Elastic constants of nematic liquid crystals of uniaxial symmetry

We study in detail the influence of molecular interactions on the Frank elastic constants of uniaxial nematic liquid crystals composed of molecules of cylindrical symmetry. A brief summary of the status of theoretical development for the elastic constants of nematics is presented. Considering a pair potential having both repulsive and attractive parts numerical calculations are reported for three systems MBBA, PAA and 8OCB. For these systems the length-to-width ratio ${x_0}$ is estimated from the experimentally proposed structure of the molecules. The repulsive interaction is represented by a repulsion between hard ellipsoids of revolution (HER) and the attractive potential is represented by the quadrupole and dispersion interactions. From the numerical results we observe that in the density range of nematics the contribution of the quadrupole and dispersion interactions are small as compared to the repulsive HER interaction. The inclusion of attractive interaction reduces the values of elastic constants ratios. The temperature variation of elastic constants ratios are reported and compared with the experimental values. A reasonably good agreement between theory and experiment is observed

A statistical-mechanical model for calculating equilibrium properties of a nematic liquid crystal

We have proposed an optimized statistical-mechanical model of a nematic liquid crystal using the method of conditional distributions due to Rott. The calculations have been carried out for hexagonal and cubic close packings with the nearest neighbour Gay-Berne intermolecular potential. The theory takes pair intermolecular correlations into account. The hexagonal close packing proves to be favourable as compared to the cubic one. Optimized values of the cell model parameter have been calculated providing the minimum Helmholtz free energy of a liquid crystal