Anisotropic wave propagation in nematic liquid crystals

Despite the fact that quantitative experimental data have been available for more than forty years now, nematoacoustics still poses intriguing theoretical and experimental problems. In this paper, we prove that the main observed features of acoustic wave propagation through a nematic liquid crystal cell – namely, the frequency-dependent anisotropy of sound velocity and acoustic attenuation – may be plausibly explained by a first-gradient continuum theory characterized by a hyperelastic anisotropic response from an evolving relaxed configuration. The latter concept – new in liquid crystal modeling – provides the first theoretical explanation of the structural relaxation process hypothesized long ago by Mullen et al. [5]. We compare and contrast our proposal with a competing theory where the liquid crystal is modeled as an isotropically compressible, anisotropic second-gradient fluid.