Unentangled Vitrimer Melts: Generalized Rouse Theory Reveals Impact of Cross-link and Backbone Chemistry on Linear Viscoelasticity

Vitrimers are polymer networks that have covalent cross-links which preserve network connectivity but permit topology fluctuations. We employ a generalized inhomogeneous Rouse model (IHR) to study the rheology of unentangled vitrimer melts. We observe that vitrimers with uniform and random cross-link distributions exhibit larger viscosities and relaxation times than gradient and blocky types. Polydimethylsiloxane vitrimer (which has a flexible backbone) shows an Arrhenius temperature dependence for viscosity, while polystyrene and poly(methyl methacrylate) vitrimers (which have rigid backbones) are only Arrhenius at high temperatures. During stress relaxation, the short time dynamics represent monomer friction, while the long time dynamics encompass a combination of network strand relaxation and cross-link exchange. Because of the different temperature dependences of the processes, time-temperature superposition fails. The effective rheological activation energy can be estimated a priori from the cross-link exchange activation energy and the backbone Williams-Landel-Ferry parameters. Based on these findings, we discuss the utility of the IHR for understanding vitrimer rheology, and best practices for characterizing the viscosity and relaxation time.