Present work is a theoretical study on the stability of the thermotropic biaxial nematic liquid crystal phase in model systems. Its main aim is to present the phase diagrams of spatially uniform liquid mesophases and to identify the molecular parameters that influence the stability of the biaxial nematic. The diagrams are obtained by means of the Local Density Functional Theory in low density approximation, and the relation between the molecular parameters of the models and macroscopic properties of the system close to the transition point are obtained by means of bifurcation analysis. We consider three model systems; the so-called L=2 model (the lowest coupling model of the orientational part of pair potential), the biaxial Gay-Berne interaction, and the bent-core system. For the second one, we also briefly investigate the temperature dependence of elastic constants in rod-like regime and in the vicinity of the Landau point and comment on the smectic phases. In every case we take into account rigid molecules. We find that the Landau points acquired from the square root rule for hard biaxial ellipsoids retain its significance, and provide qualitatively correct estimations of Landau points positions for Gay-Berne biaxial ellipsoids. In case of the bent-core model molecules build from uniaxial and biaxial Gay-Berne ellipsoids we find that the dipole-dipole interaction and degree of arms biaxiality change the stability of the biaxial nematic phase.
Phase sequences of the biaxial nematic liquid crystal in the interior of the essential triangle are studied with Wang Landau sampling. The evidence points to the existence of an intermediate unixial phase with low biaxiality in the isotropic to biaxial nematic phase sequence.
How change in molecular structure can affect relative stability and structural properties of the twist-bend nematic phase (N$_\text{TB}$)? Here we extend the mean-field model [C. Greco et al., Soft Matter, 2014, 10, 9318] for bent-shaped achiral molecules, to study the influence of arm molecular biaxiality and the value of molecule's bend angle on relative stability of N$_\text{TB}$. In particular we show that by controlling biaxiality of molecule's arms up to four ordered phases can become stable. They involve locally uniaxial and biaxial variants of N$_\text{TB}$, together with the uniaxial …
In nematic liquid crystals (NLCs), topological defects of a chiral origin play a role in phase transitions and lead to phase configurations of nontrivial topology, like those in neutron stars and helium in the A-phase. In the biaxial-uniaxial phase transition, the deformation of the orbit, as the order parameter degeneracy of the NLC, connects together an evolution of topological defects, the surface anchoring energy and elastic Frank modui. In this work we estimate the chiral gauge field presentation of the constrained Ladnau-de Gennes theory of the biaxial nematics, which have to explain the…
Thermotropic biaxial nematic phases seem to be rare, but biaxial smectic A phases less so. Here we use molecular field theory to study a simple two-parameter model, with one parameter promoting a biaxial phase and the second promoting smecticity. The theory combines the biaxial Maier-Saupe and McMillan models. We use alternatively the Sonnet-Virga-Durand (SVD) and geometric mean approximations (GMA) to characterize molecular biaxiality by a single parameter. For non-zero smecticity and biaxiality, the model always predicts a ground state biaxial smectic A phase. For a low degree of smectic ord…
Field-induced reorientation of colloidal particles is especially relevant to manipulate the optical properties of a nanomaterial for target applications. We have recently shown that surprisingly feeble external stimuli are able to transform uniaxial nematic liquid crystals (LCs) of cuboidal particles into biaxial nematic LCs. In the light of these results, here we apply an external field that forces the reorientation of colloidal cuboids in nematic LCs and sparks a uniaxial-to-biaxial texture switching. By Dynamic Monte Carlo simulation, we investigate the unsteady-state reorientation dynamics…
Colloidal cuboids have the potential to self-assemble into biaxial liquid crystal phases, which exhibit two independent optical axes. Over the last few decades, several theoretical works predicted the existence of a wide region of the phase diagram where the biaxial nematic phase would be stable, but imposed rather strong constraints on the particle rotational degrees of freedom. In this work, we employ molecular simulation to investigate the impact of size dispersity on the phase behaviour of freely-rotating hard cuboids, here modelled as self-dual-shaped nanoboards. This peculiar anisotropy,…
Stability of Biaxial Nematic Phase for Systems with Variable Molecular Shape Anisotropy
通过推广Mulder和Ruijgrok的平均场模型[Physica A { \bf 113}，145（1982）]，我们研究了分子形状的涨落对双轴双折射相稳定性的影响。我们限制自己的情况下，当分子形状各向异性，表示的对齐张量，是一个随机变量的退火类型。这种行为的原型可以在溶致体系中找到-月桂酸钾、1-癸醇和$D_2O$的混合物，其中胶束形状的分布根据实际平衡条件进行调整。具有双轴取向相的材料（其中分子形状受到波动影响）的其它实例是由柔性三聚体或四足状分子单元组成的热致材料。我们的计算表明，高斯平衡分布的变量描述分子形状（色散力）各向异性引起新的类的相图，在原来的模型中没有。取决于形状波动的性质，相对于单轴取向相，双轴取向相的稳定性可以增强或降低。在前一种情况下，朗道点分裂成两个三相点，并观察到从各向同性到双轴相的直接相变线。
Effect of the alkyl chain length of the alcohols on the nematic uniaxial-to-biaxial phase transitions in the potassium laurate/alcohol/K2SO4/water lyotropic mixture
We theoretically study the phase behaviour of monolayers of hard rod-plate mixtures using a fundamental-measure density functional in the restricted-orientation (Zwanzig) approximation. We consider both species to be subject to an attractive potential proportional to the particle contact area on the surface and with adsorption strengths that depend on the species type. Particles have board-like shape, with sizes chosen using a symmetry criterion: same volume and same aspect ratio $κ$. Phase diagrams were calculated for $κ=10$, 20 and 40 and different values of adsorption strengths. For small a…
The biaxial phase in nematic liquid crystals has been elusive for several decades after its prediction in the 1970s. A recent experimental breakthrough was achieved by Liu et al. [PNAS 113, 10479 (2016)] in a liquid crystalline medium with magnetic nanoparticles (MNPs). They exploited the different length scales of dipolar and magneto-nematic interactions to obtain an equilibrium state where the magnetic moments are at an angle to the nematic director. This tilt introduces a second distinguished direction for orientational ordering or biaxiality in the two-component system. Using coarse-graine…
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 …
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 towards 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 realising such a system unambiguously, despite encouraging predictions from MFT for example, are requiring more versatile simulational methodol…
Starting from a dynamic tensor model about two second-order tensors, we derive the frame hydrodynamics for the biaxial nematic phase using the Hilbert expansion. The coefficients in the frame model are derived from those in the tensor model. The energy dissipation of the tensor model is maintained in the frame model. The model is reduced to the Ericksen--Leslie model if the biaxial bulk energy minimum of the tensor model is reduced to a uniaxial one.
General quadratic Hamiltonian models, describing interaction between 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 c…
We employ a lattice-gas extension of the Maier--Saupe model with discrete orientation states to study the phase behavior of a statistical model for biaxial nematogenic units in mean-field theory. The phase behavior of the system is investigated in terms of the strength of isotropic interaction between anisotropic objects, as well as the degree of biaxiality and the concentration of those units. We obtain phase diagrams with isotropic phases and stable biaxial and uniaxial nematic structures, various phase coexistences, many types of critical and multicritical behaviors, such as ordinary vapor-…
We apply a recently developed technique to determine adapted coordinates for the sixth degree Landau-deGennes potential, in which the potential is specially simple, to analyze the possibility of a direct transition between the fully symmetric state and a biaxial phase in nematic liquid crystals. {Our results confirm, with simpler computations, results by Allender and Longa.
In the present work, we study minimizers of the Landau-de Gennes free energy in a bounded domain $Ω\subset \mathbb{R}^3$. We prove that at low temperature minimizers do not vanish, even for topologically non-trivial boundary conditions. This is in contrast with a simplified Ginzburg-Landau model for superconductivity studied by Bethuel, Brezis and Hélein. Merging this with an observation of Canevari we obtain, as a corollary, the occurence of biaxial escape: the tensorial order parameter must become strongly biaxial at some point in $Ω$. In particular, while it is known that minimizers cannot …
Using Monte Carlo (MC) computer simulations we explore the self-assembly and ordering behavior of a hybrid, soft magnetic system consisting of small magnetic nano-spheres in a liquid-crystalline (LC) matrix. Inspired by recent experiments with colloidal rod-matrices we focus on conditions where the sphere and rod diameters are comparable. Already in the absence of a magnetic field, the nematic ordering of the LC can stabilize formation of magnetic chains along the nematic or smectic director, yielding a state with local (yet no macroscopic) magnetic order. The chains, in turn, increase the ove…
We investigate the phase behavior of colloidal suspensions of board-like particles under the effect of an external field and assess the still disputed occurrence of the biaxial nematic (N$_\text{B}$) liquid crystal phase. The external field promotes the rearrangement of the initial isotropic (I) or uniaxial nematic (N$_\text{U}$) phase and the formation of the N$_\text{B}$ phase. In particular, very weak field strengths are sufficient to spark a direct I-N$_\text{B}$ or N$_\text{U}$-N$_\text{B}$ phase transition at the self-dual shape, where prolate and oblate particle geometries fuse into one…
We perform extensive Monte Carlo simulations to investigate the phase behaviour of colloidal suspensions of hard board-like particles (HBPs). While theories restricting particle orientation or ignoring higher ordered phases suggest the existence of a stable biaxial nematic phase, our recent simulation results on monodisperse systems indicate that this is not necessarily the case, even for particle shapes exactly in between prolate and oblate geometries, usually referred to as self-dual shape. Motivated by the potentially striking impact of incorporating biaxial ordering into display applicatio…
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 inst…
We use the Parsons Lee modification of Onsagers second virial theory within the restricted orientation approximation to analyse the phase behaviour of hard cylindrical rods confined in narrow pores Depending on the wall to wall separation we predict a number of distinctly different surface generated nematic phases including a biaxial planar nematic with variable number of layers a monolayer homeotropic and a hybrid T type structure For narrow pores we find evidence of two types of second order uniaxial biaxial transitions depending on the aspect ratio of the particles More specifically we obse…
Biaxial nematic ($N_B$) liquid crystals have been indicated as promising candidates for the design of next-generation displays with novel electro-optical properties and faster switching times. While at the molecular scale their existence is still under debate, experimental evidence, supported by theory and simulation, has unambiguously proved that suitable colloidal particles can indeed form $N_B$ fluids under specific conditions. While this discovery has sparked a widespread interest in the characterisation of the phase behaviour of $N_B$ liquid crystals, significantly less attention has been…
We use computer simulations to study the existence and stability of a biaxial nematic $N_b$ phase in systems of hard polyhedral cuboids, triangular prisms, and rhombic platelets, characterized by a long ($L$), medium ($M$), and short ($S$) particle axis. For all three shape families, we find stable $N_b$ states provided the shape is not only close to the so-called dual shape with $M = \sqrt{LS}$ but also sufficiently anisotropic with $L/S>9,11,14, 23$ for rhombi, prisms, and cuboids, respectively, corresponding to anisotropies not considered before. Surprisingly, a direct isotropic-$N_b$ trans…
We extend our previous work on monolayers of uniaxial particles [J. Chem. Phys. 140, 204906 (2014)] to study the effect of particle biaxiality on the phase behavior of liquid-crystal monolayers. Particles are modelled as board-like hard bodies with three different edge lengths $σ_1\geqσ_2\geqσ_3$, and use is made of the restricted-orientation approximation (Zwanzig model). A density-functional formalism based on the fundamental-measure theory is used to calculate phase diagrams for a wide range of values of the largest aspect ratio ($κ_1=σ_1/σ_3\in[1,100]$). We find that particle biaxiality in…
We present a high accuracy Monte Carlo simulation study of the Isotropic - Nematic phase transition of a lattice dispersion model of biaxial liquid crystals. The NI coexistence curve terminating at the Landau critical point have been determined using multiple histogram reweighting technique. A close investigation reveals a sharp departure in the nature of the $N$-$I$ coexistence curve in temperature- biaxiality parameter phase diagram in comparison to the earlier theoretical (either mean-field or computer simulation) predictions.The coexitence curve shows a change in curvature with increasing …
