Force-Extension Relation and Plateau Modulus for Wormlike Chains

TL;DR

This paper derives the force-extension relation for wormlike chains, analyzes the entanglement transition and plateau modulus, and compares theoretical predictions with experimental data to deepen understanding of polymer network mechanics.

Contribution

It introduces a comprehensive derivation of the force-extension relation and entanglement parameters for wormlike chains, including multiple scaling regimes and transition analysis.

Findings

Derived the linear force-extension relation including entropy elasticity and buckling.

Expressed entanglement length in terms of network parameters across regimes.

Compared theoretical predictions with experimental data.

Abstract

We derive the linear force-extension relation for a wormlike chain of arbitrary stiffness including entropy elasticity, bending and thermodynamic buckling. From this we infer the plateau modulus $G^0$ of an isotropic entangled solution of wormlike chains. The entanglement length $L_e$ is expressed in terms of the characteristic network parameters for three different scaling regimes in the entangled phase. The entanglement transition and the concentration dependence of $G^0$ are analyzed. Finally we compare our findings with experimental data.