Curvature elasticity in liquid crystals

Abstract

The study of curvature elasticity in liquid crystals is of great practical significance and is interesting in its own right from the points of view of understanding. The purpose of this review article is twofold. First, we provide a summarising overview till date of the developments in this field. Second, we focus on the molecular theory (SSR theory), as developed by us recently, for the elastic properties of molecular-ordered phases (liquid crystals, plastic crystals and crystalline solids) and its application to various mesophases. The article begins with a brief discussion on the symmetry, structure and types of liquid crystalline phases. This is followed by a description about distribution functions and order parameters which are considered as essential basic input concepts for the study of ordered phases. The elastic continuum theory of uniaxial nematic, smectic A, biaxial nematic, smectic C, twisted nematic, chiral smectic C and columnar liquid crystalline phases are described briefly. The methods used for measuring the elastic constants of various mesophases are examined critically. In the remaining part of the article the current status of theoretical developments are reviewed. The essential ingradients of the Landau-de-Gennes theory and its application to evaluate the elastic constants of liquid crystals are discussed. Since the formation of a liquid crystal depends on the anisotropy in the intermolecular interactions, the question concerning its role has been addressed. The hard-particle, Maier-Saupe and Van der Waals (VdW) types of theories are reviewed. The theories based on the density functional method have been found useful for studying the properties of ordered phases. We have described the application of density functional theory to study the elastostatics of liquid crystals. This includes our recent work (SSR theory) which is based on weighted density functional formalism and derives an expression for the elastic free-energy of molecular ordered phases. The application of this theory to the uniaxial and biaxial mesophases are discussed. The questions related to the elastic constants of polymer liquid crystals and the computer simulation work are also addressed. Finally, a range of unexplored problems, which can be readily addressed using SSR theory, are indicated.