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Soft Matter and Biological Physics
Eur. Phys. J. E 1, 319-336

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

A. Roy - N.V. Madhusudana

Raman Research Institute, C.V. Raman Avenue, Bangalore-560 080, India
nvmadhu@rri.ernet.in

Received 23 August 1999

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.

PACS
61.30.Cz Theory and models of liquid crystal structure - 64.70.Md Transitions in liquid crystals - 77.84.Nh Liquids, emulsions and suspensions; liquid crystals

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