Landau Theory of Nematic to Smectic-A Phase Transition

Abstract: The Maier-Saupe model of the nematic phase with an orientational order parameter is extended to the smectic $A$ phase by introducing a new order parameter, the amplitude of a density wave in the direction of the nematic preferred axis. Self-consistent equations for the two order parameters are derived from an anisotropic model interaction and are solved numerically. We calculate the order parameters, the entropy, and the specific heat as a function of temperature for several values of dimensionless interaction strength $\ensuremath{\alpha}$ for the smectic $A$ phase. The transition temperatures plotted versus $\ensuremath{\alpha}$ provide a theoretical phase diagram which resembles experimental plots of transition temperature versus alkyl chain length for homologous series of compounds. The model qualitatively reproduces chemical trends in transition entropies. Experiments are suggested to measure the order parameters in the smectic $A$ phase.

Abstract: The conformation of a smectic A can be described by a phase function φ( R ), the n -th layer corresponding to φ ( R ) = 2 πn . The role of the phase in smectics A and in superfluids is similar. This analogy leads to the following predictions for a second order smectic A↔ nematic transition: (1) the transition temperature is lowered if twist, or bend distortions are imposed: these distortions correspond to a magnetic field in superconductors. (2) the Frank coefficients K 2 and K 3 of the nematic phase must show pretransitional anomalies.

Abstract: The superconducting phase transition is predicted to be weakly first order, because of effects of the intrinsic fluctuating magnetic field, according to a Wilson-Fisher $\ensuremath{\epsilon}$-expansion analysis, as well as a generalized mean-field calculation appropriate to a type-I superconductor. Similar results hold for the phase transition from a smectic-$A$ to a nematic liquid crystal.

Abstract: From adiabatic-scanning calorimetric results it is demonstrated that in mixtures of 9CB and 10CB, two compounds of the alkylcyanobiphenyl ($n\mathrm{CB}$) series, the nematic ($N$) to smectic-$A$ ($A$) transition becomes first order for narrow $N$ ranges. From the latent heats a tricritical point is located in the phase diagram. Measurements for 7CB+ 8CB mixtures show that the specific-heat exponent $\ensuremath{\alpha}$ depends on the width of the $N$ range for continuous $\mathrm{AN}$ transitions.

Abstract: The theory of translational and orientational melting with application to liquid crystals is presented in a manner analogous to that of Kirkwood and Monroe.