Topological defects in schlieren textures of biaxial and uniaxial nematics

Point and line defects in checkerboard patterned hybrid nematic films: A computer simulation investigation

We consider a nematic liquid crystal film confined to a flat cell with homeotropic and planar patterned hybrid anchoring and show, using Monte Carlo simulations, the possibility of the system to stabilize line and point defects. The planar anchoring surface is patterned with a chessboardlike grid of squares with alternating random or parallel homogeneous planar anchoring. The simulations show only line defects when the individual domains are small enough, but also point defects when the domain size is significantly larger than the sample thickness. In the latter case, defect lines are not observed in domains with random surface anchoring, although lines and points are connected by a thick line which separates two regions with different director tilts. Increasing the anchoring strength, the defect lines appear a few layers above the surface, with the two ends just above the randomly oriented domains.

Topological Defect Guided Order Evolution across the Nematic-Smectic Phase Transition

Topological defects usually emerge and vary during the phase transition of ordered systems. Their roles in thermodynamic order evolution keep being the frontier of modern condensed matter physics. Here, we study the generations of topological defects and their guidance on the order evolution during the phase transition of liquid crystals (LCs). With a given preset photopatterned alignment, two different types of topological defects are achieved depending on the thermodynamic process. Because of the memory effect of LC director field across the Nematic-Smectic (N-S) phase transition, a stable array of toric focal conic domains (TFCDs) and a frustrated one are generated in S phase, respectively. The frustrated one transfers to a metastable TFCD array with a smaller lattice constant, and further changes to a crossed-walls type N state due to the inheritance of orientational order. A free energy on temperature diagram and corresponding textures vividly describe the phase transition process and the roles of topological defects in the order evolution across the N-S phase transition. This Letter reveals the behaviors and mechanisms of topological defects on order evolution during phase transitions. It paves a way for investigating topological defect guided order evolution which is ubiquitous in soft matter and other ordered systems.

Structural transformations of nematic disclinations

Topological defects (TDs) are a consequence of symmetry breaking phase transitions and are ubiquitous in nature. An ideal testbed for their study are liquid crystals (LCs) owing to their large response to external stimuli and their large electrical and optical anisotropies. In this paper, we perform numerical simulations of topological defects of [Formula: see text] or [Formula: see text] enforced by the confining boundary. We use the Landau-de Gennes phenomenological model in terms of the tensor nematic order parameter and the Jones beam propagation model to simulate polarized optical microscopy images. We demonstrate the structure of closed disclination loops near the boundary known as boojums that can be topologically charged or chargeless. We show that pairs of chargeless disclination loops can interact repulsively or attractively depending on if they are arranged parallel or antiparallel, respectively. Sufficiently closely spaced antiparallel pairs can rewire while parallel pairs simply exhibit stronger bending due to the repulsion.

History-dependent phase transition character

We consider history-dependent behavior in domain-type configurations in orientational order that are formed in configurations reached via continuous symmetry-breaking phase transitions. In equilibrium, these systems exhibit in absence of impurities a spatially homogeneous order. We focus on cases where domains are formed via (i) Kibble-Zurek mechanism in fast enough quenches or by (ii) Kibble mechanism in strongly supercooled phases. In both cases, domains could be arrested due to pinned topological defects that are formed at domain walls. In systems exhibiting polar or quadrupolar order, point and line defects (disclinations) dominate, respectively. In particular, the disclinations could form complex entangled structures and are more efficient in stabilizing domains. Domain patterns formed by fast quenches could be arrested by impurities imposing a strong enough random-field type disorder, as suggested by the Imry-Ma theorem. On the other hand, domains formed in supercooled systems could be also formed if large enough energy barriers arresting domains are established due to large enough systems' stiffness. The resulting effective interactions in established domain-type patterns could be described by random matrices. The resulting eigenvectors reveal expected structural excitations formed in such structures. The most important role is commonly played by the random matrix largest eigenvector. Qualitatively different behavior is expected if this eigenvector exhibits a localized or extended character. In the former case, one expects a gradual, non-critical-type transition into a glass-type structure. However, in the latter case, a critical-like phase behavior could be observed.

Co-revolving topological defects in a nematic liquid crystal

A patterned surface defect of strength m = +1 and its associated disclination lines can decompose into a pair of surface defects and disclination lines of strength m = +1/2. For a negative dielectric anisotropy liquid crystal subjected to an applied ac electric field E, these half-integer defects are observed to wobble azimuthally for E > than some threshold field and, for sufficiently large fields, to co-revolve antipodally around a central point approximately midway between the two defects. This behavior is elucidated experimentally as a function of applied field strength E and frequency ν, where the threshold field for full co-revolution scales as ν^1/2. Concurrently, nematic electrohydrodynamic instabilities were investigated. A complete field vs. frequency "phase diagram" compellingly suggests that the induced fluctuations and eventual co-revolutions of the ordinarily static defects are coupled strongly to-and driven by-the presence of the hydrodynamic instability. The observed behaviour suggests a Lehmann-like mechanism that drives the co-revolution.

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

Spontaneous Anchoring-Mediated Topography of an Orientable Fluid

A topography in a Newtonian fluid occurs if there is a disturbance near the surface. But what if there is no such disturbance? We show by optical profilometry that a thin nematic film resting on a topological-defect-patterned substrate can exhibit a hill or divot at the opposing free (air) interface in the absence of a topological disturbance at that interface. We propose a model that incorporates several material properties and that predicts the major experimental features. This work demonstrates the importance of, in particular, anisotropic surface interactions in the creation of a free-surface topography.

Transition from escaped to decomposed nematic defects, and vice versa

An escaped radial director profile in a nematic liquid crystal cell can be transformed into a pair of strength m = +1/2 surface defects (and their associated disclination lines) at a threshold electric field. Analogously, a half-integer defect pair can be transformed at a threshold electric field into a director profile that escapes into the third dimension. These transitions were demonstrated experimentally and numerically, and are discussed in terms of topologically discontinuous and continuous pathways that connect the two states. Additionally, we note that the pair of disclination lines associated with the m = +1/2 surface defects were observed to co-rotate around a common point for a sufficiently large electric field at a sufficiently low frequency.

Electric field-driven reconfigurable multistable topological defect patterns

Topological defects appear in symmetry breaking phase transitions and are ubiquitous throughout Nature. As an ideal testbed for their study, defect configurations in nematic liquid crystals (NLCs) could be exploited in a rich variety of technological applications. Here we report on robust theoretical and experimental investigations in which an external electric field is used to switch between pre-determined stable chargeless disclination patterns in a nematic cell, where the cell is sufficiently thick that the disclinations start and terminate at the same surface. The different defect configurations are stabilised by a master substrate that enforces a lattice of surface defects exhibiting zero total topological charge value. Theoretically, we model disclination configurations using a Landau-de Gennes phenomenological model. Experimentally, we enable diverse defect patterns by implementing an in-house-developed Atomic Force Measurement scribing method, where NLC configurations are monitored via polarised optical microscopy. We show numerically and experimentally that an "alphabet" of up to 18 unique line defect configurations can be stabilised in a 4x4 lattice of alternating s=±1 surface defects, which can be "rewired" multistably using appropriate field manipulation. Our proof-of-concept mechanism may lead to a variety of applications, such as multistable optical displays and rewirable nanowires. Our studies also are of interest from a fundamental perspective. We demonstrate that a chargeless line could simultaneously exhibit defect-antidefect properties. Consequently, a pair of such antiparallel disclinations exhibits an attractive interaction. For a sufficiently closely-spaced pair of substrate-pinned defects, this interaction could trigger rewiring, or annihilation if defects are depinned.

Mosaics of topological defects in micropatterned liquid crystal textures

Topological defects in the orientational order that appear in thin slabs of a nematic liquid crystal, as seen in the standard schlieren texture, behave as a random quasi-two-dimensional system with strong optical birefringence. We present an approach to creating and controlling the defects using air pillars, trapped by micropatterned holes in the silicon substrate. The defects are stabilized and positioned by the arrayed air pillars into regular two-dimensional lattices. We explore the effects of hole shape, lattice symmetry, and surface treatment on the resulting lattices of defects and explain their arrangements by application of topological rules. Last, we show the formation of detailed kaleidoscopic textures after the system is cooled down across the nematic-smectic A phase transition, frustrating the defects and surrounding structures with the equal-layer spacing condition of the smectic phase.

Complex free-energy landscapes in biaxial nematic liquid crystals and the role of repulsive interactions: A Wang-Landau study

General quadratic Hamiltonian models, describing the interaction between liquid-crystal molecules (typically with D_{2h} symmetry), take into account couplings between their uniaxial and biaxial tensors. While the attractive contributions arising from interactions between similar tensors of the participating molecules provide for eventual condensation of the respective orders at suitably low temperatures, the role of cross coupling between unlike tensors is not fully appreciated. Our recent study with an advanced Monte Carlo technique (entropic sampling) showed clearly the increasing relevance of this cross term in determining the phase diagram (contravening in some regions of model parameter space), the predictions of mean-field theory, and standard Monte Carlo simulation results. In this context, we investigated the phase diagrams and the nature of the phases therein on two trajectories in the parameter space: one is a line in the interior region of biaxial stability believed to be representative of the real systems, and the second is the extensively investigated parabolic path resulting from the London dispersion approximation. In both cases, we find the destabilizing effect of increased cross-coupling interactions, which invariably result in the formation of local biaxial organizations inhomogeneously distributed. This manifests as a small, but unmistakable, contribution of biaxial order in the uniaxial phase. The free-energy profiles computed in the present study as a function of the two dominant order parameters indicate complex landscapes. On the one hand, these profiles account for the unusual thermal behavior of the biaxial order parameter under significant destabilizing influence from the cross terms. On the other, they also allude to the possibility that in real systems, these complexities might indeed be inhibiting the formation of a low-temperature biaxial order itself-perhaps reflecting the difficulties in their ready realization in the laboratory.

Uncovering different states of topological defects in schlieren textures of a nematic liquid crystal

Topological defects are ubiquitously found in physical systems and therefore have been an important research subject of not only condensed matter physics but also cosmology. However, their fine structures remain elusive because of the microscopic scales involved. In the case of a liquid crystal, optical microscopy, although routinely used for the identification of liquid crystal phases and associated defects, does not have resolution high enough to distinguish fine structures of topological defects. Here we show that polarised and fluorescence microscopy, with the aid of numerical calculations on the orientational order and resulting image distortions, can uncover the structural states of topological defects with strength m =  ±1 in a thin cell of a nematic liquid crystal. Particularly, defects with m = +1 exhibit four different states arising from chiral symmetry breaking and up-down symmetry breaking. Our results demonstrate that optical microscopy is still a powerful tool to identify fine states of liquid crystalline defects.

Decomposition vs. escape of topological defects in a nematic liquid crystal

Nematic cells patterned with square arrays of strength m = ±1 topological defects were examined as a function of cell thickness (3 < h < 7.5 μm), temperature, and applied voltage. Thicker cells tend to exhibit an escape or partial escape of the nematic director as a means of mitigating the elastic energy cost near the defect cores, whereas thinner cells tend to favor splitting of the integer defects into pairs of half-integer strength defects. On heating the sample into the isotropic phase and cooling back into the nematic, some apparently split defects can reappear as unsplit integer defects, or vice versa. This is consistent with the system's symmetry, which requires a first order transition between the two relaxation mechanisms.

Segregation of liquid crystal mixtures in topological defects

The structure and physical properties of liquid crystal (LC) mixtures are a function of composition, and small changes can have pronounced effects on observables, such as phase-transition temperatures. Traditionally, LC mixtures have been assumed to be compositionally homogenous. The results of chemically detailed simulations presented here show that this is not the case; pronounced deviations of the local order from that observed in the bulk at defects and interfaces lead to significant compositional segregation effects. More specifically, two disclination lines are stabilized in this work by introducing into a nematic liquid crystal mixture a cylindrical body that exhibits perpendicular anchoring. It is found that the local composition deviates considerably from that of the bulk at the interface with the cylinder and in the defects, thereby suggesting new assembly and synthetic strategies that may capitalize on the unusual molecular environment provided by liquid crystal mixtures.

Liquid crystal mixtures are used in commercial applications and their composition affects their properties. Here Rahimi et al. use atomistic simulations to show that defects influence the molecular arrangement of the mixture components leading to a deviation of the local order from that of the bulk.

Spherical nematic shells with a threefold valence

We present a theoretical study of the energetics of thin nematic shells with two charge-one-half defects and one charge-one defect. We determine the optimal arrangement: the defects are located on a great circle at the vertices of an isosceles triangle with angles of 66^{∘} at the charge-one-half defects and a distinct angle of 48^{∘}, consistent with experimental findings. We also analyze thermal fluctuations around this ground state and estimate the energy as a function of thickness. We find that the energy of the three-defect shell is close to the energy of other known configurations having two charge-one and four charge-one-half defects. This finding, together with the large energy barriers separating one configuration from the others, explains their observation in experiments as well as their long-time stability.

Molecular organization of nematic liquid crystals between concentric cylinders: role of the elastic anisotropy

The orientational order in a nematic liquid crystal sample confined to an annular region between two concentric cylinders is investigated by means of lattice Monte Carlo simulations. Strong anchoring and homeotropic orientations, parallel to the radial direction, are implemented at the confining surfaces. The elastic anisotropy is taken into account in the bulk interactions by using the pair potential introduced by Gruhn and Hess [T. Gruhn and S. Hess, Z. Naturforsch. A 51, 1 (1996)] and parametrized by Romano and Luckhurst [S. Romano, Int. J. Mod. Phys. B 12, 2305 (1998); Phys. Lett. A 302, 203 (2002); G. R. Luckhurst and S. Romano, Liq. Cryst. 26, 871 (1999)], i.e., the so-called GHRL potential. In the case of equal elastic constants, a small but appreciable deformation along the cylinder axis direction is observed, whereas when the values of K(11)/K(33) if K(22)=K(33) are low enough, all the spins in the bulk follow the orientation imposed by the surfaces. For larger values of K(11)/K(33), spontaneous deformations, perpendicular to the polar plane, increase significantly. Our findings indicate that the onset of these deformations also depends on the ratio K(22)/K(33) and on the radius of the cylindrical surfaces. Although expected from the elastic theory, no tangential component of the deformations was observed in the simulations for the set of parameters analyzed.

Morphogenesis of defects and tactoids during isotropic-nematic phase transition in self-assembled lyotropic chromonic liquid crystals

We explore the structure of nuclei and topological defects in the first-order phase transition between the nematic (N) and isotropic (I) phases in lyotropic chromonic liquid crystals (LCLCs). The LCLCs are formed by self-assembled molecular aggregates of various lengths and show a broad biphasic region. The defects emerge as a result of two mechanisms: (1) surface-anisotropy that endows each N nucleus ('tactoid') with topological defects thanks to preferential (tangential) orientation of the director at the closed I-N interface, and (2) Kibble mechanism with defects forming when differently oriented N tactoids merge with each other. Different scenarios of phase transition involve positive (N-in-I) and negative (I-in-N) tactoids with nontrivial topology of the director field and also multiply connected tactoid-in-tactoid configurations. The closed I-N interface limiting a tactoid shows a certain number of cusps; the lips of the interface on the opposite sides of the cusp make an angle different from π. The N side of each cusp contains a point defect-boojum. The number of cusps shows how many times the director becomes perpendicular to the I-N interface when one circumnavigates the closed boundary of the tactoid. We derive conservation laws that connect the number of cusps c to the topological strength m of defects in the N part of the simply connected and multiply connected tactoids. We demonstrate how the elastic anisotropy of the N phase results in non-circular shape of the disclination cores. A generalized Wulff construction is used to derive the shape of I and N tactoids as a function of I-N interfacial tension anisotropy in the approximation of frozen director field of various topological charges m. The complex shapes and structures of tactoids and topological defects demonstrate an important role of surface anisotropy in morphogenesis of phase transitions in liquid crystals.

Biaxial nematic order induced by smectic fluctuations

We report on a series of measurements on the microscopic structure and the magneto-optical properties of a calamitic liquid crystalline compound in its nematic phase. Structural studies show the existence of short-range, tilted smectic order consistent with pretransitional effects above an underlying smectic phase. Concomitantly, magneto-optical results exhibit the existence of an optic axis not collinear with the uniaxial director. This apparent biaxial nature is discussed within the context of coupling between the tensor nematic and the smectic order parameters.

Biaxial-uniaxial transition in a self-assembled nematic liquid crystal by field-induced molecular conformation

A cylindrical uniaxial liquid crystal was hydrogen-bonded with a tripod-shaped molecule. As the molecular number ratio of cylindrical liquid crystal to tripod molecule converges to 2:1, |s| = 1/2 disclination defects, which are a necessary condition of biaxial nematic phase, appeared predominantly. After the application of an electric field, the |s| = 1/2 disclinations converted to |s| = 1 disclinations which imply a transition from a biaxial to uniaxial state. IR dichroism measurements support the hypothesis that the liquid crystal-tripod molecule complex undergoes a molecular conformation change from bent shape to parallel shape, and this conformation change is thought to be related to a field-induced biaxial-uniaxial transition.

Surface alignment, anchoring transitions, optical properties, and topological defects in the nematic phase of thermotropic bent-core liquid crystal A131

We study optical, structural, and surface anchoring properties of thermotropic nematic bent-core material A131. The focus is on the features associated with orientational order as the material has been reported to exhibit not only the usual uniaxial nematic but also the biaxial nematic phase. We demonstrate that A131 experiences a surface anchoring transition from a perpendicular to tilted alignment when the temperature decreases. The features of the tilted state are consistent with surface-induced birefringence associated with smectic layering near the surface and a molecular tilt that changes along the normal to the substrates. The surface-induced birefringence is reduced to zero by a modest electric field that establishes a uniform uniaxial nematic state. Both refractive and absorptive optical properties of A131 are consistent with the uniaxial order. We found no evidence of the "polycrystalline" biaxial behavior in the cells placed in crossed electric and magnetic fields. We observe stable topological point defects (boojums and hedgehogs) and nonsingular "escaped" disclinations pertinent only to the uniaxial order. Finally, freely suspended films of A131 show uniaxial nematic and smectic textures; a decrease in the film thickness expands the temperature range of stability of smectic textures, supporting the idea of surface-induced smectic layering. Our conclusion is that A131 features only a uniaxial nematic phase and that the apparent biaxiality is caused by subtle surface effects rather than by the bulk biaxial phase.

Conical soliton escape into a third dimension of a surface vortex

We present an exact three-dimensional solitonic solution to a sine-Gordon-type Euler-Lagrange equation that describes a configuration of a three-dimensional vector field n constrained to a surface p-vortex, with a prescribed polar tilt angle on a planar substrate and escaping into the third dimension in the bulk. The solution is relevant to characterization of a schlieren texture in nematic liquid-crystal films with tangential (in-plane) substrate alignment. The solution is identical to a section of a point defect discovered many years ago by Saupe [Mol. Cryst. Liq. Cryst. 21, 211 (1973)], when latter is restricted to a surface.

Computer simulations of biaxial nematics

Biaxial nematic (N(b)) liquid crystals are a fascinating condensed matter phase that has baffled, for more than thirty years, scientists engaged in the challenge of demonstrating its actual existence, and which has only recently been experimentally found. During this period computer simulations of model N(b) have played an important role, both in providing the basic physical properties to be expected from these systems, and in giving clues about the molecular features essential for the thermodynamic stability of N(b) phases. However, simulation studies are expected to be even more crucial in the future for unravelling the structural features of biaxial mesogens at the molecular level, and for helping in the design and optimization of devices towards the technological deployment of N(b) materials. This review article gives an overview of the simulation work performed so far, and relying on the recent experimental findings, focuses on the still unanswered questions which will determine the future challenges in the field.

Molecular ordering in a biaxial smectic-A phase studied by scanning transmission X-ray microscopy (STXM)

Results of STXM investigations of a binary mixture (-TNF = 2 : 1; SmA(b) 140 M 180 Iso) known to form a SmA(b) phase [T. Hegmann, J. Kain, S. Diele, G. Pelzl and C. Tschierske, Angew. Chem. Int. Ed., 2001, 40, 887] are presented. Near edge X-ray absorption fine spectra (NEXAFS) of the -TNF board-like aggregates, in particular the intensity of the low energy peaks associated with aromatic ring pi* orbitals (284.5-286.5 eV), show that the molecular plane of these aggregates is very sensitive to the relative orientation of electric field vector E of linearly polarized light, which is used to determine the molecular orientation in the LC phase. The observed strong in-plane dichroic signal suggests the predominant orientation of the -TNF aggregates to be along the smectic layer normal as well as long-range ordering of the in-plane molecular orientation (biaxiality). Orientational maps derived from series of measurements at different sample rotation angles around the specimen normal clearly show a Schlieren-type texture, and permit a detailed examination of exclusive +/-(1/2) disclination theoretically predicted for the SmA(b) phase.

Techniques for the visualization of topological defect behavior in nematic liquid crystals

We present visualization tools for analyzing molecular simulations of liquid crystal (LC) behavior. The simulation data consists of terabytes of data describing the position and orientation of every molecule in the simulated system over time. Condensed matter physicists study the evolution of topological defects in these data, and our visualization tools focus on that goal. We first convert the discrete simulation data to a sampled version of a continuous second-order tensor field and then use combinations of visualization methods to simultaneously display combinations of contractions of the tensor data, providing an interactive environment for exploring these complicated data. The system, built using AVS, employs colored cutting planes, colored isosurfaces, and colored integral curves to display fields of tensor contractions including Westin's scalar cl, cp, and cs metrics and the principal eigenvector. Our approach has been in active use in the physics lab for over a year. It correctly displays structures already known; it displays the data in a spatially and temporally smoother way than earlier approaches, avoiding confusing grid effects and facilitating the study of multiple time steps; it extends the use of tools developed for visualizing diffusion tensor data, re-interpreting them in the context of molecular simulations; and it has answered long-standing questions regarding the orientation of molecules around defects and the conformational changes of the defects.

Bulk and surface biaxiality in nematic liquid crystals

Nematic liquid crystals possess three different phases: isotropic, uniaxial, and biaxial. The ground state of most nematics is either isotropic or uniaxial, depending on the external temperature. Nevertheless, biaxial domains have been frequently identified, especially close to defects or external surfaces. In this paper we show that any spatially varying director pattern may be a source of biaxiality. We prove that biaxiality arises naturally whenever the symmetric tensor S=(Vn)(Vn)T possesses two distinct nonzero eigenvalues. The eigenvalue difference may be used as a measure of the expected biaxiality. Furthermore, the corresponding eigenvectors indicate the directions in which the order tensor Q is induced to break the uniaxial symmetry about the director n. We apply our general considerations to some examples. In particular we show that, when we enforce homeotropic anchoring on a curved surface, the order tensor becomes biaxial along the principal directions of the surface. The effect is triggered by the difference in surface principal curvatures.

Nematic textures in spherical shells

The equilibrium texture of nematic shells is studied as a function of their thickness. For ultrathin shells the ground state has four short 1/2 disclination lines but, as the thickness of the film increases, a three-dimensional escaped configuration composed of two pairs of half-hedgehogs becomes energetically favorable. We derive an exact solution for the nematic ground state in the one Frank constant approximation and study the stability of the corresponding texture against thermal fluctuations.

Lensing effects in a nematic liquid crystal with topological defects

Light traveling through a liquid crystal with disclinations perceives a geometrical background which causes lensing effects similar to the ones predicted for cosmic objects like global monopoles and cosmic strings. In this paper we explore the effective geometry as perceived by light in such media. The comparison between both systems suggests that experiments can be done in the laboratory to simulate optical properties, like gravitational lensing, of cosmic objects.

Theory of uniaxial and biaxial nematic phases in bent-core systems

We present a phenomenological theory of the uniaxial and biaxial nematic phases recently observed in bent-core mesogenic systems. To take into account the molecular anisotropy we introduce two types of symmetry transformation: "external" rotations which turn the molecules with respect to the laboratory axes and "internal" rotations which turn them with respect to the molecular axes. We show then that the description of bent-core nematic phases involves two isomorphic copies of the conventional tensor order parameter instead of one for conventional rod like and disk like molecules. The second tensor stabilizes additional monoclinic and triclinic phases and merges the calamitic and diskotic uniaxial states into a single phase. The uniaxial and biaxial phases can appear, respectively, in six and 21 distinct configurations according to the molecular axis that dominates the ordering process. We predict a number of isostructural transitions between these configurations within a thermodynamic Landau-type approach. Because bent-core molecules have the same microscopic behavior as orthorhombic micelles, the biaxial phase can be stabilized in both systems.

Selective imaging of 3D director fields and study of defects in biaxial smectic A liquid crystals

We report on the selective imaging of different director fields in a biaxial smectic A (SmAb) liquid crystal using Fluorescence Confocal Polarizing Microscopy (FCPM) and Polarizing Microscopy (PM). The patterns of two directors, namely the director n(a) perpendicular to the lamellae and the director n(b) in their planes are visualized by doping the liquid crystal with two fluorescent dyes with different orientation of the transition dipoles with respect to the lamellar matrix. The properties of defects such as disclinations and focal conic domains (FCDs) are consistent with the non-polar D2h-symmetry of the SmA(b) mesophase in the studied mixture of bent-core and rod-like molecules: (1) majority of defects in the director n(b) are half-integer "+/-1/2" disclinations; (2) the integer-strength "+/-1" defects tend to split into the "+/-1/2" disclinations. We compare the vertical cross-sections of the "+/-1" disclinations in the field in SmA(b) and uniaxial nematic samples. In SmA(b), the "+/-1" disclinations do not escape into the third dimension, while in the nematic samples with Schlieren textures they do despite the surface anchoring at the plates; the experimentally determined director field around the escaped disclination capped by a pair of surface point defects--boojums matches the one predicted recently [C. Chiccoli et al., Phys. Rev. E 66, 030701 (2002)]. The FCD structure in SmA(b) is similar to that in SmA and SmC in terms of the normal to the layers but differs significantly in terms of the director n(b) field parallel to the smectic layers. The FCDs in SmA(b) can be associated with topologically non-trivial configurations of n(b) in the surrounding matrix that are equivalent to the disclination lines.

Thermotropic biaxial nematic phase in liquid crystalline organo-siloxane tetrapodes

Infrared absorbance measurements have been carried out on two liquid crystalline organo-siloxane tetrapodes. Results unambiguously show the existence of a biaxial nematic phase below a uniaxial nematic phase. The three components of IR absorbance are used to calculate the various order parameters. On cooling, a weak first-order transition from isotropic to nematic is observed, followed by a second-order phase transition to biaxial nematic where the biaxiality parameters are found to be significantly large. Results are supported by observations from conoscopy and texture. Temperature dependences of the order parameters are well explained by the mean-field model for a biaxial phase.

Biaxial nematic phase in bent-core thermotropic mesogens

A biaxial nematic phase had been predicted with D(2h) symmetry, wherein the mesogen's long and short transverse axes are simultaneously aligned along the two orthogonal, primary and secondary directors, n and m, respectively. The unique low-angle x-ray diffraction patterns in the nematic phases exhibited by three rigid bent-core mesogens clearly reveal their biaxiality. The results of x-ray diffraction can be readily reproduced by ab initio calculations that explicitly include the bent-core shape in the form factor and assume short-range positional correlations.

Thermotropic biaxial nematic liquid crystals

We have synthesized liquid crystal (LC) mesogens based on a nonlinear oxadiazole unit that exhibit nematic phases near 200 degrees C. Polarized microscopy and conoscopy indicate that these LCs are biaxial nematics. Unambiguous and quantitative evidence for biaxiality is achieved using 2H NMR spectroscopy. "2D powder" spectra, obtained by rotating 2H-labeled samples about an axis perpendicular to the magnetic field at approximately 200 Hz, yield phase biaxiality parameters of approximately 0.1 when coupled with rigorous and proven simulations.