Mean field theory of the nematic-smectic a phase transition in a mixture of liquid crystals

Abstract

In this work we have studied using the mean field theoretical approach the nematic-smectic A phase transitions in the mixtures of liquid crystals. It is claimed in a recent work in literature that the effective free energy with a |ψ| 3 term where ψ is the smectic A order parameter, gives a nonlinear dependence of the latent heat on the concentration near the tricritical point. However, we show mathematically that within the |ψ| 3 theory this dependence of the latent heat on the concentration is linear near the tricritical point. Here, we show that only the effective free energy with the |ψ| 5 term gives the experimentally observed quadratic dependence of the latent heat on the concentration near the tricritical point. But, this solution is mathematical. The physical solution in this theory alves a linear dependence of the latent heat on the concentration. Hence, within the mean field theory with the effective free energy where the Landau amplitude expansion is made, it is not possible to explain the observed experimental results of the latent heat near the tricritical point.