General Analysis of Linear Nematic Elasticity

Abstract

The results of a general analysis of linear nematic elasticity on the basis of the five-parameter thermodynamic potential of de Gennes (DG) have been presented. It has been shown that, depending on the similarity of the material parameters to the conditions of marginal (limiting) stability, the DG potential describes the entire diversity of soft, semisoft, and harder behavior of weakly elastic nematic solids. It has been established that an additional soft mode of longitudinal stretching, acting along the director, can also exist alongside the known shear soft modes. A theorem on the special rotational invariance of the stress-tensor components, which is close to the principle of rotational invariance postulated earlier by Olmsted, has been proved. It has been shown that the stress tensor is symmetric if the shear modes are soft. In this case, the reduced DG potential is reduced to a one-parameter nematic potential. If the mode of longitudinal stretching is also soft, this dimensionless parameter contains no additional parameters. Simple shear and simple tension have been considered as an illustration of the theory elaborated.