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

Abstract

We put forward a hydrodynamic theory of nematic liquid crystals that includes both anisotropic elasticity and dynamic relaxation. Liquid remodeling is encompassed through a continuous update of the shear-stress free configuration. The low-frequency limit of the dynamical theory reproduces the classical Ericksen-Leslie theory, but it predicts two independent identities between the six Leslie viscosity coefficients. One replicates Parodi's relation, while the other-which involves five Leslie viscosities in a nonlinear way-is new. We discuss its significance, and we test its validity against evidence from physical experiments, independent theoretical predictions, and molecular-dynamics simulations.

Active nematic gels as active relaxing solids

“…The same decomposition has been recently applied to explain the hints of viscoelasticity that remain at the hydrodynamic level when a sound wave propagates inside a nematic crystals [27][28][29][30].…”

“…An analysis of this approximation for the passive case is presented in Ref. [29,30] For simplicity, I further assume that the active term only introduces a small perturbation of the passive dynamics so that the effective strain tensor B e is only a slight perturbation of its (passive) equilibrium value…”

Two-shape-tensor model for tumbling in nematic polymers and liquid crystals

“…In our previous papers [15][16][17] we have shown how nematic elastomers (NEs), nematic liquid crystals (NLCs) and nematic polymers (NPs) can be described, at the continuum level, by the same theory. A-posteriori, this is not surprising since they share the basic features of a continuum theory, namely, material symmetry and compatibility with thermo-mechanics principles.…”

“…In standard nematic elastomer theory, and in our previous works [15,16], it is assumed that the relaxed network main axis, n * , is directed along the nematic director n, at each instant of time. In so doing, the director is taken to describe, at the same time, the preferred orientation of the molecules and the relative distance of their centers of mass at equilibrium (or the direction of the natural strain in the network).…”

A Design Principle for Actuation of Nematic Glass Sheets

“…For the purpose of finding equilibrium configurations of the sheet, A nem (z) will be considered as a given field (unlike in the nematic elastomer case). Note that A nem is analogous to the plastic distortion tensor F p in elastoplasticity theory (see, e.g., [13,14] for applications to soft materials), but now in the context of 2-d bodies occupying non-Euclidean subsets of E 3 ; the main modeling hypothesis is that, to the extent allowed by compatibility and displacement boundary conditions, the 'total' deformation gradient F field attempts to generate a right stretch tensor field that equals that of A nem pointwise in order to attain minimum energy in the body.…”