From Vulcanization to Isotropic and Nematic Rubber Elasticity

TL;DR

This paper develops a Landau theory for vulcanization in nematic elastomers, linking statistical mechanics to elasticity theories and broadening their applicability to various random solids.

Contribution

It introduces a unified Landau framework for vulcanization and nematic elasticity, deriving neo-classical elasticity from fundamental principles.

Findings

Neo-classical elasticity contains classical rubber theory as a limit.

The theory applies to a wide class of random solids.

Provides a basis for studying sample fluctuations in vulcanized materials.

Abstract

A Landau theory is constructed for the vulcanization transition in cross-linked polymer systems with spontaneous nematic ordering. The neo-classical theory of the elasticity of nematic elastomers is derived via the minimization of this Landau free energy; this neo-classical theory contains the classical theory of rubber elasticity as its isotropic limit. Our work not only reveals the statistical-mechanical roots of these elasticity theories, but also demonstrates that they are applicable to a wide class of random solids. It also constitutes a starting-point for the investigation of sample-to-sample fluctuations in various forms of vulcanized matter.