Mixed spin-1/2 and spin-1 Ising model with uniaxial and biaxial single-ion anisotropy on Bethe lattice

Stability of Biaxial Nematic Phase in Model Bent-Core Systems

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…

双轴向列相及硬板状粒子流体多分散混合物中的向列-向列相分离

Biaxial nematics and nematic-nematic demixing in polydisperse mixtures of hard board-like particle fluids

本研究通过理论模拟和蒙特卡洛模拟，发现多分散性增强硬板状粒子液晶中单轴相分离并扩大双轴相稳定区，为沉降实验设计提供参考。

Enhancement by polydispersity of the biaxial nematic phase in a mixture of hard rods and plates

The phase diagram of a polydisperse mixture of uniaxial rod-like and plate-like hard parallelepipeds is determined for aspect ratios $κ=5$ and 15. All particles have equal volume and polydispersity is introduced in a highly symmetric way. The corresponding binary mixture is known to have a biaxial phase for $κ=15$, but to be unstable against demixing into two uniaxial nematics for $κ=5$. We find that the phase diagram for $κ=15$ is qualitatively similar to that of the binary mixture, regardless the amount of polydispersity, while for $κ=5$ a sufficient amount of polydispersity stabilizes the b…

Molecular simulation study of polar order in orthogonal bent core smectic liquid crystals

We explore the phase behavior and structure of orthogonal smectic liquid crystals consisting of bent-core molecules (BCMs) by means of Monte Carlo molecular simulations. A simple athermal molecular model is introduced that describes the basic features of the BCMs. Phase transitions between uniaxial and biaxial (antiferroelectric) orthogonal smectics are obtained. The results indicate the presence of local in-plane polar correlations in the uniaxial smectic phase. The macroscopic uniaxial-biaxial transformation is rationalized in terms of local polar correlations giving rise to polar domains. T…

The Isotropic-Nematic Interface with an Oblique Anchoring Condition

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…

Hierarchy of orientational phases and axial anisotropies in the gauge theoretical description of generalized nematics

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…

Phase behavior of a lattice-gas model for biaxial nematics

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-…

Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

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 …

Topological Interaction between Loop Structures in Polymer Networks and the Nonlinear Rubber Elasticity

We numerically examine the nonlinear rubber elasticity of topologically constrained polymer networks. We propose a simple and effective model based on Graessley and Pearson's topological model (GP model) for describing the topological effect. The main point is to take account of a nonequilibrium effect in the synthesis process of the polymer network. We introduce a new parameter $γ$ to describe entropic contributions from the entanglement of polymer loops, which may be determined from the structural characteristics of the sample. The model is evaluated in the light of experimental data under u…

Critical endpoint and universality class of neutron $^3P_2$ superfluids in neutron stars

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…