Molecular field theory with atomistic modeling for the curvature elasticity of nematic liquid crystals

Liquid crystals oppose a restoring force to distortions of the main alignment axis, the so-called director. For nematics this behavior is characterized by the three elastic moduli associated with the splay (K(11)), twist (K(22)), and bend (K(33)) modes; in addition, two moduli for mixed splay-bend (k(13)) and saddle-splay (k(24)) can be defined. The elastic constants are material properties which depend on the mesogen structure, but the relation between molecular features and deformations on a much longer scale has not been fully elucidated. The prediction of elastic properties is a challenge for theoretical and computational methods: atomistic simulations require large samples and must be integrated by statistical thermodynamics models to connect intermolecular correlations and elastic response. Here we present a molecular field theory, wherein expressions for the elastic constants of nematics are derived starting from a simple form of the single molecule orientational distribution function; this is parametrized according to the amount of molecular surface aligned to the nematic director. Such a model allows a detailed account of the chemical structure; moreover the conformational freedom, which is a common feature of mesogens, can be easily included. Given the atomic coordinates, the elastic constants can be calculated without any adjustable parameter at a low computational cost. The example of 4-n-pentyl,4(')-cyanobiphenyl (5CB) is used to illustrate the capability of the developed methodology; even for this mesogen, which is usually taken as a prototypal rodlike system, we predict a significant dependence of the elastic moduli on the molecular conformation. We show that good estimates of magnitude and temperature dependence of the elastic constants are obtained, provided that the molecular geometry is correctly taken into account.