Statistical field theory model for Liquid Crystal Elastomers

Liquid Crystal Elastomers (LCEs) are composed of relatively stiff liquid crystal molecules connected with flexible polymeric chains. LCEs show fast reversible shape change with temperature because of nematic-isotropic phase transition of the liquid crystals. Thus, LCEs have promising applications as thermally active soft actuators, shape memory material and artificial muscles.

Existing models for LCE response are typically based on continuum mesoscale approaches such as phase field methods. While these models provide macroscopic predictive capability once material constants are calibrated, they are unable to predict mesoscale structure and response. In particular, these methods are unable to provide insight into the behavior of LCE composites composed of active components such as liquid metals or carbon nanotubes.

We develop a statistical mechanics-based field theoretic model for LCE response to enable us to probe these questions. The polymer chain elasticity is entropic while the liquid crystalline free energy is based on the Maier-Saupe mean field theory for liquid crystals. The model is solved numerically using a finite element approach. We extend this to the many-chain setting and examine the effects of temperature, geometry and loading conditions.