General approximation of single-chain models with extensible links

Predictive constitutive models for the large deformation of soft polymer materials often seek direct theoretical connections to the underlying molecular physics. Correspondingly, many constitutive models for polymer networks are built up from statistical mechanical models for single polymer chains. Predicting large deformation scenarios such as fracture or failure often requires the single-chain models to include some extensibility beyond their purely entropic formulation. For discrete single-chain models, this is typically done by making the originally rigid links extend according to a potential energy function. While this has been accomplished in a comprehensive fashion for the simple freely jointed chain model, there is no systematic approach for other models which are more representative of real polymer chains. For this reason, an approach for general discrete single-chain models with extensible links is developed. The asymptotic theory is built for arbitrary link potentials, with little specification of other model traits, before being demonstrated by extending existing rigid-link single-chain models to include extensibility. The advances made here will aid predictive models for polymers and for general molecular stretching.