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We study the orientational transitions in a suspension of carbon nanotubes in a nematic liquid crystal induced by an external magnetic field. The case of a finite orientational anchoring of liquid crystal molecules at the surface of doped carbon nanotubes is considered. It is shown that in a magnetic field the initial homogeneous planar texture of the liquid crystal–carbon nanotubes mixture is disturbed in a threshold manner (Fréedericksz transition). The orientational and concentration distributions of the suspension are studied for different values of the magnetic field strength and segregation intensity of the impurity subsystem. The optical phase lag between ordinary and extraordinary rays of light transmitted through a layer of a liquid crystal composite is calculated. The possibility of changing the nature of the Fréedericksz transition from second order to first order is shown. This tricritical behavior is related to the redistribution of the carbon nanotubes (segregation effect) inside the layer.

We present numerical and analytical results describing the dynamics of a helical orientational structure of a ferrocholesteric liquid crystal, i.e., dilute suspension of ferromagnetic nanoparticles in a cholesteric liquid crystal, under the action of a rotating magnetic field. We employ the continuum theory to show how rotating magnetic field can untwist the helical ferrocholesteric structure and induce a ferrocholesteric–ferronematic transition. We analyze the non-stationary and stationary rotation regimes of the helical structure of a ferrocholesteric in a magnetic field. For weak fields, small and large rotational velocities the analytical expressions are obtained for the pitch of the ferrocholesteric helix. In the stationary rotational regime the orientational phase diagram of the ferrocholesteric–ferronematic transition is constructed for different values of magnetic field and angular velocities. It is shown that with increasing these parameters the transition field decreases. The dependence of a ferrocholesteric pitch on the magnetic field and its angular velocity at various material parameters is numerically obtained. We derive the analytical expression describing the divergence law for the pitch of a helix in the pre-transition region.

We study the influence of anchoring energy on the orientational structure of a cholesteric liquid crystal in a layer with soft homeotropic anchoring on the boundaries. We consider magnetic field induced transition from the uniform homeotropic nematic phase to the cholesteric phase. We show that this phase transition can occur due to the change of external magnetic field, oriented normally to the cell walls, or due to the change of the layer thickness, and can be either the first- or the second order transition. We determine the conditions of the phase transition hysteresis. We show that the variation of anchoring energy causes the change of the phase transition order, and can also lead to occurrence of the planar alignment in the layer. We also propose the method for measurement of the polar anchoring energy. We show that for some values of polar anchoring energy and the layer thickness, the initial uniform homeotropic state becomes unstable relative to small long-wave perturbations periodical along the layer.

Within the continuum theory, we study the influence of a magnetic field on the orientational and magnetic properties of a helicoidal liquid-crystal ferrosuspension, the so-called ferrocholesteric. We consider the compensated ferrocholesterics with soft planar coupling of magnetic particles with a liquid crystal matrix. We show that under the influence of a magnetic field applied perpendicularly to the axis of the helical structure of a ferrocholesteric, the unwinding of the helical structure takes place, and the transition to the ferronematic phase occurs. We study the dependence of the phase transition field on the suspension material parameters. The behavior of the average magnetization and the pitch of the helical structure as a function of a magnetic field is studied. It is shown that at soft coupling of particles with a liquid crystal matrix, the magnetization vector and the director have different pitches of the spiral structure in an external magnetic field.

A statistical theory is proposed to describe a suspension of carbon nanotubes in a nematic liquid crystal. The mean-field approach is used, and dispersion attraction, the excluded volume effects, the diamagnetism of liquid crystal molecules, and the strong diamagnetism of nanotubes are taken into account. The influence of the volume fraction of impurity, temperature, and magnetic field on the orientational ordering of a liquid crystal matrix and carbon nanotubes is studied. The concentration and temperature phase transitions in the suspension are investigated for various magnetic fields. The concentration and field shifts of the point of the phase transition between nematic and isotropic or paranematic phases are studied.

We study theoretically the unwinding of helical orientational structure of a cholesteric liquid crystal under rotating magnetic field action. We analyze the non-stationary rotation regime of the orientational structure at the initial stages of the cholesteric helix unwinding in weak magnetic fields. For small deformations of the orientational structure we analytically obtain the dependence of the pitch of the cholesteric helix on the strength and rotation velocity of a magnetic field. For the stationary rotation regime in a magnetic field, the orientational phase diagram of the cholesteric–nematic transition is constructed. We study numerically and analytically the dependences of the cholesteric helical pitch on the strength and rotation velocity of the magnetic field. We reveal that in the narrow range of rotating magnetic field strength, the reentrant cholesteric–nematic–cholesteric orientational transitions take place. We show that in the stationary rotation regime, an increase in the rotation velocity of the field leads to a decrease in the cholesteric–nematic transition field. In the absence of rotation, our results are reduced to the well-known for static magnetic fields.

The magnetic Freedericksz transition in a ferronematic representing a diluted suspension of magnetic nanoparticles in an N-(4-methoxybenzylidene)-4-butylaniline (MBBA) nematic liquid crystal was experimentally studied. The transition point was determined by means of dielectric capacitance measurements in cells of different thickness for samples with various volume fractions of ferroparticles. The effect of weak coupling between the magnetic and liquid-crystal subsystems was studied. Low concentrations of quasispherical magnetic particles were shown to decrease the magnetic Freedericksz transition threshold in comparison with a pure liquid crystal. The obtained results were theoretically substantiated. The phase diagram of the suspension was plotted, and the method of estimating the energy of coupling between magnetic particles and a liquid-crystal matrix was proposed.

A magnetic-field-induced orientational structure in a ferronematic (FN) liquid crystal (LC) layer is studied within the continuum theory. The rotation angles of the director and the magnetization and the concentration of magnetic impurity corresponding to a supertwisted orientational structure of the suspension are calculated. It is shown that the deviation angle of the director from the direction of the external field has the hysteresis region in which the orientational structure of the FN changes stepwise from a state with a positive twist of the director to a state with a negative twist. A value of the magnetic field strength is found above which orientational bistability regions arise. It is shown that orientational instability under the rotation of the field most clearly manifests itself in FNs with strong anchoring of particles to the LC matrix. It is established that the effect of magnetic segregation responsible for the redistribution of magnetic particles in the layer leads to the expansion of the hysteresis region and to a decrease in the field at which orientational instability arises. It is shown that, in FNs with soft anchoring between magnetic and LC subsystems, there exist several response modes to a quasistatic rotation of the magnetic field.

We propose a continuum theory of orientational phase transitions induced by an external magnetic field in a suspension of carbon nanotubes in a nematic liquid crystal. It is shown that in a magnetic field a non-uniform and two different uniform phases are possible in the suspension. The uniform phases of the suspension differ by the type of orientational coupling of nanotubes with the liquid crystal matrix (the planar type when the nanotubes are oriented along the matrix director, and the homeotropic type when the nanotubes are perpendicular to the director). The possibility of a redistribution of the nanotube concentration (segregation effect) is shown. The fields of orientational transitions between uniform and non-uniform phases of the suspension are found analytically. It is shown that, when the nanotubes are weakly coupled to the matrix, the magnetic field induces reentrant transitions (uniform planar phase–non-uniform phase–uniform homeotropic phase–non-uniform phase). These transitions can be of first or of second order depending on the carbon nanotubes segregation intensity.

We study the unwinding of the ferrocholesteric helical structure induced by a combined action of a magnetic field and a shear flow. Both influences are able to induce the ferrocholesteric–ferronematic transition independently; however, the differences between the magnetic field orientation and the flow alignment direction lead to a competition between magnetic and hydrodynamic mechanisms of influence on the ferrocholesteric structure. We analyze various orientations of a magnetic field relative to the direction of a shear flow. The pitch of the ferrocholesteric helix is obtained as function of the strength and the orientation angle of the magnetic field, the shear velocity gradient and a reactive parameter. Phase diagrams of ferrocholesteric–ferronematic transition and the pitch of the ferrocholesteric helix as functions of the material and the governing parameters are calculated. We find out that imposing a shear flow leads to a shift of the magnetic field threshold. The value of the critical magnetic field depends on the magnetic field orientation, the velocity gradient, and the viscous coefficients. We show that the interplay of a magnetic field and a shear flow can induce reentrant orientational transitions that are ferrocholesteric–ferronematic–ferrocholesteric.

The untwisting of the helical structure of a cholesteric liquid crystal under the action of a magnetic field and a shear flow has been studied theoretically. Both factors can induce the cholesteric–nematic transition independently; however, the difference in the orienting actions of the magnetic field and the shear flow leads to competition between magnetic and hydrodynamic mechanisms of influence on the cholesteric liquid crystal. We have analyzed different orientations of the magnetic field relative to the direction of the flow in the shear plane. In a number of limiting cases, the analytic dependences are obtained for the pitch of the cholesteric helix deformed by the shear flow. The phase diagrams of the cholesteric–nematic transitions and the pitch of the cholesteric helix are calculated for different values of the magnetic field strength and the angle of orientation, the flow velocity gradient, and the reactive parameter. It is shown that the magnetic field stabilizes the orientation of the director in the shear flow and expands the boundaries of orientability of cholesterics. It has been established that the shear flow shifts the critical magnetic field strength of the transition. It is shown that a sequence of reentrant orientational cholesteric–nematic–cholesteric transitions can be induced by rotating the magnetic field in certain intervals of its strength and shear flow velocity gradients.

Influence of magnetic field on orientation and magnetic properties of a compensated ferrocholesteric, a suspension of needle-like ferromagnetic particles in a cholesteric liquid crystal, was studied theoretically. A phase transition from a ferrocholesteric to a ferronematic state in a magnetic field oriented normally to the axis of the helical structure was considered. The dependences of the transition field to the ferronematic phase on the material parameters of the suspension and of the helical structure pitch and magnetization on the field strength were investigated. A possibility of existence of a reentrant ferrocholesteric phase was shown.

In the framework of the continuum approach we study the behavior of the orientational structure of a ferronematic liquid crystal with soft planar coupling between the liquid crystal matrix and magnetic particles in an elliptically polarized rotating magnetic field. We reveal synchronous and asynchronous oscillating regimes of orientational structure rotation for unbounded sample. We obtain the dependence of the critical angular velocity, which determines the boundary of regimes, on suspension parameters and the magnetic field for different values of its ellipticity. We show that transitions between the regimes are induced by the change in the coupling energy, the ellipticity parameter, the angular velocity, and the magnetic field. We find out that the critical angular velocity of an elliptically polarized magnetic field is always less than the critical velocity of a circularly polarized field. We analyze the stability thresholds of the orientational rotation regimes of a ferronematic liquid crystal and a nematic without magnetic admixture depending on the ellipticity of the magnetic field. We show that the presence of the magnetic particles increases the stability threshold of a synchronous oscillating regime of the suspension rotation.

On the base of molecular-statistical approach we study the phase transition between the ordered (ferromagnetic) and disordered (paramagnetic) phases in liquid-crystalline suspensions of magnetic nanoparticles in an external magnetic field. The free energy and equations of magnetic and orientational equilibrium are obtained in the framework of spherical approximation.

The magnetic-field induced orientational transition in helicoidal liquid-crystalline antiferromagnets representing compensated suspensions of magnetic nanoparticles in cholesteric liquid crystals is theoretically studied. The untwisting of a helicoidal structure and the behavior of mean magnetization as a function of the field strength and material parameters are investigated. It is shown that the magnetic subsystems in the field-untwisted ferronematic phase are not completely compensated, and the ferronematic phase is ferrimagnetic.

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.

We study the orientational response of a ferromagnetic liquid crystal that is induced by magnetic and electric fields. A modified form of the energy of the orientational interaction between magnetic impurity particles and the liquid crystal matrix that leads to bistable coupling is considered. It is shown that apart from magnetic impurity segregation, first-order orientational transitions can be due to the bistability of the potential of the orientational coupling between the director and the magnetization. The ranges of material parameters that lead to optical bistability are determined. The possibility of first-order orientational transitions is analyzed for the optical phase difference between the ordinary and extraordinary light rays transmitted through a ferronematic cell. It is shown that an electric field applied in the given geometry considerably enhances the magneto-orientational response of the ferronematic.

The orientational phases in an antiferromagnetic liquid crystal (ferronematic) based on the nematic liquid crystal with the negative anisotropy of diamagnetic susceptibility are studied in the framework of the continuum theory. The ferronematic was assumed to be compensated; i.e., in zero field, impurity ferroparticles with the magnetic moments directed parallel and antiparallel to the director are equiprobably distributed in it. It is established that under the action of a magnetic field the ferronematic undergoes orientational transitions compensated (antiferromagnetic) phase–non-uniform phase–saturation (ferrimagnetic) phase. The analytical expressions for threshold fields of the transitions as functions of material parameters are obtained. It is shown that with increasing magnetic impurity segregation parameter, the threshold fields of the transitions significantly decrease. The bifurcation diagram of the ferronematic orientational phases is built in terms of the energy of anchoring of magnetic particles with the liquid-crystal matrix and magnetic field. It is established that the Freedericksz transition is the second-order phase transition, while the transition to the saturation state can be second- or first-order. In the latter case, the suspension exhibits orientational bistability. The orientational and magnetooptical properties of the ferronematic in different applied magnetic fields are studied.

Spatial distortions of the director field and magnetization of a ferronematic (suspension of magnetic nanoparticles in a nematic liquid crystal) that are induced by simultaneous action of electric and magnetic fields are studied with allowance for the flexoelectric polarization of the liquid-crystalline matrix. Soft coupling of liquid crystal and magnetic particles and layer boundaries is considered. The dependence of the phase lag of the transmitted light on the external magnetic field is analyzed.

In the framework of continuum theory we consider magnetic field induced transitions in soft compensated ferronematic liquid crystals, i.e., suspensions of ferromagnetic nanoparticles in nematic solvents with equiprobable distribution of the particles parallel and antiparallel to the director. Such systems are liquid-crystalline analogs of antiferromagnetics. We study the sequence of re-entrant transitions (uniform compensated phase – non-uniform phase – uniform saturation phase – non-uniform phase) between phases with different orientations of the director and magnetization. These transitions take place under the magnetic field action in the case of weak coupling between disperse magnetic phase and nematic matrix. We show that these transitions can be first or second order, and obtain the expressions for determining the order of orientational transitions. For the case of first order transitions, when the ferronematic shows orientational bistability, we study magnetic field influence on the orientational behavior of the director and magnetization, redistribution of magnetic impurity, and magneto-optical response.

In the framework of continuum theory we study magnetic field induced orientational transitions in a ferronematic, i.e. suspension of single-domain magnetic particles in a nematic liquid crystal. We consider the case of negative diamagnetic susceptibility anisotropy of a liquid crystal and soft planar coupling of impurity particles with a liquid crystal matrix. We found tricritical behavior of the threshold transition in a magnetic field from perturbed state into uniform planar state. This transition can be the first or second order, depending on the parameter of the magnetic phase segregation. We analytically derive the expression for the tricritical segregation parameter that determines the character of a transition. We show that ferronematic has a large magneto-optical non-linearity which is the result of the director reorientation under external field. Comparison of results of numerical calculations with experimental data has been carried out.

The behavior of the orientational structure of a ferronematic in a rotating uniform magnetic field is investigated using the continual theory. The time-dependent system of equations describing the dynamics of the ferronematic is derived. The dependences of the angles of rotation of the director and of the magnetization of the ferronematic on the velocity of field rotation are determined for various values of the material parameters. Two regimes (synchronous and asynchronous) of rotation of the ferronematic structure are detected. In the synchronous regime, the director rotates with the frequency of the magnetic field and a constant phase delay. The asynchronous regime is characterized by a time-dependent phase delay. The dependence of the critical angular velocity of magnetic field rotation, which determines the boundary between the synchronous and asynchronous regimes, on the magnetic field strength is derived.

The influence of flexoelectric polarization induced by external electric and magnetic fields in a ferronematic liquid crystal on the orientational transitions between uniform and nonuniform phases is analyzed. The Freedericksz transition field and the saturation field as functions of ferronematic material parameters are determined. Bifurcation diagrams of orientational phases are analyzed. It is shown that the orientational transitions can be of the first or second order depending on the value of the segregation parameter of the dispersed phase.

In the framework of continuum theory we study the orientational and magnetooptical properties of ferronematics (i.e., colloidal suspensions of magnetic nanoparticles in nematic liquid crystals) with soft planar coupling of a disperse phase with a liquid crystal matrix in a magnetic field. It is shown that there is a threshold energy of coupling between the dispersed phase and the liquid crystal matrix, below which (weak coupling) ferronematic has a complex magnetooptical response to an applied magnetic field. We show that at weak coupling initially a uniform ferronematic structure under the field action undergoes the sequence of re-entrant transitions “uniform phase–non-uniform phase–uniform phase–non-uniform phase”, which can be of the first or second order depending on a segregation parameter value. The tricritical value of the segregation parameter is found analytically as a function of the material parameters of a suspension. We study magnetic field action on the optical phase lag and the capacity of a ferronematic cell. Comparison of results of numerical calculations with experimental data is carried out.

We analyze uniform orientation phases in soft ferronematics (suspensions of magnetic nanoparticles in nematic liquid crystals) induced by electric and magnetic fields. It is shown that the competition between the electric and magnetic fields can lead to various sequences of orientation transitions in a ferronematic depending on the energy of coupling between the director and magnetization. We obtain and analyze phase diagrams of these transitions. A sequence of re-entrant transitions in the orientation structure (angular phase-homeotropic phase-angular phase-planar phase) is predicted for a certain range of the coupling energies and electric field strengths.

As it is known, the Rapini-Papoular potential is suitable for description of anchoring energy between the liquid crystal and bounding surfaces in the case of small deviations of the director from the easy orientation axis. We use modified surface potential that can describe the anchoring energy at large deviations of the director more adequately. The interaction effect of a cholesteric liquid crystal with a bounding surfaces on the nature and features of cholesteric-nematic phase transitions induced by an external magnetic field is studied. We determine the conditions for existence of three different phases in a cholesteric liquid crystal layer with a finite homeotropic anchoring at the boundaries. The dependencies of the threshold fields of orientational transitions between the phases of a liquid crystal on the material parameters of the cell are calculated. Landau expansions of the total free energy of cholesteric near the transition points are constructed. We determine the tricritical values of the anisotropy parameter of the surface anchoring, which characterize the nature of transitions between the phases of a cholesteric liquid crystal.

A statistical mean-field theory is proposed for describing the magneto-orientational ordering of a composite material, namely a liquid crystal suspension of carbon nanotubes. A nematic liquid crystal with negative anisotropy of diamagnetic susceptibility with the molecules, which have long axes tending to be orthogonal to the applied magnetic field, has been considered as a dispersion medium. Since carbon nanotubes possess positive anisotropy of the diamagnetic susceptibility, they tend to align parallelly to the field, causing competition with the ordering of the liquid crystal matrix. Phase transitions induced by temperature and magnetic field have been studied for different values of the coupling energy of carbon nanotubes with a liquid crystal matrix. It is shown that depending on the temperature, magnetic field induces the transition from a highly ordered nematic phase to a weakly ordered paranematic phase with both the positive and the negative value of the order parameter of the liquid crystal, which respectively corresponds to the orientational anisotropy of the “easy-axis” and “easy-plane” types.

In the framework of continuum theory, we study magnetic field induced orientational transitions in a ferronematic, i.e., colloidal suspension of magnetic nanoparticles in a nematic liquid crystal. We consider a compensated ferronematic which is not magnetized in the absence of a field. The effect of finite coupling energy between the liquid crystal and the particle surfaces, as well as the segregation effect on the orientational transitions in a ferronematic are studied. The possibility of existence of three regimes of ferronematic orientational behavior under applied magnetic field in the case of weak coupling between the dispersed phase and a liquid crystal is established. The induced magnetic field distortions of orientational structure are shown to have a threshold character. The analytical expressions for the threshold fields are obtained. The optical phase lag and intensity of light transmitted through the ferronematic layer as functions of applied magnetic field are studied.

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.

We theoretically study the dynamics of the orientational structure of a ferronematic liquid crystal with soft planar coupling between the director and the magnetization in a rotating magnetic field. We determine critical parameters characterizing the boundary between synchronous and asynchronous rotation regimes. We show that the magnetic impurity increases the stability threshold of an asynchronous rotation regime. The critical angular velocity, the angles of the director and the magnetization rotation in each regime of orientational structure rotation are found for rigid planar coupling. We obtain that in weak magnetic fields when the main mechanism of the field influence on a ferronematic liquid crystal is associated with the effect on the magnetic particles, the critical angular velocity is linearly dependent on the field strength, while in strong magnetic fields, when the influence of a field is determined by a diamagnetic mechanism, the critical velocity is quadratically dependent on the field strength.

We study the Freedericksz transition induced by a magnetic field in a rectangular cell filled with a nematic liquid crystal. In the initial state the director of the nematic liquid crystal is uniformly aligned in the cross section plane of the cell with rigid anchoring of the director at cell walls: planar on the top and bottom walls, and homeotropic on the left and right ones. The magnetic field is directed perpendicular to the cell cross section plane. We consider two-dimensional (2D) orientational deformations of the nematic liquid crystal in the rectangular cell and determine the critical value of the Freedericksz transition field above which these orientational deformations occur. The 2D expression for the director alignment profile above the threshold of Freedericksz transition is analytically found and the profile shapes as functions of cell sizes, values of the Frank elastic constants of the nematic liquid crystal and the magnetic field are studied.

Within the continuum approach we study the equilibrium configurations of a cholesteric liquid crystal confined between two parallel plates, when a magnetic field is applied perpendicularly to the plates. We analyze the role of soft anchoring boundary conditions on magnetic-field-induced cholesteric-nematic transitions in a finite thickness cholesteric cell, treated to induce soft planar alignment. We study the stepwise behavior of cholesteric pitch as a function of the anchoring energy, the thickness of a layer, and the field strength. We analyze some kinds of soft anchoring potentials, including the case of degeneration of the easy axes. We show that the variation of the thickness or intrinsic pitch induces the the stepwise behavior of a pitch of the planar cholesteric structure, and the stepwise variations of the average tensor of diamagnetic susceptibility. The values of these jumps are determined by the anchoring energy. We find the values of critical parameters for the transitions between planar and confocal cholesteric states, and homeotropic nematic state. We show that the variation of the anchoring energy leads to change of the phase transition character; the conditions for hysteresis behavior are obtained. We show that for rather soft anchoring the confocal state is metastable, and the increase of a magnetic field leads to the direct transition between the planar cholesteric and homeotropic nematic phases. We also give a detailed derivation of the threshold and saturation properties of planar cholesteric to homeotropic nematic transition.

The Freedericksz transition in splay and bend geometry in a ferronematic (a suspension of single-domain magnetic particles in a nematic liquid crystal) is considered in the framework of the continuum theory. In zero magnetic field, the ferronematic was assumed to be compensated (i.e., having equal fractions of an impurity with magnetic moments directed parallel and antiparallel to the local director). Spatial distortions of the director and the concentration redistribution of the magnetic impurity in the ferronematic layer are studied as functions of the applied magnetic field and the segregation parameter. It is shown that the magnetic-field induced Freedericksz transition from the homogeneous to the inhomogeneous state has a threshold nature. The transition field as a function of the material parameters of the ferronematic is determined analytically. Magnetization of the ferronematic and its optical properties for a strong and weak segregation as functions of the magnetic field are studied.

Orientational transitions induced by an external magnetic field in a ferronematic (a suspension of single-domain magnetic particles in a nematic liquid crystal) are considered in the framework of the continuum theory. The surface potential of the interaction between the ferronematic and the bounding plates is used taking into account the fourth-order anisotropy (the modified Rapini potential). It is shown that the ferronematic can be in one of three phases that correspond to three types of orientational ordering: homogeneous ordering, inhomogeneous ordering, and saturation state. The influence of the segregation effect of magnetic particles on the nature of orientational transitions of the ferronematic in an external field is studied. It is established that the transitions between these phases can be of the first and second order depending on the values of the anchoring parameters and the segregation parameter. Tricritical values of the parameter of anchoring anisotropy and the segregation parameter are determined.

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.

In the framework of continuum theory we study the light transmission factor of a ferronematic liquid crystal as a function of external magnetic field, the anchoring energy with the boundary of a layer, and material parameters of a ferronematic. We show that magnetic field induced Freedericksz transition in ferronematics in twist geometry can be either a first- or second-order phase transition depending on the anchoring energy between the director and magnetic particles, i.e., it exhibits the tricritical behavior. The light transmission factor for first- or second-order transition is also studied.

A possibility of the first-order transition, as well as reentrant transitions, induced by an external magnetic field between the homeotropic phase and the hybrid homeotropically planar phase in a ferronematic liquid crystal (ferronematic) with bistable anchoring at the layer boundary is demonstrated in the framework of a continuum theory. The critical values of the material parameters of the ferronematic, the anchoring energy, the thickness of the layer, and the magnetic field strength, for which this transition is possible, are determined. The cases of positive and negative diamagnetic anisotropy of the ferronematic are considered.

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.

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.

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.

Continuum theory is used to analyze the effect of an applied magnetic field on a ferronematic (i.e. dilute suspension of needle-like magnetic particles in nematic liquid crystal) with soft homeotropic anchoring between the ferroparticles and the director, and positive diamagnetic anisotropy of the liquid-crystalline matrix. It is shown that in infinite ferronematic a peculiar Freedericksz-like transition takes place, at which by a threshold way the conditions of coupling on magnetic particles vary from homeotropic anchoring to planar one. The Freedericksz transition field and saturation field are found as a functions of material parameters of a suspension. The continuum theory predicts the existence of three ferronematic phase (homeotropic, angular, and planar) with different relative orientations of the director and magnetization. The orientational structure of these ferronematic phases is studied.

The influence of the external magnetic field on the orientational structure and magnetic properties of the ferrocholesteric is analyzed. A 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 field being applied normal to the helix. Using the continuum theory, the occurrence of magnetic-field-induced ferrocholesteric–ferronematic transition is studied. The transition field as a function of the material parameters of a ferrocholesteric is found. It is shown that rising the field strength in the ferronematic phase leads to a 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.

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 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.

In the framework of the modified model [S. V. Burylov and A. N. Zakhlevnykh, Phys. Rev. E 88, 012511 (2013)] of soft ferronematic liquid crystals, i.e., suspensions of needlelike ferroparticles in nematic solvents, we consider the ferronematic states with different mutual orientations of the director and magnetization. We study the transitions between states in an external magnetic field and show that these transitions are characterized by either continuous or discontinuous changes in the order parameter; i.e., they can be both the second-order and the first-order, respectively. In the latter case the magnetic field induced orientational hysteresis arises, which can be observed in experiments on the birefringence of ferronematic liquid crystals.

The influence of an external magnetic field on the orientational structure and magnetic properties of a ferrocholesteric (i.e. a magnetic suspension with a cholesteric liquid crystal as a carrier) is studied. Two mechanisms of the field influence on the ferrocholesteric are taken into account: the dipolar one due to the interaction between the field and the magnetic moments of the needle-like particles, and the quadrupolar one due to the diamagnetic susceptibility anisotropy of the cholesteric matrix. It is shown that a magnetic field applied normal to the ferrocholesteric helical axis leads to an untwisting of the spiral structure, and the ferrocholesteric undergoes a transition to ferronematic phase. The dependence of the ferrocholesteric-ferronematic transition critical field on the material parameters of a suspension is found. It is shown that the value of the critical field is strongly reduced if a dipolar regime of spiral untwisting is realized.

In the framework of continuum theory we study orientational transitions induced by electric and magnetic fields in ferronematics, i.e., in liquid-crystalline suspensions of ferromagnetic particles. We have shown that in a certain electric field range the magnetic field can induce a sequence of re-entrant orientational transitions in ferronematic layer: nonuniform phase --- uniform phase --- nonuniform phase. This phenomenon is caused by the interplay between the dipole (ferromagnetic) and quadrupole (dielectric and diamagnetic) mechanisms of the field influence on a ferronematic structure. We have found that these re-entrant Freedericksz transitions exhibit tricritical behavior, i.e., they can be of the first or the second order. The character of the transitions depends on a degree of redistribution of magnetic admixture in the sample exposed to uniform magnetic field (magnetic segregation). We demonstrate how electric and magnetic fields can change the order of orientational transitions in ferronematics. We show that electric Freedericksz transitions in ferronematics subjected to magnetic field have no re-entrant nature. Tricritical segregation parameters for the transitions induced by electric or magnetic fields are obtained analytically. We demonstrate the re-entrant behavior of ferronematic by numerical simulations of the magnetization and optical phase lag., Comment: 12 pages, 9 figures, to be published in Soft Matter