Anisotropic wave propagation in nematic liquid crystals

Abstract

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 - can be explained by properly accounting for two fundamental features of the nematic response: anisotropy and relaxation. The latter concept - new in liquid crystal modelling - provides the first theoretical explanation of the structural relaxation process hypothesised long ago by Mullen and co-workers [Mullen et al., Phys. Rev. Lett., 1972, 28, 799]. We compare and contrast our proposal with an alternative theory where the liquid crystal is modelled as an anisotropic second-gradient fluid.

“Fast” and “slow” pressure waves electrically induced by nonlinear coupling in Biot-type porous medium saturated by a nematic liquid crystal

“…Besides, the use of the methods of metamaterials [72][73][74] like those for pantographic structures [75][76][77] could be considered even to take into account the effects of damage [78][79][80][81][82]. Another possible extension of this model is to include surface effects [83][84][85][86][87][88][89] and the anisotropy induced by the orientation of the NLC directors, as in [90] , or as it is done in granular materials [91].…”

Liquid relaxation: A new Parodi-like relation for nematic liquid crystals

“…The hidden link between assumption (2) and flow alignment surely deserves further study, as does a proper incorporation of the degree of nematic order. A separate issue we intend to address is removing the incompressibility constraint, paying due attention to the possible role of τ 6 [19], in order to reconsider the nematoacoustic problem we tackled in [6].…”

“…The shape tensor Ψ is symmetric, positive definite, and with unit determinant. The potential Υ shr adds the following contribution to the stress tensor [6,15]:…”

“…In a previous work [6], we constructed such a theory for (slightly) compressible NLCs and applied it, with fair success, to explain quantitatively the anisotropy of sound velocity [7] and sound attenuation [8] in N -(4-methoxybenzylidene)-4-butylaniline (MBBA) over the range 2-14 MHz. The theory of nematic relaxation put forth in [6] is characterized by: (i) a neo-Hookean contribution to the strain energy where the effective shear strain enters weighted by an anisotropic shape tensor, and (ii) an isotropic gradient flow dynamics for the relaxed configuration, parameterized by a single viscosity modulus. Here we keep (i) as is, but we revise and extend (ii) by taking a gradient flow with respect to an anisotropic metric possessing the minimum symmetry compatible with the liquid crystal.…”

Encasement as a morphogenetic mechanism: The case of bending

“…The choice of including or not such an evolution for the growth components determines whether we are considering morphogenesis at stress-free conditions vs. in the presence of residual stresses. This might for instance depend on the relative time scales of growth and relaxation (see [6] for an example of how a soft material may exhibit purely elastic or apparently plastic behavior, depending on the deformation and relaxation times). We keep our study as simple as possible here, and do not consider any remodeling, so that in general the deformed shapes we characterize possess residual stresses (as, for instance, the systems considered by [25]).…”