Abstract
Recent advancements in polymer chemistry have introduced a new class of stimuli-responsive networks, called vitrimers. Due to the dynamic covalent reactions occurring above a certain temperature, vitrimers hold great promise as adaptive materials capable of shape reconfigurability, welding, and self-healing. Despite extensive experimental studies, the theoretical models for thermo-viscoelastic behavior of vitrimer networks are rare and often built upon simplifying assumptions on the network microstructure. One a priori assumption is that the constitutive strands of vitrimer networks are of uniform length. Transesterification reactions, however, are statistical processes that yield networks with polydisperse chain lengths. This contribution lays out a theoretical framework to study the effect of network polydispersity on viscoelastic properties of vitrimer networks subjected to finite deformations. To this end, the well-known 8-chain model for rubber elasticity is modified to account for vitrimer polydispersity. Assuming that the crosslinking process is uncorrelated along the primary chains, a Poisson distribution is obtained for the strand length in a random network. The free energy of the random network and consequently the components of Cauchy stress are calculated in closed form. The predictions of this constitutive model show a better agreement with the experimental results compared to the models assuming uniform chain length for the network.
