Freely jointed chain models with extensible links

TL;DR

This paper develops analytical approximations for the mechanical response of extensible freely jointed chain models, enhancing the ability to model polymer chain mechanics with bond stretching in a tractable way.

Contribution

It introduces an asymptotically correct thermodynamic theory to derive analytical approximations for extensible chain models, which are typically intractable.

Findings

Approximations match numerical results for various link potentials.

Method extends to other single-chain models and molecular stretching.

Provides a practical analytical tool for polymer mechanics modeling.

Abstract

Analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized single-chain model, such as the freely jointed chain model. To include bond stretching, the rigid links in the freely jointed chain model can be made extensible, but this almost always renders the model analytically intractable. Here, an asymptotically correct statistical thermodynamic theory is used to develop analytic approximations for the single-chain mechanical response of this model. The accuracy of these approximations is demonstrated using several link potential energy functions. This approach can be applied to other single-chain models, and to molecular stretching in general.