# Landau Theory of Nematic to Smectic-A Phase Transition

20 Jan 1998-International Journal of Modern Physics B (World Scientific Publishing Company)-Vol. 12, Iss: 2, pp 207-212

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Bell Labs

^{1}TL;DR: In this article, the Maier-Saupe model 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.

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.

854 citations

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TL;DR: The role of the phase in the second order smectic A↔ nematic transition is similar to the role of phase functions in superconductors as mentioned in this paper, where twist and bend distortions correspond to magnetic fields.

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.

681 citations

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TL;DR: 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.

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.

598 citations

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TL;DR: In this paper, it was shown that the specific heat exponent depends on the width of the $N$ range for continuous $\mathrm{AN}$ transitions, where AN is a tricritical point in the phase diagram.

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.

143 citations

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TL;DR: The theory of translational and orientational melting with application to liquid crystals is presented in this article in a manner analogous to that of Kirkwood and Monroe, and the theory is applied to liquid crystal crystallography.

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.

106 citations