A Finsler Geometry Modeling of the Liquid Crystal Elastomer

Liquid crystal elastomer (LCE) is a rubbery material composed of polymer chains and liquid crystals (LC). LCE is well known to undergo a shape transformation from the isotropic to the anisotropic phase. This shape transformation is caused by the nematic transition of the LC included in the LCE. However, the mechanism of this transformation is unknown because the interaction of LC with the bulk polymers is too complex. In this presentation, we extend the two-dimensional Finsler geometry model for membranes to a three-dimensional model for LCE. The Finsler geometry model for LCE is a coarse grained one: the Guassian bond potential S-1 is obtained by extending the one for membranes, which is originally obtained by a simple extension of the Guassian bond potential for the linear chain polymer model. The continuous Hamiltonian, which contains S1 and the curvature energy S-2, is discretized using a three-dimensional rigid sphere composed of tetrahedrons. We study the shape transformation as a phase transition between the isotropic and anisotropic phases and report the results of the transition order, obtained by the Monte Carlo simulations.