Biaxial Liquid Crystals Research Articles

Biaxial nematic order in fundamental measure theory.

Liquid crystals consisting of biaxial particles can exhibit a much richer phase behavior than their uniaxial counterparts. Usually, one has to rely on simulation results to understand the phase diagram of these systems since very few analytical results exist. In this work, we apply fundamental measure theory, which allows us to derive free energy functionals for hard particles from first principles and with high accuracy, to systems of hard cylinders, cones, and spherotriangles. We provide a general recipe for incorporating biaxial liquid crystal order parameters into fundamental measure theory and use this framework to obtain the phase boundaries for the emergence of orientational order in the considered systems. Our results provide insights into the phase behavior of biaxial nematic liquid crystals and, in particular, into methods for their analytical investigation.

Rotational diffusion of shape-switching particles dissolved in biaxial liquid crystals

ABSTRACT The interpretation of many experimental or computational studies on the orientational dynamics of molecules dissolved in liquid crystals relies on assuming some stochastic model for their time evolution. The Rotational Diffusion model is typically employed for this purpose, representing the molecules being monitored as rigid particles. However, this is not a realistic assumption for many molecules or nanoparticles in solution, and we have previously proposed a model to describe the rotational diffusion of a shape-changing particle dissolved in uniaxial fluids. Here, we extend the model allowing the host medium to be of biaxial symmetry, and we apply the theory to a simple example case, as well as exploring its general features.

Multiple ferroelectric nematic phases of a highly polar liquid crystal compound

ABSTRACT Ferroelectric nematic liquid crystals represent not only fascinating, fundamental science, but they also hold promise for new technologies including high-density power storage or sub-millisecond switching information displays. In this work, we describe the synthesis and measurements of the physical properties of a new compound, 4-nitrophenyl 4-[(2,4-dimethoxylbenzoyl)oxy]-2-fluorobenzoate (RT11001). This material exhibits multiple, highly polar, ferroelectric nematic phases that have not been previously reported. We employ a wide range of physical characterisation methods including differential scanning calorimetry (DSC), mass density measurement, optical birefringence, polarising optical microscopy (POM), dielectric spectroscopy, electric current analysis, electro-optical switching, small-angle and wide-angle x-ray scattering measurements to show that RT11001 has multiple, distinct ferroelectric phases. We argue that the highest temperature phase is a polar nematic fluid with non-polar smectic clusters. Directly below appears to be a transition to another polar nematic phase containing polar positionally ordered clusters. Lastly, there are indications of an additional, polar biaxial liquid crystal phase at lower temperatures.

The Dynamic of Rodlike Molecules in a Biaxial Liquid Crystal

The relaxation time and the polarizability of molecules with dipole moment parallel to axis in a liquid crystal are considered by a model the Brown model. The solution of this system is obtained by numerical method. Modest analytic equations relaxation is proposed, agreeing one to appreciate the behavior of the system and expecting the polarizability for different value of the barrier and anisotropy parameters, are proposed.

Quantification of nematic cell polarity in three-dimensional tissues.

How epithelial cells coordinate their polarity to form functional tissues is an open question in cell biology. Here, we characterize a unique type of polarity found in liver tissue, nematic cell polarity, which is different from vectorial cell polarity in simple, sheet-like epithelia. We propose a conceptual and algorithmic framework to characterize complex patterns of polarity proteins on the surface of a cell in terms of a multipole expansion. To rigorously quantify previously observed tissue-level patterns of nematic cell polarity (Morales-Navarrete et al., eLife 2019), we introduce the concept of co-orientational order parameters, which generalize the known biaxial order parameters of the theory of liquid crystals. Applying these concepts to three-dimensional reconstructions of single cells from high-resolution imaging data of mouse liver tissue, we show that the axes of nematic cell polarity of hepatocytes exhibit local coordination and are aligned with the biaxially anisotropic sinusoidal network for blood transport. Our study characterizes liver tissue as a biological example of a biaxial liquid crystal. The general methodology developed here could be applied to other tissues and in-vitro organoids.

Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density

In this work, we explore fluctuations during phase transitions of uniaxial and biaxial liquid crystals using a phenomenological free energy functional. We rely on a continuum-level description of the liquid crystal ordering with a tensorial parameter and a temperature dependent Landau polynomial expansion of the tensor’s invariants. The free energy functional, over a three-dimensional periodic domain, is integrated with a Gaussian quadrature and minimized with a theoretically informed Monte Carlo method. We reconstruct analytical phase diagrams, following Landau and Doi’s notations, to verify that the free energy relaxation reaches the global minimum. Importantly, our relaxation method is able to follow the thermodynamic behavior provided by other non-phenomenological approaches; we predict the first order character of the isotropic–nematic transition, and we identify the uniaxial–biaxial transition as second order. Finally, we use a finite-size scaling method, using the nematic susceptibility, to calculate the transition temperatures for 4-Cyano-4’-pentylbiphenyl (5CB) and N-(4-methoxybenzylidene)-4-butylaniline (MBBA). Our results show good agreement with experimental values, thereby validating our minimization method. Our approach is an alternative towards the relaxation of temperature dependent continuum-level free energy functionals, in any geometry, and can incorporate complicated elastic and surface energy densities.

Monte Carlo study with reweighting of uniaxial nematic liquid crystals composed of biaxial molecules.

We present a high accuracy Monte Carlo simulation study of the uniaxial nematic (N_{U}) to isotropic (I) phase transition of a lattice dispersion model of uniaxial nematics composed of biaxial molecules. The N_{U}-I coexistence curve terminating at the Landau critical point has been determined using the multiple histogram reweighting technique. A close investigation reveals a sharp departure in the nature of the N_{U}-I coexistence curve in the temperature-biaxiality parameter phase diagram in comparison to the earlier theoretical (either mean-field or computer simulation) predictions. The coexistence curve shows a change in curvature with increasing value of the degree of molecular biaxiality.

How to achieve a successful biaxial marriage.

Coupling between organic and inorganic components results in a biaxial liquid crystal

Hybrid molecular-colloidal liquid crystals.

Order and fluidity often coexist, with examples ranging from biological membranes to liquid crystals, but the symmetry of these soft-matter systems is typically higher than that of the constituent building blocks. We dispersed micrometer-long inorganic colloidal rods in a nematic liquid crystalline fluid of molecular rods. Both types of uniaxial building blocks, while freely diffusing, interact to form an orthorhombic nematic fluid, in which like-sized rods are roughly parallel to each other and the molecular ordering direction is orthogonal to that of colloidal rods. A coarse-grained model explains the experimental temperature-concentration phase diagram with one biaxial and two uniaxial nematic phases, as well as the orientational distributions of rods. Displaying properties of biaxial optical crystals, these hybrid molecular-colloidal fluids can be switched by electric and magnetic fields.

Effects of monoclinic symmetry on the properties of biaxial liquid crystals.

Tilted smectic liquid crystal phases such as the smectic-C phase seen in calamitic liquid crystals are usually treated using the assumption of biaxial orthorhombic symmetry. However, the smectic-C phase has monoclinic symmetry, thereby allowing disassociation of the principal optic and dielectric axes based on symmetry and invariance principles. This is demonstrated here by comparing optical and dielectric measurements for two materials with highly first-order direct transitions from nematic to smectic-C phases. The results show a high difference between the orientations of the principal axes sets, which is interpreted as the existence of two distinct cone angles for optical and dielectric frequencies. Both materials exhibit an increasing degree of monoclinic behavior with decreasing temperature. Due to fast switching speeds, ferroelectric smectic-C* materials are important for fast modulators and LCoS devices, where the dielectric biaxiality influences device operation.

Chiral phases in a system of biaxial molecules

ABSTRACTChiral phases in a system of biaxial molecules are investigated based on a theory of biaxial liquid crystals, which we have presented in past work. Four chiral phases are identified, corresponding to a uniaxial nematic phase, two biaxial nematic phases, and a discotic phase, respectively. We find that in the chiral uniaxial nematic phase, the pitch of the chiral structures does not depend on temperature. In contrast, in the two chiral biaxial nematic phases, as well as in the chiral discotic phase, the pitch is temperature-dependent.

Bimodal form distribution from modelling biaxial lyotropic liquid crystal solutions through a polydisperse Maier–Saupe model

ABSTRACTBiaxial nematic phases have been the subject of a long list of studies. In particular, they were found for a few lyotropic micellar solutions. There is a debate in the literature on whether the micellar aggregates should be biaxial, or if biaxiality could be the result of perpendicular alignment of uniaxial particles of cylinder-like and disc-like geometry in a mixture. Based on recent studies on the phase stability of such mixtures, we have investigated a polydisperse distribution of uniaxial particles interacting through a Maier–Saupe potential. Our calculations were developed for a general distribution of micellar anisometries. The distribution was obtained from the fitting of our results to the experimental data of Yu and Saupe’s well-known 1980 paper, near the Landau point, yielding a bimodal distribution, with the presence of two quadrupoles referred to objects of opposite symmetry, that is to prolate and oblate micelles. This result lends support to the rationalization of the biaxial phase for lyotropic systems in terms of a polydisperse mixture of rod-like and disc-like micelles.

ChemInform Abstract: Xenon in Liquid‐Crystalline Samples

AbstractReview: 18 refs.

Effect of phase symmetry on the NMR spectrum of acetonitrile oriented in a uniaxial–biaxial–uniaxial phase

We report here the measurement of the CH and the HH dipolar couplings of the methyl group of acetonitrile oriented in the biaxial liquid crystal potassium laurate/1-decanol/water system. These parameters show large variations when measured as a function of temperature. The variations follow the symmetry of the phase as the liquid crystal goes through the sequence of uniaxial – biaxial – uniaxial phases and show a close correspondence to the phase changes that occur in the liquid crystalline solvent coinciding with the onset of biaxiality. The HCH bond angle calculated after incorporating vibrational corrections to the dipolar couplings is discussed in terms of contributions in the case of the biaxial liquid crystal arising from vibration–rotation interaction effects.

Equivalent variational approaches to biaxial liquid crystal dynamics

Within the framework of liquid crystal flows, the Qian and Sheng (QS) model (Qian and Sheng 1998 Phys. Rev. E. 58, 7475. ( doi:10.1103/PhysRevE.58.7475 )) for Q -tensor dynamics is compared with the Volovik and Kats (VK) theory (Volovik and Kats 1981 Sov. Phys. 54, 122–126) of biaxial nematics by using Hamilton’s variational principle. Under the assumption of rotational dynamics for the Q -tensor, the variational principles underling the two theories are equivalent and the conservative VK theory emerges as a specialization of the QS model. Also, after presenting a micropolar variant of the VK model, Rayleigh dissipation is included in the treatment. Finally, the treatment is extended to account for non-trivial eigenvalue dynamics in the VK model and this is done by considering the effect of scaling factors in the evolution of the Q -tensor.

Reexamination of the mean-field phase diagram of biaxial nematic liquid crystals: Insights from Monte Carlo studies.

Investigations of the phase diagram of biaxial liquid-crystal systems through analyses of general Hamiltonian models within the simplifications of mean-field theory (MFT), as well as by computer simulations based on microscopic models, are directed toward an appreciation of the role of the underlying molecular-level interactions to facilitate its spontaneous condensation into a nematic phase with biaxial symmetry. Continuing experimental challenges in realizing such a system unambiguously, despite encouraging predictions from MFT, for example, are requiring more versatile simulational methodologies capable of providing insights into possible hindering barriers within the system, typically gleaned through its free-energy dependences on relevant observables as the system is driven through the transitions. The recent paper from this group [Kamala Latha et al., Phys. Rev. E 89, 050501(R) (2014)], summarizing the outcome of detailed Monte Carlo simulations carried out employing an entropic sampling technique, suggested a qualitative modification of the MFT phase diagram as the Hamiltonian is asymptotically driven toward the so-called partly repulsive regions. It was argued that the degree of (cross) coupling between the uniaxial and biaxial tensor components of neighboring molecules plays a crucial role in facilitating a ready condensation of the biaxial phase, suggesting that this could be a plausible factor in explaining the experimental difficulties. In this paper, we elaborate this point further, providing additional evidence from curious variations of free-energy profiles with respect to the relevant orientational order parameters, at different temperatures bracketing the phase transitions.

Detection of an intermediate biaxial phase in the phase diagram of biaxial liquid crystals: entropic sampling study.

We investigate the phase sequence of biaxial liquid crystals, based on a general quadratic model Hamiltonian over the relevant parameter space, with a Monte Carlo simulation which constructs equilibrium ensembles of microstates, overcoming possible (free) energy barriers (combining entropic and frontier sampling techniques). The resulting phase diagram qualitatively differs from the universal phase diagram predicted earlier from mean-field theory (MFT), as well as the Monte Carlo simulations with the Metropolis algorithm. The direct isotropic-to-biaxial transition predicted by the MFT is replaced in certain regions of the space by the onset of an additional intermediate biaxial phase of very low order, leading to the sequence N(B)-N(B1)-I. This is due to inherent barriers to fluctuations of the components comprising the total energy, and may explain the difficulties in the experimental realization of these phases.

Biaxiality-induced magnetic field effects in bent-core nematics: Molecular-field and Landau theory

Nematic liquid crystals composed of bent-core molecules exhibit unusual properties, including an enhanced Cotton-Mouton effect and an increasing isotropic (paranematic)-nematic phase transition temperature as a function of magnetic field. These systems are thought to be good candidate biaxial liquid crystals. Prompted by these experiments, we investigate theoretically the effect of molecular biaxiality on magnetic-field-induced phenomena for nematic liquid crystals, using both molecular field and Landau theory. The geometric mean approximation is used in order to specify the degree of molecular biaxiality using a single parameter. We reproduce experimental field-induced phenomena and predict also an experimentally accessible magnetic critical point. The Cotton-Mouton effect and temperature dependence of the paranematic-nematic phase transition are more pronounced with increased molecular biaxiality. We compare our theoretical approaches and make contact with recent relevant experimental results on bent-core molecular systems.

Biaxial phases in mineral liquid crystals

A review is given of liquid crystals formed in colloidal dispersions, in particular those consisting of mineral particles. Starting with the historical development and early theory, the characteristic properties related to the colloidal nature of this type of liquid crystals are discussed. The possibility to find biaxial nematic and smectic phases is described for mixtures of rods and plates and recent examples are given of biaxial liquid crystal phases of mineral particles with inherent biaxial shape.

Biaxial order parameter in the homologous series of orthogonal bent-core smectic liquid crystals

The fundamental parameter of the uniaxial liquid crystalline state that governs nearly all of its physical properties is the primary orientational order parameter (S) for the long axes of molecules with respect to the director. The biaxial liquid crystals (LCs) possess biaxial order parameters depending on the phase symmetry of the system. In this paper we show that in the first approximation a biaxial orthogonal smectic phase can be described by two primary order parameters: S for the long axes and C for the ordering of the short axes of molecules. The temperature dependencies of S and C are obtained by the Haller's extrapolation technique through measurements of the optical birefringence and biaxiality on a nontilted polar antiferroelectric (Sm-AP(A)) phase of a homologous series of LCs built from the bent-core achiral molecules. For such a biaxial smectic phase both S and C, particularly the temperature dependency of the latter, are being experimentally determined. Results show that S in the orthogonal smectic phase composed of bent cores is higher than in Sm-A calamatic LCs and C is also significantly large.