Theory of Homologous Liquid Crystals. II. Orientation Correlation Functions

Abstract

Molecular correlation functions of homologous liquid crystals are calculated statistical mechanically from a generalized McMillan hamiltonian. It goes beyond the mean-field approximation and includes the nematic and smectic fluctuations on the same footing. The expressions obtained are valid for either the isotropic(I), nematic(N) or smectic A(A) phase and are equally applicable to I-N or I-A transitions. When specified to the isotropic phase the inverse correlation function G₀ ⁻¹ shows a smooth “bending down” near T_NI or T_AI for all homologues in accordance with most experiments. The variation of the “degree” of the “bending down” with different members of a homologous series is in agreement with, e.g., the nCB and nOCB data of Muta et al. For 9CB and 11CB our G₀ ⁻¹ curve, without “inflection”, “saturation” or “dip”, agrees with the experiments of Zhang et al., but not those of Coles and Strazielle, or Pouligny et al. Supercooling temperature T* [defined by G₀ ⁻¹(T*) = 0] as function of molecular length is also calculated. Our theory is compared with others (including that of Gohin et al.).