Solitons and defects in nematic liquid crystals under a simple shear flow and in a static external magnetic field

Under a simple shear flow and in a static external magnetic field, the production of defects in the director-aligning regime of nematic liquid crystals has been investigated in terms of the Leslie-Ericksen theory. The equation of motion of the nematic director, which conforms to the driven over-damped sine-Gordon equation, has a soliton solution of the amplitude w. We show that the stationary state with the director uniformly oriented at a Leslie angle is only a metastable state and the potential, which governs the motion of the director, has a nmnber of stable stationary states. For a strong magnetic field, the higher energy barrier between the stable and unstable states leads the director to be locked along the magnetic field direction. However, at the appropriate shear rate and magnetic field the defects, which appear as a stable solitary solution, can be nucleated from a uniformly aligned nematic liquid crystal. We have calculated the stationary travelling velocity of the solitary waves and the distance between a pair of defects.     

Cascade “Melting” of a Linear Disclination in Chiral Nematic Droplets

A new structure of the elastic field of a chiral nematic liquid crystal in a cylindrical capillary with a singularity on the axis of the capillary in the form of a “melted” helical disclination has been obtained experimentally. It has been shown theoretically that the number of cylindrical surfaces, cascades at which a jump of the direction of the director orientation field n by π occurs, can be arbitrary. The particular number of cascades depends on the radius R of the cylinder and boundary conditions. An expression for the free energy of the elastic field has been obtained in the one-constant approximation of the continuum theory of liquid crystals.     

Optical properties of frustrated cholesteric liquid crystals in planar cell

ABSTRACT

We investigated the alignment director of a frustrated cholesteric liquid crystal (CLC) confined in a planar cell. Three cells with different confinement ratio (c?=?d/p) (where p is the pitch and d is the cell thickness) are prepared. Under an electric field, the CLC planar texture is transformed into a cholesteric fingerprint (CF). The results showed that CF contrast depends on c. When c?≈?2, CLC stripes are formed by a periodic CF, with a period equal to the CLC pitch. The CF is developed and slowly extended to the whole cell surface along the rubbing direction and the contrast of the grating stripes keeps unchangeable. Yet, the CLC finger borders have a different light intensity. However, when c?≈?1, the CF contrast increases with time. When c?θ between the polarizer and the CFs.     

Director dynamics near the nematic-smectic-A phase transition

The Landau-de Gennes model for the free energy of a nematic liquid crystal near the phase transition to the smectic A-phase is used to determine the frequency dependence of the fluctuation corrections to the Frank elastic constants. It is shown that the interaction of the fluctuations of the smectic order parameter and the director results in corrections to all the Frank elastic constants. In the low-frequency limit (ω→0), the corrections to the Frank elastic constants K ₂₂ and K ₃₃ are the largest, and decrease to zero in the infinite-frequency limit. The correction to K ₁₁ is negative, and vanishes in both limits. The absolute value of the correction to K ₁₁ is the largest at frequencies in the megahertz range. It is shown that in oriented nematics the interaction of the smectic fluctuations and the director limits deviations of the director from the direction of preferred orientation, as a result of which relaxation of both inhomogeneous and homogeneous distortions of the director field can be observed. It is also shown that this gives rise to a frequency interval in the megahertz range in which shear waves begin to propagate in the nematic. The propagation speed of these waves is roughly a hundred times smaller than that of sound and strongly depends on the direction of propagation. Zh. éksp. Teor. Fiz. 114, 2022–2033 (December 1998)     

Photoinduced decrease in local polarization switching fields in lithium niobate crystals

Variations in local polarization switching fields E _C in lithium niobate crystals have been investigated under laser irradiation of the z surface. It has been established that the simultaneous application of an electric field in the direction opposite to the spontaneous polarization field and laser beam leads to a decrease in the field E _C .     

High magnetic field properties of mixed terbium-yttrium ferrite garnets

Magnetization measurements in d.c. magnetic fields up to 180 kOe have been performed on polycrystalline specimens and on single crystals of mixed terbium-yttrium iron garnets: Tb _x Y_3–x Fe₅O₁₂ in the 4.2–300 K temperature range. On polycrystals (x=2.5; 2; 1; 0.37) the concentration dependence of both compensation point and spontaneous magnetization has been determined. In the single crystals (x=2; 1; 0.37) a strong magnetic anisotropy has been observed with a change of the easy direction of magnetization from [111] to [100] whenx decreases; abrupt field-induced transitions have been observed at low temperatures when the external field is applied along the [100] direction.     

Orientational Instability and Hysteresis Phenomena in a Ferronematic Liquid Crystal in a Magnetic Field

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.     

Rayleigh–Benard Convection in the homeotropic nematic liquid crystal by a Gaussian laser beam absorption

The Rayleigh–Benard Convection (RBC) were studied theoretically in the homeotropic nematic liquid crystal (NLC) cell due to the absorption of a normally incident Gaussian light beam from upper side of the cell. It was shown that a convection of hydrodynamic motion in the NLC can be induced and eventually the molecular director coupling with hydrodynamics reorients the director. An external magnetic field parallel to the director decreases the director reorientation and the radial flow velocity, while the velocity in the z direction is unaffected. The results were found to be in a range that can easily be checked experimentally.     

Helicon-phonon interaction for oblique propagation in potassium

The dispersion equation for oblique propagation of the wave in thexy plane for helicon-phonon interaction has been derived and numerical studies have been carried out on the nature of variation of the four different modes with the magnetic field and the inclination of the magnetic field with the direction of propagation.     

Surface anchoring and pitch variation in thin smectic C* layers in an electric field

The variations of the pitch of smectics C* in thin planar layers in an external electric field and their dependence on the surface anchoring are investigated theoretically. The proposed mechanism of the change in the number of half-turns of the helical structure in a finite-thickness layer upon a change in the applied field is the slip of the director on the surface of the layer through the potential barrier of surface anchoring. The equations describing the pitch variation in an external field and, in particular, the hysteresis in the jumpwise variations of the pitch for opposite directions of field variation are given and analyzed for arbitrary values of the field. For weak fields, it is found that the pitch variation in the layer is of a universal nature and is determined by only one dimensionless parameter, S _d= K ₂₂/dW, where K ₂₂ is the Frank torsion modulus, W is the surface anchoring potential, and d is the layer thickness. The possibility of direct determination of the form of the anchoring potential from the results of corresponding measurements is considered. Numerical calculations for the deviation of the director from the direction of alignment on the layer surface and pitch variations, as well as the points of pitch jumps and hysteresis in the field, are made for the Rapini model anchoring potential for values of the parameters for which the pitch variation weakly depends on the direction of the field applied in the plane perpendicular to the spiral axis of smectics C*. The changes in the pitch variation in stronger fields are discussed, and the optimal conditions for observing the discovered effects are formulated.     

Small-angle light scattering symmetry breaking in polymer-dispersed liquid crystal films with inhomogeneous electrically controlled interface anchoring

We have described the method of analyzing and reporting on the results of calculation of the small-angle structure of radiation scattered by a polymer-dispersed liquid crystal film with electrically controlled interfacial anchoring. The method is based on the interference approximation of the wave scattering theory and the hard disk model. Scattering from an individual liquid crystal droplet has been described using the anomalous diffraction approximation extended to the case of droplets with uniform and nonuniform interface anchoring at the droplet–polymer boundary. The director field structure in an individual droplet is determined from the solution of the problem of minimizing the volume density of the free energy. The electrooptical effect of symmetry breaking in the angular distribution of scattered radiation has been analyzed. This effect means that the intensities of radiation scattered within angles +θ _s and–θ _s relative to the direction of illumination in the scattering plane can be different. The effect is of the interference origin and is associated with asymmetry of the phase shift of the wavefront of an incident wave from individual parts of the droplet, which appears due to asymmetry of the director field structure in the droplet, caused by nonuniform anchoring of liquid crystal molecules with the polymer on its surface. This effect is analyzed in the case of normal illumination of the film depending on the interfacial anchoring at the liquid crystal–polymer interface, the orientation of the optical axes of droplets, their concentration, sizes, anisometry, and polydispersity.     

Formation of a temperature gradient in a hybrid-oriented liquid-crystal cell in response to shear stress

The orientational relaxation of the director, velocity, and temperature fields in a hybrid-oriented liquid-crystal cell in response to a shear stress applied to one of the cell surfaces has been investigated. The cases of the complete and partial thermal insulation of one of the cell surfaces have been considered under the condition where a constant temperature is maintained at the other cell surface. The relaxation time and the influence of the velocity field on the reorientation of the director field have been analyzed for a number of hydrodynamic regimes arising in the liquid-crystal cell under the effect of the shear stress and the temperature gradient formed over the cross section of the liquid-crystal cell.     

Peculiarities of electric polarization in bi-layered longitudinally magnetized ferrromagnetic film

Electric polarization arising in a vicinity of magnetic inhomogenety in longitudinally magnetized ferromagnetic films has been considered. A variety of polarization transformations induced by external magnetic field have been studied. It has been demonstrated that electric polarization can change continuously or with a jump-like character depending on intrinsic, mainly anisotropic properties of the layers, the direction and the value of external magnetic field.     

采用多相场法研究三维层片共晶生长的厚度效应

采用Kim,Kim,Suzuki和Ode提出的KKSO多相场模型,研究了固定层片间距不同层片厚度条件下三维过共晶层片生长形态的演化行为.研究表明,层片厚度对层片生长过程有较大影响.当层片厚度较小时,厚度效应较弱,类似于二维生长.随着层片厚度的增加,厚度效应逐渐增强并开始产生厚度方向的振荡失稳,造成层片取向的偏转.层片厚度的进一步增加,使层片宽度方向和层片厚度方向的振荡交替出现.当层片厚度大于层片宽度时,厚度效应逐渐强于宽度效应,最终宽度方向的振荡被抑制,仅在厚度方向形成类似于二维的1λ振荡. 关键词： 数值模拟 多相场 三维层片生长 层片厚度     

Magnetocaloric effect and magnetic properties in YMnO3 perovskite

The magnetic properties and magnetocaloric effect in YMnO₃ have been investigated using Monte Carlo simulations. The thermal magnetization, specific heat and magnetic entropy have been obtained for different values of exchange interactions and for a several external magnetic field values. The variation of adiabatic temperature change with the temperatures has been obtained for several values of external magnetic field. It has been found that the sample exhibited a paramagnetic to ferromagnetic phase transition at 30 K. The transition temperature of YMnO₃ has been deduced for different values of size (1/L) and different values of exchange interactions. The relative cooling power with several values of external magnetic field has been established.     

Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

The effect of magnetic field and convective flow on nematic director fluctuations

The slow orientational fluctuations of the director in the nematic state of d-PAA have been studied by real-time neutron scattering. By analysis of the measured time series we have derived the Hurst exponentH as a function of the applied magnetic field and of the applied vertical temperature difference of the sample. For zero values of both parameters we foundH0.9, indicating a high degree of temporal correlation between orientational fluctuations. At increasing field or temperature gradientH approaches a value of 0.5, corresponding to zero temporal correlations.     

Effect of magnetic fields on out-of-plane orientations of nematic liquid crystalline polymers under simple shear flow

The effect of magnetic fields on out-of-plane orientations of liquid crystalline polymers (LCPs) under simple shear flows is numerically analyzed using the Doi–Hess equation. The evolution equation for the probability distribution function of the LCP molecules is directly solved without any approximation closure. The initial director is parallel to the vorticity direction. Two cases of the magnetic fields are considered (1) the magnetic field parallel to the flow direction, and (2) the magnetic field parallel to the velocity gradient direction. For both cases a log-rolling orientation state is detected at low shear rates. However, the director is quickly aligned along the direction of magnetic fields because of the deformation of molecules. The field affects on the scalar order parameter rather than the major orientation direction for the magnetic field parallel to the flow direction. On the other hand regarding the magnetic field along the vorticity gradient direction, the effect of the magnetic field is more remarkable on the major orientation in comparison with the effect on the scalar order parameter. Also it is be found that the order parameter is increased obviously with increasing the magnetic fields. It is an efficient way to improve the performance of LCP materials.     

On the possibility of the violation of the Curie-Neumann principle in anisotropic media with dissymmetry

The dynamics of defects and their mutual transformation and annihilation in drops of a nematic-cholesteric mixture in the presence of quasistatic electric fields has been investigated by the birefringence method. Three basic independent configurations of the director distribution—static and dynamic with the right and left-handed twists of cholesteric layers around the axis parallel to the field—are formed above the threshold field. The possible mechanisms of the observed processes have been discussed. It has been shown that a certain symmetry of the causes (the nematic-cholesteric liquid crystal and field) does not necessarily lead to the corresponding symmetry of the induced structures and mechanical processes. An anisotropic distribution of the orientation of rotating spiral structures with respect to the normal to the nematic-cholesteric liquid crystal layer has been revealed.