Crosslink-to-Entanglement Transition and Crosslink Fluctuations in Polymer Networks

We use coarse-grained molecular dynamics simulations to study the mechanical properties of networks with different degrees of polymerization (DP) between crosslinks. The simulations show that there is a transition from crosslink- to entanglement-controlled network elasticity with increasing DP of network strands, n_x, which is manifested in changes in the n_x-dependence of entanglement and structural shear moduli. In particular, this crosslink-to-entanglement transition results in saturation of the network shear modulus at small deformations and renormalization of the DP of effective network strands determining nonlinear elastic response in the strongly entangled networks with n_x >n_e (DP of the network strand between entanglements). This crosslink-to-entanglement transition can also be observed from qualitative changes in the time evolution of the correlation function <(R(t+τ)-R(t))²> describing crosslink fluctuations. At short time scales, this function reflects Rouse dynamics of crosslinks, while at longer time scales, it saturates to a constant. The constant value scales linear with the DP of network strands between crosslinks n_x for n_x <n_e. However, for strongly entangled networks (n_x >n_e), the plateau saturates with increasing DP between crosslinks, n_x.