Director and Spontaneous Polarization Fluctuations in Ferroelectric Smectic- C * Cells
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TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
Director and Spontaneous Polarization Fluctuations in Ferroelectric Smectic-C* Cells S. V. Ul’yanova a
Physical Department, St. Petersburg State University, St. Petersburg, 199034 Russia e-mail: [email protected] Received March 7, 2019; revised April 15, 2019; accepted April 16, 2019
Abstract—The correlation function of the director fluctuations in a plane-parallel smectic-C* cell with a bookshelf structure is calculated far from phase transition points. The free energy takes into account the anisotropy of the Coulomb interaction of the bound charges induced by spontaneous polarization fluctuations. This correlation function of the director fluctuations is used to calculate the scattered light intensity. Taking into account the anisotropy of the permittivity in the Coulomb interaction of bound charges is shown to change a scattering indicatrix substantially. DOI: 10.1134/S1063776119080107
1. INTRODUCTION The long-term interest in ferroelectric liquid crystals is caused by their unique physical properties, which can be used in various engineering applications [1–3]. Such liquid crystals usually consist of elongated molecules and have a structure of equidistant planar layers in the equilibrium state. In smectic C (Sm-C), each layer resembles a two-dimensional liquid; that is, an order in the arrangement of the centers of mass of molecules is absent inside a layer, and an order in the average orientation of the long axes of molecules is present. This order is described by unit vector (director) n, which makes angle θ with the normal to the layers N. The projection of director n onto the plane of a smectic layer that is normalized to unity gives director c, which is traditionally used to describe Sm-C. Smectics C* (Sm-C*) are characterized by the presence of spontaneous polarization P, which is perpendicular to the normal to the layers N and to director c. From layer to layer in Sm-C*, polarization vector P and director n rotate through a certain angle about the normal to the layers and form a so-called helicoidal spiral. Here, angle θ and the polarization vector length remain unchanged. Thermal director n fluctuations and the related fluctuations of spontaneous polarization vector P cause space bound charges with density ρ = –divP. The interaction of bound charges is usually neglected: they are thought to be fully screened by ionic impurities, which are usually present in Sm-C* [1]. The interaction of partly screened bound charges was studied in [4], and this interaction in two-dimensional systems was shown to increase the longitudinal flexural modulus. The authors of [5] investigated the interac-
tion of ionic impurities with bound charges and showed that it should manifest itself in the light scattered by freely suspended smectic films. Moreover, the authors of [6] demonstrated that the interaction of bound charges and ionic impurities should increase the orientational viscosity. As was found in [7–10], the unscreened interaction of strong bound charges, which appears be
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