Stress Relaxation, Dynamics, and Plasticity of Transient Polymer Networks
We propose a theoretical framework for dealing with a transient polymer network undergoing small deformations, based on the rate of breaking and reforming of network cross-links and the evolving elastic reference state. In this framework, the characteristics of the deformed transient network at microscopic and macroscopic scales are naturally unified. Microscopically, the breakage rate of the cross-links is affected by the local force acting on the chain. Macroscopically, we use the classical continuum model for rubber elasticity to describe the structure of the deformation energy, whose reference state is defined dynamically according to when cross-links are broken and formed. With this, the constitutive relation can be obtained. We study three applications of the theory in uniaxial stretching geometry: for the stress relaxation after an instantaneous step strain is imposed, for the stress overshoot and subsequent decay in the plastic regime when a strain ramp is applied, and for the cycle of stretching and release. We compare the model predictions with experimental data on stress relaxation and stress overshoot in physically bonded thermoplastic elastomers and in vitrimer networks.