Gay-Berne Potential Research Articles

A novel orientation-dependent potential model for prolate mesogens

An intermolecular potential is introduced for the study of molecular mesogenic fluids. The model combines distinct features of the well-known Gay-Berne and Kihara potentials by incorporating dispersive interactions dependent on the relative pair orientation to a spherocylinder molecular core. Results of a Monte Carlo simulation study focused on the liquid crystal phases exhibited by the model fluid are presented. For the chosen potential parameters, molecular aspect ratio L*=5 and temperatures T*=2, 3, and 5, isotropic, nematic, smectic-A, and hexatic phases are found. The location of the phase boundaries as well as the equation of state of the fluid and further thermodynamical and structural parameters are discussed and contrasted to the Kihara fluid. In comparison to this latter fluid, the model induces the formation of ordered liquid crystalline phases at lower packing fractions and it favors, in particular, the appearance of layered hexatic ordering as a consequence of the greater attractive interaction assigned to the parallel side-to-side molecular pair configurations. The results contribute to the evaluation of the role of specific interaction energies in the mesogenic behavior of prolate molecular liquids in dense environments.

Surface ordering of diskotic liquid crystals.

We present Monte Carlo simulations of diskotic molecules using the Gay-Berne potential in a slab geometry. The disk-wall interaction is described by two different functions according to whether or not the equilibrium distance is dependent on the relative orientation of the disk to the wall. Furthermore, by changing the parameters of these potentials, we model either homeotropic (face-on) or planar (edge-on) anchoring of the disks. We have found that the isotropic-nematic transition does not change in comparison with the bulk situation. The temperature of the nematic-columnar transition, on the contrary, is found to increase for homeotropic anchoring, and decrease for planar anchoring, independently of the details of the potential. We explain the decrease of the transition temperature in the planar anchoring situation as the result of an induced frustration, due to the competition between the two orientations induced independently by the upper and lower walls.

Molecular dynamics investigation of a density-driven glass transition in a liquid crystal system.

Molecular dynamics simulations are carried out to address the density-driven glass transition in a system of rodlike particles that interact with the Gay-Berne potential. Since crystallization occurs in this system on the time scale of the simulations, direct simulation of the glass transition is not possible. Instead, glasses with isotropic orientational order are heated to a temperature T, and the relaxation times by which nematic orientational order develops are determined. These relaxation times appear to diverge at a critical density rho(c); i.e., the system can equilibrate at rho<rho(c), but it cannot equilibrate at rho>rho(c) (at the temperature T). The relaxation times follow a power-law scaling as the critical density is approached, suggesting that this density-driven glass transition concurs with mode coupling theory.

Molecular dynamics simulation study on the phase behavior of the Gay-Berne model with a terminal dipole and a flexible tail.

To study the effect of the alkyl tail and the terminal dipole on the stability of the liquid crystalline phase of mesogens, we have carried out molecular dynamics simulations for 1CB(4-methyl-4'-cyanobiphenyl) and 5CB(4-n-pentyl-4'-cyanobiphenyl) by using a coarse-grained model. In the coarse-grained model, a 5CB molecule is divided into the rigid part of 1CB moiety, which is represented by an ellipsoid, and the remaining flexible part which is represented by a chain of united atoms. The nonbonded potential between coarse-grained segments is represented by the generalized Gay-Berne (GB) potential and the potential parameters are determined by directly comparing the GB potential with the atomistic potentials averaged over the rotation of the mesogen around its axis. In addition, a dipole moment is placed at one end of the ellipsoid opposite to the flexible tail. The ordered state obtained in the polar 5CB model was assigned as the nematic phase, and the experimental static and dynamical properties were reproduced well by using this coarse-grained model. Both the dipole-dipole interactions and the thermal fluctuation of the flexible tail increase the positional disorder in the director direction, and stabilize the nematic phase. Thus, the nematic phase in the polar 5CB is induced by a cooperative effect of the flexible tail and the terminal dipole. It is noted that a local bilayer structure with head-to-head association is formed in the nematic phase, as experimentally observed by x-ray diffraction measurements.

Modeling DNA structure, elasticity, and deformations at the base-pair level.

We present a generic model for DNA at the base-pair level. We use a variant of the Gay-Berne potential to represent the stacking energy between the neighboring base pairs. The sugar-phosphate backbones are taken into account by semirigid harmonic springs with a nonzero spring length. The competition between these two interactions and the introduction of a simple geometrical constraint lead to a stacked right-handed B-DNA-like conformation. The mapping of the presented model to the Marko-Siggia and the stack-of-plates model enables us to optimize the free model parameters so as to reproduce the experimentally known observables such as persistence lengths, mean and mean-squared base-pair step parameters. For the optimized model parameters, we measured the critical force where the transition from B- to S-DNA occurs to be approximately 140 pN. We observe an overstretched S-DNA conformation with highly inclined bases which partially preserves the stacking of successive base pairs.

Computer simulations of a liquid crystalline dendrimer in liquid crystalline solvents

Molecular dynamics simulations have been carried out to study the structure of a model liquid crystalline dendrimer (LCDr) in solution. A simplified model is used for a third generation carbosilane LCDr in which united atom Lennard-Jones sites are used to represent all heavy atoms in the dendrimer with the exception of the terminal mesogenic groups, which are represented by Gay–Berne potentials. The model dendrimer is immersed in a mesogenic solvent composed of Gay–Berne particles, which can form nematic and smectic-A phases in addition to the isotropic liquid. Markedly different behavior results from simulations in the different phases, with the dendrimer changing shape from spherical to rodlike in moving from isotropic to nematic solvents. In the smectic-A phase the terminal mesogenic units are able to occupy five separate smectic layers. The change in structure of the dendrimer is mediated by conformational changes in the flexible chains, which link the terminal mesogenic moieties to the dendrimer core.

Interaction potentials for soft and hard ellipsoids.

Using results from colloid science we derive interaction potentials for computer simulations of mixtures of soft or hard ellipsoids of arbitrary shape and size. Our results are in many respects reminicent of potentials of the Gay-Berne type but have a well-defined microscopic interpretation and no adjustable parameters. Since our potentials require the calculation of similar variables, the modification of existing simulation codes for Gay-Berne potentials is straightforward. The computational performance should remain unaffected.

Influence of shape and energy anisotropies on the phase diagram of discotic molecules.

We present Monte Carlo simulations of discotic molecules using the Gay-Berne potential with shape (kappa) and energy (kappa(')) anisotropies. Following the previous work of Bates and Luckhurst [J. Chem. Phys. 104, 6696 (1996)] at kappa=0.345, kappa(')=0.2 when we determine the sequence of different phases at the same reduced pressure P(*)=50, we find an additional phase at low temperatures corresponding to an orthorhombic crystalline phase and we characterize it. Keeping the shape anisotropy fixed at kappa=0.2, we determine the evolution of the phase diagram with varying energy anisotropy. At high kappa('), low anisotropy, the system is not able to build columns while at low kappa('), the system exhibits both orthorhombic crystal as well as hexagonal liquid crystal phases over a wide range of pressures and temperatures. The domain of stability of the nematic phase is found to systematically shift towards higher pressures as kappa(') decreases.

Computer simulation of polar bent-core molecules.

Results are presented from molecular dynamics simulations in the NPT ensemble of novel bent-core liquid crystal systems. Following on from a previous study of bent-core steric shape, this study examines the effect the addition of a transverse electric dipole has on the phase diagram of a bent-core liquid crystal model. A simple model of the interaction employed a two-site Gay-Berne potential with the sites separated by +/-0.5 reduced units with a central transverse point dipole, for all models investigated. The angle between the sites 180 degrees -gamma was varied in a range gamma=10 degrees to gamma=70 degrees suggested by real molecules. The addition of the dipole to the model tended to stabilize smectic phases and increase the angle of tilted phases. As the angle gamma increased, the transition temperature to the first ordered phase decreased markedly. Smectic A, tilted smectic B, and a spontaneously polarized smectic B phases were observed in the gamma=10 degrees bent-core model. The gamma=20 degrees model showed smectic A and tilted antiferroelectric smectic B phases. The gamma=40 degrees model showed an antiferroelectric phase that exhibited unusual packing behavior. Both the gamma=20 degrees and gamma=40 degrees models demonstrated a significant phase biaxiality in the smectic B phases.

Computer simulations of pure and mixed systems of disklike particles interacting with the S-function Corner potential

The S-function potential for single-site particles has been recently introduced as an extension of the Gay–Berne potential. With the S-function potential, we can model particles of other and, possibly, more realistic shapes than Gaussian overlap ellipsoids and we can simulate mixtures in a systematic manner. As an example of both applications, we have studied via Monte Carlo computer simulation assemblies of cylindrically symmetric disklike particles of two different types. They can be considered complementary perturbations of a disk, with, respectively, a depression (red-cell, R particles) and a protuberance (ufo, U particles) at the center. The former is meant to mimic the average effect of side chains of real diskotics, while the latter is a simple representation of diskotic metallomesogens. Four systems of these kind of particles have been studied as a function of temperature: two pure cases and two 1:2 binary mixtures, so that the combined effects of shape and concentration can be observed. We have found the largest variety of phases in the pure U system where also a nematic phase is present. No such phase is observed when 13 of the U particles are replaced by R particles, as well as in the mixture 23R-13U and in the pure R system. At the lowest temperatures investigated all systems show a lattice phase except the mixture 13R-23U, whose organization is better described as a disordered columnar phase.

Towards an anisotropic bead-spring model for polymers: a Gay-Berne parametrization for benzene

Intermolecular binding energy data, determined from ab initio supermolecule calculations on the benzene dimer, are used to parametrize a Gay-Berne potential. This potential is applied in determining the structure and energetics of gas phase clusters up to and including the tetramer. Two crystal structures of benzene, Phase I and Phase II, are optimized using this model potential at 0 and 2.5GPA pressure, both at OK, and compared with experiment. Elastic constants for the Phase I crystal structure are calculated and compared with experimental data and previous theoretical results.

Brownian dynamics simulations for suspension of ellipsoids in liquid crystalline phase under simple shear flows

Brownian dynamics simulations of shear flows are carried out for various suspensions of ellipsoids interacting via the Gay-Berne potential. In this simulation all the systems of the suspension are in a liquid crystalline phase at rest. In a shear flow they exhibit various motions of the director depending on the shear rate: the continuous rotation, the intermittent rotation, the wagging-like oscillation, and the aligning. The director is almost always out of the vorticity plane when it rotates, that is the kayaking. The number density of the system and the inter-particle potential intensity significantly affect the shear rate dependence of orientation. In particular, the continuous rotation of director is maintained to higher shear rates for the system with a stronger potential. Furthermore, the rheological properties are examined. The shear-thinning in viscosity is observed, but the negative first normal difference is not obtained.

The effects of molecular shape and quadrupole moment on tilted smectic phase formation

Results are presented from constant NPT Monte Carlo simulations of two systems based on the biaxial internally rotated Gay-Berne (IRGB) potential. First, the effect of increasing molecular elongation is considered, and it is shown that a change in aspect ratio from 3:1 to 4:1 leads to nematic and tilted smectic J phases being replaced by smectic A and tilted smectic G phases, respectively. Second, the effect of a longitudinal electric quadrupole on the phase behaviour of the IRGB model is examined. The presence of a moderate quadrupole moment results in the smectic G phase being replaced by a smectic J; the onset pressure of the smectic J increases monotonically as the quadrupole moment is increased, although the integrity of the tilted layers improves. In addition, the region of smectic A stability is found to persist for moderate quadrupole moment values. For the largest quadrupole moment considered, domains comprising poorly defined, tilted layers are formed but fail to develop into coherent smectic structures. This observation is ascribed to the competition between the unique tilt direction favoured by the biaxial IRGB potential and the random tilt direction of the uniaxial quadrupole-quadrupole interactions.

A domain decomposition molecular dynamics program for the simulation of flexible molecules of spherically-symmetrical and nonspherical sites. II. Extension to NVT and NPT ensembles

Abstract We describe the algorithms for NVT and NPT-ensemble simulations developed within the parallel molecular dynamics program GBMOLDD. This program uses the domain decomposition algorithm and is targeted at large-scale simulations of molecular systems (particularly polymers and liquid crystals) composed of both spherically-symmetric and nonspherical sites. The nonspherical sites can be described either by a Gay–Berne potential or by soft repulsive spherocylinders. The molecules can be of arbitrary topology and the intramolecular forces are described via standard force fields. We tested the stability of both leap-frog and velocity-Verlet integrators on two “real-life” systems—a nematic liquid crystal phase of 1944 one-site Gay–Berne molecules and on 512 flexible liquid-crystalline dimers. In both cases the algorithm demonstrates good stability over the typical simulation times required for new phase formation and/or molecular relaxation processes.

Computer simulation of apolar bent-core and rodlike molecules.

Bent-core molecules have received much interest due to their biaxiality and novel phase ordering. It is, therefore, of interest to model the characteristic shape of these molecules and observe the effect on liquid crystal mesophase formation in a computer simulation study. A simple model of the interaction employed a two-site Gay-Berne potential with the sites separated by +/-0.5 reduced units for all models. The angle between the two sites, 180 degrees -gamma, was varied from gamma=0 degrees to gamma=70 degrees and influenced the phase behavior markedly. The rodlike model formed isotropic, nematic, smectic-A, and smectic-B, phases. Results for the bent-core models show that as the angle gamma increases the transition temperature to the ordered phase decreases. As gamma increases the nematic phase is first destabilized then stabilized with respect to the smectic phase and a tilted smectic-B phase is seen at gamma=20 degrees. For gamma=40 degrees a "TGB-like" phase is identified as the system cools whereas for gamma=70 degrees no ordered phase is formed.

Density-functional theory of the columnar phase of discotic Gay–Berne molecules

We propose a density-functional theory for the study of the phase behavior of discotic molecules interacting via a Gay–Berne potential. The attractions are treated perturbatively in a van der Waals-type manner while the virial series of the repulsions is resummed approximately with the inclusion of the exact second-order Onsager result. On this basis we have studied the isotropic (I)–nematic (N)–columnar (Co) phase behavior for various aspect ratios of the discotic molecules. For small aspect ratios (i.e., large nonsphericities) the phase diagram is found to involve a I–N–Co triple point where the two I–N and N–Co first-order transitions are transformed into a direct I–Co first-order transition. For larger aspect ratios the domain where the N-phase is stable shrinks and disappears above a critical value of the aspect ratio. When compared to the available simulation data it is found that the theory underestimates this critical aspect ratio.

Rigid-body formalism for simulating macromolecules

Abstract In our work we aim at developing a model where macromolecules are represented on a mesoscopic level as an assembly of rigid bodies which interact via arbitrary bonded and non-bonded interactions. For the non-bonded interactions we use a variant of the Gay–Berne potential, while the bonded interactions are split into an orientational part and a harmonic bond between two arbitrary points in the respective material frames.

A general-purpose coarse-grained molecular dynamics program

In this article, we describe a general-purpose coarse-grained molecular dynamics program COGNAC ( COarse Grained molecular dynamics program by NAgoya Cooperation). COGNAC has been developed for general molecular dynamics simulation, especially for coarse-grained polymer chain models. COGNAC can deal with general molecular models, in which each molecule consists of coarse-grained atomic units connected by chemical bonds. The chemical bonds are specified by bonding potentials for the stretching, bending and twisting of the bonds, each of which are the functions of the position coordinates of the two, three and four atomic units. COGNAC can deal with both isotropic and anisotropic interactions between the non-bonded atomic units. As an example, the Gay–Berne potential is implemented. New potential functions can be added to the list of existing potential functions by users. COGNAC can do simulations for various situations such as under constant temperature, under constant pressure, under shear and elongational deformation, etc. Some new methods are implemented in COGNAC for modeling multiphase structures of polymer blends and block copolymers. A density biased Monte Carlo method and a density biased potential method can generate equilibrium chain configurations from the results of the self-consistent field calculations. Staggered reflective boundary conditions can generate interfacial structures with smaller system size compared with those of periodic boundary conditions.

Liquid crystal phases of achiral banana-shaped molecules: a computer simulation study

The phase behaviour of achiral banana-shaped molecules was studied by computer simulation. The banana-shaped molecules were described by model intermolecular interactions based on the Gay-Berne potential. The characteristic molecular structure was considered by joining two calamitic Gay-Berne particles through a bond to form a biaxial molecule of point symmetry group C 2v with a suitable bending angle. The dependence on temperature of systems of N=1024 rigid banana-shaped molecules with bending angle φ =140° has been studied by means of Monte Carlo simulations in the isobaric-isothermal ensemble (NpT). On cooling an isotropic system, two phase transitions characterized by phase transition enthalpy, entropy and relative volume change have been observed. For the first time by computer simulation of a many-particle system of banana-shaped molecules, at low temperature an untilted smectic phase showing a global phase biaxiality and a spontaneous local polarization in the layers, i.e. a local polar arrangement of the steric dipoles, with an antiferroelectric-like superstructure could be proven, a phase structure which recently has been discovered experimentally. Additionally, at intermediate temperature a nematic-like phase has been proved, whereas close to the transition to the smectic phase hints of a spontaneous achiral symmetry breaking have been determined. Here, in the absence of a layered structure a helical superstructure has been formed. All phases have been characterized by visual representations of selected configurations, scalar and pseudoscalar correlation functions, and order parameters.

1324 Gay-Berne ポテンシャル回転楕円体粒子によるライオトロピック液晶系の単純せん断流れのブラウン動力学シミュレーション

1324 Gay-Berne ポテンシャル回転楕円体粒子によるライオトロピック液晶系の単純せん断流れのブラウン動力学シミュレーション