Liquid Crystal Elastomers and Phase Transitions in Actin Rod Networks

Abstract

In this article, we construct and analyze models of anisotropic crosslinked polymers employing tools from the theories of nematic liquid crystals and liquid crystal elastomers. The anisotropy of these systems stems from the presence of rigid rod molecular units in the network. We construct energy functionals for compressible and incompressible elastomers as well as for rod-fluid networks. The theorems on the minimization of these energies combines methods of isotropic nonlinear elasticity with the theory of lyotropic liquid crystals. Two of the theorems refer to incompressible elastomers, in the cases that the bulk liquid crystal energy is given by the well-known polynomial form of the Landau--de Gennes theory and also in the case of a singular potential. Another theorem refers to compressible elastomers, and in the last row, the rod density is taken as a main field of the model. We apply our results to the study of phase transitions in networks of rigid rods, in order to model the behavior of actin filament systems found in the cytoskeleton. Our results show a good agreement with the molecular dynamics experiments reported in the literature as well as with some laboratory experiments. The model does not include polydispersity effects due to variable rod shape and size, and it does not account either for phase transitions to lamellar phases.