Viscoelastic Response of Crosslinked Rubber: Coarse-Grained Molecular Dynamics and Time-Temperature Superposition

Abstract

The viscoelastic response of crosslinked rubber was investigated using coarse-grained molecular dynamics simulations combined with time-temperature superposition. Crosslinked polymer networks containing different numbers of crosslinkers were generated using a dynamic reaction probability model and their mechanical responses were analyzed by Green-Kubo-based stress autocorrelation and uniaxial tensile simulations. The relaxation master curves were constructed from the relaxation modulus and loss tangent, extending the accessible timescale by nearly seven orders of magnitude beyond that directly attainable in the simulation. Increasing the number of crosslinkers slowed the stress relaxation, reduced the peak value of the loss tangent, and increased the equilibrium modulus, indicating that crosslinking suppressed the viscous relaxation and enhanced the elastic network constraints. Stress decomposition further revealed that intermediate-time relaxation is strongly affected by negative cross-correlations between the pair and bonded stresses, whereas the long-time equilibrium elasticity in highly crosslinked systems is sustained mainly by the autocorrelation and cross-correlation of the backbone-bond and crosslink-bond stresses. In addition, uniaxial tensile simulations showed that crosslinking promotes chain orientation and that crosslink bonds undergo greater stretching than backbone bonds near the onset of strain hardening. These results provide a molecular-scale picture of how crosslinking governs both the stress relaxation and elastic reinforcement of rubber.