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Nematic elastomers: from a microscopic model to macroscopic elasticity theory.

Xiangjun Xing¹, Stephan Pfahl, Swagatam Mukhopadhyay

¹Physics Department, Syracuse University, Syracuse, New York 13244, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 23, 2008

Summary

A new Landau theory explains gelation in polymer networks with nematic ordering. This framework unifies theories of elasticity for nematic elastomers and isotropic materials, revealing universal principles.

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Area of Science:

Polymer Physics
Soft Matter Physics
Materials Science

Background:

Cross-linked polymer systems can exhibit spontaneous nematic ordering.
Understanding the gelation transition and elasticity in these systems is crucial.
Existing theories for elasticity often lack a unified microscopic basis.

Purpose of the Study:

To construct a Landau theory for the gelation transition in nematic polymer networks.
To derive phenomenological elasticity theories from a microscopic model.
To establish the universality of these elasticity descriptions.

Main Methods:

Development of a Landau theory based on symmetry principles and an order parameter for the amorphous solid state.
Substantiation using a microscopic model of cross-linked dimers.
Minimization of Landau free energy under nematic order conditions.

Main Results:

The theory successfully explains the gelation transition in nematic polymer systems.
Minimization yields neoclassical theory for nematic elastomers and classical theory for isotropic elasticity.
The derived theories are shown to be universal mean-field descriptions.

Conclusions:

A unified Landau theory provides a microscopic foundation for elasticity in polymer gels.
The theory bridges the gap between microscopic models and macroscopic elasticity descriptions.
This work demonstrates the universality of mean-field elasticity theories for chemical gels and vulcanized media.