Effect of crosslinking agent types on the tensile properties of polyisoprene rubber

The impacts of crosslinking bond types on the equilibrium kinetics and uniaxial tensile properties of polyisoprene rubber were investigated by using molecular dynamics (MD) simulations. We analyze the changes in mean square displacement, glass transition temperature, and end-to-end vector autocorrelation function of different crosslinked systems during the equilibrium process. It was found that the mobility of polysulfide crosslinked systems was more limited compared with that of monosulfide and disulfide bonds. In addition, during uniaxial stretching, the polysulfide-bonded crosslinked system could exhibit better tensile strength, and the stress response was significantly improved. The above research results help to understand the mechanical properties and deformation mechanism of crosslinked polyisoprene rubber and provide certain reference values for improving the performance of related materials.


Introduction
Rubber materials find extensive use in diverse fields, including automobile, electronics, construction, and medical devices, owing to their excellent wear resistance, corrosion resistance, adhesion, and high elasticity [1] .However, in its unprocessed state, it often fails to meet the requirements of practical working conditions due to insufficient strength.Therefore, to enhance the mechanical performance of the material, a common practice involves heating and curing it with a vulcanizing agent to form a cross-linked network structure.Alternatively, fillers like silica are added, or the composite with fibers and metals is employed to improve its properties.Among them, vulcanization treatment has been widely researched and developed, with a certain degree of reliability and controllability.In the traditional vulcanization process, sulfur decomposes to form sulfur molecules with different numbers of sulfur atoms, including mono-sulfur (-S-), disulfide (-S-S-), and poly-sulfur (-Sx-) atoms.Among them, single sulfur atoms may participate in short-chain cross-linking, while double sulfur atoms may participate in forming longer cross-linking chains than single sulfur atoms.Multisulfur atoms typically refer to structures containing three or more sulfur atoms, and these structures may give rise to extremely long cross-linking chains.Therefore, different sulfur molecules, when reacting with the double-bonded carbon atoms on the rubber polymer chains, will form cross-linking networks of varying degrees.To explore the mechanisms and distinctions in the cross-linking networks formed by vulcanized cross-linking agents of different lengths, further investigation at the molecular scale is necessary.However, traditional experimental methods make it difficult to accurately control the formation of cross-linking agent types and are unable to obtain the specific positions and movements of molecules or atoms.
Given the complex internal structural evolution during the stretching deformation of cross-linked systems, the swift progress in computer technology has offered a novel research approach for this purpose.Molecular dynamics simulations combine classical mechanics with statistical mechanics, establishing a relationship between microscopic structure and macroscopic performance by calculating and analyzing the mechanical properties of materials.For instance, Chen et al. [2] simulated the thermal conductivity and mechanical behavior of polyisoprene at different degrees of polymerization.Rottach et al. [3] , through molecular dynamics simulations, investigated the influence of cross-linking on the constitutive behavior and internal structure of polymer networks.However, there is a dearth of research utilizing computational simulation methods to investigate how cross-linking agent types affect the mechanical properties of rubber materials.
Therefore, taking polyisoprene rubber as an example, molecular dynamics simulation methods were used to construct network models cross-linked by different types of sulfur molecules (composed of single sulfur, disulfide, and polysulfide atoms).The influence of crosslinking agent types on the dynamic mechanical properties of the IR rubber system during equilibrium and stress response during uniaxial tension was analyzed and studied.From the perspective of molecular scale, the close relationship between the structure of crosslinking agents and the mechanical properties of infrared rubber during stretching has been deeply revealed.

Modelling
The model was constructed by using Material Studio (MS) molecular simulation software developed by Accelrys.Through the Visualizer module, the established isoprene molecular monomer was generated into a high degree of polymerization polyisoprene rubber molecular chain.Each established molecular chain was subjected to structure optimization and energy minimization.Then, the Monte Carlo method was used in the Amorphous Cell module to fill the rubber molecular chains into the unit cell lattice and establish a periodic model.The molecular chain length is 100, and the number of chains is 30.The adoption of the PCFF force field could effectively simulate the static and dynamic mechanical properties of polyisoprene rubber.Cross-linking bonds were then introduced into the model via MS Perl scripts, by randomly selecting two double-bonded carbon atoms on two of the rubber molecular chains as reaction sites.If the distance d between them matches 0.25 nm < d < 0.75 nm, the sulfur atoms will bond with the C atoms in the C=C bond.The C=C bond is converted to a C-C bond, and the disulfide bond structure is attached to the rubber molecular chain via a carbon-sulfur bond (C-S).Finally, the Forcite geometry optimization was performed by using the Smart algorithm to eliminate local irrational structures in the model and to adjust the distance of the C-S bond and angle in the model.In this study, a crosslinking agent molecule was composed of 1, 2, or 4 sulfur atoms (Ncs=1, 2, and 4) to simulate the monosulfide, disulfide, and polysulfide crosslinking agents.The modeling process is shown in Figure 1.

Molecular dynamics simulation methods
Structural optimization of different crosslinked IR rubber models and computational analysis of kinetic properties were carried out by using LAMMPS software.Before conducting the dynamic equilibrium simulation of the cross-linking system, it was necessary to employ periodic boundary conditions to eliminate the finite size and edge effects in the simulation [4] .The NVT and NPT ensembles were employed to bring the cross-linking system to an equilibrium state.Initially, the model underwent a stepwise dynamic simulation within the NVT ensemble.We use the Nose Hooper method to control the temperature at 500 K to achieve short-term equilibrium of the system and reduce internal stress.Subsequently, the NPT ensemble was employed for a 5 10 1 step dynamic simulation, maintaining the temperature at 500 K to obtain the optimal structure of the model.Finally, the temperature was lowered to 300 K for a 1 ns NPT equilibrium simulation to bring the system to a stable state.After reaching equilibrium, different cross-linking models were subjected to tensile simulations along the x-axis by using an engineering strain rate of , with a maximum tensile strain of 3.0 and a stretching time of 300 ps.To eliminate the random deviation of the data, 100 steps were used as a reference to take 1 sample every 10 steps forward, a total of 5 samples were taken, and the stress values of these 5 samples were averaged.The molecular visualization was conducted by using OVITO software.

Dynamic equilibrium performance analysis
This section calculates and analyzes the changes in mean-square displacements, end-to-end vector autocorrelation functions, and glass transition temperatures of the IR rubber model.The goal is to elucidate and predict the impact of crosslinking agent types on their kinetic properties during the equilibrium state process.
The influence of crosslinker type on the ability of polymer segments to move can be further characterized by calculating the system's glass transition temperature.Staged cooling was used to reduce the temperature of the system from 500 K to 100 K, with each stage cooling by 50 K.The statistically collected data were plotted against the density of the simulated box versus temperature.The glass transition temperature of the system was obtained by linearly fitting the temperature at the intersection point.Figure 2 gives the variation rule of the glass transition temperature of IR rubber with the parameters of the type of cross-linking bond in the system.With the increase of Ncs, the glass transition temperature of IR rubber is gradually increased.This means that higher Ncs can more effectively inhibit the movement of molecular chains within the crosslinking system, which makes the molecular movement of the material near the glass transition temperature more strongly restricted.Therefore, high Ncs cross-linking systems require higher temperatures to begin movement, and this result is consistent with the experimental law [5] .Mean Squared Displacement (MSD) serves as a metric to characterize the average distance traveled by particles in space over time and is extensively employed to delineate the translational dynamics of the system [6] .Figure 3 (a) illustrates the time evolution of the MSD curves for molecular chain segments within various cross-linked IR rubber systems at a temperature of 300 K. Looking at the whole picture, with the increase of relaxation time, the diffusion rate of crosslinked IR rubber system gradually tends to level off, and the system tends to be stable.With the increasing Ncs, the change of molecular chain means square displacement in the cross-linked IR rubber system decreases.This indicates that the increasing Ncs can more effectively limit the diffusion ability of the molecular chain in the system.The end-to-end vector autocorrelation function ( ) P t described the correlation between terminal units of polymer chains and was commonly employed to characterize the rotational dynamics of polymer chains or segments [7] , as given by: Where ( ) e t and (0) e denote the end-to-end unit vectors for each molecular chain at time t and the initial time, respectively; < > denotes the average of the system by using different time origins.The end-vector autocorrelation function of the molecular chain in the crosslinked IR rubber system shows a decreasing trend with the increase in relaxation time.This trend slows down with the increase of Ncs in the system, which reflects that the rotational ability of the molecular chain segments gradually weakens with the increase of Ncs in the system.The primary reason for this phenomenon is the constraint of crosslinking on the molecular chains, leading to the inhibition of rotational motion of the chain segments.This constraint effect significantly intensifies with the increase of Ncs in the system.

Uniaxial tensile properties
Uniaxial tensile simulation experiments were carried out to investigate the effect of cross-linking bond type on the mechanical properties of IR systems.A uniaxial stretching simulation was performed along the x-axis direction at a constant strain rate of , and the total volume of the simulated box was maintained constant during stretching.Figure 4 presents the variation rule of the stress-strain curve with the Ncs parameter for the IR rubber model during stretching.From Figure 4 (a), when the strain is less than 0.15, the stress increases linearly with the strain, which satisfies Hooke's law and exhibits quite good elasticity.The system reaches its maximum yield limit when the strain is 0.15.This is because as the strain increases, the molecular chains gradually become more ordered.However, within a certain strain range, the interaction between chain segments is insufficient to resist the increase of external strain.When a certain strain is reached, the interactions between the chain segments begin to affect the overall behavior of the material, leading to a reduction in stress.This critical value is often referred to as the "yield point" or "stress maximum" of the material.After reaching the yield point, the stress slowly decreases with the increase of strain, which is a strain-softening phenomenon.A turnaround occurs after the stress decreases to a local minimum.When the strain is greater than 1, the value of stress starts to enhance continuously with the increase in strain, and after the strain is greater than 2.5, the stress increases exponentially.The stress values of the system at the same strain are positively correlated with the magnitude of Ncs.For instance, at a strain of 3, the stress response of the system with Ncs=4 is significantly higher than that of the system with Ncs=1, which is approximately four times higher.

Conclusions
The effect of the cross-linking bond type Ncs on the structure and properties of polyisoprene rubber materials was systematically investigated through molecular dynamics simulation (MD) methods.
Analyses showed that an increase in Ncs within the system during equilibrium diminished the motility of the molecular chain segments.This was specifically manifested as an increase in the glass transition temperature, which represents the chain segment mobility of the entire IR system.Simultaneously, there was a decrease in the mean square displacement of the molecular chain, indicating a reduction in the translational ability of the entire chain.Additionally, there was a decrease in the terminal vector autocorrelation function, reflecting a decline in the rotational ability of the chain segment.During uniaxial stretching, the IR system exhibits a stronger stress response with the increase of Ncs.The findings from this research contribute to an improved understanding of how cross-linking structures affect the mechanical properties of polyisoprene rubber.This provides valuable insights for enhancing the performance of related materials.

Figure 2 .
Figure 2. Density versus temperature for different crosslinked IR rubber systems.

Figure 3 .
Figure 3. (a) Mean square displacement; (b) End-to-end vector autocorrelation function over time for different crosslinked IR rubber systems.

Figure 4 .
Figure 4. Variation of stress-strain curves for different Ncs systems.