Theoretical study of nematic to isotropic transition in porous media

Experimental observations show that the N-I transition temperature (T_{NI}) for liquid crystals embedded in solid porous materials is lower compared to that of the bulk liquid crystals and T_{NI} is reduced linearly with the inverse pore diameter. To explain this, various theoretical studies have been proposed. We propose to use the mean field approach. We modify the Maier-Saupe mean field theory to include the disordering effects of porosity as a disordering surface potential. A molecule near the surface is assumed to feel the mean field potential (the Maier-Saupe type) and also the surface induced potential. We calculate the values of the nematic order parameter and hence find the T_{NI} for different pore diameters. The weighted average of the order parameter is calculated considering the cylindrical symmetry of the pores. Our calculations on the variation of T_{NI} with pore diameter agree with experimental data. Also, the calculated values of specific heat peak decrease with decrease in pore radius, in agreement with experimental trends.