Layer distortions induced by a magnetic field in planar samples of smectic C liquid crystals

Abstract

This article derives theoretical results for the onset of the Helfrich-Hurault transition in smectic C liquid crystals induced by a magnetic field applied parallel to the smectic layers. A suitable quadratic energy in terms of the smectic layer displacement u is derived from the nonlinear version of the smectic C energy. This energy is minimized via averaging to enable the calculation of a critical field strength Hc for the onset of layer distortions. Comparisons are made with known results for the corresponding geometry in the smectic A case. An estimate for the value of the smectic C elastic constant A12 can also be made by considering characteristic length scales

Fredericks Transition in Pure and Nanodoped Surface Stabilized Ferroelectric Liquid Crystals

“…Also, we assume the system is free from dislocation of layer thickness. Hence, the layer normal must fulfill the constraint [13] ∇ × a = 0,…”

Threshold properties of nanodoped surface stabilized ferroelectric liquid crystals under electric and magnetic fields

“…The restoring orientational elastic torques, acts on the system and the presence of a spontaneous polarization leads to the torques on P and c-director. In an applied field, the coupling between the polarization and the c-director leads to additional torques on c [22,24,26]. The director is strongly anchored at the boundaries and therefore, the external field can cause an inhomogeneous texture.…”

“…Also, we assume that the system is free from dislocation of layer thickness [22,23]. Hence, the layer normal must fulfill the constraint [24] ∇ Â a ¼ 0:…”

“…The undulating deformation of layers and layer compressions induced by the external fields in a SSFLC, with strong anchoring condition on the walls are neglected, too. It is reasonable assumption, because the field strength needed to make these distortions is typically very stronger than the threshold values of Fredericks transition [11,24]. In this work, we mainly focus on the Fredericks transitions of a nanodoped ferroelectric system under simultaneous applied electric and magnetic fields whose properties were not well studied in the literatures and in our previous work as well.…”

Structure of smectic-Aliquid crystals in nonuniform domains: Modeling the impact of imperfect boundaries

“…Specifically, smectic liquid crystals are layered structures with a well-defined interlayer distance, which is in the range 20 − 80Å [66, p. 6]. These layers may be described by a scalar function Φ that can be used to investigate layer undulations [64,65,68,67,74,76,22,43,42,69,73,71,72,75] and is often assumed to be of the form Φ(x, y, z, t) = x + u(x, y, z, t) (or Φ(x, y, z, t) = z + u(x, y, z, t) depending on the layer orientation), where u denotes layer undulations. However, this ansatz does not accurately describe the underlying features of the smectic layers.…”