Polymer field theory applied to Liquid Crystal Elastomers

Existing continuum and micromechanical elastic models for rubbery polymers do not explicitly account for the inter-segment interaction in a cross-linked network. To address this limitation and understand the physics of chain interactions, we have developed a statistical mechanics-based field theoretic model for elastomers.

In the many-chain setting, we use statistical field theory to account for inter-segment interaction using an excluded volume approach. We account for the network averaging the chain response over orientation space, and connect to the macroscale using an affine-deformation approximation.

The resulting model is solved numerically using a finite element approach to obtain the total free energy and equilibrium elastomer density as a function of applied deformation gradient. We find that in the absence of inter-segment interaction, elastic response of the polymer chain matches with the classical rubber elasticity, whereas a sufficiently strong inter-segment interaction leads to unexpected instabilities in the structure and response of the polymer network.

We extend our model to Liquid Crystal Elastomers (LCEs). We probe the detailed structure and response of LCEs, and examine the effects of temperature, geometry and loading conditions on LCE response.