Theory of Side-chain Liquid Crystal Elastomers

Liquid crystal elastomers, formed by incorporating liquid crystal moieties into polymer networks, have wide applications in smart materials due to their stimuli-responsive and energy storage properties. However, a detailed theoretical understanding of such materials is still lacking. Here, we develop a self-consistent field theory of side-chain liquid crystal elastomers by combining the affine network theory for polymer networks and freely-jointed chain model for liquid crystal polymers. Particularly, the coupling between the nematic ordering of the LC moieties and the orientation of chain segments is systematically treated by distinguishing the globalized contribution from the localized "hinge" effect. The theory relates nematic ordering and shape change with various molecular parameters. Through numerical computations, we investigate the effects of crosslink density, "hinge" configuration and external stress on nematic ordering and shape deformation upon phase transition. Furthermore, we predict the critical phase behaviors if the applied stress is strong enough. This work provides fundamental insight into the phase and elastic behaviors of liquid crystal elastomers, which plays a key step towards the rational design of such smart materials at the molecular level.