Mechanics of Polymer Networks with Dynamic Bonds

Incorporation of dynamic, reversible bonds into the polymer network of soft gels has been exploited as a strategy to enhance fracture toughness and to enable self-healing. Gels with dynamic bonds often exhibit macroscopic viscoelasticity which can be traced back to the kinetics of bond dissociation and reformation. This chapter discusses recent efforts in developing constitutive models to connect the molecular-level bond kinetics to the continuum-level viscoelasticity. Two different modeling approaches are described using a model system, i.e., hydrogel with dynamic physical crosslinks and static chemical crosslinks. Both approaches are based on the theoretical framework of continuum mechanics and thermodynamics and aim to quantify how the total network free energy is governed by macroscopic deformation and molecular kinetics. In the first approach, the network is treated as a collection of polymer chains formed at different instants along the loading history. These chains experience different extent of deformation and thus carry different free energy. The total free energy is the sum of contributions from all chains. The second approach considers a statistical distribution of the chain end-to-end vectors, which evolves upon macroscopic deformation and reaction of dynamic bonds. The total free energy is calculated by integrating the single-chain free energy over the chain distribution space. These two approaches, capable of capturing the time-dependent mechanical behaviors of hydrogels with reversible crosslinks, can be extended to model the macroscopic mechanics induced by other molecular mechanisms such as bond exchange and chain scission.