Free energy of liquid crystals with slowly changing parameters of orientational order

The entropy formulation of the three-parameter law of corresponding states in the Holleran-Hammes form, permitting the geometric correspondence of the form (anisotropy) of molecules to be taken into account, served as the basis for obtaining the dependence of the anisotropy of the component of the free energy G of a liquid crystal on the temperature T, pressure P, and relative anisotropy of b of the van der Waals repulsion parameter. An expression is derived for the functional G of a liquid crystal which is weakly inhomogeneous (over the molecular length), making it possible to find the spatial distribution not only for the directions of orientational order (director field) but also its magnitude (field of Tsvetkov parameter η). An appendix studies the dependence of the pitch of the spiral (helicoid) of a cholesteric liquid crystal (weakly doped nematic liquid crystal) on T, P, b, η, and the concentration of the active additive. The theoretical results obtained are compared with experiment. © 1978 Plenum Publishing Corporation.