Multiscale analysis of sulfur-bridge topology and linear mechanical response in natural rubber

Context: Sulfur vulcanization determines the mechanical response of natural rubber, but sulfur content or average crosslink density alone cannot describe how mono-, di-, and polysulfidic bridges are converted into elastically effective network structures. Here, topology-resolved networks with controlled sulfur-bridge architectures were compared at sulfur contents of 0.6, 1.3, and 2.5 parts per hundred rubbers (phr). At fixed sulfur content, monosulfidic-rich networks generated more backbone subdivision points, shorter and less dispersed strands, fewer dangling and loop defects, and higher active-strand densities. Polysulfidic-rich networks consumed more sulfur atoms per bridge and consequently exhibited longer and more heterogeneous strands, more primitive defects, lower equilibrium shear moduli, and enhanced dissipative relaxation. These results show that sulfur-bridge architecture regulates linear mechanical behavior mainly through the realized mesoscopic topology rather than through sulfur content alone. Methods: All-atom (AA) sulfur-vulcanized cis-1,4-polyisoprene networks were generated using the CURE procedure in HTPolyNet, coupled to GROMACS, with the General AMBER Force Field parameters. One polyisoprene repeat unit was mapped to one coarse-grained rubber bead, whereas sulfur atoms were retained explicitly. Coarse-grained bonded interactions were obtained from mapped atomistic distributions, and rubber-bead nonbonded interactions were represented by a Lennard–Jones potential parameterized through iterative Boltzmann inversion. Free volume was evaluated with OVITO, and retained entanglement constraints were extracted using Z1+ primitive path analysis. Custom graph-based routines identified soluble clusters, dangling strands, loop strands, and active strands. Equilibrium shear moduli were estimated using a phantom force-balance network, and frequency-dependent moduli were calculated from the eigenvalue spectrum of a normal-mode connectivity matrix.