Pressure-induced phase transitions in liquid crystals: A molecular field approach

Abstract

A rigorous microscopic treatment of a nematic fluid system based on a pairwise interaction potential is immensely complex. For studying such systems molecular field theories are often the standard method of choice. In this paper we have chosen a simple effective potential U=u_{4}/v^{4}-u_{2}/v^{2}-Au_{2}/v^{2}〈P_{2}〉P_{2}(cosϑ) to study an isothermal-isobaric ensemble describing a liquid crystalline system. Using this we have studied in particular the pressure dependence of liquid crystalline phase transitions.

A Molecular Field Approach to Pressure Induced Phase Transitions in Liquid Crystals : Smectic-Nematic transition

“…Any realistic theoretical model of liquid crystals which allow volume fluctuation must include both repulsive and attractive interactions. In [5] we had used a molecular field approach by adapting the Maier Saupe potential for this purpose by adding an isotropic volume dependent term. In this paper we further extend that work by following the development by McMillan [24] that included another term to account for the translational periodicity.…”

“…where u 4 , u 2 , A and α are constants and v is the volume of the fluid per molecule. Here the volume dependence of the isotropic terms has been chosen to mimic the scaling behavior of the familiar Lennard-Jones potential [5]. Both Maier Saupe and McMillan models were on fixed lattices.…”

“…Here we are singling out its volume dependence since we are going to use the saddle point method where the integral is only over volume. Since N 1 we can use the saddle point approximation [5] to write (upto a multiplicative constant which we ignore)…”

“…In 2018 [5] we had presented a molecular field theory to study pressure induced phase transitions in liquid crystals. A simple effective potential was chosen to discuss in particular the N-I phase transition.…”

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Since a rigorous microscopic treatment of a nematic fluid system based on a pairwise interaction potential is immensely complex we had introduced a simple mean field potential which was a modification of the Maier-Saupe potential in a previous paper [5]. Building up on that here we have modified that potential to take into account the various aspects of a smectic A-nematic phase transition.

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