Symmetries and Elasticity of Nematic Gels

A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these novel materials.Comment: 21 pages, 4 eps figure

Electro-Mechanical Fredericks Effects in Nematic Gels

The solid nematic equivalent of the Fredericks transition is found to depend on a critical field rather than a critical voltage as in the classical case. This arises because director anchoring is principally to the solid rubbery matrix of the nematic gel rather than to the sample surfaces. Moreover, above the threshold field, we find a competition between quartic (soft) and conventional harmonic elasticity which dictates the director response. By including a small degree of initial director misorientation, the calculated field variation of optical anisotropy agrees well with the conoscopy measurements of Chang et al (Phys.Rev.E56, 595, 1997) of the electro-optical response of nematic gels.Comment: Latex (revtex style), 5 EPS figures, submitted to PRE, corrections to discussion of fig.3, cosmetic change