Gay-Berne Mesogens Research Articles

Nematic phases from nearly spherical mesogens: applying the approximate non-conformal (ANC) theory

A coarser model for the Gay-Berne mesogen is developed using the interaction potential from the Approximate Non-Conformal (ANC) theory. The ANC potential contains both repulsive and attractive contributions. We modify intermolecular attractions by conditioning them with a Hess-Su orientation-dependent term. This imparts an anisotropic contribution to the energy of the system. The softness parameter s of the ANC potential is probed to qualitatively identify a threshold capable of sustaining a nematic phase. We construct phase diagrams for each value of s from molecular dynamics simulations and characterise bulk samples to outline phase regions. We find that a softness parameter or higher supports the emergence of a nematic phase. The stability of the nematic region is enhanced as , corresponding to the conventional Lennard-Jones interaction. The stability of the nematic phase for nearly-spherical mesogens with increasing s leads to a gradual loss in spherical symmetry despite no imposed shape anisotropy. Thus, the energy anisotropy becomes more pronounced and is capable of prompting the emergence of the nematic phase in this model.

Dynamic self-assembly of active particles in liquid crystals

We studied a binary mixture of self propelling (active) and standard (passive), Gay-Berne mesogens using a molecular dynamics technique. We found that in a certain range ofactive particle concentration, propelling force and temperature, here identified, a liquid crystalline sample where active particles are initially randomly distributed can form self-assembling parallel streams (lanes) of active particles flowing in opposite directions. As far as we are aware this is the first microscopic study showing the dynamic self organization of active particles in thermotropic liquid crystals.

Long-range decay of pair correlations and nematic ordering in a two-dimensional system of Gay-Berne mesogens

Isothermal-isobaric(NPT) Monte-Carlo simulation has been used to investigate the nature of pair-correlations and ordering in a two-Dimensional system of soft ellipses with aspect ratio κ=3 interacting via the Gay-Berne potential. The system is found to exhibit an isotropic phase (with exponential decay of orientational correlations) and a nematic phase (with algebraic decay of orientational correlations) as we suitably change temperature and pressure. The large distance decay exponent of the orientational correlations is found to converge around an universal value of 0.5 with the increase in pressure along an isotherm. The algebraic decay of orientational correlation in the low temperature phase shows that the nematic lacks true-long range orientational order. This has been substantiated by the system size dependence of the nematic order parameter. We have found the emergence of localized nematic patches separated by disclinations on increasing the pressure in the isotropic phase. No abrupt change is observed in pressure-density plot corresponding to the isotherms studied in this work.

A Bidimensional Gay-Berne Calamitic Fluid: Structure and Phase Behavior in Bulk and Strongly Confined Systems

A bidimensional (2D) thermotropic liquid crystal (LC) is investigated with Molecular Dynamics (MD) simulations. The Gay-Berne mesogen with parameterization GB(3, 5, 2, 1) is used to model a calamitic system. Spatial orientation of the LC samples is probed with the nematic order parameter: a sharp isotropic-smectic (I-Sm) transition is observed at lower pressures. At higher pressures, the I-Sm transition involves an intermediate nematic phase. Topology of the orthobaric phase diagram for the 2D case differs from the 3D case in two important respects: 1) the nematic region appears at lower temperatures and slightly lower densities, and 2) the critical point occurs at lower temperature and slightly higher density. The 2D calamitic model is used to probe the structural behavior of LC samples under strong confinement when either planar or homeotropic anchoring prevails. Samples subjected to circular, square, and triangular boundaries are gradually cooled to study how orientational order emerges. Depending on anchoring mode and confining geometry, characteristic topological defects emerge. Textures in these systems are similar to those observed in experiments and simulations of lyotropic LCs.

Shape, chirality and internal order of freely suspended nematic nanodroplets

We investigate the properties of freely suspended nematic nanodroplets of increasing size formed by elongated Gay–Berne mesogens, using extensive molecular dynamics simulations. We find that the nanodroplets have an elongated shape with an aspect ratio changing with size and that in the 50–100 nm size range (N ≈ 50 000–100 000 particles) they show a spontaneous symmetry breaking of the surface bipolar director field into a twisted pattern, whose chirality we quantify with a specific index. The droplets are found to be inhomogeneous in terms, e.g. of the local orientational order, and a detailed description of their internal and interfacial structure is given.

Effects of anchoring strength on the diffusivity of nanoparticles in model liquid-crystalline fluids

The diffusivity of a nanoparticle suspended in a liquid crystal is investigated in the limit of nematic ordering and under isotropic conditions. Molecular simulations are performed with the liquid-crystalline solvent represented at the level of Gay–Berne mesogens in the canonical (N,V,T) ensemble. The mesogen–colloid interaction strength is varied to induce anchoring that ranges from parallel to perpendicular. Mean square displacements, orientational correlation functions, and relative colloidal diffusivities are reported for different types of mesogenic anchoring on the nanoparticle. The Gay–Berne parametrization is contextualized with respect to experimental observations, and a specific set of parameters is found to reproduce the characteristic ratio of mesogenic diffusivities observed in recent experiments. The results presented in this work provide a means to determine anchoring strength at small length scales, and the parameterizations provided in this work could serve as a starting point to interpret experimental data for nanoparticle suspensions in liquid-crystals at a molecular level.

Applications of Wang-Landau sampling to determine phase equilibria in complex fluids

Applications of the Wang-Landau algorithm for simulating phase coexistence at fixed temperature are presented. The number density is sampled using either volume scaling or particle insertion/deletion. The resulting algorithms, while being conceptually easy, are of comparable efficiency to existing multicanonical methods but with the advantage that neither the chemical potential nor the pressure at phase coexistence has to be estimated in advance of the simulation. First, we benchmark the algorithm against literature results for the vapor-liquid transition in the Lennard-Jones fluid. We then demonstrate the general applicability of the algorithm by studying vapor-liquid coexistence in two examples of complex fluids: charged soft spheres, which exhibit a transition similar to that in the restricted primitive model of ionic fluids, being characterized by strong ion pairing in the vapor phase; and Stockmayer fluids with high dipole strengths, in which the constituent particles aggregate to form chains, and for which the very existence of a transition has been widely debated. Finally, we show that the algorithm can be used to locate a weak isotropic-nematic transition in a fluid of Gay-Berne mesogens.

X-ray scattering patterns of model liquid crystals from computer simulation: Calculation and analysis

We have simulated the x-ray scattering patterns for the isotropic, nematic, smectic A, and smectic B phases formed by the Gay–Berne model mesogen GB(4.4,20.0,1,1). We have used these scattering patterns for two quite different purposes. First, they have been employed to confirm the previous identification of the phases formed by this Gay–Berne mesogen, building on the considerable knowledge base created from x-ray scattering studies of real liquid crystal phases. Second, we have analyzed the simulated scattering patterns to obtain quantitative structural information about the mesophases using several approximate routes. The structural parameters include the nearest neighbor separation, the layer spacing, and translational order parameters of the smectic phase and the singlet orientational distribution function of the nematic phase. Since these quantities have already been determined from previous simulations, we are able to provide a unique test of the approximations used to extract them from the scattering patterns. The success of this investigation has required the use of sensibly large systems and so we have sought to understand, in a quantitative manner, how the size and geometry of the system influences the scattering pattern.

Computer Simulation of the Field-Induced Alignment of the Smectic a Phase of the Gay-Berne Mesogen Gb(4.4,20.0,1,1)

As an aid to understanding the mechanism for the field-induced alignment of the smectic A phase we have attempted to simulate this process for the Gay-Berne model mesogen GB(4.4,20.0,1,1). The results for the quasi-dynamical behaviour of the alignment process obtained from a constant pressure-constant temperature Monte Carlo simulation are discussed. It is found that the molecules realign parallel to the field without destroying the layer structure and, more or less, as a monodomain in the simulations. This is qualitatively in agreement with the results obtained from recent deuterium NMR and small angle X-ray experiments. In addition, the relationship between the box shape and structures formed during the alignment process is discussed. The choice of box is found to be important for the simulation of the field-induced alignment process.

Shear-induced structural changes of a smectic-A phase: a computer simulation study.

We have carried out a Monte Carlo simulation of a thin sample of the smectic-A phase of the Gay-Berne mesogen GB(4.4,20.0,1,1) sandwiched between two plates and subject to shear. The smectic layers are perpendicular to the confining plates and are pinned at the boundaries. The thickness of the samples studied ranges from about three to twenty molecules. The layers tilt progressively with increasing shear, but rearrange themselves at a critical shear. At this critical shear the layers melt near the center of the sample and reform with a reduced tilt consistent with the layer pinning at the walls. The pseudodynamics of this process as the smectic layers melt and are reformed have been followed during the simulation. The critical layer tilt at which slippage takes place tends to a constant value for thick samples, but for very thin samples the critical shear tends toward half a smectic layer, with a significantly reduced translational order near the sample center just before the critical shear. The simulation results are consistent with the predictions of the mean field theory of this phenomenon developed by Mottram et al.

Representation of pair correlations in nematics

A complete expansion of equilibrium pair correlation functions for a uniaxial nematic phase composed of axially symmetric, non-polar and chiral molecules is proposed. Full advantage is taken of the symmetry of the nematic state and of the molecules. The explicit analysis and classification of the terms involving spherical harmonics with indices not exceeding 4 is given and illustrated using computer simulations for the nematic phase of a Gay-Berne mesogen. The theory is contrasted with the commonly used approach employing invariants that describe orientational correlations in molecular fluids. The role of the new representation in obtaining a correct understanding of a variety of observables, like the elastic constants, is demonstrated. In particular, the long-standing puzzle concerning the splay-bend degeneracy is resolved.

Field-Induced Alignment of the Directors in the Smectic A Phase. Experiment and Simulation

In contrast to nematics far less is known about the alignment of the directors in a smectic A phase by an external field. To characterise this process, which necessarily involves the flow of the molecules, we have undertaken an NMR investigation of the smectic A phase of 4-octyl-4′-cyanobiphenyl. The results of these experiments have revealed that, as expected, the alignment of the directors is a complex process strongly influenced by the nature of the containing surface for the smectic A phase. To assist in understanding the alignment process we have used computer simulations to study the field induced alignment of the directors in the smectic A phase formed by the Gay-Berne mesogen GB(4.4,20.0,1,1).

Computer simulation studies of anisotropic systems. XXXII. Field-induction of a smectic A phase in a Gay–Berne mesogen

Molecular field theory predicts the induction of a smectic A phase by the application of a field, either magnetic or electric, to a nematic phase. This intriguing behavior results from an enhancement of the orientational order which is coupled to the translational order and so shifts the smectic A-nematic transition. To test this prediction we have investigated a system of Gay–Berne mesogenic molecules subject to an applied field of second rank using isothermal–isobaric Monte Carlo simulations. The results of our calculations are compared with the Kventsel–Luckhurst–Zewdie molecular field theory of smectogens, modified to include the effect of an external field. We have also used the simulations to explore the possibility of inducing more ordered smectic phases with stronger fields.

Cage Effects in the Orientational Dynamics of a Gay-Berne Mesogen

The dynamical features of a Gay-Berne mesogen have been investigated through an analysis of molecular dynamics simulation data. The cage potential confining instantaneously the orientational motion of the molecules, for both the isotropic and nematic phases have been defined and parameterised. The statistical analysis of the data obtained from the MD simulations show that no significant differences exist in the local structural and dynamical properties of the cage in the isotropic and nematic phases, but that a clear dependence of the cage potential does exist with respect to its orientation in the nematic phase.

A STOCHASTIC CAGE MODEL FOR THE ORIENTATIONAL DYNAMICS OF SINGLE MOLECULES IN NEMATIC PHASES

A stochastic cage model for the orientational dynamics of a molecule in isotropic and nematic phases of a liquid crystal has been developed, following the methodology introduced in Refs. 1, 2. The model has been parameterized on the basis of statistical data obtained from the analysis of Molecular Dynamics (MD) simulations of a Gay–Berne mesogen and is based on the general assumption of a timescale separation between the fast inertial librational motion inside the instantaneous cage potential and the slow diffusive motion of the cage itself. The model is able to reproduce single molecule time correlation functions both for the angular momentum and the reorientation of the long molecular axis of the molecule. A complete description of the dynamics of a Gay–Berne particle is given with a single set of physical parameters, from a very fast (hundreds of femtoseconds) timescale up to a timescale of nanoseconds.

Computer simulation studies of anisotropic systems. XXX. The phase behavior and structure of a Gay–Berne mesogen

The Gay–Berne potential is proving to be a valuable model with which to investigate the behavior of liquid crystals using computer simulation techniques. The potential contains four independent parameters which control the anisotropy in the attractive and repulsive interactions. The choice of these parameters is not straightforward and it would seem that those employed in some simulations are not strictly appropriate for mesogenic rodlike molecules. Here we report a detailed computer simulation study of Gay–Berne particles interacting via a potential parametrized to reflect the anisotropic forces based on a fit to a realistic mesogenic molecule. The behavior of the phases and the transitions between them have been investigated for a system of 2000 particles using isothermal–isobaric Monte Carlo simulations. At low pressures, this Gay–Berne mesogen exhibits isotropic, smectic A and smectic B phases but, as the pressure is increased, so a nematic phase is added to the sequence. The nature of the phase transitions and the phase diagram are compared where possible with those of real mesogens. The structures of the four phases have been investigated in detail for a larger system of 16 000 particles using canonical molecular dynamics simulations at state points taken from the phase diagram determined from the Monte Carlo simulations. A wide range of singlet and pair distribution functions were evaluated together with orientational correlation coefficients and, for the smectic phases, a bond orientation correlation function. The results for these properties were used to identify the phases, to consider their structure at a quantitative level and, where possible, to make contact with experimental studies and the predictions of theories of liquid crystals. It would appear that with this parametrization, the Gay–Berne potential provides a powerful tool with which to understand the behavior of real liquid crystals and to test the predictions of theory.

A molecular dynamics study of a steric multipole model of liquid crystal molecular geometry

We report results from a series of molecular dynamics simulations designed to study the phase behaviour of model rod-like liquid crystal molecules with different geometries interacting via the Gay-Berne potential. Following the classification of molecular geometry in terms of a multipole expansion in steric asymmetry, two models have been studied in detail: a zigzag model defined as a steric quadrupole and a triangle model defined as a longitudinal steric dipole, and comparison has been made with a cylindrical model. Results from the NVE ensemble indicate that the model steric quadrupole delays the temperature of onset of the nematic phase. Extensive simulations in the NPT ensemble demonstrate a similar trend in the temperature of onset of the smectic B phase, with a lower temperature of onset observed with the steric quadrupole than the steric dipole. Local antiparallel steric ordering within a layer was observed with the model steric dipole in the crystal B phase but not with the model steric quadrupole. This structure is in agreement with experimental results and with the prediction of the generalized molecular asymmetry model. The steric quadrupole demonstrated a rippled structure through the smectic B phase, increasing in amplitude and wavelength sufficiently to tilt molecules along a wave with respect to the system director as the system was cooled. This structure was almost absent in the final crystal structure simulated. The ensemble also allowed comparison with experiment and agreement, scaled with respect to the single-site Gay-Berne mesogen, was found to be good.

Monte Carlo simulation of discotic Gay–Berne mesogens with axial dipole

R. Berardi, S. Orlandi and C. Zannoni, J. Chem. Soc., Faraday Trans., 1997, 93, 1493 DOI: 10.1039/A607571A

Computer-simulation studies of anisotropic systems. Part XXIV.—Constant-pressure investigations of the smectic B phase of the Gay–Berne mesogen

Molecular dynamics simulation studies of the smectic B phase of the Gay–Berne model mesogen at constant volume suggest that the structure of the phase may be influenced by the periodic images. To avoid this problem we have undertaken an isothermal–isobaric Monte Carlo simulation of this phase. The ability of the dimensions of the simulation box to change during the course of the simulation should allow the layered structure of the phase to be commensurate with the periodic images. The structure of the smectic B phase has been characterised using the radial distribution function, an in-plane distribution function normal to the director and the number density along the director. In addition, these distributions have been augmented with images constructed from configurations taken from the production stage of the simulation. Such images have proved to be of particular value in exploring the positions of particles in one layer relative to those in an adjacent layer; these reveal an unexpected structure for the phase. They have also allowed us to see that the layers in the smectic B phase have a slightly rippled structure. The thermodynamic properties have also been determined as a function of temperature and through the smectic B–isotropic transition. Since these results are obtained at constant pressure this facilitates comparison with the behaviour of real mesogens which are usually studied under the same condition. The agreement between simulation and experiment is found to be good.

Computer simulation studies of anisotropic systems

The Gay-Berne potential is proving to be of considerable value in computer simulation studies of liquid crystals. However, the parameters employed in the potential were chosen by comparison with that for a line of four Lennard-Jones centres; they may not, therefore, be appropriate for mesogenic molecules. To see if this is the case we have estimated the parameters in the Gay-Berne potential by comparison with the site-site potential constructed for p-terphenyl, which has a molecular structure typical of many mesogens. Unlike the Gay-Berne potential the site-site potential is biaxial, and a method for projecting out this biaxiality is proposed. The resultant uniaxial model has then been used to obtain values for the parameters occurring in the Gay-Berne potential. These are found to differ significantly from those proposed originally; they are, we believe, more appropriate for investigations of the behaviour of liquid crystals. Our own molecular dynamics simulations, based on the new parametrization, reveals the existence of isotropic, nematic and smectic A phases. The results, in common with those from previous studies, indicate that the structure of the isotropic and nematic phases of the Gay-Berne mesogen are dominated by short range anisotropic repulsive forces. In marked contrast, the stability of the smectic A phase is found to be critically dependent upon the anisotropy in the attractive forces.