Angular structure of radiation scattered by monolayer of polydisperse droplets of nematic liquid crystal

We considered light scattering by a polydisperse ensemble of droplets of a nematic liquid crystal. To model light scattering by a monolayer of polymer-dispersed spherical droplets of a nematic liquid crystal with cylindrical symmetry of its internal structure, we proposed a semianalytical modeling method. The method is based on interference approximation of the theory of multiple wave scattering, anomalous diffraction approximation, and effective-medium approximation. The method takes into account cooperative optical effects in concentrated, partially ordered layers and can be used to analyze the small-angle structure of the intensity of scattered radiation in relation to the concentration, size, polydispersity of liquid crystal droplets, orientation of their optical axes, and refractive indices of the liquid crystal and polymer. The obtained relations can be applied to solving direct and inverse problems of light scattering in composite liquid crystal materials using data of polarization measurements. We present graphical results of solving the direct problem for components of the polarization vector of scattered wave. These results illustrate the formation of an angular structure for monolayers with a high concentration of polydisperse droplets of the liquid crystal in the range of small scattering angles (0 < θ _s ≤ 8°).     

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.     

Stability of cellulose lyotropic liquid crystal emulsions

We studied a new kind of W/O emulsions based on a lyotropic liquid crystal as the aqueous droplet phase. The cholesteric phase, a solution hydroxypropyl cellulose in water was dispersed in the continuous oil matrix, paraffin oil or heptane. We made a specific choice of surfactant in order to impose director anchoring conditions at the oil-water interface and orient the liquid crystal inside the droplet. The strong anchoring conditions resulted in a topological defect inside the droplets of size above the critical value R^*. The defect elastic energy creates a barrier against droplet coalescence, the effect of topological size selection. We have studied the orientation of the director inside the droplets and their size distribution.     

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.     

Coherent transmission and angular structure of light scattering by monolayer films of polymer dispersed liquid crystals with inhomogeneous boundary conditions

We consider monolayer polymer films with oriented droplets of a nematic liquid crystal (LC). Relations for the coherent transmission coefficients of a layer of oriented ellipsoidal droplets and for the intensity of light scattered by monolayers of spherical and spheroidal droplets have been obtained. The amplitude-phase screen model and the interference approximation of the theory of multiple wave scattering have been used. To describe light scattering by an individual ellipsoidal droplet with inhomogeneous surface binding, we have developed an anomalous diffraction approximation. For monolayers of spherical LC droplets, the coherent scattering coefficients and the angular scattering structure have been analyzed. The internal structure of nematic droplets have been calculated by the relaxation method based on the solution of the minimization problem of the free energy volume density. We have studied basic regular features of light scattering by a monolayer with homogeneous and inhomogeneous boundary conditions at the LC-polymer interface. We show that, for films that contain droplets with inhomogeneous boundary conditions of the tangentially normal type, the angular structure of the scattered light is asymmetric with respect to the polar scattering angle.     

Inhomogeneous threshold director reorientation in a planar nematic flexoelectric cell with finite anchoring energy

The dependence of the threshold parameters and the period of the electric-field-induced spatially periodic reorientation of the director in a flexoelectric nematic liquid crystal (NLC) on the anchoring conditions at the surface of a planar NLC cell has been studied. The threshold electric field and the corresponding wave-number of the periodic structure of the director field have been numerically calculated for arbitrary values of the anchoring energy. In the case of strong anchoring, the corresponding analytical expressions are obtained in a single-constant approximation. A decrease in the azimuthal anchoring energy leads to an increase in the intervals of possible values of the flexoelectric parameter ν and the ratio K₂/K₁ of the Frank elastic constants. A decrease in the polar anchoring energy leads to narrowing of these intervals as compared to the case of infinitely strong anchoring at the NLC cell surface.     

Study on the algorithm of computational ghost imaging based on discrete fourier transform measurement matrix

We have developed a model and realized an algorithm for the calculation of the coefficient of coherent (direct) transmission of light through a layer of liquid crystal (LC) droplets in a polymer matrix. The model is based on the Hulst anomalous diffraction approximation for describing the scattering by an individual particle and the Foldy-Twersky approximation for a coherent field. It allows one to investigate polymer dispersed LC (PDLC) materials with homogeneous and inhomogeneous interphase surface anchoring on the droplet surface. In order to calculate the configuration of the field of the local director in the droplet, the relaxation method of solving the problem of minimization of the free energy volume density has been used. We have verified the model by comparison with experiment under the inverse regime of the ionic modification of the LC-polymer interphase boundary. The model makes it possible to solve problems of optimization of the optical response of PDLC films in relation to their thickness and optical characteristics of the polymer matrix, sizes, polydispersity, concentration, and anisometry parameters of droplets. Based on this model, we have proposed a technique for estimating the size of LC droplets from the data on the dependence of the transmission coefficient on the applied voltage.     

Study of intrinsic anchoring in nematic liquid crystals based on modified Gruhn-Hess pair potential

A nematic liquid crystal slab composed of N molecular layers is investigated using a simple cubic lattice model, based upon the molecular pair potential which is spatially anisotropic and dependent on elastic constants of liquid crystals. A perfect nematic order is assumed in the theoretical treatment, which means the orientation of the molecular long axis coincides with the director of liquid crystal and the total free energy equals to the total interaction energy. We present a modified Gruhn-Hess model, which is relative to the splay-bend elastic constant K₁₃. Furthermore, we have studied the free nematic interfacial behavior (intrinsic anchoring) by this model in the assumption of the perfect nematic order. We find that the preferred orientation at the free interface and the intrinsic anchoring strength change with the value of modification, and that the director profile can be determined by the competition of the intrinsic anchoring with external forces present in the system. Also we simulate the intrinsic anchoring at different temperatures using Monte Carlo method and the simulation results show that the intrinsic anchoring favors planar alignment and the free interface is more disordered than the bulk.     

Surface driven transition in a nematic liquid crystal cell

Surface driven reorientation effects in a nematic liquid crystal cell caused by light-induced changes of the anchoring parameters were studied. Theoretical consideration of one-dimensional flat distributions of the director has shown that the director can undergo threshold reorientation between hybrid, homeotropic, and planar alignments as the anchoring energy varies continuously. The threshold reorientation takes place when the reference and light-induced easy axes are perpendicular. In the one-elastic-constant approximation the light-induced transition was found to be of second order as shown by a critical increase of the director thermal fluctuations in the vicinity of the transition point. These effects were experimentally studied in the cells containing 5CB liquid crystal aligned by the photosensitive azo-containing polymer layer. Zh. éksp. Teor. Fiz. 112, 2045–2055 (December 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

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.     

Influence of the structure of the director field on the optical properties of a nematic liquid-crystal droplet

The changes in the optical properties of a spherical, bipolar, liquid-crystal droplet due to the change in structure of its director field under the influence of an applied external field are investigated on the basis of calculations using the nested-ellipsoids model in the discretedipole approximation. Graphs are plotted for the attenuation efficiency factor and the angular structure of the scattered radiation for the two typical cases of strong and weak dependence of the optical properties of the droplet on the change in structure of its director field. Zh. Tekh. Fiz. 69, 86–90 (November 1999)     

The structural instabilities in ferronematic based on liquid crystal with negative diamagnetic susceptibility anisotropy

The studied ferronematic is a nematic liquid crystal (ZLI1695) of low negative anisotropy of the diamagnetic susceptibility (χ_a<0) doped with the magnetic particles Fe₃O₄. Structural instabilities are interpreted within Burylov and Raikher's theory. The high magnetic fields were oriented perpendicular (Freedericksz transition) or parallel to the initial director. Using capacitance measurements the Freedericksz threshold magnetic field of the ferronematic B_FN, and the critical magnetic field B_max, at which the initial parallel orientation between the director and the magnetic moment of magnetic particles breaks down, have been determined. The values of these quantities have been used to estimate the surface density of the anchoring energy W of liquid crystal molecules on the surface of the magnetic particles. The obtained values indicate a soft anchoring of the liquid crystal on the magnetic particles with a preferred parallel orientation of the magnetic moment of magnetic particles and the director.     

Dynamic light scattering at the ice water interface during freezing

The 488 nm radiation of an argon laser is scattered quasi-elastically at the [0001]-face (basal plane) of a growing ice crystal. The scattering plane is the basal plane. The Rayleigh-linewidth is proportional to the square of the scattering vector. One measures about 2 krad/s at a scattering angle of 90°. The linewidth does not depend on the growth rate. Scattering is only observed once a critical growth rate ν_crit = 1,5 μ m?s has been exceeded. Then the scattering intensity depends linearly on the growth rate in the range between 0,03 μ m?s and 2,5 μ m?s. Once the surface is molten scattering vanishes and does not reappear until the growth rate has again exceeded the threshold ν_crit. The coherence properties of the scattered light indicate that the thickness of the scattering layer is less than 6 μ m. The observations are interpreted in terms of a fluctuating interface. The decay time of the fluctuations has been calculated. Satisfactory agreement with the observed Rayleigh linewidth is obtained.     

液晶表面锚定能的温度依赖性研究

通过测量扭曲液晶盒中的液晶分子的实际扭曲角及摩擦方向与液晶分子的界面指向矢之间的方位偏角，用自行建立的液晶方位表面锚定能的测量方法，测定了５ＣＢ液晶与摩擦的聚酰亚胺界面的锚定能及其温度依赖性，并用热力学理论进行了分析．实验结果表明，随着温度的增加液晶的表面锚定能Ｅ_ａ是减小的，从２５.５℃时的５.０×１０^－5Ｊ／ｍ²减小到３５℃时的５.０×１０^－6Ｊ／ｍ²；同时，外推长度ｄ_e随 关键词：     

Optical birefringence and anisotropic scattering in acrylate based holographic polymer dispersed liquid crystals

In this work, we experimentally study the evolution of the diffraction efficiency and birefringence of a holographic polymer dispersed liquid crystal grating. It is shown that the onset of birefringence coincides closely with the moment when TE and TM polarizated probes start to diffract differently. Light scattering, caused by liquid crystal droplets, is also monitored to understand the dynamics of droplet formation and growth. It is shown that the onset of anisotropic scattering and birefringence also occur almost simultaneously.     

Electro-optical phase shift in polymer dispersed liquid crystals

An anisotropic version of the Maxwell Garnett approximation is applied for studying the electro-optical phase modulation by polymer dispersed liquid crystals (PDLC). The PDLC contain bipolar liquid crystal droplets that can be reoriented by an external field causing a change in the optical birefringence. This approach provides an explicit link between the droplet orientation distribution and the electro-optical phase shift. For aligned droplets we find that the sharpness of the change in the birefringence may be controlled by selecting the initial orientation. For a planar distribution we find sharp transitions with a hysteresis loop whose width depends on the droplet concentration. For a random distribution, the droplet orientation and the optical phase shift change more gradually with the applied field. These results demonstrate that PDLC may be suitable for a wide range of electro-optic applications based on their field-induced phase modulation properties. In addition, it is apparent that the optical phase shift is quite sensitive to changes in droplet orientation. It should therefore be useful for studying reorientation phenomena in PDLC, overcoming the problems due to light scattering in these materials. Received 25 November 1999 and Received in final form 20 January 2000     

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.     

Photoinduced gratings in a Sn<Subscript>2</Subscript>P<Subscript>2</Subscript>S<Subscript>6</Subscript> ferroelectric crystal with the period depending on the optical pump power

The light scattering in the form of ring structures in Sn₂P₂S₆ crystals at the propagation of intense laser pump radiation along the b crystallographic axis is detected. Radiation passing through a crystal is completely scattered into a cone whose angle increases with the pump power and decreases reversibly with a decrease in this power. The observed effect can be attributed to a spontaneous increase in the amplitude of photoinduced bulk diffraction gratings and to the scattering of light on them in the directions where the phase increments of the photorefractive and diffraction natures compensate each other. A similar type of scattering was observed previously in other photorefractive crystals, but the appearance of gratings with the period easily varied by varying the pump power is demonstrated for the first time.     

Elastic Scattering of Two Photons by a Multicharged Atomic Ion

The elastic scattering of two X-ray photons by a multicharged atomic ion has been studied theoretically. A pronounced resonance structure and strong angular anisotropy of differential scattering cross section have been predicted in the energy range of a scattered photon from ?ω–I_1s to ?ω+I_1s (where is the energy of the incident photon and is the ionization energy threshold of the shell of the ion). The absolute value of the observed cross section has been quantitatively estimated.