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We revisited the nematic-isotropic (NI) transition of the Lebwohl-Lasher lattice model with a detailed investigation of samples containing 200 x 200 x 200 particles. The large-scale Monte Carlo (MC) simulations involved were carried out following the standard Metropolis, as well as the cluster MC Wolff algorithms. A notable free-energy barrier was observed between the isotropic and nematic phase, leading to long-lived metastable states and hysteresis. We provide an improved estimate of the nematic-isotropic transition temperature TNI, of the supercooling and superheating temperatures, of the temperature of divergence of pretransitional effects TC* as well as an analysis of the size distribution of the ordered domains above TNI, contributing to a better understanding of this transition of key importance for liquid crystals. This article is part of the theme issue 'Topics in mathematical design of complex materials'. [ABSTRACT FROM AUTHOR]

The Gay–Berne (GB) potential has proved highly successful in the simulation of liquid crystal phases, although it is fairly demanding in terms of resources for simulations of large (e.g., N>105) systems, as increasingly required in applications. Here, we introduce a soft-core GB model, which exhibits both liquid crystal phase behavior and rapid equilibration. We show that the Hamiltonian replica exchange method, coupled with the newly introduced soft-core GB model, can effectively speed up the equilibration of a GB liquid crystal phase by frequent exchange of configurations between replicas, while still recovering the mesogenic properties of the standard GB potential. [ABSTRACT FROM AUTHOR]

A brief review and personal perspective of modelling and simulations of liquid crystals and of how this has dramatically changed over the years, from idealised lattice to molecular level and now to predictive atomistic models. [ABSTRACT FROM AUTHOR]

A Monte Carlo method for studying anisotropic systems with a new type of boundary conditions is proposed. The missing interactions at the sample box surface are replaced by interactions with ghost molecules. The orientations of these ghost particles are sampled from a ‘‘least biased’’ singlet distribution obtained self-consistently from the order parameter inside the sample. The method is tested on the Lebwohl–Lasher model with 125 and 1000 particles. Results for the transition temperature and order parameters are in good agreement with those obtained from simulation of much larger systems. The method is fairly general and should be applicable in a variety of simulations. Here we show that it can also be used to study director fluctuations in nematogen models. [ABSTRACT FROM AUTHOR]

We present large-scale lattice Monte Carlo simulations of nematic ordering in the vicinity of submicron objects — colloids or viruses — of different shapes (spherical, cubical or icosahedral) immersed in a nematic liquid crystal. We simulate polarized light transmission patterns for the various particles and find that they are distinguishable, suggesting that they might be useful for object shape recognition or, in case of viruses, for diagnostic purposes. [ABSTRACT FROM AUTHOR]

Liquid crystal elastomers (LCE)polymernetworks constructedwith liquid crystal unitsare functional materials characterizedby a pronounced coupling between elastic strain and liquid crystallineorientational ordering. When prepared by polymerization and cross-linkingin the isotropic phase, and then cooled (“isotropic genesis”),a polydomain LCE presents an extraordinary “supersoft”elastic behavior under unidirectional pulling, with a plateau-likelow elastic modulus region in the stress–strain curve, beforeturning into a monodomain LCE where a standard elastic resistanceis recovered. The physical mechanism of this behavior is of greatinterest, but still mysterious. This work investigates its origin,reproducing the experiment and succeeding to observe the plateau-likestress–strain behavior by means of large-scale molecular iso-stressMonte Carlo simulations. The results not only show that the basicmolecular mechanism behind supersoft elasticity hinges on local domainrotation and growth but also suggest that this is assisted by a newlyproposed dissipation of the elastic energy stored in the defects createdby the isotropic genesis process, explaining also the irreversibilityobserved in main-chain LCE. [ABSTRACT FROM AUTHOR]

We present a detailed Monte Carlo study of the effects of biaxiality on the textures of nematic films with specific homeotropic boundary conditions. We have used the Straley generalized Hamiltonian for a wide range of biaxial parameters and the differences obtained in the polarized microscopy images are analyzed for the various cases. [ABSTRACT FROM AUTHOR]

We present a Monte Carlo simulation study of the phase behavior and molecular organizations observed in a system of nanoparticles constituted by a central spherical core with attached mesogenic groups, which we model with a set of suitable Gay–Berne units connected by flexible spacers. We show that the choice of radial or tangential orientation of the attached mesogenic groups with respect to the surface of the core is crucial for the resulting phase behavior. [ABSTRACT FROM PUBLISHER]

Swollen elastomer liquid crystals undergo significant deformations by application of an electric field perpendicular to their alignment axis, as shown in experiments by Urayama et al. [Urayama Κ, Honda S, Takigawa Τ (2006) Macromolecules 39:1943-1949]. Here we clarify this surprising effect at the molecular level using largescale Monte Carlo simulations of an off-lattice model based on a soft Gay-Berne potential. We provide the internal change of molecular organization, as well as the key observables during the actuation cycle. [ABSTRACT FROM AUTHOR]

We present a Monte Carlo study of external field-induced switching in nematic elastomers, employing a coarse-grained shearable lattice model. In large enough systems a full-wavelength Fréedericksz effect is observed --as opposed to the half-wavelength effect seen in ordinary nematics-- that clearly reflects in simulated polarized light textures, as well as in deuterium magnetic resonance spectra. The reorientation of mesogenic units is accompanied by pronounced shear deformations. [ABSTRACT FROM AUTHOR]

We have investigated with extensive Monte Carlo simulations in the isothermal isobaric ensemble a system of N=8192 elongated attractive-repulsive biaxial Gay-Berne (GB) particles. We have found uniaxial and biaxial nematic phases and a biaxial orthogonal smectic phase in this thermotropic model system. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We study the relation between the chirality of a discotic mesogen and that of the chiral columnar aggregates that they can spontaneously form by self-assembly. We discuss first the different types of chiral columns that can be in principle obtained. We introduce then a simple two-site Gay–Berne dissymmetric molecular model where chirality can be easily varied and perform extensive NPT Monte Carlo simulations of samples of these particles for different chiralities. At low temperatures we find nematic discotic and columnar mesophases formed by overall chiral columns and we analyze the results in terms of suitably defined observables and chiral correlation functions. We find that, at least for our model system, the columnar chirality is not originating from a regular helical or spiral arrangement of particles but it is mainly due to one-particle high-chirality defects separated by low-chirality domains. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Abstract We present a Monte Carlo study of the effects of elastic anisotropy on the textures of nematic droplets with different boundary conditions. Simulated polarized optical microscopy (POM) images are analysed for uniaxial nematics with radial, bipolar and toroidal boundaries and for numerous combinations of the splay, twist and bend elastic constant values. An atlas of simulated textures is presented as an aid to understanding new experimental results. Highlights • An investigation of the relation between polarized optical microscopy images and elastic constants in nematics droplets • Monte Carlo simulations of POM textures in nematic sdroplets with different surface alignment • An analysis of cases where POM can provide information on elastic anisotropy and boundary conditions [ABSTRACT FROM AUTHOR]

The molecular organization of a nematic film sandwiched between two planar randomly aligned surfaces is studied by means of detailed Monte Carlo simulations. The formation as well as the evolution of topological defects induced by these particular boundary conditions are investigated. The resulting defect structure is compared with the one induced by hybrid aligned surfaces. The observation of such defects and some features of their structures can be associated with geometric parameters of the film and with properties of the confining surfaces. [ABSTRACT FROM AUTHOR]

Computer simulations of 2D nematic systems with quenched disorder placed on the oriented boundary have been performed to test the Feldman-Vinokur hypothesis which suggests that the long-range order is destroyed in that case. Our results for various system sizes and different percentages of disorder at the boundary do not necessarily confirm this hypothesis. [ABSTRACT FROM AUTHOR]

We have simulated, using a Monte Carlo method, a system of apolar Gay–Berne discotic particles without dipoles and with two or three dipoles symmetrically embedded in the disc. The dipoleless system can form nematic and hexagonal columnar mesophases. Adding two in‐plane antiparallel radial dipoles has the effect of destabilizing the columnar ordering, in favour of a fully interdigitated arrangement of the molecular stacks, with strong correlations in the plane perpendicular to the director and large biaxiality. No columnar phase is observed for the systems with three planar radial dipoles with threefold symmetry up to very low temperatures. Finally, on decreasing the strength of the three dipoles, a columnar non‐interdigitated phase is observed. [ABSTRACT FROM AUTHOR]

Abstract: We propose a simple coarse-grained lattice model for liquid crystal elastomers and show, through large scale Monte Carlo simulations, that it can reproduce stress–strain, order, light transmission, and other experiments, including temperature effects. We focus both on homogeneously and inhomogeneously crosslinked materials. [Copyright &y& Elsevier]

We have performed a Monte Carlo simulation study of a system of ellipsoidal particles with donor-acceptor sites modelling complementary hydrogen-bonding groups in real molecules. We have considered elongated Gay-Berne particles with terminal interaction sites allowing particles to associate and form dimers. The changes in the phase transitions and in the molecular organization and the interplay between orientational ordering and dimer formation are discussed. Particle flip and dimer moves have been used to increase the convergency rate of the Monte Carlo (MC) Markov chain. [ABSTRACT FROM AUTHOR]

We have studied nematic hybrid films with homeotropic alignment at the top surface and various controlled degrees of in plane ordering, going from a random degenerate organization to a completely uniform alignment along one direction, at the bottom one. We show, by Monte Carlo (MC) computer simulations and experiments on photopatterned films with the bottom support surface fabricated with in-plane order similar to the simulated ones, that the point defects observed in the case of random planar orientations at the bottom tend to arrange along a filament as the surface ordering is sufficiently increased. MC simulations complement the polarized microscopy texture observations allowing to inspect the 3D structure of the defects and examine the role of elastic constants. [ABSTRACT FROM AUTHOR]

We have performed a detailed Monte Carlo study of photonic devices based on nematic liquid crystal infiltrated in polydimethylsiloxane (PDMS) and in Silicon-Organic Hybrid (SOH) channels, to be used as waveguides. The simulations of a simple model of these slot waveguide shifters have shown the effect of an applied electric external field in two cases with different surface alignments, i.e. planar SOH and homeotropic PDMS. We have investigated the effect of the external field on the optical transmission and the ordering across the cell. [ABSTRACT FROM AUTHOR]

Liquid crystal phases formed by bent-shaped (or “banana”) molecules are currently of great interest. Here we investigate by Monte Carlo computer simulations the phases formed by rigid banana molecules modeled combining three Gay-Berne sites and containing either one central or two lateral and transversal dipoles. We show that changing the dipole position and orientation has a profound effect on the mesophase stability and molecular organization. In particular, we find a uniaxial nematic phase only for off-center dipolar models and tilted phases only for the one with terminal dipoles. [ABSTRACT FROM AUTHOR]

We present a short overview of recent investigations of the equilibrium tilt angle profile in a cell limited by two concentric cylinders filled with nematic liquid crystals (NLC), both in presence and in absence of an external electric field. The analyses are carried out by recalling some recent results obtained in the framework of the elastic continuum theory and Monte Carlo (MC) simulations, or suitable combinations of both approaches. These are very powerful tools to face the richness of the configurations of NLC in complex geometries. In particular, they are helpful in providing a comprehension of the molecular organisation of these systems for what concerns the spontaneous Fréedericksz-like transition, connected with the phenomenon of escaping into the third dimension. Some concluding remarks and perspectives points towards some remarkable features of confined systems in soft matter. [ABSTRACT FROM AUTHOR]

We present detailed Monte Carlo simulations of a simple model of a nematic liquid crystal slot waveguide shifter, investigating the effect of an applied electric external field. The simulations are based on the Lebwohl-Lasher lattice spin model with boundary conditions chosen to mimic the planar alignment as in Silicon Organic Hybrid waveguides and the homeotropic anchoring appropriate for Polydimethylsiloxane polymer walls. The external field is modeled by adding a term to the Hamiltonian which describes its coupling to the mesogenic molecules. We have investigated the effect of the external field on the optical transmission and the ordering across the cell. [ABSTRACT FROM AUTHOR]

We present detailed Monte Carlo simulations of a simple model of a nematic liquid crystal channel waveguide investigating the effect of an applied electric external field. The simulations are based on the Lebwohl-Lasher lattice spin model with boundary conditions chosen to mimic the homeotropic anchoring appropriate for PDMS polymer walls. The external field is modeled by adding an additional term to the Hamiltonian which describes its coupling to the mesogenic molecules. We have investigated the effect of the external field on the optical transmission and the ordering across the cell. [ABSTRACT FROM AUTHOR]

We revisit the classical problem of the molecular orientation inside a hybrid cell filled with liquid-crystals with various elastic constant anisotropies by means of Monte Carlo simulations using the Gruhn-Hess effective pair potential. We find some unstable defect lines and we discuss their arising in the system. We study the effects of the elastic anisotropy on the profiles of the director close to the surface with weak anchoring. Our findings indicate that the elastic theory and computer simulations are in good qualitative agreement while quantitatively some discrepancies are found mainly when the ratio K11/K33is larger than one. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations of lattice spin models are employed to investigate the effects of an external field on the creation and evolution of inversion walls in nematic films with conical boundary conditions. The simulations, based on the well known Lebwohl-Lasher potential, allow to produce simulated polarized microscopy images which are followed during their evolution when the field is applied. [ABSTRACT FROM AUTHOR]

We present detailed Monte Carlo (MC) simulations of a nematic cell with homeotropic boundary conditions at the four confining surfaces. The simulations are based on the Lebwohl-Lasher lattice spin model with boundary conditions chosen to mimic the cell anchoring. We have investigated the model using a standard Metropolis Monte Carlo method to study the optical transmission and the ordering through the cell. [ABSTRACT FROM AUTHOR]

Nematic systems confined to a bounded volume are particularly interesting because they present stable structure defects induced by the anchoring conditions on the surface. Here we present a Monte Carlo study of a hybrid nematic film with various strengths of coupling with the surfaces. [ABSTRACT FROM PUBLISHER]

We present a simple Monte Carlo study of orientational ordering in a nematic liquid crystal with embedded chiral nanostructures. The nanostructures are shown to impose bulk chiral order in the nematic only for large enough values of the chiral pitch. [ABSTRACT FROM AUTHOR]

A hybrid (weak-strong anchoring) cylindrical cell with antagonistic boundary conditions (planar–homeotropic) at the outer confining surface and at a central coaxial cylindrical core and filled with nematic liquid crystals is investigated by means of the Elastic Theory and Monte Carlo Simulations. The director orientation profile on the surface characterized by weak anchoring is built as a function of the extrapolation length and other relevant parameters. By considering the angle on the surface as an order parameter, a transition in the orientation is found when the extrapolation length becomes smaller than a critical value and the orientation of the surface with strong anchoring is dominant. The order parameter critical exponent is numerically calculated, and the mean field value (β≈1/2) is found in all cases. These transitions are essentially confirmed by Monte Carlo simulations even if some numerical discrepancies are found. The analysis show similarities between planar and cylindrical geometries, but non-usual consequences are found more easily in the latter one. [ABSTRACT FROM AUTHOR]

We present a detailed computer simulation study of the formation and evolution of topological defects in thin biaxial nematic films. We have used the Straley generalized Hamiltonian and a wide range of biaxial parameters to generate and explore a variety of mesophases. The differences obtained for the various cases are analyzed for thin biaxial nematic films with random planar (Schlieren) surface alignment. [ABSTRACT FROM PUBLISHER]

Monte Carlo simulations of lattice spin models are employed to investigate the creation of inversion walls in nematic films with specific boundary conditions. The simulations, based on the well known Lebwohl-Lasher potential, allow to produce simulated polarized microscopy images which are followed during their evolution and analysed for different film thicknesses. [ABSTRACT FROM AUTHOR]

We present an investigation of the ordering in a nematic liquid-crystal film confined between two cylindrical surfaces with antagonistic (radial and planar) anchoring alignments. A Monte Carlo study of a Lebwohl-Lasher model with suitable boundary conditions has been performed to calculate the ordering and the molecular organization for different film thicknesses. The simulation results are compared with some theoretical predictions obtained with the elastic continuum approach. The agreement between theory and simulation is improved as the thickness decreases. [ABSTRACT FROM AUTHOR]

We present a Monte Carlo study of the effects of elastic anisotropy on the textures of nematic films with specific random hybrid boundary conditions. The polarized microscopy images and their evolution are analyzed in uniaxial systems for different values of the elastic constants. [ABSTRACT FROM AUTHOR]

We present a Monte Carlo study of a liquid crystal-polymer interface, focusing on a single cell with boundary conditions tailored to mimic the main features of the system and we examine the effect of an external applied field. A simple lattice spin model, based on the Lebwohl-Lasher hamiltonian, has been employed to represent the nematic and the polymer molecules. The orientations of the spins representing the low molar mass nematic molecules are updated during the simulations while the polymer chain units are kept frozen. The model allows us to investigate the molecular organization and the ordering expected across the cell. Moreover the response to the change in external field intensity and duration pulse is also studied. [ABSTRACT FROM AUTHOR]

We present a joint molecular dynamics (MD)/kinetic Monte Carlo (KMC) study aimed at the atomistic description of charge transport in stacks of liquid-crystalline tetraalkoxy-substituted, metal-free phthalocyanines. The molecular dynamics simulations reproduce the major structural features of the mesophases, in particular, a phase transition around 340 K between the rectangular and hexagonal phases. Charge transport simulations based on a Monte Carlo algorithm show an increase by 2 orders of magnitude in the hole mobility when accounting for the rotational and translational dynamics. The results point to the formation of dynamical structural defects along the columns. [ABSTRACT FROM AUTHOR]

We present detailed Monte Carlo (MC) simulations of a nematic film with antagonistic boundary conditions corresponding to homeotropic and homogeneous planar anchoring at the two surfaces. The simulations are based on the Lebwohl-Lasher lattice spin model with boundary conditions chosen to mimic the cell anchoring. We have investigated the model using both a standard Metropolis and a reweighting Monte Carlo method recently implemented for continuous systems. [ABSTRACT FROM AUTHOR]

We present a Monte Carlo study of a simple model of a liquid crystal-polymer system under the effect of an external applied field. A lattice spin model, based on the Lebwhol-Lasher Hamiltonian and generalized with suitable boundary conditions, has been employed to investigate the molecular organization and to predict the ordering across a sample cell. [ABSTRACT FROM AUTHOR]

Abstract: We perform Monte Carlo simulations of a mixture of soft ellipsoids with embedded quadrupoles as a model of various small molecules dissolved in nematic liquid crystals. We find that Gay–Berne ellipsoids with distributed embedded quadrupoles qualitatively reproduce the trend in the order parameters observed experimentally in NMR spectra. In contrast, ellipsoids with a single embedded quadrupole cannot reproduce the negative order parameter of acetylene in EBBA. [Copyright &y& Elsevier]

We have studied a lattice spin model of nematic liquid crystal-polymer composite films by means of extensive Monte Carlo simulations over a distributed computing network. The Condor processing system installed on the Italian Nuclear Physics Institute computer network was used. The use of several geometries and boundary conditions allowed us to investigate a wide number of different realistic or speculative models. Many of the simulations differ only by a small number of parameters and they can be effectively performed in parallel. The results of the simulations can be analyzed globally when all the computations are completed and then for example, employed to extrapolate phase diagrams or other complex physical quantities. They provide an effective example of wide area distributed computing applications which could be also implemented in future GRID approaches. [ABSTRACT FROM AUTHOR]

We set up a model for discotic liquid crystal dimers and study, by means of Monte Carlo simulations, their phase behaviour and self–assembling properties, in comparison with the simpler monomeric case. Each discotic dimer is described by two oblate Gay–Berne ellipsoids connected by a flexible spacer, modelled by a harmonic “spring” of three different lengths. We find that dimerization in general yields produces a significant change on the phase behaviour, with an increase of the columnar–nematic transition temperature, a widening of the nematic region and the apparent suppression of the crystalline phase in favour of the columnar phase up to very low temperatures. Longer spacers prove to ease the formation of columns and to increase the orientational order. [ABSTRACT FROM AUTHOR]

In this work we consider the stability of columnar liquid crystals formed by discotic molecules differing only in one core substituent. In particular we concentrate on the 1-substituted 2, 3, 6, 7, 10, 11 hexaalkyloxy triphenylene family, and more specifically on the methoxy derivatives, studying the effects of seven α-substituents (H, Br, CH3, Cl, F, NH2, NO2) on the shape and electronic properties, calculated at density functional level, and relating them with the phase behaviour of the corresponding hexyloxy derivatives. In a second step, we use the optimized structures and the atomic charges in a simplified Monte Carlo simulation of systems of molecules arranged in a columnar fashion, to try to shed light on the consequences of functionalization on the stacking behaviour. [ABSTRACT FROM AUTHOR]

Abstract: We present a Monte Carlo simulation study of the phase behaviour and molecular organization of a system of fullerene-based mesogens, represented by a three-site model composed of a fullerene sphere and two mesogenic moieties rigidly attached to it. It is shown that a combination of suitably modified Lennard-Jones and Gay–Berne attractive–repulsive potentials allows a satisfactory qualitative modeling of the interactions between the fullerene derivatives under investigation. Indeed, simulation results show that, despite the crude representation of the molecular structure, our model generates nematic and smectic phases, thus accounting qualitatively for the basic experimental observations on the class of compounds considered. [Copyright &y& Elsevier]

Monte Carlo simulations of polarizing microscope textures for confined nematic droplets are presented. We consider uniaxial and biaxial cases with various boundary conditions and different values of the molecular biaxiality. The analysis of these optical textures should be of interest in assigning and characterizing biaxial nematic system, an issue of great current interest. [ABSTRACT FROM AUTHOR]

We present a Monte Carlo (MC) simulation of a nematic film with boundary conditions that vary from a homogeneous to a homeotropic anchoring at one surface while having a homogeneous anchoring at the other one. The simulations are based on the Lebwohl–Lasher lattice spin model with suitable boundary conditions to mimic the cell. We have investigated temperature effects on the molecular organization inside the system by calculating the internal energy, the heat capacity and the standard nematic order parameter. [ABSTRACT FROM AUTHOR]

We present a Monte Carlo study of a nematic droplet with boundary conditions that vary from an homeotropic to a bipolar anchoring. We follow the change in the molecular organisation inside the droplet as the boundary conditions vary by calculating order parameters and experimental observables like Deuterium NMR line shapes and polarized microscopy textures. [ABSTRACT FROM AUTHOR]

The purpose of this research is to investigate the thermodynamical behavior of a nematic liquid crystal sample confined to an annular cylindrical region and subjected to a radial anchoring alignment at the cylinder surfaces. The study is carried out by means of a combination of Monte Carlo simulations and of a theoretical approach based on the Landau–de Gennes formalism. The analytical model shows that the order instabilities cover the whole sample, while from the computer simulation one deduces that these instabilities are evident in a region far from the surfaces while some order remain close to them, and decreases more slowly as the temperature increases. • The study is carried out by means of a combination of Monte Carlo simulations and of a theoretical approach based on the LandauŰde Gennes formalism. • Both approaches show that the order close to the outer surface is slightly higher than the order close to the internal surface. • The analytical model shows that the some order instabilities cover the whole sample when a critical temperature is reached. • The computer simulation presents some instabilities in a region far from the surfaces while some order remain close to them. [ABSTRACT FROM AUTHOR]