Shear Dynamic Modulus of Nematic Elastomers: Modified Rouse Model

Abstract

We develop a microscopic theory of dynamic mechanical properties of nematic elastomers taking the chain structure of network strands explicitly into account. We use an approach in which network strands are modeled as a sequence of Gaussian subchains, whose elasticity constants and friction coefficients are different for motions parallel and perpendicular to the LC-director: K∥ ≠ K⊥ and ζ∥ ≠ ζ⊥ (a modified Rouse model). We show that the dynamic modulus of an ordered nematic elastomer, G∗ = G′ + iG′′, should demonstrate a frequency behavior very similar to that of usual (nonordered) rubbers; especially, it should display a frequency domain with a Rouse-like behavior, G′ ≅ G′′ ∼ ω1/2, a feature which is confirmed by experiments. In contrast to the usual rubbers, nematic elastomers are characterized by the anisotropy of the dynamic mechanical behavior with respect to the LC director, n. In agreement with experiment we show that for prolate systems in the D-geometry (when n is parallel to the shear velocity) G′D greatly decreases around the nematic isotropic phase transition, whereas in the V-geometry (when n is perpendicular to the shear plane) GV′ does not demonstrate such a singularity. We discuss the predictions of our theory for other geometries under shear deformation.