A. N. Zakhlevnykh

First Order Orientational Transitions in Ferronematic Liquid Crystals

The influence of external magnetic field on the orientational structure of a ferronematic liquid crystal is analyzed. We use modified Rapini potential for the anisotropic part of coupling energy between the ferronematic and the limiting surfaces. We show that under magnetic field action one of three ferronematics phases is possible: the uniform state, the disturbed state and the saturation state. We find that the transition between these ferronematic phases can be either the first- or the second order transition depending on the surface anchoring anisotropy and segregation parameter. We show the influence of the segregation effect on the orientational transitions in ferronematics.

Mean-field description of the order–disorder phase transition in ferronematics

A mean-field theory is developed describing in what way a small amount of ferromagnetic nanoparticles embedded in a nematic liquid-crystalline matrix affects the order parameters and the temperature of the nematic–isotropic phase transition. In such a suspension, often termed ferronematic, the ability of the particles to be aligned by the magnetic field results in occurrence of a partially oriented (paranematic) state above the transition temperature. This fact entails the possibility of field-tuning the transition temperature in both ways: up and down. The pertinent field-dependencies are obtained and analyzed. The same description applies to liquid-crystalline suspensions of ferroelectric nanoparticles tuned by the electric field.

Freedericksz Transition in Compensated Ferronematic Liquid Crystals

In the framework of continuum theory, the Freedericksz transition in ferronematic, i.e., suspension of monodomain magnetic particles in nematic liquid crystal, is studied. In the absence of a magnetic field, the suspension is supposed to be compensated, i.e., it contains equal numbers of magnetic particles with magnetic moments oriented in parallel and antiparallel to local director. Spatial distortions of director and concentrational redistribution of magnetic admixture in ferronematic layer under the influence of a magnetic field are studied. Threshold character of magnetic field induced Freedericksz transition from homogeneous to inhomogeneous state is shown. Transition field as a function of ferronematic material parameters is analytically found. Magnetization of ferronematic is studied.

Structure of the Domain Walls in Soft Ferrocholesterics

Abstract Using the continuum theory the influence of the external magnetic field on the ferrocholesteric — ferronematic phase transition is analyzed. The field being applied normal to the helix. Soft homeotropic coupling between the magnetic particles and the cholesteric molecules is assumed. The diamagnetic anisotropy of the matrix is chosen to be positive. In this case the dipolar and quadrupolar mechanisms of orientational interaction with the external field compete with each other. The transition field as a function of the material parameters of a ferrocholesteric is found. The reentrant ferrocholesteric and ferronematic phases are discussed. It is shown that rising the field strength in the ferronematic phase leads to the change in the coupling between the particles and the director from homeotropic to planar one. A study on the structure of the domain walls in ferronematic phase is undertaken.

Statistical Theory of Nematic Liquid Crystals Composed of Biaxial Ellipsoidal Particles

Abstract Statistical theory of nematic liquid crystal whose constituent molecules are biaxial ellipsoids is proposed. The method is suggested which enables one to calculate exactly the second virial coefficient for the system of biaxial ellipsoidal particles and to obtain a simple approximation formula for the third one. By means of the so-called y-expansion, the thermodynamic potential of the system is constructed and equations of the thermodynamic and orientational state are obtained. The influence of the anisometric degree (i.e. the measure of biaxiality) of the particles on the features of orientational behavior and phase transitions among the isotropic, uniaxial and biaxial nematic phases is studied. A phase diagram for a system of biaxial ellipsoids has been calculated. It is shown that the so-called self-dual point takes place with high degree of accuracy. In the limiting cases (molecules are spheres or ellipsoids of revolution) our results are identical with earlier known ones.

Reentrant Phase Transitions in Ferronematic Liquid Crystals

Within the continuum theory we study the influence of codirectional electric and magnetic fields on the orientational structure of a ferronematic layer taking into account the segregation effects. Recently in [Phys. Rev. E 81, 051710 (2010)] the tricritical behavior of the magnetic Freedericksz transition in ferronematics has been theoretically predicted. This paper shows that an external electric field can change the character of this transition. We find reentrant Freedericksz transitions in ferronematic liquid crystals subjected to the electric and magnetic fields. These transitions can be either first- or second-order ones. We derive the analytical expression for the width of the area of the reentrant orientational transitions.

Shear Flow of a Ferronematic in a Magnetic Field

We examine the effect of shear flow on the orientational phase transitions induced by magnetic field in ferronematics. Continuum approach based on the generalized Leslie-Ericksen theory is used to describe the dynamics of a ferronematic. We consider the steady state shear flow of unbounded ferronematic with constant velocity gradient in the uniform magnetic field. Stationary solutions for the director and the magnetization are obtained as functions of the magnetic field strength for the different material parameters. Our results show that shear flow can leads to the shift of the field thresholds or to a “smoothing” of the transitions in a ferronematic.

One-Dimensional Structures in Ferrocholesteric Film with Weak Homeotropic Anchoring on the Layer Boundaries

Abstract We consider one-dimensional structures of a ferrocholesteric film with weak anchoring of homeotropic type on the boundaries of the layer. We assume that the external magnetic field is oriented normal to the plane of the layer and diamagnetic anisotropy of cholesteric liquid crystal matrix is positive. We find that two kinds of ordering can exist in the layer with weak homeotropic anchoring on its boundaries: ferronematic (FN) and ferrocholesteric (FC) states. It is shown that variation of the surface anchoring strength between the cholesteric molecules and layer boundaries can induce the FN-FC transition, and can lead to a change of the phase transition character from the first order to second order one. The critical parameters of the transition between FC and FN states are determined as a function of FC material parameters. At present study of orientational and magnetic properties of FN-FC transition the so-called segregation effect are taken into account: the concentration redistribution of the magnetic admixture under the influence of a magnetic field.

Magnetic Freedericksz Transition in Ferronematic Layer Under Shear Flow

Within the framework of continuum theory we analyze the Freedericksz transition in a ferronematic layer under the combined influence of magnetic field and shear flow. The stationary equations for concentration of magnetic particles, planar director and magnetization fields are obtained. We perform numerical calculations of the angles of the director and the magnetization rotation for different values of magnetic field strength, reactive parameter and Ericksen number. We show that in the general case shear flow “smoothes” the Freedericksz transition in ferronematics. For ferronematics with non-flow-aligning nematic matrix we calculate stationary orientations of the director and magnetization in the shear plane.

On a simple molecular–statistical model of a liquid-crystal suspension of anisometric particles

A molecular–statistical mean-field theory is constructed for suspensions of anisometric particles in nematic liquid crystals (NLCs). The spherical approximation, well known in the physics of ferromagnetic materials, is considered that allows one to obtain an analytic expression for the free energy and simple equations for the orientational state of a suspension that describe the temperature dependence of the order parameters of the suspension components. The transition temperature from ordered to isotropic state and the jumps in the order parameters at the phase-transition point are studied as a function of the anchoring energy of dispersed particles to the matrix, the concentration of the impurity phase, and the size of particles. The proposed approach allows one to generalize the model to the case of biaxial ordering.