Simple theory of transitions between smectic, nematic, and isotropic phases.

Abstract

The transitions between smectic, nematic, and isotropic phases are investigated in the framework of a unified molecular-statistical approach. The new translational order parameter is different from the one introduced in K. Kobayashi [Phys. Lett. A 31, 125 (1970)] and W. L. McMillan [Phys. Rev. A 4, 1238 (1971)]. The variance of the square sine of intermolecular shift angle along the director is introduced to take self-consistently into account the most probable location of the molecules with respect to each other, which is unique for every liquid crystal (LC) material and is mainly responsible for the order parameters and phase sequences. The mean molecular field was treated in terms of only two parameters specific to any intermolecular potential of elongated molecules: (1) its global minimum position with respect to the shift of two interacting molecules along the director and (2) its inhomogeneity/anisotropy ratio. A simple molecular model is also introduced, where the global minimum position is determined by the linking groups elongation Δ/d, while the inhomogeneity/anisotropy ratio Gβ/Gγ is determined by the ratio of electrostatic and dispersion contributions. All possible phase sequences, including abrupt/continuous transformation between the smectic and nematic states and the direct smectic-isotropic phase transition, are predicted. The theoretical prediction is in a good agreement with experimental data for some simple materials correlating with our molecular model, but it is expected to be valid for any LC material.