Biaxial Nematic Research Articles

To be or not to be – nematic liquid crystals from shape-persistent V-shaped nematogens with the ‘magic angle’

ABSTRACTThe tetrahedral bending angle in V-shaped nematogens was claimed to be the optimum for finding a biaxial nematic liquid crystal phase. The benzo[1,2-b:4,3-b’]dithiophene core, recently successfully applied as a tetrahedral bending unit in mesogens with lateral flexible chains, is here embedded in a scaffold with only terminal chains, which conventionally promotes the formation of nematic phases at low temperature. A series of new mesogens has been successfully prepared, realising hockey-stick, hockey-stick dimer and V-shaped molecular topologies. Only the hockey-stick mesogens assemble in uniaxial nematic phases over a broad temperature range. Single crystal structure analysis of a hockey-stick and V-shaped compound reveal remarkable similarities with the benzodithiophene core wrapped by aliphatic chains. A model explaining the absence of nematic mesophases in the family of V-shaped, shape-persistent mesogens with terminal aliphatic chains is presented and results in the proposal of a new design for biaxial nematogens.

Hierarchy of orientational phases and axial anisotropies in the gauge theoretical description of generalized nematic liquid crystals.

The paradigm of spontaneous symmetry breaking encompasses the breaking of the rotational symmetries O(3) of isotropic space to a discrete subgroup, i.e., a three-dimensional point group. The subgroups form a rich hierarchy and allow for many different phases of matter with orientational order. Such spontaneous symmetry breaking occurs in nematic liquid crystals, and a highlight of such anisotropic liquids is the uniaxial and biaxial nematics. Generalizing the familiar uniaxial and biaxial nematics to phases characterized by an arbitrary point-group symmetry, referred to as generalized nematics, leads to a large hierarchy of phases and possible orientational phase transitions. We discuss how a particular class of nematic phase transitions related to axial point groups can be efficiently captured within a recently proposed gauge theoretical formulation of generalized nematics [K. Liu, J. Nissinen, R.-J. Slager, K. Wu, and J. Zaanen, Phys. Rev. X 6, 041025 (2016)2160-330810.1103/PhysRevX.6.041025]. These transitions can be introduced in the model by considering anisotropic couplings that do not break any additional symmetries. By and large this generalizes the well-known uniaxial-biaxial nematic phase transition to any arbitrary axial point group in three dimensions. We find in particular that the generalized axial transitions are distinguished by two types of phase diagrams with intermediate vestigial orientational phases and that the window of the vestigial phase is intimately related to the amount of symmetry of the defining point group due to inherently growing fluctuations of the order parameter. This might explain the stability of the observed uniaxial-biaxial phases as compared to the yet to be observed other possible forms of generalized nematic order with higher point-group symmetries.

PA19 屈曲型液晶分子のネマチック相における二軸性の可能性(物理・物性)

PA19 屈曲型液晶分子のネマチック相における二軸性の可能性(物理・物性)

Molecular field theory for biaxial nematics formed from liquid crystal dimers and inhibited by the twist-bend nematic.

Liquid crystal dimers with odd spacers are good candidates as materials for biaxial nematic phases (NB). The dimers are flexible molecules sustaining biaxial conformations, and couplings between the conformational and orientational distributions could be expected to stabilise NB. We apply a molecular field theory for flexible molecules developed elsewhere to study a simple system made up of dimers composed of two cylindrically symmetric mesogenic groups. Our model allows for two idealised conformations: one linear and one bent at a tetrahedral angle. For a restricted set of chain lengths, the model predicts a first-order reentrant phase transition from the NB phase into a low temperature uniaxial nematic phase (NU). However the formation of the biaxial nematic could be blocked by the appearance of a twist-bent nematic.

Spontaneous chiral symmetry breaking in liquid crystals

Motivated by new experimental observations we generalize the Landau-like approach to include the direct phase transition between isotropic liquid (I) and heliconical nematic liquid crystal (NTB) structure. We show that depending on the Landau expansion coefficients, our model allows either direct I–NTB transition, or the sequence of the phases I–N–NTB with the classical nematic liquid crystal (N) sandwiched between the isotropic liquid and heliconical nematic liquid crystal. Which of these two situations is realized depends on how strong is the first order phase transition from the isotropic liquid. If it is strong enough the system undergoes I–N–NTB sequence, and for the very weak first order phase transition I–NTB transformation occurs. Furthermore in the latter case the NTB structure can be biaxial heliconical nematic liquid crystal.

Can multi-biaxial mesogenic mixtures favour biaxial nematics? A computer simulation study.

Extending the range of existence of biaxial nematic phases is key to their use in applications. Here, we have investigated using extensive molecular dynamics (MD) simulations of a coarse-grained model the possible advantages of using mesogenic mixtures. We have studied the phase organisation of five thermotropic mixtures of biaxial Gay-Berne (GB) ellipsoidal particles having the same volume, but different shapes and interactions, with aspect ratios ranging from rod-like to disc-like and, choosing fractional compositions so as to model a Gaussian dispersity of shapes. The parameterisation is based on a previous GB model with biaxialities of opposite sign for steric and attractive interactions which was shown to exhibit a stable biaxial nematic phase. We found that mixing different biaxial GB particles has an overall stabilising effect on the biaxial nematic phase with respect to temperature, layering and, to some extent also demixing. The mixtures show a decrease of ordering transition temperatures, a widening of nematic temperature ranges, and the formation of smectic phases at lower temperatures.

Core Structure and Non-Abelian Reconnection of Defects in a Biaxial Nematic Spin-2 Bose-Einstein Condensate.

We calculate the energetic structure of defect cores and propose controlled methods to imprint a nontrivially entangled vortex pair that undergoes non-Abelian vortex reconnection in a biaxial nematic spin-2 condensate. For a singular vortex, we find three superfluid cores in addition to depletion of the condensate density. These exhibit order parameter symmetries that are different from the discrete symmetry of the biaxial nematic phase, forming an interface between the defect and the bulk superfluid. We provide a detailed analysis of phase mixing in the resulting vortex cores and find an instability dependent upon the orientation of the order parameter. We further show that the spin-2 condensate is a promising system for observing spontaneous deformation of a point defect into an "Alice ring" that has so far avoided experimental detection.

Erratum to Perturbed hedgehogs: continuous deformation of point defects in biaxial nematic liquid crystals

Erratum to Perturbed hedgehogs: continuous deformation of point defects in biaxial nematic liquid crystals

Role of kosmotrope-chaotrope interactions at micelle surfaces on the stabilization of lyotropic nematic phases.

Three lyotropic quaternary systems of ionic surfactants were prepared to investigate the role of kosmotrope-chaotrope interactions at the micelle surfaces on stabilizing the different nematic phases. The ionic surfactants were potassium laurate (KL), sodium dodecylsulfate (SDS) and tetradecyltrimethylammonium bromide (TDTMABr), where KL is a kosmotrope surfactant, and others are chaotrope. The first system consisted of KL/decanol (DeOH)/water/alkali sulfate and the second of SDS/DeOH/water/alkali sulfate. The third system was prepared by adding sodium salts of chaotropic or kosmotropic anions to the primary mixture of TDTMABr/DeOH/water, separately. The characteristic textures of discotic nematic (N D), biaxial nematic (N B) and calamitic nematic (N C) phases were identified under polarizing light microscope. Laser conoscopy was employed to determine the uniaxial-to-biaxial phase transitions. The kosmotrope-kosmotrope or chaotrope-chaotrope interactions between the head groups of the surfactants and the ions of the electrolytes led to the stabilization of the N D phase. On the other hand, kosmotrope-chaotrope interactions stabilize the N B and/or N C phases.

Generalized Liquid Crystals: Giant Fluctuations and the Vestigial Chiral Order ofI,O, andTMatter

The physics of nematic liquid crystals has been subject of intensive research since the late 19th century. However, because of the limitations of chemistry the focus has been centered around uni- and biaxial nematics associated with constituents bearing a $D_{\infty h}$ or $D_{2h}$ symmetry respectively. In view of general symmetries, however, these are singularly special since nematic order can in principle involve any point group symmetry. Given the progress in tailoring nano particles with particular shapes and interactions, this vast family of "generalized nematics" might become accessible in the laboratory. Little is known since the order parameter theories associated with the highly symmetric point groups are remarkably complicated, involving tensor order parameters of high rank. Here we show that the generic features of the statistical physics of such systems can be studied in a highly flexible and efficient fashion using a mathematical tool borrowed from high energy physics: discrete non-Abelian gauge theory. Explicitly, we construct a family of lattice gauge models encapsulating nematic ordering of general three dimensional point group symmetries. We find that the most symmetrical "generalized nematics" are subjected to thermal fluctuations of unprecedented severity. As a result, novel forms of fluctuation phenomena become possible. In particular, we demonstrate that a vestigial phase carrying no more than chiral order becomes ubiquitous departing from high point group symmetry chiral building blocks, such as $I$, $O$ and $T$ symmetric matter.

Optical Simulation of Viewing Angle Property of Biaxial Nematic Bent-Core Liquid Crystal

The conventional liquid crystal displays (LCDs) have been using optically uniaxial liquid crystal (LC) medium and this often causes a significant image change at oblique viewing angles. We simulated the viewing angle properties of the biaxial nematic (Nb) phase of a bent-core liquid crystal (BLC) and compared the results with the vertically aligned (VA)- and the in-plane switching (IPS)-LCDs. The Nb phase of the BLC showed a smaller transmittance at the dark state as well as a greater contrast ratio at wide viewing angle. The viewing angle property of the Nb-mode without any compensation film was slightly superior to the IPS-mode with the compensation films eliminating the decross of the polarizers at oblique viewing angle.

Soft ellipsoid potential for biaxial molecules

A soft ellipsoid contact pair potential model for biaxial molecules is proposed considering the configuration dependent energy anisotropy explicitly alongwith their geometrical aspects. Analytic expressions of forces and torques for this coarse-grained potential are provided to make it convenient for molecular dynamics simulation study. Additionally, some molecular dynamics simulations are performed to generate biaxial smectic and nematic liquid crystal phases.

Molecular field theory for polar, biaxial bent-core nematics

ABSTRACTWe have studied a polar, biaxial nematic liquid crystal formed from bent-core molecules using molecular field theory. The model includes a simple Heisenberg-form dipolar intermolecular interaction in addition to the usual quadrupolar nematic interaction, and mimics a system consisting of nematogenic bent-core molecules with a large transverse dipole along the bisector of the two molecular arms. Such systems are regarded as good candidates for biaxial nematic liquid crystals. In principle, the molecular dipoles can align, thus stabilising the ordering of the minor axes. Our calculations predict that, for suitable values of the bent-core interarm angle, the biaxial nematic phase can be stabilised at higher temperatures than in the absence of the transverse dipole. In general, the transverse macroscopic polar order stabilises the biaxial nematic phase. In particular, for a large enough dipolar interaction, the Landau point in the pure biaxial nematic develops into a line of first-order polar biaxial nematic-to-isotropic phase transitions.

Conoscopic image of a biaxial nematic phase in a sodium decyl sulfate – decanol – D2O mixture

ABSTRACTThe nematic phases of a lyotropic system NadS/ decanol/ heavy water are investigated using optical conoscopy and image processing. The phase diagram obtained from these lyotropic materials predicts the occurrence of a direct phase transition, which does not present the biaxial nematic phase, between the discotic (ND) and calamitic (NC) nematic phases. A biaxial nematic (NB) phase is optically characterized and confirmed through conoscopic image, inside the biaxial range, between the two uniaxial nematic phases. Also, their respective transition points are determined by means of image processing. The NB phase observed here is discussed as part of the nature of the micellar configuration of lyotropic materials which exhibit uniaxial nematic phases.

Lattice model for biaxial and uniaxial nematic liquid crystals.

We use a lattice gas model to describe the phase transitions in nematic liquid crystals. The phase diagram displays, in addition to the isotropic phase, the two uniaxial nematics, the rod-like and discotic nematics, and the biaxial nematic. Each site of the lattice has a constituent unit that takes only six orientations and is understood as being a parallelepiped brick with the three axes distinct. The possible orientations of a brick are those in which its axes are parallel to the axes of a Cartesian reference frame. The analysis of the model is performed by the use of a mean-field approximation and a Landau expansion of the free energy.

New phase diagrams in the mixture of rods and plates of biaxial nematic liquid crystals

Experiments have shown an unusual phase transition between a stable biaxial nematic phase and a coexistence region of the two uniaxial nematic phases in lyotropic liquid crystals. We propose a Landau model to describe this interesting phase behavior. The model considering both rod-like molecules and plate-like molecules is discussed with great details. The possibility of the various phases including the coexistence phases is explored by means of variation of the concentration. The model describes the first theoretical observation of the phase transition between two biaxial nematic phases. The theoretical predictions are found to be in good qualitative agreement with available experimental results.

Landau theory for uniaxial nematic, biaxial nematic, uniaxial smectic-A, and biaxial smectic-A phases

ABSTRACTWe use the Landau theory of phase transitions to obtain the global phase diagram concerning the uniaxial nematic, biaxial nematic, uniaxial smectic-A and biaxial smectic-A phases. The transition between the biaxial nematic and biaxial smectic is continuous as well as the transition between the nematic phases and the transition between the smectic phases. The transition from uniaxial nematic and uniaxial smectic is continuous with a tricritical point. The tricritical point may be absent and the entire transition becomes continuous. The four phases meet at a tetracritical point.

Director structures with dominant in-plane alignment in hybrid planar films of biaxial nematic liquid crystals: A Monte Carlo study

Equilibrium director structures in two thin hybrid planar films of biaxial nematics are investigated through Markov chain Monte Carlo simulations based on a lattice Hamiltonian model within the London dispersion approximation. While the substrates of the two films induce similar anchoring influences on the long axes of the liquid crystal molecules (viz. planar orientation at one end and perpendicular, or homeotropic, orientations at the other), they differ in their coupling with the minor axes of the molecules. In Type-A film the substrates do not interact with the minor axes at all (which is experimentally relatively more amenable), while in Type-B, the orientations of the molecular axes at the surface layer are influenced as well, by their biaxial coupling with the surface. Both films exhibit expected bending of the director associated with the ordering of the molecular long axes due to surface anchoring. Simulation results indicate that the Type-A film hosts stable director structures in the biaxial nematic phase of the LC medium, with the primary director lying in the plane of the film. High degree of this stable order thus developed could be of practical interest for potential applications. Type-B film, on the other hand, experiences competing interactions among the minor axes due to incompatible anchoring influences at the bounding substrates, apparently leading to frustration.

Perturbed hedgehogs: continuous deformation of point defects in biaxial nematic liquid crystals

A spherically symmetric isolated point defect in a 3D uniaxial nematic liquid crystal sample is often called a {\it radial hedgehog}. We use topological methods to describe local configurations of uniaxial and biaxial states into which a hedgehog naturally deforms under small perturbations: these include the biaxial torus and split core configurations studied in the literature using analytical and numerical methods. The topological results here take no account of the governing physical laws but provide a library of options from which the physics must make a choice.

On the Landau--de Gennes Elastic Energy of Constrained Biaxial Nematics

In the Landau--de Gennes theory, a nematic liquid crystal is described by a tensor order parameter, ${\bf Q}$, which, at each point of the region $\Omega$ occupied by the system, is a symmetric, traceless $3 \times 3$ matrix. The free-energy density $\psi$ of nematic liquid crystals is expanded into powers of the components ${\bf Q}_{ij}$ of ${\bf Q}$ and ${\bf Q}_{ij,k}$ of its gradient $\nabla {\bf Q}$, and can be decomposed in the sum $\psi = \psi_B + \psi_E$ of the bulk part $\psi_B({\bf Q})$ and the elastic part $\psi_E({\bf Q}, \nabla {\bf Q})$. A most common expression for $\psi_E$ is given by the four-constant approximation $\psi_E({\bf Q},\nabla {\bf Q}) = L_1 {\bf Q}_{ij,j}{\bf Q}_{ik,k} + L_2 {\bf Q}_{ik,j}{\bf Q}_{ij,k} + L_3 {\bf Q}_{ij,k}{\bf Q}_{ij,k} + L_4 {\bf Q}_{lk}{\bf Q}_{ij,l}{\bf Q}_{ij,k} $ [J. M. Ball, The Mathematics of Liquid Crystals, Cambridge Centre for Analysis short course, 2012, https://people.maths.ox.ac.uk/ball/teaching.shtml, H. Mori, E. C. Gartland, Jr., J. R. Kelly, and P. J. Bos, Jap. J. Appl. Phys., 38 (1999), pp. 135--146, N. J. Mottram and C. Newton, Introduction to $Q$-tensor theory, Technical report, Department of Mathematics, University of Strathclyde, Glasgow, UK, 2004, arXiv:1409.3542 [cond-mat.soft], 2014]. For general ${\bf Q}$-tensors, it was shown that if $L_4\neq 0$, the corresponding free-energy functional is unbounded from below [J. M. Ball, The Mathematics of Liquid Crystals, Cambridge Centre for Analysis short course, 2012, https://people.maths.ox.ac.uk/ball/teaching.shtml, J. M. Ball and A. Majumdar, Mol. Cryst. Liq. Cryst., 525 (2010), pp. 1--11]. On the other hand, if $L_4=0$ and $L_1$, $L_2$, and $L_3$ satisfy appropriate conditions, the elastic part of the energy functional is bounded and coercive [T. A. Davis and E. C. Gartland, Jr., SIAM J. Numer. Anal., 35 (1998), pp. 336--362, L. Longa, D. Monselesan, and H.-R. Trebin, Liq. Cryst., 2 (1987), pp. 769--796]. In the constrained theory in which ${\bf Q}$ has position independent eigenvalues, only the elastic energy has to be considered, since the bulk energy is constant. For constrained uniaxial systems, it is known that if $L_4\neq 0$, the elastic density $\psi_E$ reduces to the classical Oseen--Frank density, and relations among $L_1$, $L_2$, $L_3$, and $L_4$ can be obtained so that the energy is coercive [J. M. Ball and A. Zarnescu, Arch. Ration. Mech. Anal., 202 (2011), pp. 493--535, J. L. Ericksen, Inequalities in liquid crystal theory, Phys. Fluids, 9 (1966), pp. 1205--1207, L. Longa, D. Monselesan, and H.-R. Trebin, Liq. Cryst., 2 (1987), pp. 769--796]. In this paper we address the question of coercivity for constrained biaxial systems. Conditions on $L_1$, $L_2$, $L_3$, and $L_4$ guaranteeing coercivity of the energy, and hence the existence of minimizers, are established. In particular, we shall obtain the constrained biaxial counterpart of the classical Ericksen conditions for the constrained uniaxial case. For the proof, after deriving a Cartesian representation for $\psi_E$ in terms of the three orthonormal eigenvector fields of ${\bf Q}$, we use the identification of the order parameter space with the eightfold quotient of ${\mathbb S}^3 \cong Sp(1)$ by the quaternion group ${\mathcal H}$ and the description, in this model, of the condition for the frame indifference of Landau--de Gennes energy densities as given in [D. Mucci and L. Nicolodi, Arch. Ration. Mech. Anal., 206 (2012), pp. 853--884].