Theoretical Studies of the Structure of Intermediate Chiral Smectic Phases with Increasing Periodicity

Abstract

Different approaches to the description of the structure of intermediate chiral smectic C* phases are discussed and the concept of the “discrete” flexoelectric effect is introduced that describes a polarization induced in a smectic layer by a difference in director orientation in the two other layers adjacent to it. It is shown that the “discrete” flexoelectric effect is determined by electrostatic dipole-quadrupole interaction between positionally correlated molecules located in adjacent smectic layers. It is also shown that a simple discrete model proposed in the literature can be used to describe the whole sequence of intermediate chiral smectic C* phases with increasing periods, and to determine the non-planar structure of each phase without additional assumptions. In this sequence the phases with three and four layer periodicity have the same structure, as observed in the experiment. The theory predicts also the structure of intermediate phases with longer periods that have not been studied experimentally so far. The influence of long-range interaction between polarization fluctuations in different layers, proposed by Prost and Bruinsma, is also considered. Several intermediate phases are shown to be suppressed by this interaction, while the stability of the phases three and four layer periodicity is increased.