Molecular field treatment of nematic liquid crystals

Abstract

The Maier-Saupe theory of the nematic mesophase is extended to rod-like molecules interacting with a perfectly general anisotropic potential. The resulting series expansion for the pseudo-potential accounts quantitatively for the observed temperature dependence of the orientational order, even when the expansion is restricted to just the first two terms. However, the agreement can only be obtained if the expansion coefficients are assumed to depend on the inverse fourth power of the molar volume. The orientational molar enthalpy of transition calculated with the parameters determined by fitting the orientational order is qualitatively correct, although rather too large. The theory is also modified to allow for deviations from a spherically symmetric distribution of the inter-molecular vector in the mesophase. A comparison of this new expression for the pseudo-potential with that derived by Chandrasekhar and Madhusudana reveals that certain of their assumptions are invalid. Finally, calculations made with the new pseudo-potential indicate that a modification of the Maier-Saupe theory based solely on deviations from a spherically symmetric distribution cannot yield quantitative agreement with theory.