Modes of Molecular-Chain Fluctuation in Polymer Cross-Linked Networks under Tensile Deformation

The fluctuation mode of molecular-chain conformations in polymer cross-linked networks during macroscopic deformation has not yet been fully clarified. To address this issue, coarse-grained models of polyisoprene cross-linked networks with different cross-linking densities and degrees of polymerization were constructed, and uniaxial tensile molecular dynamics simulations were performed. After sufficient relaxation, long-time conformations of molecular chains in near-equilibrium states were extracted. Based on these conformations, the mean paths of molecular chains and the envelope surfaces of their conformations were obtained. Combined with results from the Z1+ method, the evolution of primitive-path length and orientation, trajectory-envelope volume, and confining-tube diameter during deformation was quantitatively analyzed. For the entangled cross-linked networks studied here, the results show that (1) the primitive-path lengths of chains in different directions all increase with stretch ratio, with only weak differences between the two selected initial-orientation groups; (2) chain segments initially distributed both along and perpendicular to the stretching direction gradually orient toward the stretching direction as deformation increases; (3) the spatial volume available for chain fluctuation remains essentially unchanged during deformation; and (4) the equivalent tube diameter decreases with increasing chain extension and network cross-link density while showing only weak dependence on initial orientation. These results indicate that, during deformation, local chain segments progressively orient toward the tensile direction while the mean-path contour length increases, whereas radial fluctuations decrease with increasing tensile deformation. Therefore, the evolution of molecular chain motion is more appropriately described by the primitive path rather than by the end-to-end vector. This study reveals the characteristics of constrained chain motion in cross-linked networks under deformation and can guide the mechanical analysis and constitutive modeling of polymer cross-linked networks.