Linear viscoelasticity of nematic liquid crystalline polymers

A general phenomenological equation is given for the viscoelasticity of nematic fluids in small‐amplitude deformations. It is a time integral containing three independent relaxation moduli, which are coefficients of the terms γαβ, γαμnμnβ+nαnνγνβ, and γμνnμnνnαnβ, where γαβ is the rate‐of‐deformation tensor and nα is the director. For small amplitudes, the equation reduces to Ericksen's transversely isotropic fluid. The three moduli are computed for the Doi theory for concentrated solutions of rodlike polymers. Even for a monodisperse system, the Doi theory yields two relaxation times, one corresponding to relaxation parallel to the director, the other transverse to it. The predictions of the Doi theory obtained for the linear viscoelastic moduli G′ and G″ depend on director orientation. Calculations of G′ and G″ are made (1) for the director orientation established during slow steady shearing and (2) in the quiescent state, where it is assumed that because of defects or domains, the director varies ...