Liquid crystal was discovered in 1888. However, it was only after the observation of dynamic scattering in nematics in 1968 and the subsequent application in displays that liquid crystal, as a field of research, has obtained its vitality and importance as we know it today.† Not surprisingly, it was in the early years of this modern era of liquid crystals that China ventured into this exciting “new” field.1-16

Liquid Crystal Research in China: 1970-1982

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 TNI or TAI 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 molecula...

Theory of Homologous Liquid Crystals. II. Orientation Correlation Functions

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.

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

The rigorous formula of Suzuki for correlation function of classical systems and Ising model is generalized and applied to the rotationally invariant Maier-Saupe Hamil-tonian of liquid crystals.The results show that the microscopic treatment of the correlation function and magnetic Cotton-Mouton coefficient by one of the authors is indeed correct within the approximation stated. The random phase approximation results of Vertogen and van der Meer is improved. A scheme to describe the thermodynamics of liquid crystals beyond the mean field approximation is proposed.

Lin Lei

Papers

Generalized suzuki formula and its application in liquid crystals