Landau-Ginzburg mean-field theory for the nematic to smectic-Cand nematic to smectic-Aphase transitions

Abstract

A Landau-Ginzburg free energy is presented that yields a nematic to smectic-$A$ (NA) transition, a nematic to smectic-$C$ (NC) transition, and a Lifshitz point (at the boundary between the NA and NC transitions). Fluctuation enhancements of the Frank elastic constants are calculated. For the NC transition, all three elastic constants $K_1$, $K_2$, and $K_3$ diverge as ${\xi }^2$, where $\xi$ is the correlation length for fluctuations of the smectic order parameter. At the Lifshitz point, $K_1$ and $K_2$ diverge as $\ln \xi$ whereas $K_3$ diverges as $\xi$.