Landau Model of the Phase Transitions for Description of Commensurate Polar Smectic Structures

Abstract

Calculations of polar structures with frustration interaction are often difficult and require complicated numerical calculations. A simple approach based on Landau model is given to describe the manifold of commensurate structures. The power of the used method is shown on the example of polar liquid crystals. Our approach allows to perform analytical study that shows the nature of formation of different structures. In spite of its simplicity this approach is fruitful. Fluctuation of the modulus of the order parameter leads to decrease in the energy and formation of stable phases with six, three, five and ten layer periodicity. Results of analytical studies correlate with experimental data and numerical calculations.

Keywords:

• Polar liquid crystals
• smectic subphases
• two-component order parameter

Acknowledgment

This work was supported in part by RFFI Grants No. 11-02-01028, 11-02-92610-KO and by Grant MK-2458.2011.2.