A static and dynamic theory for photo-flexoelectric liquid crystal elastomers and the coupling of light, deformation and electricity

Photoactive nematic liquid crystal elastomers permit generation of large mechanical deformation through impingement by suitably polarized light. The light-induced deformation in this class of soft matter allows for devices such as transducers and robots that may be triggered wirelessly. While there is no ostensible direct coupling between light and electricity in nematic liquid crystal elastomers, in this work, we take cognizance of the fact that the phenomenon of flexoelectricity is universal and present in all dielectrics. Flexoelectricity involves generation of electrical fields due to strain gradients or conversely, the production of mechanical deformation through electrical fields. Barring some specific contexts, the flexoelectric effect is in general rather weak in hard materials. However, due to the facile realization of strain gradients (e.g. flexure) in soft materials, we expect flexoelectricity to be highly relevant for liquid crystal elastomers thus, prima facie, furnishing a deformation-mediated mechanism to couple light and electricity. In this work, we develop nonlinear equilibrium and dynamical models for photo-flexoelectric nematic liquid crystal elastomers and analyze the precise conditions underpinning an appreciable coupling between light and electricity. A careful scaling analysis reveals that there is an optimal size-scale at which the flexoelectricity-mediated photo-electric effect is maximized. We find that with conservative estimates of the flexoelectric coefficients of these materials, the electrical power generation is rather modest for typical optical load. However, our proposed coupling is an appropriate modality for optical sensing. Furthermore, design of next-generation liquid crystal elastomers with high flexoelectricity as well as exploitation of size-effects could ameliorate extraction of electrical power from light illumination.