A rouse-tube model of dynamic rubber viscoelasticity

The dynamic-mechanical response of a polymer network has been calculated using a stress-based Rouse model formalism. In contrast to the previous work, this improved formulation incorporates appropriate boundary conditions and provides a smooth crossover from the classical equilibrium result of rubber elasticity to the short time-scale relaxation. We develop a consistent implementation of the classical tube model, which is merged with the Rouse dynamics to take into account the entanglement effects. In a polymer network, crosslinks prevent the global reptation and constraint release. Entanglements thus acquire a different topological meaning and have a much stronger effect on the resulting mechanical response. We construct a dynamic stress tensor for a polymer network, which naturally covers the whole frequency/time range. Using this stress tensor, we first examine the equilibrium response to small shear and uniaxial deformations, and then investigate the linear dynamic response of a network for all the cases where the stress-tensor computations are analytically tractable.