A simple molecular theory of smectic-C liquid crystals

Abstract

Smectogenic organic compounds are made of rod-like molecules, which often have dipolar groups with lateral components. We argue that since the groups are generally off-axis, the electrostatic contribution to the intermolecular interaction between the neighbours in a smectic layer favours a tilting of the molecules. We develop a mean-field theory of the smectic-$\chem{C}$ (SmC) phase based on a single-particle potential of the form $u\propto\sin 2\theta \cos \phi$, consistent with the biaxial nature of the phase, where $\theta$ and $\phi$ are the polar and azimuthal angles, respectively. The hard-rod interactions which favour the smectic-A (SmA) phase with non-zero tilt are also included to construct phase diagrams involving isotropic, nematic, SmA and SmC phases. The topology of the phase diagrams, the calculated temperature variation of tilt angle in the SmC phase and the specific-heat jump across the SmA-SmC transition compare favourably with experiments.