Temperature Evolution of a Smectic Liquid Crystal with Inner Degrees of Freedom

Abstract

Abstract A statistical model of the smectic A mesophase with inner degrees of freedom (MIDF-model) is formulated in which the interlayer interaction of molecules is described in the McMillan approximation and the intramolecular interaction account is fulfilled in the pseudo-spin approximation. In terms of the variational Feynman-Bogoljubov principal the MIDF-model free energy depending on three order parameters: orientational (P2), conformational (1−x) and mixed translationally-orientational (ωP 2⟨ ones and also on four control parameters: a sizeless temperature (t), effective length (ε), rigidity (y) and characteristic size of central core (a) of molecules is calculated. By means of numerical methods the investigation of equilibrium equations is fulfilled which allows to separate qualitatively different versions of the smectic liquid crystal temperature evolution to which different versions of dependence ⟨P2⟩ x and ⟨ωP 2⟩ on t, of the state diagrams in coordinates “ε–γ” and of the phase diagrams in variables “t-y” of the MIDF-model correspond. A fundamentally new result of the paper is an establishing of the conditions at which a conformational disorder increase causes successive isostructural phase transitions in stability ranges of the system's smectic and nematic states. Those are realized in accordance to one of following schemes: coSm (conformationally ordered smectic)—cdSm (conformationally disordered smectic)—N (nematic)‒IL (isotropic liquid), coSm‒cdSm‒IL and Sm‒coN (conformationally ordered nematic)‒cdN (conformationally disordered nematic)—IL which are found experimentally in lipids, alkylammonium compounds, p-n−octyloxybenzoic acids.