Anisotropic elasticity and relaxation in nematic liquid crystals
As early as 1972, Mullen and coworkers showed experimentally that the director alignment of a nematic liquid crystal induces an anisotropic, frequency dependent sound speed in nematic liquid crystals. Similarly, Selinger and co-workers have studied a liquid crystal cell where the nematic molecules can be realigned by an ultrasonic wave, leading to a change in the optical transmission through the cell. The existing theoretical models for this acousto-optic effect propose a free energy that depends on the density gradient thus describing the nematic liquid crystal as a compressible second grade fluid. In this talk we will show that that the angular dependence of the sound speed can be easily reproduced by introducing a simple anisotropic term in the stress tensor, thus providing a simpler first-grade model for the acousto-optic effect. The simplest term is non-hyperelastic, but we show that it can be interpreted as the quasi-incompressible approximation of an elastic term which couples the director orientation with the strain. More interestingly, the frequency dependence of the anisotropic sound speed can be recovered by assuming an irreversible relaxation of the reference configuration with respect to which the strain is measured.