Landau theory of the nematic-smectic a tricritical phase transition in a binary mixture of liquid crystals

Abstract

We have developed in this study a thermodynamic model for the nematic-smectic A (NA) tricritical phase transition of a binary mixture of liquid crystals in analogy with the model for quasi fluid mixtures due to Griffiths. Using the Landau theory with a symmetrical TCP, we have predicted the critical behaviours of the nematic susceptibility, order parameter and the specific heat discontinuity in the vicinity of the TCP.

Our predictions for the tricritical exponents for the order parameter and the specific heat discontinuity are those predicted by the mean field theory (β=1/4 and α=1/2) with a symmetrical TCP. Our exponent value of γ=1/2 for the nematic susceptibility does not agree with the mean field value of γ=1.

Our predicted values agree with those obtained experimentally for some binary mixtures of liquid crystals. This means that the mean field model with a symmetrical TCP is capable of describing the nematic-smectic A tricritical phase transition for a symmetrical binary mixture of liquid crystals.

Key Words:

• Landau theory
• NA transition
• liquid crystals