The isotropic-to-nematic transition in a two-dimensional fluid of hard needles is studied using grand canonical Monte Carlo simulations, multiple histogram reweighting, and finite size scaling. The transition is shown to be of the Kosterlitz-Thouless type, via a direct measurement of the critical exponents eta and beta, of the susceptibility and order parameter, respectively. At the transition, eta=1/4 and beta=1/8 are observed, in excellent agreement with Kosterlitz-Thouless theory. Also the shift in the chemical potential of the nematic susceptibility maximum with system size is in good agreement with theoretical expectations. Some evidence of singular behavior in the density fluctuations is observed, but no divergence, consistent with a negative specific heat critical exponent. At the transition, a scaling analysis assuming a conventional critical point also gives reasonable results. However, the apparent critical exponent beta_eff obtained in this case is not consistent with theoretical predictions.
We perform extensive Monte Carlo simulations of a two-dimensional bent hard-needle model in both its chiral zig-zag and its achiral bow-shape configurations and present their phase diagrams. We find evidence for a variety of stable phases: isotropic, quasi-nematic, smectic-C, anti-ferromorphic smectic-A, and modulated-nematic. This last phase consists of layers formed by supramolecular arches. They create a periodic modulation of the molecular polarity whose period is sensitively controlled by molecular geometry. We identify transition densities using correlation functions together with approp…
We propose a lattice model to simulate the influence of porous medium on the Nematic - Isotropic transition of liquid crystal confined to the pores. The effects of pore size and pore connectivity are modelled through a disorder parameter. Monte Carlo calculations based on the model leads to results that compare well with experiments.
We have employed the Density Functional Theory formalism to investigate the nematic-isotropic capillary transitions of a nematogen confined by walls that favor antagonist orientations to the liquid crystal molecules (hybrid cell). We analyse the behavior of the capillary transition as a function of the fluid-substrate interactions and the pore width. In addition to the usual capillary transition between isotropic-like to nematic-like states, we find that this transition can be suppressed when one substrate is wet by the isotropic phase and the other by the nematic phase. Under this condition t…
A system of hard rectangles of size $m\times mk$ on a square lattice undergoes three entropy driven phase transitions with increasing density for large enough aspect ratio $k$: first from a low density isotropic to an intermediate density nematic phase, second from the nematic to a columnar phase, and third from the columnar to a high density sublattice phase. In this paper we show, from extensive Monte Carlo simulations of systems with $m=1,2$ and $3$, that the transition density for the isotropic-nematic transition is $\approx A_1/k$ when $k \gg 1$, where $A_1$ is independent of $m$. We esti…
The nematic-to-isotropic orientational phase transition, or equivalently the $RP^2$ model, is considered in two dimensions and the question of the nature of the phase transition is addressed. Using powerful conformal techniques adapted to the investigation of critical properties of two-dimensional scale-invariant systems, we report strong evidences for a transition governed by topological defects analogous to the Berezinskii-Kosterlitz-Thouless transition in two-dimensional XY model.
Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior and universality for the isotropic-nematic phase transition in a system of long straight rigid rods of length $k$ ($k$-mers) on two-dimensional lattices. The nematic phase, characterized by a big domain of parallel $k$-mers, is separated from the isotropic state by a continuous transition occurring at a finite density. The determination of the critical exponents, along with the behavior of Binder cumulants, indicate that the transition belongs to the 2D Ising universality class for squ…
Monte Carlo simulations have been carried out for a system of monomers on square lattices that, by decreasing temperature or increasing density, polymerize reversibly into chains with two allowed directions and, at the same time, undergo a continuous isotropic-nematic (I-N) transition. The results show that the self-assembly process affects the nature of the transition. Thus, the determination of the critical exponents indicates that the universality class of the I-N transition changes from two-dimensional Ising-type for monodisperse rods without self-assembly to q=1 Potts-type for self-assemb…
Computer simulations are presented of the isotropic-to-nematic transition in a liquid crystal confined between two parallel plates a distance H apart. The plates are neutral and do not impose any anchoring on the particles. Depending on the shape of the pair potential acting between the particles, we find that the transition either changes from first-order to continuous at a critical film thickness H=Hx, or that the transition remains first-order irrespective of H. This demonstrates that the isotropic-to-nematic transition in confined geometry is not characterized by any universality class, bu…
We present simulation data of first-order isotropic-to-nematic transitions in lattice models of liquid crystals and locate the thermodynamic limit inverse transition temperature $ε_\infty$ via finite-size scaling. We observe that the inverse temperature of the specific heat maximum can be consistently extrapolated to $ε_\infty$ assuming the usual $α/ L^d$ dependence, with $L$ the system size, $d$ the lattice dimension and proportionality constant $α$. We also investigate the quantity $ε_{L,k}$, the finite-size inverse temperature where $k$ is the ratio of weights of the isotropic to nematic ph…
We present Monte Carlo simulation results of the two-dimensional Zwanzig fluid, which consists of hard line segments which may orient either horizontally or vertically. At a certain critical fugacity, we observe a phase transition with a two-dimensional Ising critical point. Above the transition point, the system is in an ordered state, with the majority of particles being either horizontally or vertically aligned. In contrast to previous work, we identify the transition as being of the liquid-gas type, as opposed to isotropic-to-nematic. This interpretation naturally accounts for the observed…
We develop a free energy functional for an inhomogeneous system that contains both symmetry conserved and symmetry broken parts of the direct pair correlation function. These correlation functions are found by solving the Ornstein- Zernike equation with the Percus-Yevick closure relation. The method developed here gives the pair correlation functions in the ordered phase with features that agree well with the results found by computer simulations. The theory predicts accurately the isotropic-nematic transition in a system of anisotropic molecules and can easily be extended to study other order…
In liquid-crystalline elastomers, the nematic order parameter and the induced strain vary smoothly across the isotropic-nematic transition, without the expected first-order discontinuity. To investigate this smooth variation, we measure the strain as a function of temperature over a range of applied stress, for elastomers crosslinked in the nematic and isotropic phases, and analyze the results using a variation on Landau theory. This analysis shows that the smooth variation arises from quenched disorder in the elastomer, combined with the effects of applied stress and internal stress.
The isotropic-nematic phase behavior of length polydisperse hard rods with arbitrary length distributions is calculated. Within a numerical treatment of the polydisperse Onsager model using the Gaussian trial function Ansatz we determine the onset of isotropic-nematic phase separation, coming from a dilute isotropic phase and a dense nematic phase. We focus on parent systems whose lengths can be described by either a Schulz or a `fat-tailed' log-normal distribution with appropriate lower and upper cutoff lengths. In both cases, very strong fractionation effects are observed for parent polydisp…
We consider the effects of polydispersity on isotropic-nematic phase equilibria in thermotropic liquid crystals, using a Maier-Saupe theory with factorized interactions. A sufficient spread (approx. 50%) in the interaction strengths of the particles leads to phase separation into two or more nematic phases, which can in addition coexist with an isotropic phase. The isotropic-nematic coexistence region widens dramatically as polydispersity is increased, leading to re-entrant isotropic-nematic phase separation in some regions of the phase diagram. We show that similar phenomena will occur also f…
We present the first calculations of the pressure tensor profile in the vicinity of the planar interface between isotropic liquid and nematic liquid crystal, using Onsager's density functional theory and computer simulation. When the liquid crystal director is aligned parallel to the interface, the situation of lowest free energy, there is a large tension on the nematic side of the interface and a small compressive region on the isotropic side. By contrast, for perpendicular alignment, the tension is on the isotropic side. There is excellent agreement between theory and simulation both in the …
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…
We study the phase behaviour of hard rods with length polydispersity, treated within a simplified version of the Onsager model. We give a detailed description of the unusual phase behaviour of the system when the rod length distribution has a "fat" (e.g. log-normal) tail up to some finite cutoff. The relatively large number of long rods in the system strongly influences the phase behaviour: the isotropic cloud curve, which defines the where a nematic phase first occurs as density is increased, exhibits a kink; at this point the properties of the coexisting nematic shadow phase change discontin…
We revisit the classic problem of the structure of the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory, refining previous analytic treatments of biaxiality at the interface. We compare our analysis with numerical results obtained through a highly accurate spectral collocation scheme for the solution of the Landau-Ginzburg-de Gennes equations. In comparison to earlier work, we obtain improved agreement with numerics for both the uniaxial and biaxial profiles, accurate asymptotic results for the decay of biaxial order on both nematic and isotropic sides of the interface and a…
We introduce a density-functional formalism based on the Parsons-Lee and the generalized van der Waals theories in order to describe the thermodynamics of anisotropic particle systems with steric interactions. For ellipsoids of revolution, the orientational distribution function is obtained by minimizing the free energy functional and the equations of state are determined. The system exhibits a nematic-isotropic discontinuous transition, characterized by a phase separation between nematic and isotropic phases at finite as well low packing fractions. The model presents a phase behavior which is…
We predict the possible existence of a new phase of liquid crystals near the nematic-isotropic ($ NI $) transition. This phase is an achiral, tilt-analogue of the blue phase and is composed of a lattice of {\em double-tilt}, escape-configuration cylinders. We discuss the structure and the stability of this phase and provide an estimate of the lattice parameter.
The focus of our work is to identify conditions for the presence of an isotropic-nematic phase transition in the context of a generic system with isotropic competing interactions. The comment 0709.4205 criticizes our results by showing that the low temperature fluctuations of a stripe phase in 2d diverge linearly in the thermodynamic limit. The analysis is restricted to the stripe phase and does not apply to the central result of our letter. We show, contrary to what is suggested in the comment, that the model introduced by D. G. Barci and D. A. Stariolo in PRL98, 200604 (2007) undergoes an is…
Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse percolation of straight rigid rods on triangular lattices. In the case of standard (inverse) percolation, the lattice is initially empty(occupied) and linear $k$-mers ($k$ linear consecutive sites) are randomly and sequentially deposited on(removed from) the lattice, considering an isotropic and nematic scheme. The study is conducted by following the behavior of four critical concentrations with the size $k$, determined for a wide range of $k$ : $(i)$[$(ii)$] standard isotropic[nematic] p…
A Landau theory is constructed for the vulcanization transition in cross-linked polymer systems with spontaneous nematic ordering. The neo-classical theory of the elasticity of nematic elastomers is derived via the minimization of this Landau free energy; this neo-classical theory contains the classical theory of rubber elasticity as its isotropic limit. Our work not only reveals the statistical-mechanical roots of these elasticity theories, but also demonstrates that they are applicable to a wide class of random solids. It also constitutes a starting-point for the investigation of sample-to-s…
When captured by a flat nematic-isotropic interface, colloidal particles can be dragged by it. As a result spatially periodic structures may appear, with the period depending on a particle mass, size, and interface velocity~\cite{west.jl:2002}. If liquid crystal is sandwiched between two substrates, the interface takes a wedge-like shape, accommodating the interface-substrate contact angle and minimizing the director distortions on its nematic side. Correspondingly, particles move along complex trajectories: they are first captured by the interface and then `glide' towards its vertex point. Ou…
By computer simulations of systems of ellipsoids, we study the influence of the isotropic/nematic phase transition on the direct correlation functions (DCF) in anisotropic fluids. The DCF is determined from the pair distribution function by solving the full Ornstein-Zernike equation, without any approximations. Using a suitable molecular-fixed reference frame, we can distinguish between two qualitatively different contributions to the DCF: One which preserves rotational invariance, and one which breaks it and vanishes in the isotropic phase. We find that the symmetry preserving contribution is…
Dynamical heterogeneity in a system of Gay-Berne ellipsoids near its isotropic-nematic (I-N) transition and also in an equimolar mixture of Lennard-Jones spheres and Gay-Berne ellipsoids in deeply supercooled regime is probed by the time evolution of non-Gaussian parameter (NGP). The appearance of a dominant second peak in the rotational NGP near the I-N transition signals the growth of pseudonematic domains. Surprisingly such a second peak is instead observed in the translational NGP for glassy binary mixture. Localization of orientational motion near the I-N transition is found to be respons…
We present large-scale molecular dynamics simulations of a nematic-isotropic interface in a system of repulsive ellipsoidal molecules, focusing in particular on the capillary wave fluctuations of the interfacial position. The interface anchors the nematic phase in a planar way, i.e., the director aligns parallel to the interface. Capillary waves in the direction parallel and perpendicular to the director are considered separately. We find that the spectrum is anisotropic, the amplitudes of capillary waves being larger in the direction perpendicular to the director. In the long wavelength limit…
When liquid-crystalline elastomers pass through the isotropic-nematic transition, the orientational order parameter and the elastic strain vary rapidly but smoothly, without the expected first-order discontinuity. This broadening of the phase transition is an important issue for applications of liquid-crystalline elastomers as actuators or artificial muscles. To understand this behavior, we develop a lattice model of liquid-crystalline elastomers, with local directors coupled to a global strain variable. In this model, we can consider either random-bond disorder (representing chemical heteroge…
In a recent PRL Barci and Stariolo (BS) generalized the well known Brazovskii model to include an additional rotationally invariant quartic interaction and study this model in two dimensions (2d). Depending on the parameters of the model, BS find two transitions: a first order isotropic-lamellar (striped) or a second order isotropic-nematic (which they speculate to be in the Kosterlitz-Thouless universality class). Using a simple symmetry argument, I show that the striped phase found by BS can not exist in 2d. Furthermore, I argue that based on the coarse-grained action used by BS it is imposs…
Wang and Landau proposed recently, a simple and flexible non-Boltzmann Monte Carlo method for estimating the density of states, from which the macroscopic properties of a closed system can be calculated. They demonstrated their algorithm by cocontinuous energy spectrum. We propose in this paper modifications nsidering systems with discrete energy spectrum. We find that the Wang-Landau algorithm does not perform well when the system has continuous energy spectrum. We propose in this paper modifications to the algorithm and demonstrate their performance on a lattice model of liquid crystalline s…
We discuss 2D systems with Ising symmetry and competing interactions at different scales. In the framework of the Renormalization Group, we study the effect of relevant quartic interactions. In addition to the usual constant interaction term, we analyze the effect of quadrupole interactions in the self consistent Hartree approximation. We show that in the case of repulsive quadrupole interaction, there is a first order phase transition to a stripe phase in agreement with the well known Brazovskii result. However, in the case of attractive quadrupole interactions there is an isotropic-nematic s…
By means of a molecular model, we examine hybrid nematic films with antagonistic anchoring angles where one of the surfaces is in the strong anchoring regime. If anchoring at the other surface is weak, and in the absence of wetting by the isotropic phase, the anchoring transition may interact with the capillary isotropic-nematic transition in interesting ways. For general anchoring conditions on this surface we confirm the existence of the step-tilt, biaxial phase and the associated transition to the linear, constant-tilt-rotation, configuration. The step-like phase is connected with the bulk …
We use numerical simulations to investigate the hydrodynamic behavior of the interface between nematic (N) and isotropic (I) phases of a confined active liquid crystal. At low activities, a stable interface with constant shape and velocity is observed separating the two phases. For nematics in homeotropic channels, the velocity of the interface at the NI transition increases from zero (i) linearly with the activity for contractile systems and (ii) quadratically for extensile ones. Interestingly, the nematic phase expands for contractile systems while it contracts for extensile ones, as a resul…
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…
Scaled particle theory for a binary mixture of hard discorectangles and for a binary mixture of hard rectangles is used to predict possible liquid-crystal demixing scenarios in two dimensions. Through a bifurcation analysis from the isotropic phase, it is shown that isotropic-nematic demixing is possible in two-dimensional liquid-crystal mixtures composed of hard convex bodies. This bifurcation analysis is tested against exact calculations of the phase diagrams in the framework of the restricted-orientation two-dimensional model (Zwanzig model). Phase diagrams of a binary mixture of hard disco…
We studied the dynamics of isotropic-nematic transitions in liquid crystalline polymers by integrating time-dependent Ginzburg-Landau equations. In a concentrated solution of rodlike polymers, the rotational diffusion constant Dr of the polymer is severely suppressed by the geometrical constraints of the surrounding polymers, so that the rodlike molecules diffuse only along their rod directions. In the early stage of phase transition, the rodlike polymers with nearly parallel orientations assemble to form a nematic polydomain. This polydomain pattern with characteristic length l, grows with se…
The elastic interactions between objects embedded in a nematic liquid crystal are usually caused by the average distorsion-rather than by the fluctuations-of the nematic orientational field. We argue that for sufficiently small particles, the nematic-mediated interaction originates purely from the fluctuations of the nematic director. This Casimir interaction decays as d^(-6), d being the distance between the particles, and it dominates van der Waals interactions close to the isotropic-to-nematic transition. Considering the nematic as a polymer solvent, we show that the onset of this Casimir i…
Density functional theory is used to study colloidal hard-rod fluids near an individual right-angled wedge or edge as well as near a hard wall which is periodically patterned with rectangular barriers. The Zwanzig model, in which the orientations of the rods are restricted to three orthogonal orientations but their positions can vary continuously, is analyzed by numerical minimization of the grand potential. Density and orientational order profiles, excess adsorptions, as well as surface and line tensions are determined. The calculations exhibit an enrichment [depletion] of rods lying parallel…
A theory of thermotropic nematic liquid crystals in which molecules form internally ordered clusters is presented. The formulation is based on the same mean field approximation and form of the anisotropic potential used in the Maier-Saupe theory. A uniaxial nematic and two macroscopically isotropic phases are predicted. One of the isotropic phases consists of thermodynamically stable clusters with internal orientational order. The nematic phase shows cybotactic order throughout its range of stability. This order persists above the transition temperature, either as a stable feature or as a pret…
Polyhedral nematics are examples of exotic orientational phases that possess a complex internal symmetry, representing highly non-trivial ways of rotational symmetry breaking, and are subject to current experimental pursuits in colloidal and molecular systems. The classification of these phases has been known for a long time, however, their transitions to the disordered isotropic liquid phase remain largely unexplored, except for a few symmetries. In this work, we utilize a recently introduced non-Abelian gauge theory to explore the nature of the underlying nematic-isotropic transition for all…
We investigate the behavior of disclination loops in the vicinity of the first order nematic-isotropic transition in the Lebwohl-Lasher and related models. We find that two independent measures of the transition temperature, the free energy and the distribution of disclination line segments, give essentially identical values. We also calculate the distribution function D(p) of disclination loops of perimeter p and fit it to a quasiexponential form. Below the transition, D(p) falls off exponentially, while in the neighborhood of the transition it decays with a power law exponent approximately e…
We have used the density functional theory to study the effect of molecular elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A phase transitions of a fluid of molecules interacting via the Gay-Berne intermolecular potential. We have considered a range of length-to-width parameter $3.0\leq x_0\leq 4.0$ in steps of 0.2 at different densities and temperatures. Pair correlation functions needed as input information in density functional theory are calculated using the Percus-Yevick integral equation theory. Within the small range of elongation, the phase diagram shows s…
Polydispersity is believed to have important effects on the formation of liquid crystal phases in suspensions of rod-like particles. To understand such effects, we analyse the phase behaviour of thin hard rods with length polydispersity. Our treatment is based on a simplified Onsager theory, obtained by truncating the series expansion of the angular dependence of the excluded volume. We describe the model and give the full phase equilibrium equations; these are then solved numerically using the moment free energy method which reduces the problem from one with an infinite number of conserved de…
We examine dense self-gravitating stellar systems dominated by a central potential, such as nuclear star clusters hosting a central supermassive black hole. Different dynamical properties of these systems evolve on vastly different timescales. In particular, the orbital-plane orientations are typically driven into internal thermodynamic equilibrium by vector resonant relaxation before the orbital eccentricities or semimajor axes relax. We show that the statistical mechanics of such systems exhibit a striking resemblance to liquid crystals, with analogous ordered-nematic and disordered-isotropi…
High-resolution ac-calorimetry has been carried out on dispersions of aerosils in the liquid crystal octyloxycyanobiphenyl (8OCB) as a function of aerosil concentration and temperature spanning the crystal to isotropic phases. The liquid-crystal 8OCB is elastically stiffer than the previously well studied octylcyanobiphenyl (8CB)+aerosil system and so, general quenched random disorder effects and liquid-crystal specific effects can be distinguished. A double heat capacity feature is observed at the isotropic to nematic phase transition with an aerosil independent overlap of the heat capacity w…
We analyse the effect of a continuous spread of particle lengths on the phase behavior of rodlike particles, using the Onsager theory of hard rods. Our aim is to establish whether ``unusual'' effects such as isotropic-nematic-nematic (I-N-N) phase separation can occur even for length distributions with a single peak. We focus on the onset of I-N coexistence. For a log-normal distribution we find that a finite upper cutoff on rod lengths is required to make this problem well-posed. The cloud curve, which tracks the density at the onset of I-N coexistence as a function of the width of the length…
We study the statistical properties of orientation and rotation dynamics of elliptical tracer particles in two-dimensional, homogeneous and isotropic turbulence by direct numerical simulations. We consider both the cases in which the turbulent flow is generated by forcing at large and intermediate length scales. We show that the two cases are qualitatively different. For large-scale forcing, the spatial distribution of particle orientations forms large-scale structures, which are absent for intermediate-scale forcing. The alignment with the local directions of the flow is much weaker in the la…
We introduce a model for a fluid of polydisperse rounded hard rectangles where the length and width of the rectangular core are fixed, while the roundness is taken into account by the convex envelope of a disk displaced along the perimeter of the core. The diameter of the disk has a continuous polydispersity described by a Schultz distribution function. We implemented the scaled particle theory for this model with the aim to studying: (i) the effect of roundness on the phase behavior of the one-component hard-rectangle fluid, and (ii) how polydispersity affects phase transitions between isotro…
We construct a phenomenological Landau-de Gennes theory for hard colloidal rods by performing an order parameter expansion of the chemical-potential dependent grand potential. By fitting the coefficients to known results of Onsager theory, we are not only able to describe the isotropic-nematic phase transition as function of density, including the well-known density jump, but also the isotropic-nematic planar interface. The resulting theory is applied in calculations of the isotropic core size in a radial hedgehog defect, the density dependence of linear defects of hard rods in square confinem…
We introduce a minimal model for a collection of self-propelled apolar active particles, also called as `active nematic', on a two-dimensional substrate and study the order-disorder transition with the variation of density. The particles interact with their neighbours within the framework of the Lebwohl-Lasher model and move asymmetrically, along their orientation, to unoccupied nearest neighbour lattice sites. At a density lower than the equilibrium isotropic-nematic transition density, the active nematic shows a first order transition from the isotropic state to a banded state. The banded st…
