Monte Carlo simulations of spherocylinders interacting with site-dependent square-well potentials

Monte Carlo simulations are performed to study the self-assembly of a dilute system of spherocylinders interacting with square-well potential. The interactions are defined between randomly placed sites on the axis of the spherocylinder, akin to the interacting groups on a rigid rodlike molecule. This model therefore also serves as a minimal coarse-grained representation of a system of low molecular weight or stiff polymers with contour lengths significantly lower than the persistence length, interacting predominantly with short-range interactions (e.g., hydrogen bonding). The spherocylinder concentration, square-well interaction strength and range, and fraction of interacting sites are varied to study the phase behavior of the system. We observe the formation of dispersed, bundled, and network configurations of the system that may be compared with previous atomistic simulation results of weak polyelectrolytes.

Elastic response of colloidal smectic liquid crystals: Insights from microscopic theory

Elongated colloidal rods at sufficient packing conditions are known to form stable lamellar or smectic phases. Using a simplified volume-exclusion model, we propose a generic equation of state for hard-rod smectics that is robust against simulation results and is independent of the rod aspect ratio. We then extend our theory by exploring the elastic properties of a hard-rod smectic, including the layer compressibility (B) and bending modulus (K_{1}). By introducing weak backbone flexibility we are able to compare our predictions with experimental results on smectics of filamentous virus rods (fd) and find quantitative agreement between the smectic layer spacing, the out-of-plane fluctuation strength, as well as the smectic penetration length λ=sqrt[K_{1}/B]. We demonstrate that the layer bending modulus is dominated by director splay and depends sensitively on lamellar out-of-plane fluctuations that we account for on the single-rod level. We find that the ratio between the smectic penetration length and the lamellar spacing is about two orders of magnitude smaller than typical values reported for thermotropic smectics. We attribute this to the fact that colloidal smectics are considerably softer in terms of layer compression than their thermotropic counterparts while the cost of layer bending is of comparable magnitude.

A Monte Carlo approach to study the effect of ions on the nucleation of sulfuric acid-water clusters

The nucleation of sulfuric acid-water clusters is a significant contribution to the formation of aerosols as precursors of cloud condensation nuclei (CCN). Depending on the temperature, there is an interplay between the clustering of particles and their evaporation controlling the efficiency of cluster growth. For typical temperatures in the atmosphere, the evaporation of H 2 SO 4  H 2 O clusters is more efficient than the clustering of the first, small clusters, and thus their growth is dampened at its early stages. Since the evaporation rates of small clusters containing an HSO 4 - $$ {\mathrm{HSO}}_4^{-} $$ ion are much smaller than for purely neutral sulfuric acid clusters, they can serve as a central body for the further attachment of H 2 SO 4  H 2 O molecules. We here present an innovative Monte Carlo model to study the growth of aqueous sulfuric acid clusters around central ions. Unlike classical thermodynamic nucleation theory or kinetic models, this model allows to trace individual particles and thus to determine properties for each individual particle. As a benchmarking case, we have performed simulations at T = 300 K $$ T=300\kern0.5em \mathrm{K} $$ a relative humidity of 50% with dipole and ion concentrations of c dipole = 5 × 10 8 - 10 9 cm - 3 $$ {c}_{dipole}=5\kern0.5em \times \kern0.5em {10}^8-{10}^9\kern0.5em {\mathrm{cm}}^{-3} $$ and c ion = 0 - 10 7 cm - 3 $$ {c}_{ion}=0-{10}^7\kern0.5em {\mathrm{cm}}^{-3} $$ . We discuss the runtime of our simulations and present the velocity distribution of ionic clusters, the size distribution of the clusters as well as the formation rate of clusters with radii R ≥ 0.85 nm $$ R\ge 0.85\kern0.5em \mathrm{nm} $$ . Simulations give reasonable velocity and size distributions and there is a good agreement of the formation rates with previous results, including the relevance of ions for the initial growth of sulfuric acid-water clusters. Conclusively, we present a computational method which allows studying detailed particle properties during the growth of aerosols as a precursor of CCN.

Two-temperature activity induces liquid-crystal phases inaccessible in equilibrium

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 observed in equilibrium for the respective aspect ratios. In particular, we find a nematic phase for L/D=3 and a smectic phase for L/D=2 above a critical activity.

Hidden scale invariance in the Gay-Berne model

This paper presents a numerical study of the Gay-Berne liquid crystal model with parameters corresponding to calamitic (rod-shaped) molecules. The focus is on the isotropic and nematic phases at temperatures above unity, where we find strong correlations between the virial and potential-energy thermal fluctuations, reflecting the hidden scale invariance symmetry. This implies the existence of isomorphs, which are curves in the thermodynamic phase diagram of approximately invariant physics. We study numerically one isomorph in the isotropic phase and one in the nematic phase. In both cases, good invariance of the dynamics is demonstrated via data for the mean-square displacement and the reduced-unit time-autocorrelation functions of the velocity, angular velocity, force, torque, and first- and second-order Legendre polynomial orientational order parameters. Deviations from isomorph invariance are observed at short times for the orientational time-autocorrelation functions, which reflects the fact that the moment of inertia is assumed to be constant and thus not isomorph-invariant in reduced units. Structural isomorph invariance is demonstrated from data for the radial distribution functions of the molecules and their orientations. For comparison, all quantities were also simulated along an isochore of similar temperature variation, in which case invariance is not observed. We conclude that the thermodynamic phase diagram of the calamitic Gay-Berne model is essentially one-dimensional in the studied regions as predicted by isomorph theory, a fact that potentially allows for simplifications of future theories and numerical studies.

Heating leads to liquid-crystal and crystalline order in a two-temperature active fluid of rods

We report phase separation and liquid-crystal ordering induced by scalar activity in a system of soft repulsive spherocylinders (SRSs) of shape anisotropy L/D=5 using molecular dynamics (MD) simulations. Activity is introduced by increasing the temperature of half of the SRSs (labeled hot) while maintaining the temperature of the other half constant at a lower value (labeled 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 particles. Activity also drives the cold particles through a phase transition to a more ordered state and the hot particles to a state of less order compared to the initial equilibrium state. The cold components of a homogeneous isotropic structure acquire nematic and, at higher activity, crystalline order. Similarly, the cold zone of a nematic initial state undergoes smectic and crystal ordering above a critical value of activity while the hot component turns isotropic. We find that the hot particles occupy a larger volume and exert an extra kinetic pressure, confining, compressing, and provoking an ordering transition of the cold-particle domains.

Phase behavior of hard cylinders

Using isobaric Monte Carlo simulations, we map out the entire phase diagram of a system of hard cylindrical particles of length (L) and diameter (D) using an improved algorithm to identify the overlap condition between two cylinders. Both the prolate L/D > 1 and the oblate L/D < 1 phase diagrams are reported with no solution of continuity. In the prolate L/D > 1 case, we find intermediate nematic N and smectic SmA phases in addition to a low density isotropic I and a high density crystal X phase with I-N-SmA and I-SmA-X triple points. An apparent columnar phase C is shown to be metastable, as in the case of spherocylinders. In the oblate L/D < 1 case, we find stable intermediate cubatic (Cub), nematic (N), and columnar (C) phases with I-N-Cub, N-Cub-C, and I-Cub-C triple points. Comparison with previous numerical and analytical studies is discussed. The present study, accounting for the explicit cylindrical shape, paves the way to more sophisticated models with important biological applications, such as viruses and nucleosomes.

Demixing and tetratic ordering in some binary mixtures of hard superellipses

We examine the fluid phase behavior of binary mixtures of hard superellipses using the scaled particle theory. The superellipse is a general two-dimensional convex object that can be tuned between the elliptical and rectangular shapes continuously at a given aspect ratio. We find that the shape of the particle affects strongly the stability of isotropic, nematic, and tetratic phases in the mixture even if the side lengths of both species are fixed. While the isotropic-isotropic demixing transition can be ruled out using the scaled particle theory, the first order isotropic-nematic and the nematic-nematic demixing transition can be stabilized with strong fractionation between the components. It is observed that the demixing tendency is strongest in small rectangle-large ellipse mixtures. Interestingly, it is possible to stabilize the tetratic order at lower densities in the mixture of hard squares and rectangles where the long rectangles form a nematic phase, while the squares stay in the tetratic order.

The role of the dipole moment orientations in the crystallization tendency of the van der Waals liquids - molecular dynamics simulations

Computer simulations of model systems play a remarkable role in the contemporary studies of structural, dynamic and thermodynamic properties of supercooled liquids. However, the commonly employed model systems, i.e., simple-liquids, do not reflect the internal features of the real molecules, e.g., structural anisotropy and spatial distribution of charges, which might be crucial for the behavior of real materials. In this paper, we use the new model molecules of simple but anisotropic structure, to studies the effect of dipole moment orientation on the crystallization tendency. Our results indicate that proper orientation of the dipole moment could totally change the stability behavior of the system. Consequently, the exchange of a single atom within the molecule causing the change of dipole moment orientation might be crucial for controlling the crystallization tendency. Moreover, employing the classical nucleation theory, we explain the reason for this behavior.

Automated Tracking of Biopolymer Growth and Network Deformation with TSOAX

Studies of how individual semi-flexible biopolymers and their network assemblies change over time reveal dynamical and mechanical properties important to the understanding of their function in tissues and living cells. Automatic tracking of biopolymer networks from fluorescence microscopy time-lapse sequences facilitates such quantitative studies. We present an open source software tool that combines a global and local correspondence algorithm to track biopolymer networks in 2D and 3D, using stretching open active contours. We demonstrate its application in fully automated tracking of elongating and intersecting actin filaments, detection of loop formation and constriction of tilted contractile rings in live cells, and tracking of network deformation under shear deformation.

Speeding up Monte Carlo simulation of patchy hard cylinders

The hard cylinder model decorated with attractive patches proved to be very useful recently in studying physical properties of several colloidal systems. Phase diagram, elastic constants and cholesteric properties obtained from computer simulations based on a simple hard cylinder model have been all successfully and quantitatively compared to experimental results. Key to these simulations is an efficient algorithm to check the overlap between hard cylinders. Here, we propose two algorithms to check the hard cylinder overlap and we assess their efficiency through a comparison with an existing method available in the literature and with the well-established algorithm for simulating hard spherocylinders. In addition, we discuss a couple of optimizations for performing computer simulations of patchy anisotropic particles and we estimate the speed-up which they can provide in the case of patchy hard cylinders.

Elastic moduli of a smectic membrane: a rod-level scaling analysis

Chiral rodlike colloids exposed to strong depletion attraction may self-assemble into chiral membranes whose twisted director field differs from that of a 3D bulk chiral nematic. We formulate a simple microscopic variational theory to determine the elastic moduli of rods assembled into a bidimensional smectic membrane. The approach is based on a simple Onsager-Straley theory for a non-uniform director field that we apply to describe rod twist within the membrane. A microscopic approach enables a detailed estimate of the individual Frank elastic moduli (splay, twist and bend) as well as the twist penetration depth of the smectic membrane in relation to the rod density and shape. We find that the elastic moduli are distinctly different from those of a bulk nematic fluid, with the splay elasticity being much stronger and the curvature elasticity much weaker than for rods assembled in a three-dimensional nematic fluid. We argue that the use of the simplistic one-constant approximation in which all moduli are assumed to be of equal magnitude is not appropriate for modelling the structure-property relation of smectic membranes.

Perturbation Theory versus Thermodynamic Integration. Beyond a Mean-Field Treatment of Pair Correlations in a Nematic Model Liquid Crystal

The phase behavior and structure of a simple square-well bulk fluid with anisotropic interactions is described in detail. The orientation dependence of the intermolecular interactions allows for the formation of a nematic liquid-crystalline phase in addition to the more conventional isotropic gas and liquid phases. A version of classical density functional theory (DFT) is employed to determine the properties of the model, and comparisons are made with the corresponding data from Monte Carlo (MC) computer simulations in both the grand canonical and canonical ensembles, providing a benchmark to assess the adequacy of the DFT results. A novel element of the DFT approach is the assumption that the structure of the fluid is dominated by intermolecular interactions in the isotropic fluid. A so-called augmented modified mean-field (AMMF) approximation is employed accounting for the influence of anisotropic interactions. The AMMF approximation becomes exact in the limit of vanishing density. We discuss advantages and disadvantages of the AMMF approximation with respect to an accurate description of isotropic and nematic branches of the phase diagram, the degree of orientational order, and orientation-dependent pair correlations. The performance of the AMMF approximations is found to be good in comparison with the MC data; the AMMF approximation has clear advantages with respect to an accurate and more detailed description of the fluid structure. Possible strategies to improve the DFT are discussed.

Fundamental measure theory for non-spherical hard particles: predicting liquid crystal properties from the particle shape

Density functional theory (DFT) for hard bodies provides a theoretical description of the effect of particle shape on inhomogeneous fluids. We present improvements of the DFT framework fundamental measure theory (FMT) for hard bodies and validate these improvements for hard spherocylinders. To keep the paper self-contained, we first discuss the recent advances in FMT for hard bodies that lead to the introduction of fundamental mixed measure theory (FMMT) in our previous paper (2015 Europhys. Lett. 109 26003). Subsequently, we provide an efficient semi-empirical alternative to FMMT and show that the phase diagram for spherocylinders is described with similar accuracy in both versions of the theory. Finally, we present a semi-empirical modification of FMMT whose predictions for the phase diagram for spherocylinders are in excellent quantitative agreement with computer simulation results.

Three-Phase Coexistence in Colloidal Rod-Plate Mixtures

Aqueous suspensions of clay particles, such as montmorillonite (MMT) platelets and sepiolite (Sep) rods, tend to form gels at concentrations around 1 vol %. For Sep rods, adsorbing sodium polyacrylate to the surface allows for an isotropic-nematic phase separation to be seen instead. Here, MMT is added to such Sep suspensions, resulting in a complex phase behavior. Across a range of clay concentrations, separation into three phases is observed: a lower, nematic phase dominated by Sep rods, a MMT-rich middle layer, which is weakly birefringent and probably a gel, and a dilute top phase. Analysis of phase volumes suggests that the middle layer may contain as much as 6 vol % MMT.

Hard-body models of bulk liquid crystals

Hard models for particle interactions have played a crucial role in the understanding of the structure of condensed matter. In particular, they help to explain the formation of oriented phases in liquids made of anisotropic molecules or colloidal particles and continue to be of great interest in the formulation of theories for liquids in bulk, near interfaces and in biophysical environments. Hard models of anisotropic particles give rise to complex phase diagrams, including uniaxial and biaxial nematic phases, discotic phases and spatially ordered phases such as smectic, columnar or crystal. Also, their mixtures exhibit additional interesting behaviours where demixing competes with orientational order. Here we review the different models of hard particles used in the theory of bulk anisotropic liquids, leaving aside interfacial properties and discuss the associated theoretical approaches and computer simulations, focusing on applications in equilibrium situations. The latter include one-component bulk fluids, mixtures and polydisperse fluids, both in two and three dimensions, and emphasis is put on liquid-crystal phase transitions and complex phase behaviour in general.

Depletion-interaction effects on the tunneling conductivity of nanorod suspensions

We study by simulation and theory how the addition of insulating spherical particles affects the conductivity of fluids of conducting rods, modeled by spherocylinders. The electrical connections are implemented as tunneling processes, leading to a more detailed and realistic description than a discontinuous percolation approach. We find that the spheres enhance the tunneling conductivity for a given concentration of rods and that the enhancement increases with rod concentration into the regime where the conducting network is well established. By reformulating the network of rods using a critical path analysis, we quantify the effect of depletion-induced attraction between the rods due to the spheres. Furthermore, we show that our conductivity data are quantitatively reproduced by an effective-medium approximation, which explicitly relates the system tunneling conductance to the structure of the rod-sphere fluid.

Polydispersity stabilizes biaxial nematic liquid crystals

Inspired by the observations of a remarkably stable biaxial nematic phase [van den 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 regime in between uniaxial nematic and smectic states.

High-level virial theory of hard spheroids

We present a method for calculating high-order virial expansions of the isotropic-nematic phase transition which we apply here to hard spheroids. Studying a range of aspect ratios, for both oblate and prolate particles, we obtain equations of state, coexistence densities, and nematic order parameters, using expansions truncated at up to eighth virial level. For particles of large aspect ratios our results show rapid convergence, with truncation at sixth order sufficient to give excellent agreement with simulation data. For more spherical particles the convergence is less rapid, with results for up to eighth-order theory approaching but still not reaching simulation data. Our results indicate that high-order viral expansions are better suited to predicting equations of state than coexistence densities. We also test the validity of using the Onsager trial function to approximate the orientational distribution function, finding only small errors when making this approximation.

Thermodynamic stability of the cubatic phase of hard cut spheres evaluated by expanded ensemble simulations

The system of hard cut spheres (disk-shaped particles formed by symmetrically truncating the end caps of a sphere) exhibits an intriguing "cubatic" phase with cubic orientational symmetry. However, it is unclear whether this phase is metastable with respect to the columnar phase. We attempt to provide an answer to this question by carrying out free energy calculations by the expanded ensemble Monte Carlo method. We conclude that there may be a very small region of cubatic stability in the vicinity of the isotropic-cubatic phase transition, but that that transition would need to be determined more accurately to obtain a definitive answer. We also comment on the efficacy of the expanded ensemble method for these kinds of calculations.

Cholesteric order in systems of helical Yukawa rods

We consider the interaction potential between two chiral rod-like colloids which consist of a thin cylindrical backbone decorated with a helical charge distribution on the cylinder surface. For sufficiently slender helical rods a simple scaling expression is derived which relates the chiral 'twisting' potential to the microscopic properties of the particles, such as the internal helical pitch, charge density and electrostatic screening parameter. To predict the behaviour of the macroscopic cholesteric pitch of the fluid bulk phase we invoke a simple second-virial theory generalized to treat anisotropic states with weakly twisted director fields. It is shown that, while particles with weakly coiled helices always form a cholesteric phase whose helical sense is commensurate with that of the internal helix, more strongly coiled rods lead to the formation of a cholesteric state of opposite sense. The correlation between the helical symmetry at the microscopic and macroscopic scale is found to be very sensitive to the pitch of the Yukawa helix. Mixing helical particles of sufficiently disparate length and internal pitch may give rise to a demixing of the uniform cholesteric phase into two fractions with a different macroscopic pitch. Our findings could be relevant to the interpretation of experimental observations in systems of cellulose and chitin microfibres, DNA and fd virus rods.

Phase behavior of colloidal superballs: shape interpolation from spheres to cubes

The phase behavior of hard superballs is examined using molecular dynamics within a deformable periodic simulation box. A superball's interior is defined by the inequality |x|(2q)+|y|(2q)+|z|(2q)≤1 , which provides a versatile family of convex particles (q≥0.5) with cubelike and octahedronlike shapes as well as concave particles (q<0.5) with octahedronlike shapes. Here, we consider the convex case with a deformation parameter q between the sphere point (q=1) and the cube (q=∞). We find that the asphericity plays a significant role in the extent of cubatic ordering of both the liquid and crystal phases. Calculation of the first few virial coefficients shows that superballs that are visually similar to cubes can have low-density equations of state closer to spheres than to cubes. Dense liquids of superballs display cubatic orientational order that extends over several particle lengths only for large q. Along the ordered, high-density equation of state, superballs with 1<q<3 exhibit clear evidence of a phase transition from a crystal state to a state with reduced long-ranged orientational order upon the reduction of density. For q≥3 , long-ranged orientational order persists until the melting transition. The width of the apparent coexistence region between the liquid and ordered, high-density phase decreases with q up to q=4.0. The structures of the high-density phases are examined using certain order parameters, distribution functions, and orientational correlation functions. We also find that a fixed simulation cell induces artificial phase transitions that are out of equilibrium. Current fabrication techniques allow for the synthesis of colloidal superballs and thus the phase behavior of such systems can be investigated experimentally.

Role of anisotropy for protein-protein encounter

Protein-protein interactions comprise both transport and reaction steps. During the transport step, anisotropy of proteins and their complexes is important both for hydrodynamic diffusion and accessibility of the binding site. Using a Brownian dynamics approach and extensive computer simulations, we quantify the effect of anisotropy on the encounter rate of ellipsoidal particles covered with spherical encounter patches. We show that the encounter rate k depends on the aspect ratios xi mainly through steric effects, while anisotropic diffusion has only a little effect. Calculating analytically the crossover times from anisotropic to isotropic diffusion in three dimensions, we find that they are much smaller than typical protein encounter times, in agreement with our numerical results.

Liquid crystalline and antinematic behavior of shape-persistent macrocycles from molecular-dynamics simulations

In this work we present a molecular-dynamics study of a coarse-grained (CG) model for a system of planar shape-persistent macrocycles (SPMs). SPMs are synthetic organic rigid macromolecules typically comprised of meta- and para-aromatics groups connected by acetylene and/or diacetylene units. In the CG model, each SPM is represented as a rigid hexagonal arrangement of 24 soft-repulsive spheres, resembling a large ring or hoop. The supramolecular arrangement of these macrocycles at high pressures is studied using N-P-T molecular-dynamics simulation both by expansion of an initial hexagonal lattice structure and also by compression of an isotropic phase. In both cases, systems under consideration exhibit an isotropic-smectic-A phase transition, which is detected by monitoring relevant order parameters and analyzing snapshots of equilibrium configurations. The smectic-A phase is unique; although the molecules form layers, the system presents antinematic order where the orientation of the molecular axes is perpendicular to the direction of the layers themselves. Due to their planar geometry, the SPM molecules would be expected to form columnar or nematic phases. On the contrary, these phases seem suppressed by a novel smectic-A phase, formed by the mutual interpenetration of the cycles. These results are a unique example of how molecular nonconvexity can, by itself, induce mesomorphism in anisotropic systems.

Effective shape and phase behavior of short charged rods

We explicitly calculate the orientation-dependent second virial coefficient of short charged rods in an electrolytic solvent, assuming the rod-rod interactions to be a pairwise sum of hard-core and segmental screened-Coulomb repulsions. From the parallel and isotropically averaged second virial coefficient, we calculate the effective length and diameter of the rods, for charges and screening lengths that vary over several orders of magnitude. Using these effective dimensions, we determine the phase diagram, where we distinguish a low-charge and strong-screening regime with a liquid crystalline nematic and smectic phase, and a high-charge and weak-screening regime with a plastic crystal phase in the phase diagram.

The Percus-Yevick approximation for quadrupolar molecular fluids

The Percus-Yevick integral equation theory has been solved to study the equilibrium and structural properties of quadrupolar Gay-Berne fluids. The method used involves an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. All the terms of harmonic coefficients which involve l indices up to less than or equal to 6 have been considered. Molecules with length-to-breadth ratios 3.0 and 4.0 have been considered and results are reported for different densities, temperatures, and quadrupole moments. The values of pair correlation functions have been compared with the available computer simulation results.

Theory and computer simulation for the cubatic phase of cut spheres

The phase behavior of a system of hard-cut spheres has been studied using a high-order virial theory and by Monte Carlo simulation. The cut-sphere particles are disks of thickness L formed by symmetrically truncating the end caps of a sphere of diameter D . The virial theory predicts a stable nematic phase for aspect ratio LD=0.1 and a stable cubatic phase for LD=0.15-0.3 . The virial series converges rapidly on the equation of state of the isotropic and nematic phases, while for the cubatic phase the convergence is slower, but still gives good agreement with the simulation at high order. It is found that a high-order expansion (up to B8 ) is required to predict a stable cubatic phase for LD> or =0.15 , indicating the importance of many-body interactions in stabilizing this phase. Previous simulation work on this system has focused on aspect ratios LD=0.1 , 0.2, and 0.3. We expand this to include also LD=0.15 and 0.25, and we introduce a fourth-rank tensor to measure cubatic ordering. We have applied a multiparticle move which dramatically speeds the attainment of equilibrium in the nematic phase and therefore is of great benefit in the study of the isotropic-nematic phase transition. In agreement with the theory, our simulations confirm the stability of the nematic phase for LD=0.1 and the stability of the cubatic phase over the nematic for LD=0.15-0.3 . There is, however, some doubt about the stability of the cubatic phase with respect to the columnar. We have shown that the cubatic phase found on compression at LD=0.1 is definitely metastable, but the results for LD=0.2 were less conclusive.

Simulation and theory of hybrid aligned liquid crystal films

We present a study of the effects of nanoconfinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential, extending earlier work by two of us [D. J. Cleaver and P. I. C. Teixeira, Chem. Phys. Lett. 338, 1 (2001)]. Here, we consider the case of hybrid films, where one of the substrates induces strongly homeotropic anchoring, while the other favors either weakly homeotropic or planar anchoring. These systems are investigated using both Monte Carlo simulation and density-functional theory, the latter implemented at the level of Onsager's second-virial approximation with Parsons-Lee rescaling. The orientational structure is found to change either continuously or discontinuously depending on substrate separation, in agreement with earlier predictions by others. The theory is seen to perform well in spite of its simplicity, predicting the positional and orientational structure seen in simulations even for small particle elongations.

Elastic constants of hard thin platelets by Monte Carlo simulation and virial expansion

In this paper we present an investigation into the calculation of the Frank elastic constants of hard platelets via molecular simulation and virial expansion beyond second order. Monte Carlo simulations were carried out and director fluctuations measured as a function of wave vector k, giving the elastic constants through a fit in the low-k limit. Additionally, the virial expansion coefficients of the elastic constants up to sixth order were calculated, and the validity of the theory determined by comparison with the simulation results. The simulation results are also compared with experimental measurements on colloidal suspensions of platelike particles.