Elasticity coefficients of nematic liquid crystals

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Abstract
A Ginsburg–Landau type ansatz for the Gibbs free energy is introduced which involves the alignment tensors of ranks 2 and 4 and their spatial derivatives. It is applicable to both the isotropic and nematic phases. The Frank elasticity coefficients of the nematic phase are expressed in terms of the equilibrium order parameters and phenomenological coefficients which are related to bare correlation length coefficients. The full anisotropy of the elasticity coefficients is obtained and their experimentally observed temperature dependence can be reproduced for all of the ten substances which have been analyzed.