A fluid constituted of hard spherocylinders is studied using a density functional theory for non-spherical hard particles, which can be written as a function of weighted densities. This is based on an extended deconvolution of the Mayer $f$-function for arbitrarily shaped convex hard bodies in tensorial weight functions, which depend each only on the shape and orientation of a single particle. In the course of an examination of the isotropic- nematic interface at coexistence the functional is applied to anisotropic and inhomogeneous problems for the first time. We find good qualitative agreement with other theoretical predictions and also with Monte-Carlo simulations.
The scaled particle theory is developed for the description of thermodynamical properties of a mixture of hard spheres and hard spherocylinders. Analytical expressions for free energy, pressure and chemical potentials are derived. From the minimization of free energy, a nonlinear integral equation for the orientational singlet distribution function is formulated. An isotropic-nematic phase transition in this mixture is investigated from the bifurcation analysis of this equation. It is shown that with an increase of concentration of hard spheres, the total packing fraction of a mixture on phase…
We develop the scaled particle theory to describe the thermodynamic properties and orientation ordering of a binary mixture of hard spheres (HS) and hard spherocylinders (HSC) confined in a disordered porous medium. Using this theory the analytical expressions of the free energy, the pressure and the chemical potentials of HS and HSC have been derived. The improvement of obtained results is considered by introducing the Carnahan-Starling-like and Parsons-Lee-like corrections. Phase diagrams for the isotropic-nematic transition are calculated from the bifurcation analysis of the integral equati…
Orientational ordering and phase behaviour of a binary mixture of hard spheres and hard spherocylinders
我们使用$NP_nAT$系综Monte Carlo（MC）方法研究了硬球（HS）和硬球柱（HSCs）二元混合物在各向同性和非均质状态下的结构和流体相行为。该方法允许一个估计的各向同性-双相变的位置，并观察共存相之间的组合物的不对称性，与预期的增加的HSC浓度在双相。这与先前报道的MC模拟形成鲜明对比，其中使用传统的各向同性$NPT$系综。我们进一步将模拟结果与使用单流体和多流体近似扩展原始Parsons-Lee理论的两种分析理论的理论预测进行比较[Malijevskeln { \it at al} J. Chem. Phys. \textbf{129}，144504（2008）]。在单流体理论中，混合物的性质被映射到一个有效的单组分HS系统上，而在多流体理论中，混合物的组分被表示为单独的有效HS颗粒。比较结果表明，无论是一个和多流体的方法提供了一个合理的准确的定量描述的混合物，包括各向同性的HSC-HS混合物的取向顺序的程度和各向同性的-HSC-HS相边界的预测。
A generalized Van der Waals approach is developed for anisotropic fluids in disordered porous media. As the reference system a hard spherocylinder fluid in a disordered porous medium is considered and described in the framework of the scaled particle theory with the Carnahan-Starling and Parsons-Lee corrections. The attractive part of interaction is treated in the framework of the mean field approximation in which due to orientational dependence of the excluded volume of two spherocylinders, a coupling between attractive and repulsive contributions is found. We focus on spherocylinder fluids w…
Using Monte Carlo simulations, we investigate the electrical conductivity of networks of hard rods as a function of the volume fraction for two tunneling conductance models. For a simple, orientationally independent tunneling model, we observe non-monotonic behaviour of the bulk conductivity as a function of volume fraction at the isotropic-nematic transition. However, this effect is lost if one allows for anisotropic tunneling. We also compute the mesh number of the Kirchhoff network, which turns out to be a simple alternative to the computationally expensive conductivity of large systems in …
We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rate $\dotγ$. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. Considering a range of packing fractions $ϕ$ and particle asphericities $α$ at small $\dotγ$, we study the angular rotation $\dotθ_i$ and the nematic orientational ordering $…
We use numerical simulations to study the flow of athermal, frictionless, soft-core two dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rate $\dotγ$. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. We study the resulting spatial structure of the sheared system, and compute correlation functions of the velocity, the particle density, the nematic order parameter, and the particle angular velocit…
The scaled particle theory (SPT) approximation is applied for the study of the influence of a porous medium on the isotropic-nematic transition in a hard spherocylinder fluid. Two new approaches are developed in order to improve the description in the case of small lengths of spherocylinders. In one of them, the so-called SPT-CS-PL approach, the Carnahan-Starling (CS) correction is introduced to improve the description of thermodynamic properties of the fluid, while the Parsons-Lee (PL) correction is introduced to improve the orientational ordering. The second approach, the so-called SPT-PL ap…
Using overdamped Brownian dynamics simulations we investigate the isotropic-nematic (IN) transition of self-propelled rods in three spatial dimensions. For two well-known model systems (Gay-Berne potential and hard spherocylinders) we find that turning on activity moves to higher densities the phase boundary separating an isotropic phase from a (nonpolar) nematic phase. This active IN phase boundary is distinct from the boundary between isotropic and polar-cluster states previously reported in two-dimensional simulation studies and, unlike the latter, is not sensitive to the system size. We th…
Shape-tension coupling produces nematic order in an epithelium vertex model
Rudolf Peierls Centre For Theoretical Physics, University of Oxford（鲁道夫·派尔斯理论物理中心，牛津大学）；School of Science and Engineering, University of Dundee（邓迪大学科学与工程学部）；School of Life Sciences, University of Dundee（邓迪大学生命科学学部）
In equilibrium hard-rod fluids, and in effective hard-rod descriptions of anisotropic soft-particle systems, the transition from the isotropic (I) phase to the nematic phase (N) is observed above the rod aspect ratio L/D = 3.70 as predicted by Onsager. We examine the fate of this criterion in a molecular dynamics study of a system of soft repulsive spherocylinders rendered active by coupling half the particles to a heat bath at a higher temperature than that imposed on the other half. We show that the system phase separates and self-organizes into various liquid-crystalline phases that are not…
We derive a fully covariant theory of the hydrodynamics of nematic and polar active surfaces, subjected to internal and external forces and torques. We study the symmetries of polar and nematic surfaces and find that in addition to 5 different types of in-plane isotropic surfaces, polar and nematic surfaces can be classified into 5 polar, 2 pseudopolar, 5 nematic and 2 pseudonematic types of surfaces. We give examples of physical realisations of the different types of surfaces we have identified. We obtain expressions for the equilibrium tensions, moments, and external forces and torques actin…
In dense biological tissues, cell types performing different roles remain segregated by maintaining sharp interfaces. To better understand the mechanisms for such sharp compartmentalization, we study the effect of an imposed heterotypic tension at the interface between two distinct cell types in a fully 3D model for confluent tissues. We find that cells rapidly sort and self-organize to generate a tissue-scale interface between cell types, and cells adjacent to this interface exhibit signature geometric features including nematic-like ordering, bimodal facet areas, and registration, or alignme…
We report phase separation and liquid-crystal ordering induced by scalar activity in a system of Soft Repulsive Spherocylinders (SRS) of aspect ratio $L/D = 5 $. Activity was introduced by increasing the temperature of half of the SRS (labeled \textit{`hot'}) while maintaining the temperature of the other half constant at a lower value (labeled \textit{`cold'}). The difference between the two temperatures scaled by the lower temperature provides a measure of the activity. Starting from different equilibrium initial phases, we find that activity leads to segregation of the hot and cold particle…
Nematic interfaces are thin fluid films, ideally two-dimensional, endowed with an in-plane degenerate nematic order. In this letter we examine a generalisation of the classical Plateau problem to an axisymmetric nematic interface bounded by two coaxial parallel rings. The equilibrium interface shape results from the competition between surface tension, which favours the minimization of the interface area, and the nematic elasticity which instead promotes the alignment of the molecules along a common direction. We find two classes of equilibrium solutions with intrinsically uniform alignments: …
Stochastic kinetics reveal imperative role of anisotropic interfacial tension to determine morphology and evolution of nucleated droplets in nematogenic films
