and anti-corrosion properties of the material after the use of modifiers. For instance, Feng et al. [19] studied EVA-modified RC, finding that EVA interacted with the cement matrix, enhancing the composite material’s shear performance and toughness index. Kang et al. [20] studied the effect of surface treatment of rubber particles on the compressive strength of RC, illustrating the bridging effect of silane coupling agent (SCA) molecules between rubber and cement. Han et al. [21] simulated the erosion of sodium chloride solution in the nanopores of rubber concrete, revealing the transmission mechanism of chloride ions in rubber concrete. Yu et al. [22] used silane coupling agents to modify rubber concrete to study its anti-corrosion and anti-chloride properties, showing that the addition of silane reduces the movement rate of water molecules in capillary pores, thereby inhibiting the transmission of corrosive ions. These studies demonstrate that MD can effectively simulate the dynamic mechanical behavior of atoms at the two-phase interface. At the same time, most studies are based on modifying rubber to enhance its mechanical properties and corrosion resistance [19,23]. However, studies on RC at the nanoscale under high-temperature conditions have not been reported, making it necessary to conduct detailed research on the mechanisms affecting the macroscopic mechanical properties of RC at the nanoscale under high temperatures.

To reveal the effects of temperature on the RC interface at the nanoscale, and knowing that cracks start to appear at the two-phase interface around 500 K [2], the temperatures in molecular dynamics simulations were controlled in medium–low ranges (300 K, 320 K, 340 K, 360 K) and high temperatures (500 K, 700 K). The flowchart of this study is shown in Figure 1. It is worth noting that the macro data collection on the left side of Figure 1 was compared with existing studies, and this study did not conduct actual experiments. Additionally, given the high natural rubber content in waste tires, which maintains more stable physical properties and molecular structures at high temperatures [23], this study primarily focuses on natural rubber. We used MD numerical simulation methods to construct an interface model of natural rubber (NR) and calcium silicate hydrate (C-S-H), the main source of concrete strength, and conducted a detailed study of the NR/C-S-H nanoscale interface. The interface structure is shown in Figure 2. Binding energy was used to analyze the mutual attraction and repulsion at the two-phase interface under high temperatures (Section 3.1). The radius of gyration was used to observe the looseness and tightness of rubber molecules (Section 3.2). The interface structure and chemical bond connections were used to understand the distribution of atoms and chemical bond connections at high temperatures (Section 3.3). Interface dynamic behavior was used to observe the movement of major atoms and the stability of chemical bonds at the interface under high temperatures (Section 3.4). The effects of temperature on the structure and dynamic behavior of the two-phase interface were studied from multiple angles. We also collected data on RC compressive strength, stress–strain behavior, and microstructural changes at high temperatures in the laboratory, and correlated the MD analysis results with macroscopic phenomena, revealing the mechanisms of high-temperature degradation of RC interface structure and compressive strength. This study explored the mechanism of degradation of macroscopic mechanical properties of RC caused by high temperature at the nanoscale, providing nanoscale insights for optimizing RC.

2. Simulation Method

Many studies have confirmed the effectiveness of MD simulation, which can accurately characterize material properties and effectively predict mechanical responses [20,24]. This study used the Materials Studio (2023) molecular dynamics simulation software to create an interface model of calcium silicate hydrate (C-S-H) and natural rubber (NR). The system was subjected to geometric optimization, annealing, and molecular dynamics simulations based on the COMPASS force field. Temperature was controlled as the independent variable to analyze the effect of high temperatures on molecular interactions at the two-phase interface. This work used a 24-core CPU (Intel i7-14650HX, Intel, Santa Clara, CA, USA) for computation.

2.1. Model Construction

After cement hydration, the main hydration products include calcium silicate hydrate gel (C-S-H), calcium aluminate silicate hydrate (C-A-S-H), and calcium hydroxide (CH). However, C-S-H occupies the main volume in the cement gel and is the primary source of concrete material strength [25,26]. Therefore, C-S-H can be used as the matrix model. C-S-H is an imperfect crystal similar to the mineral tobermorite. Tobermorite 11 Å was selected as the initial configuration of the model, with lattice parameters of 6.69 Å × 7.39 Å × 22.77 Å (a × b × c). To make the model’s physical and mechanical properties closer to reality, the methods reported by Kovačević and Chen et al. [27,28] were used. First, the water molecules inside the unit cell were removed, and the unit cell was orthogonalized and treated with supercell (3 × 2 × 1). Second, to achieve a Ca/Si ratio of 1.7, SiO₂ was randomly deleted from the silicon chains, removing some silicate tetrahedra [29]. Third, the Grand Canonical Monte Carlo (GCMC) method was used to hydrate the C-S-H skeleton [30], and the model was hydrated to saturation. Finally, the C-S-H structure was geometrically optimized and relaxed under the NPT ensemble (constant temperature and pressure, 298 K, 1 bar) for 300 ps with a 1 fs time step. This process constructs the equilibrium configuration of C-S-H. It has been reported that this modeling method can produce realistic C-S-H, consistent with experimental results from X-ray diffraction (XRD) and nuclear magnetic resonance (NMR) tests [31,32,33]. This model was used as the cement gel model for this study. Subsequently, the model was cut along the [001] direction to obtain the C-S-H surface model [34]. The modeling process is shown in Figure 3-Path2.

The main component of NR (natural rubber) is cis-1,4-polyisoprene, with the molecular formula [CH2CH=C(CH3)CH2]n. First, hydrogen and carbon atoms were used to draw the NR monomer. According to previous studies [35,36] and convergence test results, when the degree of polymerization is 16, key interface information can be captured while alleviating the computational load. Therefore, this paper uses 16 NR monomers to combine to form a rubber chain. Using the amorphous cell module, five rubber chains were combined to form a polymer (temperature 298 K, precision Fine). The modeling process is shown in Figure 3-Path1. After modeling, the total number of atoms in the rubber polymer was 660. Ten configurations were output, and the configuration with the lowest energy was retained as the initial NR model. The build layer tool was used to create the NR/C-S-H interface model, maintaining periodicity in the X-Y direction. Fix the outermost atoms along the z-direction to avoid periodic effects on the simulation results in the z-direction. The dimensions of the interface model are x = 20.205 Å, y = 26.939 Å, z = 43.816 Å, with α = β = γ = 90°. This size has been validated to effectively capture interface interactions, ensuring simulation accuracy while reducing computational resources. The interface model is shown in the right part of Figure 3, with a total of 1716 atoms in the interface. This modeling method has been validated by researchers [35,36].

2.2. Simulation Details

Different force fields can yield varying simulation results, and the choice of force field is a critical part of the simulation, depending on the type of structure being studied. The COMPASS force field [37] is a high-quality force field that integrates parameters for both organic and inorganic materials, making it well suited for simulating calcium silicate structures. Since the interface model constructed in this study is a hybrid structure composed of organic and inorganic materials, the COMPASS force field can describe the potential parameters of this structure [38,39]. Experimental validations have also shown that the COMPASS force field matches experimental data [24,40]. Therefore, the COMPASS force field was used for numerical simulations in this study.

The process of constructing the interface model and molecular simulation is shown in Figure 4. First, we used the smart algorithm to perform geometric optimization on each model, with the optimization quality set to fine and the maximum number of iterations set to 20,000 steps. The structural optimization of the 300 K interface model is shown in Figure 5a. It can be seen that as the number of optimization steps increases, the energy rapidly decreases and stabilizes after 200 steps, indicating that the number of iterations is sufficient to achieve a stable structure. Subsequently, the surface atoms of the constructed interface model were constrained, and geometric optimization was performed again with the same parameter settings as before. This ensures that the interface model reaches an equilibrium state. Next, the system was annealed for five cycles, with the temperature range set from 300 K to 700 K, and each cycle consisted of 1000 steps. This method eliminates unreasonable structures, allowing us to select the lowest energy configuration from multiple configurations, providing the best starting point for subsequent dynamic simulations. In the forcite module, molecular dynamics simulations were performed in two main steps. In the first step, the interface model was run for 500 ps under the NPT ensemble (constant number of atoms N, pressure P, and temperature T) with a time step of 1.0 fs. The parameter changes of the system during this process are shown in Figure 5b. It can be seen that after 30 ps, the fluctuations in temperature and density stabilize, indicating that the structure has reached a more stable state at the target temperature. In the second step, the interface model was run for 1 ns under the NVT ensemble (constant number of atoms N, volume V, and temperature T) with the same time step. At this point, the total energy and potential energy of the system are both in a stable state, proving that the relaxation time is sufficient. The main purpose of this step is to collect data and dynamic trajectory information, which will be used for statistical analysis in the subsequent analysis section. The Nosé thermostat [41] and Andersen barostat [42] were used in the MD simulation to maintain the temperature and pressure in the structure. Electrostatic and van der Waals (vdW) interactions were summed using the Ewald and atom-based methods, respectively. To speed up the calculation, the cutoff distance and buffer width were set to 12.5 Å and 1 Å, respectively. In addition, three independent simulations were run, and the results showed that all three simulations converged to similar structures and energy values, thereby proving the reliability of the simulation results.

2.3. Model Verification

To ensure the accuracy of the model, this section verifies the rationality of each component and the overall model used in the simulations. The comparison of model parameters in this study is shown in

Table 1. Comparison of model parameters in this study.

	C-S-H	Comparison Value	NR	Comparison Value	NR/C-S-H	Comparison Value
Density (g/cm3)	2.6	2.44 [43], 2.604 [24]	0.864	0.897 [34]
Young’s modulus (GPa)	90.25	77.0–129.7 [33,44]	1.836	1.893 [45]
Bulk modulus (GPa)					34.76	34.68 [22]
Shear modulus (GPa)					15.75	12.35 [22]

. First, the C-S-H and NR models were validated in terms of density (ρ) and Young’s modulus (E). The density and Young’s modulus of the C-S-H model constructed in this study are 2.6 g/cm³ and 90.25 GPa, respectively. The experimental density for this structure is 2.604 g/cm³, and Young’s modulus ranges from 77.0 to 129.7 GPa. The density and Young’s modulus of the NR model in this study are 0.864 g/cm³ and 1.836 GPa, respectively, while the literature reports values of 0.897 g/cm³ and 1.893 GPa. These data are close to previous research results, proving that the two-component models are relatively reasonable. Additionally, the overall NR/C-S-H interface model was also comparatively validated. Due to the lack of experimental data to support the model, only the mechanical properties of the model were comparatively validated. The bulk modulus (K) and shear modulus (G) of the model from the literature [23] were compared with those of the model in this study, as shown in Table 1. It can be observed that the data of this model are very close to those in the literature. Therefore, it can be concluded that the interface model constructed in this study is relatively reasonable.

3. Results and Discussion

The binding energy, radius of gyration, interface structure, chemical bond connections, and dynamic behavior of the interface model directly affect the bonding ability and compressive strength of RC [16,46]. Therefore, this study investigates the effects of high temperatures on atomic interactions at the two-phase interface from these aspects.

3.1. Binding Energy

The cohesive energy can quantitatively analyze the adhesion ability between two-phase interfaces, visually indicating whether there is mutual attraction or repulsion between the two-phase structures [47]. It can also explain the mechanism of crack formation at the macroscopic scale and the reasons for the decrease in bonding performance. Through cohesive energy, we can clearly understand the influence of temperature on the adhesion ability of NR/C-S-H interfaces. The cohesive energy between the C-S-H substrate and NR is calculated according to Equation (1). Here, the total energy in the system (E_Total) consists of potential energy (E_P) and kinetic energy (E_K). The potential energy is composed of diagonal terms of bond energy, cross terms of bond energy, and non-bonding energy. When the cohesive energy value obtained is negative, it indicates mutual attraction between NR and C-S-H interfaces; otherwise, they repel each other.

$$E_{int}=E_{Total}-E_{CSH}-E_{NR}$$

(1)

$$E_{Total}=E_P+E_K$$

(2)

$$E_P=E_{val-diag}+E_{val-cross}+E_{non-bond}$$

(3)

where $E_{int}$ is the interaction energy between C-S-H and NR; E_Total is the total energy of the system; $E_{CSH}$ is solely the energy of C-S-H; and $E_{NR}$ is solely the energy of NR.

Table 2. System total energy composition.

Temperature	ETotal (kcal/mol)	EP (kcal/mol)			EK (kcal/mol)
		Total	vdW	Elec
300 K	−101,283	−102,806	10,504	−125,821	1523.403
320 K	−101,056	−102,692	10,580	−125,786	1635.868
340 K	−100,725	−102,463	10,503	−125,127	1738.107
360 K	−100,757	−102,597	10,604	−125,958	1840.353
500 K	−99,738	−102,294	10,743	−126,928	2556.043
700 K	−98,097	−101,676	10,906	−127,854	3578.466

provides a detailed breakdown of the components of the total energy in the system at different temperatures, where positive values indicate repulsion and negative values indicate attraction. From the data in the table, it is evident that potential energy (E_P) is the primary component of the total energy, while kinetic energy (E_K) constitutes less than 5%. Furthermore, in the composition of potential energy, the contribution of electrostatic forces is significant, whereas van der Waals forces contribute relatively less. Further observation of the influence of temperature on the system energy reveals an inverse relationship between temperature and the magnitude (absolute value) of the total energy. When the temperature is 300 K and 360 K, the total energy is 101,283 kcal/mol and 100,757 kcal/mol, respectively, with a decrease of 0.519%. Meanwhile, at temperatures of 500 K and 700 K, the total energy decreases to 99,738 kcal/mol and 98,097 kcal/mol, respectively, with reductions of 1.525% and 3.146%. Additionally, as the temperature increases, the values of electrostatic forces and van der Waals forces both increase, while the absolute value of the total potential energy decreases.

The microscale interface of RC in reference [2], as shown in Figure 6a, reveals that at a temperature of 294 K, the rubber particles bond tightly with the cement, whereas with increasing temperature, noticeable cracks appear between the rubber and cement. Observing the cohesive energy calculation results in Figure 6b, it is found that the cohesive energies of all systems are negative, indicating good interfacial compatibility between them. As the temperature rises, the absolute values of the cohesive energies at the interfaces between the two phases gradually decrease. When the temperature is 300 K, 320 K, 340 K, and 360 K, the changes in binding energy values are not significant. At 300 K and 360 K, the binding energies are 189.52 kcal/mol and 180.77 kcal/mol, respectively, with a decrease of 4.62%. However, at high temperatures, the reduction in binding energy becomes more pronounced. When the temperature reaches 700 K, the binding energy value is 165.66 kcal/mol, a decrease of 12.59%. This indicates that high temperatures weaken the binding energy between NR and C-S-H, leading to the decrease in bonding performance shown in Figure 6a, which is one of the reasons for the appearance of cracks at the interface. Similar to existing research results [47,48], the larger the binding energy value between interfaces, the stronger the interatomic interaction, which has a positive effect on the macroscopic mechanical properties and durability of materials.

3.2. Radius of Gyration

The gyration radius is an important parameter that describes the compactness of molecules, with its numerical value reflecting the conformation and dynamic behavior of molecular chains. For the same molecule, a smaller gyration radius value and amplitude indicate a more compact molecule and a more stable system. By analyzing the molecular gyration radius within the system at different temperatures, we can understand the effect of temperature on the density of the internal structure. This section analyzes the evolution of the rubber molecule’s mass-weighted gyration radius to illustrate changes in the rubber molecule’s conformation. The calculation of the gyration radius is shown in Equation (4).

$$R_g=\sqrt{{\sum }_{i=1}^N [m_i\cdot (r_i-r_c{)}^2]/M}$$

(4)

where M is the total mass; $m_i$ is the mass of atom I; and $r_i-r_c$ is the distance from atom i to the center of mass.

Through comparison, it was found that the average gyration radius values are approximately the same between temperatures of 300 K and 320 K–500 K. Therefore, only the gyration radii at 300 K, 360 K, and 700 K are plotted. The results are shown in Figure 7, indicating that the average gyration radius at 700 K is approximately 6.15 Å, with significant fluctuations. The system becomes loose and unstable, possibly resulting in internal voids in the structure, leading to a decrease in compressive strength. This is because at high temperatures, the cohesive energy of the system decreases, weakening the cohesion, and making the rubber chains more prone to stretch and expand, resulting in an extended molecular state. At 300 K, the internal thermal energy of rubber molecules is lower, causing the molecular chains to maintain a compact or coiled state. Yun et al. [48] analyzed the effect of temperature on the gyration radius of tannic acid, concluding that high temperatures cause single-bond rotations, increasing the gyration radius, which validates the above analysis. It is worth noting that there is a decrease in the average gyration radius at 360 K. This could be because, within the temperature range of 300 K to 500 K, the decrease in cohesive energy did not weaken cohesion to the extent necessary to change the molecular chain conformation, thus limiting the extension of the molecular chains to some extent.

3.3. Interface Structure and Chemical Bond Analysis

Current researchers [8] have found through macroscopic experiments that the compressive strength of RC gradually decreases as the temperature increases. This section analyzes the interface structure and chemical bonds through relative concentration distribution (RCD) and radial distribution function (RDF) to clarify the atomic strength distribution and chemical bond states at different temperatures [49], revealing the mechanism of temperature’s effect on RC compressive strength.

3.3.1. RCD

Relative concentration distribution can reflect the distribution of atomic density along specific directions [50,51]. It is used to assess the spatial positions of atoms in C-S-H and NR. This model system is constructed as a layered structure along the Z direction (001). Therefore, the relative concentration of atoms is analyzed only along the Z direction. The relative concentration is calculated according to Equation (5) [24].

$$\mathrm{R}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}[\mathrm{s}\mathrm{e}\mathrm{t}{]}_{slab}=[\mathrm{s}\mathrm{e}\mathrm{t}{]}_{slab}/[\mathrm{s}\mathrm{e}\mathrm{t}{]}_{bulk}$$

(5)

where [set]_slab = (no.atoms in system)/(volume of slab); and [set]_bulk = (total no.atoms in system)/(volume of system).

Since the concentration distribution phenomena between 320 K and 500 K are similar to those at 300 K, comparisons were made only between the concentration distributions at 300 K and 700 K. From Figure 8a,c, it can be observed that the atomic concentration distribution along the Z direction (0 0 1) is nearly symmetric. Multiple strong Si, H_water, and O_water peaks are present in the C-S-H on both sides, with water molecules’ characteristic peaks located between the Si peaks, indicating a strong affinity of C-S-H for water molecules and a stable framework structure. Furthermore, atoms in NR and C-S-H show linear changes and atomic crossings within the 9–14 Å and 24–29 Å regions, indicating good compatibility between NR and cement. It is noteworthy that at a temperature of 300 K, there are fewer water molecules in the atomic cross-section, which helps the atoms in NR to form chemical bonds with the matrix. However, when the temperature rises to 700 K, the number of water molecules increases significantly. Figure 8b,d provide a more intuitive view of the atomic distribution along the Z direction in the system. While the distribution of atoms in C-S-H and NR regions is relatively uniform at both temperatures, there is a significant difference in the proportion of water molecules at the interface: 6% at 300 K compared to 16% at 700 K. Because NR cannot form hydrogen bonds with water molecules (see Section 3.3.2), this hinders the ionic and covalent interactions between NR and the matrix. Our simulation results are consistent with existing MD studies on different material interfaces at high temperatures, both confirming the trend of water molecules transferring to the interface at high temperatures [48].

3.3.2. RDF

The radial distribution function (RDF) allows for a deeper understanding of the spatial relationship between rubber and cementitious bases [52]. RDF describes the probability g(r) of finding another atom within a certain range around a central atom, reflecting the degree of molecular aggregation. The first prominent peak in RDF corresponds to the atomic bond length [29], forming the basis of static structural analysis. Thus, RDF graphs can be used to observe the interaction modes and strengths between atoms. RDF is calculated according to Equation (6) [34].

$$g_{AB}(r)=1/⟨{\rho }_B{⟩}_{local}·{\displaystyle \frac{1}{N_A}}·{\sum }_{i\in A}^{N_A} {\sum }_{i\in B}^{N_B} \delta (r_{ij}-r)/4\pi r^2$$

(6)

where $g_{AB}\left(r\right)$ is the probability of finding particle B within the range around particle A; r is the distance between each pair of atoms; N is the number of atoms; and ${⟨{\rho }_B⟩}_{local}$ is the average total shell density of particle B around particle A.

The stability of the interface mainly depends on the atomic interactions within the interface. According to the rules of hydrogen bond formation, hydrogen bonds can only form when the distance between O atoms and H atoms is less than 2.45 Å [53]. Observing Figure 9a,b, it is found that characteristic peaks are located near 2.75 Å and 2.61 Å, respectively, or there is no distinct peak phenomenon at certain temperatures. Moreover, the bond lengths of all characteristic peaks at all temperatures are greater than the threshold for hydrogen bond formation, indicating that O_water and O_C-S-H cannot form hydrogen bonds with H_NR. This reveals that the interaction between NR and C-S-H interfaces mainly relies on covalent and ionic bond interactions. Figure 9c shows that at 300 K, the characteristic peak of the Si-H_NR bond is at 2.89 Å. With increasing temperature, the bond length of the characteristic peak increases and its intensity decreases. This indicates that at higher temperatures, the spatial correlation between Si_C-S-H and H_NR decreases, and high temperatures weaken the interaction between Si_C-S-H and H_NR, reducing the orderliness of the bonds. This is because, under high-temperature conditions, water molecules tend to accumulate at the interface (Section 3.3.1), hindering the chemical bond formation between NR and the matrix. Figure 9d shows that the characteristic peak of the Ca-H_NR bond is near 3 Å at all temperatures, and high temperatures similarly weaken the interaction between Ca_C-S-H and H_NR. However, at 340 K, the characteristic peak is highest, indicating strong interaction between Ca-H_NR bonds. This corresponds to the binding energy discussed earlier, where at this temperature, the binding energy value slightly increases. In summary, hydrogen bonds cannot be formed at the interface between the two phases, and the interactions mainly rely on covalent bonds and ionic bonds. Additionally, as the temperature increases, water molecules tend to accumulate at the interface, hindering the connection between NR and the matrix, thereby gradually decreasing the system’s binding energy. This is one of the reasons why the compressive strength of RC decreases under high-temperature conditions.

3.4. NR/C-S-H Dynamic Behavior

The previous section mainly revealed the atomic distribution and chemical bond states. In addition to characterizing the RC interface structure and chemical bonds, considering the dynamic behavior of the model system is also crucial. This section analyzes the mean square displacement (MSD) and time correlation function (TCF) of the system to more intuitively reveal the stability of atoms and chemical bonds in the system [16].

3.4.1. MSD

The mean square displacement (MSD) can more intuitively display the dynamic behavior of atoms at the interface between NR and C-S-H phases. In molecular dynamics, each atom is constantly in motion, and MSD can effectively analyze the diffusion between atoms. MSD is calculated according to Equation (7) [54]. The diffusion coefficient D is 1/6 of the slope of the MSD-t curve. The D value is obtained by taking 1/6 of the slope of the MSD curve, which exhibits a linear relationship, as shown in Equation (8) [55]. A larger value indicates that atoms diffuse away from their initial positions at a faster rate.

$$MSD=⟨{\mid r_i\left(t\right)-r_i\left(0\right)\mid }^2⟩$$

(7)

$$\begin{array}{c}D=1/6N*\underset{t\to \mathrm{\infty }}{lim} {\displaystyle \frac{d}{dt}}{\sum }_{i=1}^N ⟨{\left|r_i\left(t\right)-r_i\left(0\right)\right|}^2⟩\end{array}$$

(8)

where r(t) and r(0) are the positions of the atom at times t and 0, respectively, and N is the total number of particles to be averaged.

The MSD and diffusion coefficients of the main atoms in the system are shown in Figure 10 and

Table 3. Diffusion coefficient of the main atoms at the interface.

Temperature	HNR	CNR	Ca
300 K	0.08	0.04	0.008
320 K	0.23	0.138	0.041
340 K	0.247	0.131	0.018
360 K	0.241	0.115	0.022
500 K	0.397	0.256	0.043
700 K	1.835	1.473	0.063

, respectively. From Figure 10a,b, and Table 3, it can be observed that the MSD values of H and C atoms in NR vary proportionally with temperature. The changes in MSD values correspond to the diffusion coefficients. At 300 K, the MSD values of both atoms are close to 0, with diffusion coefficients of 0.08 and 0.04, respectively. When the temperature is between 320 K and 360 K, the MSD values of both atoms in NR rise slowly, and their diffusion coefficients are below 0.3. When the temperature is at 500 K and 700 K, the MSD values show a rapid upward trend, with D values reaching up to 1.835. This indicates that at 300 K, the atoms in NR move more slowly and are more likely to pair with the matrix to form chemical bonds. As the temperature increases, the atoms move faster, weakening the interactions with the matrix. This phenomenon is consistent with existing research results [48]. Additionally, from Figure 10c and Table 3, it can be observed that the MSD values of Ca atoms in C-S-H increase with temperature but remain relatively small, with MSD values below 0.7 and diffusion coefficients D below 0.07. The above situation occurs because water molecules gather at the interface at high temperatures, and then the atoms in NR move faster to find a suitable position to bond with the matrix. The C-S-H skeleton has high stability, and the position deviation of atoms in the system is small at high temperatures.

3.4.2. TCF

The interactions between molecules are dynamic processes, and the TCF can describe the dynamic behavior of molecules at the two-phase interface. It can assess the stability of chemical bonds. Since the RDF analysis above indicates that hydrogen bonds cannot form in the system, this study focuses on the stability of covalent and ionic bonds in the system. The dynamic characteristics of interfacial connections can be further analyzed. The TCF is calculated according to Equation (9) [56].

$$C\left(t\right)=\left[\delta b\left(t\right)\delta b\left(0\right)\right]/\left[\delta b\left(0\right)\delta b\left(0\right)\right]$$

(9)

where the value is either 0 or 1. When the connection between atomic pairs is stable, the TCF remains at 1. When there is no connection between atomic pairs, the TCF is 0. Over time, the TCF value of chemical bonds between atoms will fluctuate between 1 and 0. Observing the deviation of the TCF from the value of 1 reflects the stability of atomic pairs.

Figure 11 shows the TCF of the main chemical bonds in NR/C-S-H. From Figure 11a, it can be seen that the TCF of the Si-H_NR chemical bond remains above 0.99 at 300 K, indicating that the chemical bonds formed between NR and C-S-H are consistently stable at this temperature. Furthermore, as the temperature increases, the TCF of Si-H_NR shows a continuous decline, dropping to around 0.8 at 700 K. This indicates that as the temperature rises, the available sites on the substrate for bonding with rubber decrease, leading to reduced interfacial chemical bonding and stability. This phenomenon is similar to the current research results on inorganic organic material interfaces. The same phenomenon can be observed in Figure 11b, where high temperatures affect the interfacial chemical bonding, which may be the reason for the decrease in the material’s compressive strength and ultimate stress. In summary, high temperatures affect the stability of chemical bonds between NR molecules and C-S-H, leading to reduced compressive strength and bonding strength. Additionally, the literature [13] indicates that the ultimate stress of RC decreases at high temperatures, which is consistent with the MSD and TCF analysis results mentioned above. At high temperatures, the molecular motion of NR is faster, seeking coordination sites with the matrix, thus reducing the stability of chemical bonds at the two-phase interface. This explains from a nanoscale perspective that this is one of the reasons why high temperatures lead to a decrease in RC ultimate stress.

In summary, the reduction in RC bonding performance, compressive strength, and ultimate stress under high-temperature conditions is mainly due to the atomic arrangement at the interface, the state of chemical bond connections, and their stability. These research results demonstrate that high temperatures weaken the interaction between C-S-H and NR atoms, preventing hydrogen bonding at the interface. Therefore, when excellent fire resistance is required in practical engineering, modifiers can be added to optimize structural properties. For example, interfacial coupling agents can be used to increase the number of hydrogen bonds at the interface and enhance the stability of the chemical bonds, thereby ensuring structural safety [20]. Previous studies have focused on the performance of modified materials while neglecting the atomic interactions at the RC interface itself under the influence of temperature. This is why this paper delves deeply into the interface between C-S-H and NR. This study mainly focuses on the nanoscale perspective, and the macroscopic and microscopic material properties are selected from existing literature data comparisons, which is a limitation of this study. In the future, macro and micro experiments will be conducted to achieve more rigorous scale bridging.

4. Conclusions

In this study, we used MD simulation methods to systematically analyze the impact of temperature on the interfacial mechanical properties of RC from various aspects, including binding energy, radius of gyration, static structure, and interface evolution. Through nanoscale research and analysis, we revealed the weakening mechanisms of temperature on the mechanical properties of RC structures, providing theoretical support for the engineering application and material improvement and optimization of RC. The research results indicate the following:

(1)

NR and C-S-H have good interfacial compatibility, but high temperatures reduce the binding energy, leading to noticeable cracking at the two-phase interface. Additionally, C-S-H has a stable skeleton with its atoms being less affected by temperature. However, atoms in NR are significantly affected by temperature; the higher the temperature, the faster the atomic movement and the poorer the stability. Notably, the number of available rubber sites on the substrate decreases at high temperatures, reducing the stability of Si-H_NR and Ca-H_NR bonds, and leading to a decrease in the peak stress of the material.

(2)

Under high temperatures, the rotation of chemical bonds in rubber molecules causes an increase in the radius of gyration, resulting in a looser molecular state. At 300 K, the radius of gyration is relatively small, and the molecular chains within the system are relatively compact. Additionally, within the temperature range of 300 K-500 K, the reduction in cohesive energy does not reach the threshold to alter the conformation of molecular chains, limiting their expansion.

(3)

High temperatures have little impact on the RCD. Water molecules aggregate at the two-phase interface under high temperatures, hindering the formation of chemical bonds between NR and the matrix. NR cannot form hydrogen bonds with C-S-H. Silicon atoms connect rubber to the substrate by forming H_NR-Si bond chains. However, high temperatures increase the bond length of chemical bonds and reduce their bonding strength, leading to a decrease in RC compressive strength.