A chiral axial next nearest neighbour xy-model for antiferroelectric liquid crystals

Abstract

We describe a chiral axial next nearest neighbour xy-model to account for the various subphases exhibited by antiferroelectric liquid crystals made of chiral rod-like molecules. The assumed form of the interlayer interactions is based on physical processes which are discussed. Using a discrete model, the predicted sequence of transitions is SmA-SmC$^*_\alpha$-SmC$^*_\beta$-FIH-FII-FIL-SmC*A, where FI stands for a ferriphase, as seen in many compounds. The ferri and SmC$^*_\alpha$ phases are characterized by relatively large angles between the c-vectors of successive layers and occur only when the compounds have high optical purity. The calculated field induced structures exhibit a plateau of the apparent tilt angle at $\sim\theta/3$, where $\theta$ is the tilt angle of the molecules in the ferriphase. The conoscopic figures in the presence of a field and ellipsometric parameters in the absence of a field have also been generated, which agree extremely well with the experimental results. Recent anomalous X-ray scattering studies prove the xy-character of the configurations, though the commensurate structures that are found in the ferriphase require an extension of the model to include lock-in terms.