Statistical theory of orientational order in nematic liquid crystals

Abstract

Assuming a model based on dispersion and repulsion interactions, it is shown that the orientational potential energy of a molecule in a nematic liquid crystal is expressible as, where U_i= −(u₀ + u₂ cos² θ_i + u₄ cos⁴ θ_i + u₆ cos⁴ θ_i + ....), u₀ = w₀₀ + w₀₂ cos² θ + w₀₄ cos⁴ θ + .... u₂ = w₂₀ + w₂₂ cos² θ + w₂₄ cos⁴ θ + ...., etc., W_mn = W_nm, and θ is the angle which the long axis of the molecule makes with the uniaxial direction of the medium. Using a slightly simplified form of this function, a statistical theory of long range orientational order in the nematic state is developed. The thermodynamic properties of the ordered system are evaluated relative to those of the completely disordered one, and the conditions of equilibrium are discussed. The constants of the potential function are determined for p-azoxyanisole that lead to a theoretical curve for the degree of orientational order and a volume change at the nematic-isotropic transition point in good agreement with observations. However, the predicted latent heat of the nematic-isotropic transition is significantly higher than the experimental value suggesting that a certain degree of short range order persists in the liquid phase. The calculated latent heat of transition as well as the specific heat and the compressibility of the liquid crystal fit the experimental data when a correction factor is included in the theory to allow for the effect of short range order. The magnetic birefringence of the liquid phase gives an independent estimate of the short range order which confirms the previous calculations.