Using Density Functional Theory we theoretically study the orientational properties of uniform phases of hard kites -- two isosceles triangles joined by their common base. Two approximations are used: Scaled Particle Theory, and a new approach which better approximates third virial coefficients of two-dimensional hard particles. By varying some of their geometrical parameters kites can be transformed into squares, rhombuses, triangles, and also very elongated particles, even reaching the hard-needle limit. Thus a fluid of hard kites, depending on the particle shape, can stabilize isotropic, nematic, tetratic and triatic phases. Different phase diagrams are calculated, including those of rhombuses, and kites with two of their equal interior angles fixed to $90^{\circ}$, $60^{\circ}$ and $75^{\circ}$. Kites with one of their unequal angles fixed to $72^{\circ}$, which have been recently studied via Monte Carlo simulations, are also considered. We find that rhombuses and kites with two equal right angles and not too large anisometry stabilise the tetratic phase but the latter stabilize it to a much higher degree. By contrast, kites with two equal interior angles fixed to $60^{\circ}$ stabilize the triatic phase to some extent, although it is very sensitive to changes in particle geometry. Kites with the two equal interior angles fixed to $75^{\circ}$ have a phase diagram with both tetratic and triatic phases, but we show the nonexistence of a particle shape for which both phases are stable at different densities. Finally the success of the new theory in the description of orientational order in kites is shown by comparing with Monte Carlo simulations for the case where one of the unequal angles is fixed to $72^{\circ}$. These particles also present phase diagrams with stable tetratic and triatic phases.
We re-examine the ordering behavior of a one-dimensional fluid of freely rotating hard needles, where the centers of mass of the particles are restricted to a line. Analytical equations are obtained for the equation of state, order parameter and orientational correlation functions using the transfer-matrix method if some simplifying assumptions are applied for either the orientational freedom or the contact distance between two needles. The two-state Zwanzig model accounts for the orientational ordering, but it produces unphysical pressure at high densities and there is no orientational correl…
Freezing of charged colloids on square or triangular two-dimensional periodic substrates has been recently shown to realize a rich variety of orientational orders. We propose a theoretical framework to analyze the corresponding structures. A fundamental ingredient is that a non spherical charged object in an electrolyte creates a screened electrostatic potential that is anisotropic at any distance. Our approach is in excellent agreement with the known experimental and numerical results, and explains in simple terms the reentrant orientational melting observed in these so called colloidal molec…
We discuss some interesting physical features stemming from our previous analytical study of a simple model of a fluid with dipolar-like interactions of very short range in addition to the usual isotropic Baxter potential for adhesive spheres. While the isotropic part is found to rule the global structural and thermodynamical equilibrium properties of the fluid, the weaker anisotropic part gives rise to an interesting short-range local ordering of nearly spherical condensation clusters, containing short portions of chains having nose-to-tail parallel alignment which runs antiparallel to adjace…
We study orientational ordering of $2$-dimensional closely packed Janus particles by extensive Monte Carlo simulations. For smaller patch sizes the system remains in the plastic crystal phase where the rotational degrees of freedom are disordered down to the lowest temperatures. There the liquid consist of dimers and trimers of the attractive patches. For large enough patch sizes, the system exhibits a thermodynamic transition into a phase with stripe patterns of the patches breaking the three-fold rotational symmetry. Our results strongly suggests that the latter is a 2nd order phase transiti…
The concept of symmetry breaking has been a propelling force in understanding phases of matter. While rotational symmetry breaking is one of the most prevalent examples, the rich landscape of orientational orders breaking the rotational symmetries of isotropic space, i.e. $O(3)$, to a three-dimensional point group remain largely unexplored, apart from simple examples such as ferromagnetic or uniaxial nematic ordering. Here we provide an explicit construction, utilizing a recently introduced gauge theoretical framework, to address the three-dimensional point-group-symmetric orientational orders…
The combinations of particle aspect ratio and enthalpic-barrier templates that lead to translational and orientational ordering of monolayers of rectangular particles are determined using Monte Carlo simulations and density functional theory. For sufficiently high enthalpic barriers, we find that only specific combinations of particle sizes and template spacings lead to ordered arrays. The pattern multiplication factor provided by the template extends to approximately ten times the smallest dimension of the particle.
We study an experimental system of hard granular squares in two dimensions, energized by vibration. The interplay of order in the orientations and positions of anisotropic particles allows for a rich set of phases. We measure the structure and dynamics of steady states as a function of particle density. This allows us to identify a progression of phases in which a low density isotropic fluid gives way to a phase with tetratic orientational order, short-range translational correlations, and slowed rotational dynamics. In this range of density we also observe a coupling between the molecular ori…
Orientational ordering and close packing properties of quasi-one-dimensional hard Gaussian overlap particles
Institute for Applied Physics, University of Tübingen（蒂宾根大学应用物理研究所）；Physics Department, Centre for Natural Sciences, University of Pannonia（佩奇大学自然科学中心物理系）
Orientational ordering and correlations in a quasi-one-dimensional hard-dumbbell fluid
Universidad de Extremadura（埃斯特雷马杜拉大学）；University of Pannonia（潘诺尼亚大学）；Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura（埃斯特雷马杜拉大学先进科学计算研究所）
Arrangement of interacting particles on a sphere is historically a well known problem, however, ordering of particles with anisotropic interaction, such as the dipole-dipole interaction, has remained unexplored. We solve the orientational ordering of point dipoles on a sphere with fixed positional order with numerical minimization of interaction energy and analyze stable configurations depending on their symmetry and degree of ordering. We find that a macrovortex is a generic ground state, with various discrete rotational symmetries for different system sizes, while higher energy metastable st…
We examine the ordering behavior of hard plate-like particle in a very narrow slit-like pore using the Parsons-Lee density functional theory and the restricted orientation approximation. We observe that the plates are orientationally ordered and align perpendicularly (face-on) to the walls at low densities, a first order layering transition occurs between uniaxial nematic structures having n and n+1 layers at intermediate densities and even a phase transition between a monolayer with parallel (edge-on) orientational order and n layers with perpendicular one can be detected at high densities. I…
We report an experimental study of the development of orientational order in a crumpled sheet, with a particular focus on the role played by the geometry of confinement. Our experiments are performed on elastomeric sheets immersed in a fluid, so that the effects of plasticity and friction are suppressed. When the sheet is crumpled either axially or radially within a cylinder, we find that the sheet aligns with the flat or the curved wall, depending on the aspect ratio of the cylinder. Nematic correlations develop between the normals of the sheets at relatively low volume fractions and the crum…
Based on Monte Carlo (MC) computer simulations we study the structure formation of a system of magnetic nanorods. Our model particles consist of fused spheres with permanent magnetic dipole moments, as inspired by recent experiments. The resulting system behaves significantly different from a system of hard (non-magnetic) rods or magnetic rods with a single longitudinal dipole. In particular, we observe for the magnetic nanorods a significant decrease of the percolation threshold (as compared to non-magnetic rods) at low densities, and a stabilization of the high-density nematic phase. Moreove…
Self-assembly of particles with short-range attraction and long-range repulsion (SALR) interactions on a flat and on a spherical surface is compared. Molecular dynamics (MD) simulations are performed for the two systems having the same area and the density optimal for formation of stripes of particles. Structural characteristics, e.g. a cluster size distribution, a number of defects and an orientational order parameter (OP), as well as the specific heat, are obtained for a range of temperature. In both cases, the cluster size distribution becomes bimodal and elongated clusters appear at the te…
Dense assemblies of self propelled particles, also known as active or living glasses are abundantaround us, covering different length and time scales: from the cytoplasm to tissues, from bacterialbio-films to vehicular traffic jams, from Janus colloids to animal herds. Being structurally disorderedas well as strongly out of equilibrium, these systems show fascinating dynamical and mechanicalproperties. Using extensive molecular dynamics simulation and a number of different dynamicaland mechanical order parameters we differentiate three dynamical steady states in a sheared modelactive glassy sy…
The orientational order of nematic liquid crystals is traditionally studied by means of the second-rank ordering tensor $\mathbb{S}$. When this is calculated through experiments or simulations, the symmetry group of the phase is not known \emph{a-priori}, but needs to be deduced from the numerical realisation of $\mathbb{S}$, which is affected by numerical errors. There is no generally accepted procedure to perform this analysis. Here, we provide a new algorithm suited to identifying the symmetry group of the phase. As a by product, we prove that there are only five phase-symmetry classes of t…
Can a bath of isotropic but active particles promote ordering of anisotropic but passive particles? In this paper, we uncover a fluctuation-driven mechanism by which this is possible. Somewhat counter-intuitively, we show that the passive particles tend to be more ordered upon increasing the noise-strength of the active isotropic bath. We first demonstrate this in a general dynamical model for a non-conserved order parameter (model A) coupled to an active isotropic field and then concentrate on two examples, i. a collection of polar rods on a substrate in an active isotropic bath and ii. a pas…
We theoretically studied electric double layer by using the mean-field approach including the non-uniform size effect and the orientational ordering of water dipoles in electrolyte solution. Performing the minimization of the free energy, the resulting ion and water distribution functions are determined numerically in the process of solving the Poisson's equation. The effect of non-uniform ionic size and orientational ordering of water dipoles on stratification of counterions of different size in multicomponent electrolyte solution near the charged surface are presented and discussed. Spatial …
Under an electric field, chiral smectic liquid crystals transit usually to the unwound SmC* phase where the helical structure is completely unrolled. Sometimes the sample transits initially towards an intermediate polar state before the total destruction of the helix. Based on the extension of the H-T model, a theoretical study of these field-induced phase transitions was carried out. Two hypotheses of the dynamics that give rise to the appearance of the intermediate phase have been discussed. The results of a numerical analysis confirm the known experimental results; the intermediate phase ha…
We present a method of organizing incoherent motion of a colloidal suspension to produce synchronized, coherent motion. This method exploits general features of rotational response to time-dependent forcing, and it does not require interaction between the particles. We report two methods of achieving orientational alignment of an ensemble of identical colloids by means of a time-dependent, but spatially uniform forcing: a) a piecewise constant force alternating between two directions and b) a force uniformly rotating about an axis. The physical origin of the forcing may be e.g., sedimentation …
We numerically simulate the uniform athermal shearing of bidisperse, frictionless, two dimensional spherocylinders and three dimensional prolate ellipsoids. We focus on the orientational ordering of particles as an asphericity parameter $α\to 0$ and particles approach spherical. We find that the nematic order parameter $S_2$ is non-monotonic in the packing fraction $ϕ$, and that as $α\to 0$ $S_{2}$ stays finite at jamming and above. The approach to spherical particles thus appears to be singular. We also find that sheared particles continue to rotate above jamming, and that particle contacts p…
The response of a suspension under a variety of static or alternating external fields strongly depends on the equilibrium electric double layer that surrounds the colloidal particles in the suspension. The theoretical models for salt-free suspensions can be improved by incorporating non-uniform size effects and orientational ordering of water dipoles neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann approach. Our model including non-uniform size effects and orientational ordering of water dipoles seems to have quite a promising effect because the model can p…
Orientational ordering driven by mechanical distortion of soft substrates plays a major role in material transformation processes such as elastocapillarity and surface anchoring. We present a theoretical model of the orientational response of anisotropic rods deposited onto a surface of a soft, elastic substrate of finite thickness. We show that anisotropic rods exhibit a continuous isotropic-nematic phase transition, driven by orientational interactions between surface deposited rods. This interaction is mediated by the deformation of the underlying elastic substrate, and is quantified by the…
Microswimmers typically operate in complex environments. In biological systems, often diverse species are simultaneously present and interact with each other. Here, we derive a (time-dependent) particle-scale statistical description, namely a dynamical density functional theory, for such multi-species systems, extending existing works on one-component microswimmer suspensions. In particular, our theory incorporates the effect of external potentials, but also steric and hydrodynamic interactions between swimmers. For the latter, a previously introduced force-dipole-based minimal (pusher or pull…
In order to investigate the orientational ordering of molecular dipoles and the associated electronic properties, we studied the adsorption of chlorogallium phthalocyanine molecules (GaClPc, Pc=C_32N_8H_16) on Cu(111) using the X-ray standing wave technique, photoelectron spectroscopy, and quantum chemical calculations. We find that for sub-monolayer coverages on Cu(111) the majority of GaClPc molecules adsorb in a 'Cl-down' configuration by forming a covalent bond to the substrate. For bilayer coverages the XSW data indicate a co-existence of the 'Cl-down' and 'Cl-up' configuration on the sub…
We investigate the translational and rotational relaxation dynamics of a crowded two-dimensional system of monodisperse Penrose kites, in which crystallization, quasi-crystallization, and nematic ordering are suppressed, from low to high area fractions along the metastable ergodic fluid branch. First, we demonstrate a decoupling between both the translational and the rotational diffusion coefficients and the relaxation time: the diffusivities are not inversely proportional to the relaxation time, neither in the low-density normal liquid regime nor in the high-density supercooled regime. Our si…
We present the first nearly atomistic molecular dynamics study of nanorod-nanorod association in explicit solvent, showing that inter-rod forces can be dominated by microscopic factors absent in common continuum descriptions. Specifically, we find that alkane ligands on faceted CdS nanorods in n-hexane undergo a temperature-dependent order-disorder transition akin to that of self-assembled monolayers on macroscopic substrates. This collective ligand alignment organizes nearby solvent molecules, strongly influencing the statistics of rod-rod separation. The strong temperature-dependence of this…
We examine the ordering properties of rectangular hard rods with length L and diameter D at a single planar wall and between two parallel hard walls using the second-virial density functional theory. The theory is implemented in the three-state Zwanzig approximation, where only three mutually perpendicular directions are allowed for the orientations of hard rods. The effect of varying shape anisotropy is examined at L/D=10, 15 and 20. In contact with a single hard wall, the density profiles show planar ordering, damped oscillatory behavior, and wall induced surface ordering transition below th…
Recently there have been several considerations by different authors of viscosity and the Green-Kubo stress correlation function from the microscopic perspective. In most of these and earlier works the atomic level stress is the minimal element of stress. It is also possible to consider, for pairwise interaction potentials, as the minimal elements of stress, the stress tensors associated with the pairs of interacting particles. From this perspective, the atomic level stress is not the minimal stress element, but a sum of all pair stress elements in which involved a selected particle. In this p…
The effect of out-of-plane orientational freedom on the orientational ordering properties of a monolayer of hard ellipsoids is studied using Parsons-Lee scaling approach and replica exchange Monte Carlo computer simulation. Prolate and oblate ellipsoids exhibit very different ordering properties, namely, the axes of revolution of prolate particles tend to lean out, while those of oblate ones prefer to lean into the confining plane. The driving mechanism of this is that the particles try to maximize the available free area on the confining surface, which can be achieved by minimizing the cross …
Previous particle-based computer simulations have revealed a significantly more pronounced tendency of spontaneous global polar ordering in puller (contractile) microswimmer suspensions than in pusher (extensile) suspensions. We here evaluate a microscopic statistical theory to investigate the emergence of such order through a linear instability of the disordered state. For this purpose, input concerning the orientation-dependent pair-distribution function is needed, and we discuss corresponding approaches, particularly a heuristic variant of the Percus test-particle method applied to active s…
We report a hybrid mesophase consisting of magnetic nanorods confined between the non-ionic surfactant bilayers of a lamellar phase. The magnetic field-induced ordering of the nanorods was measured experimentally and modeled by a two-dimensional Onsager theory including the third virial coefficient. The nanorods are strongly confined in layers, with no orientational coupling from one layer to the next. At high volume concentration they exhibit spontaneous in-plane orientational ordering and form a stack of independent two-dimensional nematic systems. This isotropic-nematic transition is first-…
Orientational Ordering of Janus Particle Arrays as Classical Compass Spin Systems
University of Science and Technology of China（中国科学技术大学）；Shanghai Research Center for Quantum Science（上海量子科学研究中心）；CAS Center for Excellence in Quantum Information and Quantum Physics（中国科学院量子信息与量子物理卓越创新中心）；Hefei National Laboratory（合肥国家实验室）；Brandeis University（布兰迪斯大学）；Martin A. Fisher School of Physics, Brandeis University（布兰迪斯大学马丁·A·费舍尔物理学院）；University of Virginia（弗吉尼亚大学）；Department of Physics, University of Virginia（弗吉尼亚大学物理系）；Department of Mathematics, University of Virginia（弗吉尼亚大学数学系）
Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits stable isotropic, nematic, smectic A, columnar, plastic crystalline and orientationally ordered crystalline phases. As far as the dynamics is concerned, the translational density is a conserved order parameter while the orientational ordering is non-conserved. The derived phase-field-crystal model can serve for efficient numerical investigations of various none…
The nucleation kinetics of the rotator phase in hard cuboctahedra, truncated octahedra, and rhombic dodecahedra is simulated via a combination of Forward Flux Sampling and Umbrella Sampling. For comparable degree of supersaturation, the polyhedra are found to have significantly lower free-energy barriers and faster nucleation rates than hard spheres. This difference primarily stems from localized orientational ordering, which steers polyhedral particles to pack more efficiently. Orientational order hence fosters here the growth of orientationally disordered nuclei.
The plant microtubule cortical array is a striking feature of all growing plant cells. It consists of a more or less homogeneously distributed array of highly aligned microtubules connected to the inner side of the plasma membrane and oriented transversely to the cell growth axis. Here we formulate a continuum model to describe the origin of orientational order in such confined arrays of dynamical microtubules. The model is based on recent experimental observations that show that a growing cortical microtubule can interact through angle dependent collisions with pre-existing microtubules that …
We develop a classical density functional theory (DFT) for two site associating fluids in spatially uniform external fields which exhibit orientational inhomogeneities. The Helmholtz free energy functional is obtain using Wertheim's thermodynamic perturbation theory and the orientational distribution function is obtained using DFT in the canonical ensemble. It is shown that an orienting field significantly enhances association by ordering the molecules thereby reducing the entropic penalty of association. It is also shown that association enhances orientational order for fixed field strength.
We study structure and fluid-phase behaviour of a binary mixture of hard spheres (HSs) and hard spherocylinders (HSCs) in isotropic and nematic states using the $NP_nAT$ ensemble Monte Carlo (MC) method in which a normal pressure tensor component is fixed in a system confined between two hard walls. The method allows one to estimate the location of the isotropic-nematic phase transition and to observe the asymmetry in the composition between the coexisting phases, with the expected increase of the HSC concentration in the nematic phase. This is in stark contrast with the previously reported MC…
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 $…
There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases the complete translational and rotational symmetry exist, whereas in a solid phase both symmetries are broken. In intermediate phases between liquid and solid, which include liquid crystal and plastic crystal phases, only one of the two symmetries is preserved. Among the fundamental states of matter, the liquid state is most poorly understood. We argue that it is …
Two-Stage Ordering Kinetics in Binary Mixtures of Ellipsoidal Particles
Vellore Institute of Technology（维罗尔理工大学）；Jawaharlal Nehru University（贾瓦哈拉尔·尼赫鲁大学）；Indian Institute of Science Education and Research Berhampur（贝拉姆普尔印度科学教育研究所）
The triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion, introduced in [J. Pekalski, A. Ciach and N. G. Almarza, arXiv:1401.0801 [cond-mat.soft]] is studied by Monte Carlo simulation. Introduction of appropriate order parameters allowed us to construct a phase diagram, where different phases with patterns made of clusters, bubbles or stripes are thermodynamically stable. We observe, in particular, two distinct lamellar phases - the less ordered one with global orientational order and the more ordered one with both orientational and translational order. Our re…
We investigate the obstructed motion of tracer (test) particles in crowded environments by carrying simulations of two-dimensional Gaussian random walk in model fibrinogen monolayers of different orientational ordering. The fibrinogen molecules are significantly anisotropic and therefore they can form structures where orientational ordering, similar to the one observed in nematic liquid crystals, appears. The work focuses on the dependence between level of the orientational order (degree of environmental crowding) of fibrinogen molecules inside a layer and non-Fickian character of the diffusio…
