Bulk Nematic Liquid Crystals Research Articles

Magneto-optically reorientation-induced image reconstruction in bulk nematic liquid crystals.

We theoretically propose the magneto-optically reorientation-induced image reconstruction in bulk nematic liquid crystals (NLCs). The underlying signals are reinforced and recovered at the expense of scattering noise under reorientation-induced self-focusing nonlinearity. The intensity perturbation gain is derived and the numerical results are presented to show the response of NLC molecules to the diffusive images. The nonlinear image recovery is influenced by the input light intensity, the magnetic field direction, and the correlation length. The results suggest an alternative approach to detect noisy images and promote the application of NLCs in image processing.

Fourth-order nematic elasticity and modulated nematic phases: a poor man’s approach

ABSTRACTWe propose an extension of Frank-Oseen’s elastic energy for bulk nematic liquid crystals which is based on the hypothesis that the fundamental deformations allowed in nematic liquid crystals are splay, twist and bend. The extended elastic energy is a fourth-order form in the fundamental deformations. The existence of bulk spontaneous modulated or deformed nematic liquid crystal ground states is investigated. The analysis is limited to bulk nematic liquid crystals in the absence of limiting surfaces and/or external fields. The non deformed ground state is stable only when Frank-Oseen’s elastic constants are positive. In case where at least one of them is negative, the ground state becomes deformed. The analysis of the stability of the deformed states in the space of the elastic parameters allows to characterise different types of deformed nematic phases. Some of them are new nematic phases, for instance a twist – splay nematic phase is predicted. Inequalities between second-order elastic constants which govern the stability of the twist–bend, splay–bend, and splay–twist states are obtained. Their stability in respect to triple splay–bend–twist deformations is investigated.

Magnetic routing of light-induced waveguides

Among photofunctional materials that can be employed to control the propagation of light by modifying their properties, soft dielectrics such as nematic liquid crystals (NLCs) stand out for their large all-optical response. Through reorientation, the molecular distribution of NLCs can be modified by the electric field of light, permitting functional operations and supporting self-localized light beams or spatial optical solitons. To date, the generation and routing of such solitons have been limited by the boundary conditions employed to tailor the properties of NLCs in planar cells or capillaries. Here we report on spatial solitons in bulk NLCs with no lateral anchoring, where the application of an external magnetic field effectively controls the direction of propagation and the angular steering of the self-trapped wavepackets. Our results entail a completely new approach to the routing of self-localized beams and light-induced waveguides in three dimensions, without the usual limitations imposed by transverse boundary conditions.

Large-scale self-organization of reconfigurable topological defect networks in nematic liquid crystals.

Topological defects in nematic liquid crystals are ubiquitous. The defects are important in understanding the fundamental properties of the systems, as well as in practical applications, such as colloidal self-assembly, optical vortex generation and templates for molecular self-assembly. Usually, spatially and temporally stable defects require geometrical frustration imposed by surfaces; otherwise, the system relaxes because of the high cost of the elastic energy. So far, multiple defects are kept in bulk nematic liquid crystals by top-down lithographic techniques. In this work, we stabilize a large number of umbilical defects by doping with an ionic impurity. This method does not require pre-patterned surfaces. We demonstrate that molecular reorientation controlled by an AC voltage induces periodic density modulation of ions accumulated at an electrically insulating polymer interface, resulting in self-organization of a two-dimensional square array of umbilical defects that is reconfigurable and tunable.

Weak anchoring for a two-dimensional liquid crystal

We study the weak anchoring condition for nematic liquid crystals in the context of the Landau–De Gennes model. We restrict our attention to two dimensional samples and to nematic director fields lying in the plane, for which the Landau–De Gennes energy reduces to the Ginzburg–Landau functional, and the weak anchoring condition is realized via a penalized boundary term in the energy. We study the singular limit as the length scale parameter ε→0, assuming the weak anchoring parameter λ=λ(ε)→∞ at a prescribed rate. We also consider a specific example of a bulk nematic liquid crystal with an included oil droplet and derive a precise description of the defect locations for this situation, for λ(ε)=Kε−α with α∈(0,1]. We show that defects lie on the weak anchoring boundary for α∈(0,12), or for α=12 and K small, but they occur inside the bulk domain Ω for α>12 or α=12 with K large.

Assembly and control of 3D nematic dipolar colloidal crystals

Topology has long been considered as an abstract mathematical discipline with little connection to material science. Here we demonstrate that control over spatial and temporal positioning of topological defects allows for the design and assembly of three-dimensional nematic colloidal crystals, giving some unexpected material properties, such as giant electrostriction and collective electro-rotation. Using laser tweezers, we have assembled three-dimensional colloidal crystals made up of 4 μm microspheres in a bulk nematic liquid crystal, implementing a step-by-step protocol, dictated by the orientation of point defects. The three-dimensional colloidal crystals have tetragonal symmetry with antiparallel topological dipoles and exhibit giant electrostriction, shrinking by 25-30% at 0.37 V μm(-1). An external electric field induces a reversible and controllable electro-rotation of the crystal as a whole, with the angle of rotation being ~30° at 0.14 V μm(-1), when using liquid crystal with negative dielectric anisotropy. This demonstrates a new class of electrically highly responsive soft materials.

Lagrange solution for three wavelength solitary wave clusters in nematic liquid crystals

We investigate the interaction of three optical solitary waves propagating with angular momentum in bulk nematic liquid crystals. The resulting cluster of solitary waves, or nematicons, is shown to orbit about its common centre of “mass”. An elongated isosceles triangle configuration is derived, this solution being the equivalent of the Lagrange solution of Newtonian gravitation. This triangle solution is found to be stable owing to diffractive radiation. A modulation theory explains the existence of the triangle solution as due to the non-monotonicity of an effective potential for the interaction of the solitary waves. This modulation theory also gives good agreement with numerical solutions for the trajectories of the nematicons in the three colours. Finally, it is shown that a cut-off in the shed diffractive radiation prevents the break-up of the triangle due to radiative losses.

Two-color, nonlocal vector solitary waves with angular momentum in nematic liquid crystals

The propagation and interaction of two solitary waves with angular momentum in bulk nematic liquid crystals, termed nematicons, have been studied in the nonlocal limit. These two spinning solitary waves are based on two different wavelengths of light and so are referred to as two-color nematicons. Under suitable boundary conditions, the two nematicons can form a bound state in which they spin about each other. This bound state is found to be stable to the emission of diffractive radiation as the nematicons evolve. In addition this bound state shows walk-off due to dispersion. Using an approximate method based on the use of suitable trial functions in an averaged Lagrangian of the two-color nematicon equations, modulation equations for the evolution of the individual nematicons are derived. These modulation equations are extended to include the diffractive radiation shed as the nematicons evolve. Excellent agreement is found between solutions of the modulation equations and full numerical solutions of the nematicon equations. The shed diffractive radiation is found to play a much lesser role in the nonlocal limit than in the local limit.

Defects in nematic membranes can buckle into pseudospheres

Many factors influence the shapes of living and manufactured membranes. In addition to boundary conditions, surface tension, and curvature, the ordering of particles embedded in or attached to a membrane can strongly influence its equilibrium shape. As a simple model of such ordering, we consider rodlike particles that align to form a so-called nematic phase in the plane of the membrane. We call any sheet with such embedded orientational order a nematic membrane. Nematic membranes can occur in biological cells, liquid crystal films, manufactured materials, and other soft matter systems. By formulating the free energy of nematic films using tensor contractions from differential geometry, we elucidate the elastic terms allowed by symmetry, and indicate differences from hexatic membranes. We find that topological defects in the orientation field can cause the membrane to buckle over a size set by the competition between surface tension and in-plane elasticity. In the absence of bending rigidity the resulting shape is universal, known as a parabolic pseudosphere or a revolved tractrix. This buckling is the two-dimensional analog of the bent cores of line defects that are frequently observed in bulk nematic liquid crystals. Bending costs oppose such buckling and modify the shape in a predictable manner. In particular, the anisotropic rigidities of nematic membranes lead to different shapes for aster and vortex defects, in principle enabling measurement of couplings specific to nematic membranes.

Novel Defect Structures in Nematic Liquid Crystal Shells

We use double-emulsion drops to experimentally investigate the defect structures of spherical shells of nematic liquid crystals. We uncover a rich scenario of coexisting defect structures dictated by the unavoidable finite thickness of even the thinnest shell and by the thickness variation around the sphere. These structures are characterized by a varying number of disclination lines and pairs of surface point defects on the inner and outer surfaces of the nematic shell. In the limit of very thick shells the defect structure ultimately merges with that of a bulk nematic liquid crystal drop.

NONLINEAR AND ELECTRO-OPTICS OF NANO-DISPERSED NEMATIC LIQUID CRYSTALS WITH TUNABLE NEGATIVE-, ZERO-, AND POSITIVE INDICES

We present a review of recent progress in the studies of the nonlinear- and electro-optics of liquid crystals, particularly in their meta-material forms. An analytical expression for the "ultimate" optical nonlinearity of nematic liquid crystals is obtained, and several routes to realizing such optical nonlinearities are discussed. We also describe two approaches for realizing tunable or reconfigurable negative-zero-positive index materials: (1) planar nano-structured frequency selective surfaces [FSS] containing nematic liquid crystals; (2) core-shell nano-spheres randomly distributed in bulk nematic liquid crystal matrix. Such metamaterials can be designed for applications in the visible-infrared, as well as Terahertz and microwave regimes. These liquid crystalline meta-materials are capable of supra-nonlinearities characterized by refractive index changing coefficients of over 1 cm2/watt and microseconds response times.

Anisotropic diffusion of light in polymer dispersed liquid crystals

Anisotropic diffusion of light was experimentally first observed in bulk nematic liquid crystals. The origin of anisotropy in such a system is due to the optical anisotropy of nematic liquid crystal and to anisotropic scattering of light from nematic orientational fluctuations. In polymer dispersed liquid crystals (PDLCs) anisotropic scatterers-i.e., nematic droplets-are embedded in an optically isotropic polymer. The anisotropy of diffusion of light in this system therefore depends only on the anisotropic scattering from a single nematic droplet and on the average orientation of the droplets in PDLCs. In the absence of an external field droplets in PDLCs are randomly oriented and diffusion of light is isotropic. In an external field the droplets are on average oriented in the direction of the external field and the diffusion of light becomes anisotropic. We calculated the diffusion tensor and expected anisotropy of the diffusion of light as a function of an external field, kR , and volume fraction using the theory developed for bulk nematic liquid crystals. Our calculations show that the anisotropy of diffusion tensor can have both the signs and that the magnitude of diffusion constants increase with increasing external field.

Annihilation Dynamics of the Disclination Loop in Bulk Nematic Liquid Crystals

We investigate the annihilation dynamics of the disclination loop in bulk nematic liquid crystals. This work is based on the Frank free energy and the nematodynamics equations. The dissipation of energy is calculated by two methods. In the first method, the dissipation of energy is obtained from the Frank free energy. In the second method, it is calculated by the nematodynamics equations. Finally, we obtain the equation of motion and annihilation velocity of the disclination loop.

Optical Diffraction Properties of Polymer Dispersed Liquid Crystals Switched by Interdigitated Electrodes

ABSTRACT We investigated optical properties of a polymer dispersed liquid crystal (PDLC) film in-plane switched by a periodic pattern of interdigitated electrodes. Such a system acts as a thin optical phase grating which diffraction efficiency strongly depends on polarization state of the incident light. The intensity and dynamic response of various diffraction orders were analyzed as a function of the applied voltage amplitude. Our results demonstrate that by using a PDLC very effective phase gratings with response times below 10 ms can be achieved at the expense of slightly higher driving fields than needed for the similar bulk nematic liquid crystal gratings.

Nonlinear Wave Propagation and Spatial Solitons in Nematic Liquid Crystals

Optical spatial solitons have been demonstrated in bulk nematic liquid crystals. We present an overview of our recent experimental results on nonlinear wave propagation in nematic liquid crystals, focusing on spatial solitons through the reorientational nonlinear response. Various phenomena, including spatial readdressing, weak signal guiding and two-soliton interactions, are observed in voltage biased planar cells.

Signal readdressing by steering of spatial solitons in bulk nematic liquid crystals

Fully three-dimensional spatial solitons in bulk nematic liquid crystals form self-consistent waveguides that are able to confine a weak, collinear copolarized signal at different wavelengths and with large trapping angles. We use a milliwatt cw source to generate a soliton and, by angular steering of the soliton, spatially readdress the guided signal.

Light Scattering and Photon Correlation Spectroscopy of Filled and Confined Liquid Crystals

We present the results of photon correlation spectroscopy investigations of the influence of the confinement and interfaces on the behavior of nematic liquid crystals (NLC) filled with aerosil particles as well as dispersed in porous matrices of different pore geometry and size. The experiments show significant changes in physical properties of LC in such confinements and suggest that there is some evidence for glass-like dynamical behavior, although bulk LC do not have glassy properties. In NLC with nanoparticle network, at least two well identified decays were observed. We attribute the first decay to the director fluctuations of the bulk NLC. The second, glass-like decay, could be related to director dynamics in surface layers at aerosil - LC interface. The mode corresponding to motions of individual aerosil nanoparticles was not detected. This confirms that the aerosil particles form a network in the LC.

Critical behaviour of nematic liquid crystals in oblique magnetic fields

The static critical behaviour of a bulk nematic liquid crystal sample in an oblique magnetic field is analysed. When a magnetic field is applied at a suitable angle alpha with respect to the initially homogeneous nematic director, a spatially inhomogeneous director pattern can be formed. The transition to the deformed state and the formation of walls between the domains resulting from the two equally stable configurations above the transition are studied. The width of the walls is found to diverge at the transition. The critical exponents corresponding to the transition and wall formation are shown to be characteristic of a mean field second order phase transition.

Phase ordering in bulk uniaxial nematic liquid crystals

The phase-ordering kinetics of a bulk uniaxial nematic liquid crystal is addressed using techniques that have been successfully applied to describe ordering in the O(n) model. The method involves constructing an appropriate mapping between the order-parameter tensor and a Gaussian auxiliary field. The mapping accounts both for the geometry of the director about the dominant charge 1/2 string defects and biaxiality near the string cores. At late-times t following a quench, there exists a scaling regime where the bulk nematic liquid crystal and the three-dimensional O(2) model are found to be isomorphic, within the Gaussian approximation. As a consequence, the scaling function for order-parameter correlations in the nematic liquid crystal is exactly that of the O(2) model, and the length characteristic of the strings grows as $t^{1/2}$. These results are in accord with experiment and simulation. Related models dealing with thin films and monopole defects in the bulk are presented and discussed.

Dynamic light scattering in polymer-dispersed liquid crystals

A polymer dispersed liquid crystal was studied by dynamic light scattering. In the experiments, where no electric field is applied, the system exhibits additional slow dynamics to the ones observed in bulk nematic liquid crystals. This slow dynamics gradually disappears with an increasing electric field. While the measured time intensity correlation function does not depend on the scattering vector in the system where no field is applied due to the multiple scattering, its dependence on the electric field shows expected size effects. In confined systems, with typical size $d$, there are no eigenmodes of the orientational fluctuations in droplets with the wave vectors less than the minimal wave vector ${q}_{\mathrm{min}}\ensuremath{\sim}\ensuremath{\pi}/d$. We observed a quadratic dependence of the inverse relaxation time on the scattering vector down to a certain scattering vector, below which the relaxation time remains constant. The size calculated from this minimal scattering vector is in agreement with the average droplet size obtained from scanning electron microscope photographs and the atomic force microscope images of our sample. The electric field changes the temperature behavior of the inverse relaxation time near the nematic-isotropic phase transition, which increases with the temperature when the electric field is applied, but decreases when the field is absent.