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Franck Vernerey (University of Colorado Boulder)
Statistical Mechanics of Dynamic Polymer Networks. Exploring the Interplay Between Viscoelasticity, Damage and Fracture.
A large majority of soft biological materials are made of elastic molecular networks with changing topology, allowing to accommodate growth, remodeling, and self-healing over time. Such behaviors can now be replicated in synthetic polymers through the synthesis of networks whose chains are connected by weak molecular bonds, which under thermal fluctuations can permanently associate and dissociate. In contrast to their elastic counterparts, these networks therefore exhibit a myriad of new physics (flow, elastic deformation, self-healing, programmability, actuation, ...) that can be controlled by network topology, bond dynamics, and deformation rate. The link between molecular mechanisms, loading history, and the time-dependent response of the network is however poorly understood.
The presentation will tackle this challenge by providing an overview of the inner workings of these networks together with ways to characterize their response using concepts in statistical mechanics. This will allow us to derive conditions for which a network can transition from a viscous fluid to an elastic solid depending on the Weissenberg number, that measures the competition between the rates of loading and bond dynamics. We will see that for intermediate Weissenberg numbers, bond dynamics not only depends on force, but can also be coupled with chain rupture. In this case, we observe nonlinear interplay between the network elasticity, flow and damage which is at the origin of nonlinear rheology and rate-dependent fracture.These concepts are used to illustrate the puzzling response of various dynamics networks, ranging from the nonlinear rheological behavior of fire-ant aggregations to the transient fracture of vitrimers, a new class of dynamic polymers.