Linear Viscoelasticity of Nematic Liquid Crystalline Polymers

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Abstract
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 γ̇ αβ , γ̇ αμ n μ n β +n α n ν γ̇ νβ , and γ̇ μν n μ n ν n α n β , where γ̇ αβ is the rate‐of‐deformation tensor and n α 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 viscoelasticmoduli 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 from place to place so that it samples all orientations with equal probability. The linear viscoelasticmoduli for case (2) are computed by averaging with equal weighting over all possible orientations of the director. By analogy with similar calculations done previously for polycrystalline solids, upper bounds for the moduli are estimated by assuming all domains experience equal strains, lower bounds by assuming all domains experience equal shear stresses. The results suggest that at polymer concentrations just above the critical concentration needed to produce a nematic phase, the modulus in the quiescent state may be lower than that in the sheared state, in qualitative agreement with some recent experiments of Moldenaers and Mewis.

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