Simple Molecular Model for the Smectic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi></mml:math>Phase of Liquid Crystals

TLDR

The study extends the Maier‑Saupe nematic model to the smectic A phase by adding a density‑wave amplitude order parameter and proposes experiments to measure these order parameters. Self‑consistent equations for the nematic and smectic order parameters are derived from an anisotropic interaction, solved numerically, and used to compute temperature‑dependent order parameters, entropy, and specific heat for various interaction strengths. The resulting phase diagram of transition temperatures versus interaction strength reproduces experimental trends of transition temperature versus alkyl chain length, and the model qualitatively captures chemical trends in transition entropies.

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.