Algebraic theory of linear viscoelastic nemattodynamics Part 2: Linear viscoelastic nematic viscoelasticity

TL;DR

This paper develops a comprehensive linear viscoelastic nematodynamics theory for liquid crystal polymers, incorporating magnetic field effects, and simplifies to minimal parameter models under certain conditions.

Contribution

It introduces a unified, elegant operator-based framework for linear viscoelastic nematodynamics, including magnetic field effects and soft deformation modes.

Findings

The theory accounts for non-symmetric stresses under magnetic fields.

Simplified models with 6 and 2 parameters are derived for specific conditions.

Linear nematodynamics reduces to LEP-like equations with modified coefficients.

Abstract

This second part of paper develops a theory of linear viscoelastic nematodynamics applicable to LCP. The viscous and elastic nematic components in theory are described by using the LEP approach for viscous nematics and de Gennes free energy for weakly elastic nematic elastomers. The case of applied external magnetic field exemplifies the occurrence of non-symmetric stresses. In spite of multi- (10) parametric character of the theory, the use of nematic operators presents it in an elegant form. When the magnetic field is absent, the theory is simplified for symmetric case with 6 parameters, and takes an extremely simple, 2-parametric form for viscoelastic nematodynamics with possible soft deformation modes. It is shown that the linear nematodynamics is always reduced to the LEP-like equations where the coefficients are changed for linear memory functionals whose parameters are calculated from original viscosities and moduli.