Behavior of inclusions with different value and orientation of topological dipoles in ferroelectric smectic films

Cholesteric droplets in ferroelectric free-standing films with tunable anchoring on the droplet boundary are investigated. A droplet and satellite topological defect(s) form a topological dipole. We obtained droplets with different angles α between two radial lines from the droplet center to −1/2 topological defects. Droplets with parallel dipoles form linear chains in which the interparticle distances decrease with increasing the defect angle α. For the first time, the dependence of the interparticle distance on the angle between topological defects was measured. We can adjust the magnitude and orientation of topological dipoles formed by the droplets. For the first time, the droplets with antiparallel topological dipoles were prepared in a smectic film. Interaction of the droplets with parallel and antiparallel dipoles differs drastically. Formation of antiparallel dipoles leads to a decomposition of the droplet pairs and chains of droplets. Our observations may be used to change the magnitude, anisotropy of the interparticle interaction, and structures of inclusions in liquid crystal media. The article is published in the original.     

Energetics of 2D colloids in free-standing smectic-C films

The formation of regular colloid patterns in free-standing smectic films at the transition from the smectic-C to the isotropic or nematic phase is well known experimentally. The self-organization of isotropic or nematic droplets is caused by their mutual interaction, mediated by elastic distortions of the local director in the surrounding liquid crystal. These distortions are related to the anchoring conditions of the director at the droplet border. We describe analytically the energetics of the liquid crystal environment of a single droplet in one-constant approximation. A method of complex analysis, Conformal Mapping, is employed. Following a suggestion of Dolganov et al. (Phys. Rev. E. 73, 041706 (2006)), energetics of chain and grid patterns built from the colloids are investigated numerically in order to explain experimentally observed formations and their director fields.     

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.     

Fabrication of PDLC films based on acrylic monomers and study of the electric field effect on the alignment structure of liquid crystal droplets in PDLC films

Polymer Dispersed Liquid Crystal (PDLC) films are prepared by the polymerization induced method of phase separation. Initial configurations of the director of liquid crystal droplets inside the films are found using a polarized microscope. The effect of an electric field on the alignment structure of droplets is studied. Two mechanisms of droplet orientation by the electric field are determined as smooth and spontaneous. The processes observed are compared with the results of electro-optical studies.     

Branching of colloidal chains in capillary-confined nematics

We report on the observation of colloidal chain assembly and branching inside capillaries filled with a nematic liquid crystal. Because of the homeotropic anchoring of liquid crystalline molecules on the capillary and colloidal droplet surfaces, the assembly of droplets along the capillary axis is expected, producing a transformation of the nematic director field from an escape-radial to quasiradial configuration. However, the subsequent over time branching of the straight colloidal chains is counterintuitive. By numerical simulations, we demonstrate that chain branching can occur by overcoming an energy barrier and can at least dwell as a metastable configuration. Moreover, manipulation of colloidal chains by electric fields and their gradients demonstrates various regimes of chain behavior in electric fields.     

Water droplets in a spherically confined nematic solvent: A numerical investigation

Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains [Poulin et al., Science 275, 1770 (1997)]. The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all the surfaces. Between each pair of water droplets a point defect in the liquid crystalline order was found in accordance with topological constraints. This point defect causes a repulsion between the water droplets. In our numerical investigation we limit ourselves to a chain of two droplets. For such a complex geometry we use the method of finite elements to minimize the Frank free energy. We confirm an experimental observation that the distance d of the point defect from the surface of a water droplet scales with the radius r of the droplet like .When the water droplets are moved apart, we find that the point defect does not stay in the middle between the droplets, but rather forms a dipole with one of them. This confirms a theoretical model for the chaining. Analogies to a second order phase transition are drawn. We also find the dipole when one water droplet is suspended in a bipolar nematic drop with two boojums, i.e., surface defects at the outer boundary. Finally, we present a configuration where two droplets repel each other without a defect between them. Received 11 December 1998     

Friedericksz threshold field in bipolar nematic droplets with strong surface anchoring

A numerical method has been developed for calculating the director configuration in ellipsoidal droplets of a nematic liquid crystal with strong tangential anchoring in a uniform magnetic field of an arbitrary orientation. A relation has been obtained for determining the Friedericksz threshold corresponding to the beginning of the reorientation of the central region of a droplet when the field is orthogonal to the biopolar axis. The effect of the breaking of the orthogonal condition on the threshold character of the orientation process is considered. The reorientation of the ensemble of bipolar droplets of the 5CB nematic liquid crystal dispersed in polyvinyl butyral has been studied by the magneto-optical method. Comparative analysis of calculation data and measured values of the threshold field has been performed.     

Multiferroic based on nanoparticles consisting of a silica nucleus and a shell of spin-variable iron complexes

Cholesteric droplets dispersed in a polymer with homeotropic surface anchoring are studied. A director configuration with the bipolar distribution of the axis of the helix is formed in droplets. The untwisting of the helical structure (i.e., an increase in the pitch of the helix) is experimentally observed at a decrease in the size of droplets. This dependence is analyzed for liquid crystal droplets with various concentrations of the chiral addition. A proposed empirical relation describes well the correlation of the helix pitch and the size of droplets in the studied samples.     

Phase transition in ellipsoidal droplets of nematic liquid crystals

We developed a simple method for the calculation of the director field distribution in the droplets of nematic liquid crystals (LCs) of any shape, allowing for the interaction of LCs with the droplet surface, as well as the influence of constant electric field. In contrast to different approaches, the approach that is developed in the present paper does not require any simplifying suppositions about the structure of the LC director field. The elastic-continuum theory is used, complemented with the possibility of consideration of point and linear defects. Calculations are performed using the Monte Carlo method on a simple grid. The triangulation technique is used to take the boundary conditions of droplets of a complex shape into account. The developed approach can be used for investigation of the properties of polymer-dispersed liquid crystals (PDLCs). The topological phase transitions in the nematic LC 4-cyano-4′-pentyl-biphenyl (5CB) in spherical and ellipsoidal droplets are investigated in this paper.     

Dimer structures formed in smectic films by inclusions with parallel and antiparallel topological dipole moments

Self-organization of cholesteric and nematic droplets in smectic free-standing films is investigated. Strong tangential anchoring at the droplet boundary leads to nucleation of a topological defect and formation of a topological dipole from the droplet and the defect. The interaction between droplets results in assembly of the droplets in dimers and line chains. Topological dipoles of the droplet-defect pairs can be oriented in dimers with polar (ferroelectric) and nonpolar (antiferroelectric) ordering. In this paper we found novel dimer structures formed by droplets with different handedness of the c-director field near the droplets. Depending on the relative magnitude of the droplet dipoles the resulting structure may be dipolar or quadrupolar. Formation of antiferroelectric dimers is discussed on the basis of electromagnetic analogy.     

Continuous director-field transformation of nematic tactoids

We theoretically investigate the director field inside spindle-shaped nematic droplets, known as tactoids. Tactoids typically form in dispersions of rod-like colloidal particles. By optimising the bulk elastic and surface energies, we find that the director field crosses over smoothly from a homogeneous to a bipolar configuration with increasing droplet size, in a process that we postulate to involve two virtual point defects that move in from infinity towards the poles on the surface of the droplet. Our calculations show that these hypothesised virtual defects become true surface point defects or boojums only in the limit of infinite droplet volume, and that the more elongated the droplets are, the larger their volume has to be before a uniform director field distorts so as to become discernibly bipolar. The theory agrees well with available experimental data on the size dependence of the aspect ratio of tactoids.Received: 31 October 2003, Published online: 2 March 2004PACS: 61.30.St Lyotropic phases - 64.70.Md Transitions in liquid crystals - 81.16.Dn Self-assembly - 82.70.Dd Colloids     

Nematic order in nanoscopic liquid crystal droplets

We have used atomistic molecular-dynamics simulations to model the detailed molecular configuration of 5CB (4-n-pentyl-4'-cyanobiphenyl) molecules in the form of a nanoscopic liquid crystal droplet in a vacuum microgravity environment. We find the equilibrium state of droplets consisting of as few as 26 or 50 molecules to exhibit significant nematic ordering. The shape of the droplets is also anisotropic, but there is little angular correlation between the nematic director and the long axis of the droplet. Some tendency to micelle formation is observed in droplets of 50 molecules.     

Orientational structure transformations caused by the electric-field-induced ionic modification of the interface in nematic droplets

The films of a polymer-dispersed nematic liquid crystal doped with an ionic surfactant were studied. The surface-anchoring modification effect caused by the local increase in the concentration of surface-active ions was observed at the polymer-liquid crystal interface under the action of an electric field. The modification of the boundary conditions leads to the transformation of the orientational structure of the nematic droplets and, as a result, to an appreciable change in their texture patterns and light-scattering efficiency at the interfaces. The monopolar director configurations (normal and curved) arising in the process of orientational structure transformations are considered and their typical textures are demonstrated. The possibility that the monopolar structure can be formed is theoretically substantiated by the computer simulation of the director field in a nematic droplet with the boundary conditions corresponding to the experiment.     

Hydrodynamics of nematic liquid crystals due to direct volume expansion

Hydrodynamics of planar nematic liquid crystal molecules under the influence of horizontal pressure gradient was studied, theoretically. The pressure gradient is due to nematic liquid crystal volume expansion which is a consequence of the incompressibility of the liquid. The resulting director reorientation which is due to coupling between the director orientation and fluidity of the liquid is calculated numerically for the hard and weak anchoring conditions at the cell walls.     

挠曲电效应对向列相液晶盒电光效应的影响

研究挠曲电效应对向列相液晶盒电光效应的影响.通过变分理论得到液晶指向矢满足的微分方程和边界条件,利用差分迭代的方法计算强锚定和弱锚定液晶盒中液晶指向矢的分布情况.借助琼斯矩阵的方法,计算两种液晶盒电光特性曲线.此外,在计算中同时考虑了挠曲电表面和体积效应.     

Ultrasound emulsification: effect of ultrasonic and physicochemical properties on dispersed phase volume and droplet size

Ultrasonic emulsification of oil and water was carried out and the effect of irradiation time, irradiation power and physicochemical properties of oil on the dispersed phase volume and dispersed phase droplet size has been studied. The increase in the irradiation time increases the dispersed phase volume while decreases the dispersed phase droplets size. With an increase in the ultrasonic irradiation power, there is an increase in the fraction of volume of the dispersed phase while the droplet size of the dispersed phase decreases. The fractional volume of the dispersed phase increases for the case of groundnut oil-water system while it is low for paraffin (heavy) oil-water system. The droplet size of soyabean oil dispersed in water is found to be small while that of paraffin (heavy) oil is found to be large. These variations could be explained on the basis of varying physicochemical properties of the system, i.e., viscosity of oil and the interfacial tension. During the ultrasonic emulsification, coalescence phenomenon which is only marginal, has been observed, which can be attributed to the collision of small droplets when the droplet concentration increases beyond a certain number and the acoustic streaming strength increases.     

c-director relaxation around a vortex of strength +1 in free-standing smectic-C films

The relaxation of director fields in freely suspended smectic films is studied experimentally by means of polarizing microscopy, and analyzed by solving the torque balance equation under appropriate initial and boundary conditions. We consider in particular the role of anchoring conditions of the c-director at particles and defects in the film. The structure of regular relaxation patterns allows to determine the elastic anisotropy of smectic materials. The splay elastic constant can exceed the bend constant by a factor of two and more. A remarkable consequence of this anisotropy is the stick-slip-like relaxation around a central defect of topological strength s = + 1.     

Light scattering by a nematic liquid crystal droplet: Wentzel–Kramers–Brillouin approximation

Light scattering by an optically anisotropic liquid crystal (LC) droplet of a nematic in an isotropic polymer matrix is considered in the Wentzel–Kramers–Brillouin (WKB) approximation. General relations are obtained for elements of the amplitude matrix of light scattering by a droplet of arbitrary shape and for the structure of the director field. Analytic expressions for the amplitude matrices are derived for spherical LC droplets with a uniformly oriented structure of local optical axes for strictly forward and strictly backward scattering. The efficiency factors of extinction and backward scattering for a spherical nonabsorbing LC droplet depending on the LC optical anisotropy, refractive index of the polymer, illumination conditions, and orientation of the optical axis of the droplet are analyzed. Verification of the obtained solutions has been performed.     

Evolution of temperature of a droplet of liquid composite fuel interacting with heated airflow

The macroscopic patterns of a temperature change at the center of a droplet of three-component (coal, water, petroleum) composite liquid fuel (CLF) were studied using a low-inertia thermoelectric converter and system of high-speed (up to 10⁵ frames per second) video recording during the induction period at different heating intensity by the air flow with variable parameters: temperature of 670?870 K and motion velocity of 1?4 m/s. The studies were carried out for two groups of CLF compositions: fuel based on brown coal and coal cleaning rejects (filter cake). To assess the effect of liquid combustible component of CLF on characteristics of the ignition process, the corresponding composition of two-component coal-water fuel (CWF) was studied. The stages of inert heating of CLF and CWF droplets with characteristic size corresponding to radius of 0.75?1.5 mm, evaporation of moisture and liquid oil (for CLF), thermal decomposition of the organic part of coal, gas mixture ignition, and carbon burnout were identified. Regularities of changes in the temperature of CLF and CWF droplets at each of identified stages were identified for the cooccurrence of phase transitions and chemical reactions. Comparative analysis of the times of ignition delay and complete combustion of the droplets of examined fuel compositions was performed with varying droplet dimensions, temperatures, and oxidant flow velocity.     

Stability of Disclinations in Nematic Liquid Crystals

In the light of φ-mapping method and topological current theory, the stability of disclinations around a spherical particle in nematic liquid crystals is studied. We consider two different defect structures around a spherical particle: disclination ring and point defect at the north or south pole of the particle. We calculate the free energy of these different defects in the elastic theory. It is pointed out that the total Frank free energy density can be divided into two parts. One is the distorted energy density of director field around the disclinations. The other is the free energy density of disclinations themselves, which is shown to be concentrated at the defect and to be topologically quantized in the unit of (k-k₂₄)π/2. It is shown that in the presence of saddle-splay elasticity a dipole (radial and hyperbolic hedgehog) configuration that accompanies a particle with strong homeotropic anchoring takes the structure of a small disclination ring, not a point defect.