We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rod-like and disc-like molecules. A quenched distribution of shapes leads to the existence of a stable biaxial nematic phase, in qualitative agreement with experimental findings for some ternary lyotropic liquid mixtures. An annealed distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times, to show that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure.
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…
Inspired by the observations of a remarkably stable biaxial nematic phase [E.v.d. Pol et al., Phys. Rev. Lett. 103, 258301 (2009)], we investigate the effect of size polydispersity on the phase behavior of a suspension of boardlike particles. By means of Onsager theory within the restricted orientation (Zwanzig) model we show that polydispersity induces a novel topology in the phase diagram, with two Landau tetracritical points in between which oblate uniaxial nematic order is favored over the expected prolate order. Additionally, this phenomenon causes the opening of a huge stable biaxiality …
Monte Carlo simulation performed on a lattice system of biaxial molecules possessing $D_{2h}$ symmetry and interacting with a second rank anisotropic dispersion potential yields three distinct macroscopic phases depending on the biaxiality of the constituent molecules. The phase diagram of such a system as a function of molecular biaxiality is greatly modified when a transverse dipole is considered to be associated with each molecule so that the symmetry is reduced to $C_{2v}$. Our results indicate the splitting of the Landau point i.e. the point in the phase diagram where a direct transition …
With the aim of investigating the stability conditions of biaxial nematic liquid crystals, we study the effect of adding a non-adsorbing ideal depletant on the phase behavior of colloidal hard boardlike particles. We take into account the presence of the depletant by introducing an effective depletion attraction between a pair of boardlike particles. At fixed depletant fugacity, the stable liquid crystal phase is determined through a mean-field theory with restricted orientations. Interestingly, we predict that for slightly elongated boardlike particles a critical depletant density exists, whe…
We analyze the global phase diagram of a Maier-Saupe lattice model with the inclusion of disorder degrees of freedom to mimic a mixture of oblate and prolate molecules (discs and cylinders). In the neighborhood of a Landau multicritical point, solutions of the statistical problem can be written as a Landau-de Gennes expansion for the free energy. If the disorder degrees of freedom are quenched, we confirm the existence of a biaxial nematic strucure. If orientational and disorder degrees of freedom are allowed to thermalize, this biaxial solution becomes thermodynamically unstable. Also, we use…
The possible symmetries of the biaxial nematic phase are examined against the implications of the presently available experimental results. Contrary to the widespread notion that biaxial nematics have orthorhombic symmetry, our study shows that a monoclinic ($C_{2h}$) symmetry is more likely to be the case for the recently observed phase biaxiality in thermotropic bent-core and calamitc tetrapode nematic systems. The methodology for differentiating between the possible symmetries of the biaxial nematic phase by NMR and by IR spectroscopy measurements is presented in detail. The manifestations …
We use density-functional theory, of the fundamental-measure type, to study the relative stability of the biaxial nematic phase, with respect to non-uniform phases such as smectic and columnar, in fluids made of hard board-like particles with sizes $σ_1>σ_2>σ_3$. A restricted-orientation (Zwanzig) approximation is adopted. Varying the ratio $κ_1=σ_1/σ_2$ while keeping $κ_2=σ_2/σ_3$, we predict phase diagrams for various values of $κ_2$ which include all the uniform phases: isotropic, uniaxial rod- and plate-like nematics, and biaxial nematic. In addition, spinodal instabilities of the uniform …
We study the symmetry and the spatial uniformity of orientational order of the biaxial nematic phase in the light of recent experimental observations of phase biaxiality in thermotropic bent-core and calamitic-tetramer nematics. We present evidence supporting monoclinic symmetry, instead of the usually assumed orthorhombic. We describe the use of deuterium NMR to differentiate between the possible symmetries. We present the spatial aspects of biaxial order in the context of the cluster model, wherein macroscopic biaxiality can result from the field-induced alignment of biaxial and possibly pol…
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 study a class of models for \sbentcore molecules using low density version of Local Density Functional Theory. Arms of the molecules are modeled using two- and three Gay-Berne (GB) interacting units of uniaxial and biaxial symmetry. Dipole-dipole interactions are taken into account by placing a dipole moment along the ${\mathcal{C}}_2$symmetry axis of the molecule. The main aim of the study is to identify molecular factors that can help stabilizing the biaxial nematic phase. The phase diagrams involving isotropic ($I$), uniaxial ($N_U$) and biaxial ($N_B$) nematic phases are determined at g…
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 introduce shape fluctuations in a liquid-crystalline system by considering an elementary Maier--Saupe lattice model for a mixture of uniaxial and biaxial molecules. Shape variables are treated in the annealed (thermalized) limit. We analyze the thermodynamic properties of this system in terms of temperature $T$, concentration $c$ of intrinsically biaxial molecules, and a parameter $Δ$ associated with the degree of biaxiality of the molecules. At the mean-field level, we use standard techniques of statistical mechanics to draw global phase diagrams, which are shown to display a rich structur…
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 are the uniaxial and biaxial nematics. Generalizing the familiar uniaxial and biaxial nematics to phases characterized by an arbitrary point group symmetry, referred to as \emph{generalized n…
We present numerical and analytic results for uniaxial and biaxial order at the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory. We study the case where an oblique anchoring condition is imposed asymptotically on the nematic side of the interface, reproducing results of previous work when this condition reduces to planar or homoeotropic anchoring. We construct physically motivated and computationally flexible variational profiles for uniaxial and biaxial order, comparing our variational results to numerical results obtained from a minimization of the Ginzburg-Landau-de Genn…
We give a criterion to test a non-biaxial behavior of infinitely thin hard platelets of $D_{2h}$ symmetry based upon the components of three order parameter tensors. We investigated the nematic behavior of monodisperse infinitely thin rectangular hard platelet systems by using the criterion. Starting with a square platelet system, and we compared it with rectangular platelet systems of various aspect ratios. For each system, we performed equilibration runs by using isobaric Monte Carlo simulations. Each system did not show a biaxial nematic behavior but a uniaxial nematic one, despite of the s…
Orientational and positional ordering properties of liquid crystal monolayers are examined by means of Fundamental-Measure Density Functional Theory. Particles forming the monolayer are modeled as hard parallelepipeds of square section of size $σ$ and length $L$. The particle centers of mass are restricted to a flat surface and three possible and mutually perpendicular orientations (in-plane and along the layer normal) of their uniaxial axes are allowed. We find that the structure of the monolayer depends strongly on particle shape and density. In the case of rod-like shapes, particles align a…
We study the effect of flexibility and bend angle on systems of hard semiflexible boomerangs. These are modelled as two rodlike segments joined at one end with an angle that can fluctuate about a preferred angle. We use a second-virial theory for semiflexible chains with two segments, and numerically solve for the full orientation distribution function as a function of the four angles that determine the boomerang's orientation. We plot the single segment distributions as a function of two angles as well as the interarm angle distribution. For stiff boomerangs, we find prolate, oblate, and biax…
We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of …
We perform statistical mechanics calculations to analyze the global phase diagram of a fully-connected version of a Maier-Saupe-Zwanzig lattice model with the inclusion of couplings to an elastic strain field. We point out the presence of uniaxial and biaxial nematic structures, depending on temperature $T$ and on the applied stress $σ$. Under uniaxial extensive tension, applied stress favors uniaxial orientation, and we obtain a first-order boundary, along which there is a coexistence of two uniaxial paranematic phases, and which ends at a simple critical point. Under uniaxial compressive ten…
The rich mesophase polymorhism and the phase sequence of board-like colloids depends critically on their shape anisometry. Implementing extensive Monte Carlo simulations, we calculated the full phase diagram of sterically interacting board-like particles, for a range of experimentally accessible molecular dimensions/anisometries of colloids of this shape. A variety of self organized mesophases including uniaxial and biaxial nematics, smectic, cubatic and columnar phases have been identified. Our results demonstrate clearly that the molecular anisometry influences critically not only the struct…
Topological defects and the short-distance behavior of the structure factor in nematic liquid crystals
从理论上研究了含有拓扑缺陷的双折射系统中波矢幅值k较大的光的光的散射。在大k时，结构因子S（k）主要由幂律贡献所支配，幂律贡献来自与拓扑缺陷相关的奇异序参数变化和指向矢的横向热涨落。这些缺陷（双向错和刺猬）导致形式为rho A k^{-xi}（"Porod尾“）的贡献，其中rho是给定类型缺陷的数密度，A是无量纲Porod振幅，xi是整数值Porod指数。的Porod振幅和指数计算的所有类型的拓扑稳定的缺陷发生在单轴和双轴向列在两个或三个空间维度。的范围内的波矢量的散射强度的贡献，由于缺陷占主导地位的贡献，由于热波动的估计，它的结论是，对于实验上可访问的缺陷密度的范围内的可观测性的Porod尾部扩展超过一个到三十年的散射波矢量的大小k。分析了现有的单轴向列相序实验结果，并提出了我们的研究结果的应用程序的光散射研究的其他系统包含大量的缺陷。
We study the thermodynamics and critical behavior of neutron $^3P_2$ superfluids in the inner cores of neutron stars. $^3P_2$ superfluids offer a rich phase diagram including uniaxial/biaxial nematic phases, the ferromagnetic phase, and the cyclic phase. Using the Bogoliubov-de Gennes (BdG) equation as superfluid Fermi liquid theory, we show that a strong (weak) magnetic field drives the first (second) order transition from the dihedral-two biaxial nematic phase to dihedral-four biaxial nematic phase in low (high) temperatures, and their phase boundaries are divided by the critical endpoint (C…
