Theory of Homologous Liquid Crystals. I. Phase Diagrams and the Even-Odd Effect

Publisher Website
Google Scholar
Abstract
Effect of the molecular length d in a homologous series of liquid crystal is considered. The McMillan hamiltonian is generalized to be H = F(d)Σi>-V(I j)- The mean-field form of the hamiltonian is derived explicitly and systematically for the first time. For F(d) - d Λ, results of McMillan and Lee et al. are recovered with correction when Λ = I and Λ = 0, respectively. Different types of the isotropic-nematic-smectic A phase diagrams are explained and new ones are predicted. The even-odd effect may be understood when the width of the molecule is also included in our formalism. As illustrations, even-odd variations of transition temperatures, order parameters and supercooling temperatures are calculated showing good agreement with experiments.