Gay-Berne Particles Research Articles

A Monte Carlo simulation study of associated liquid crystals

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.

Computer Simulations using a Quadrupolar Gay-Berne Model

Systems of Gay-Berne particles with longitudinal and transverse linear quadrupoles are studied by molecular dynamics simulations. Attention is paid to the characterisation of the smectic phase as a function of the quadrupole magnitude and direction. It is found that the longitudinal quadrupole destabilises the formation of the smectic phase whereas the transverse quadrupolar Gay-Beme system demonstrates a greatly extended smectic A region. The smectic phase is found to be sensitive to the magnitude of the longitudinal quadrupole with smectic A, B and C phases observed. A simulated annealing method for characterising a smectic C phase is described.

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.

Computer simulations using a longitudinal quadrupolar Gay–Berne model: effect of the quadrupole magnitude on the formation of the smectic phase

Systems of Gay–Berne particles with longitudinal linear quadrupoles are studied by molecular dynamics simulations. The effect of the magnitude of the quadrupole on the smectic phase is investigated. It is found that the quadrupole destabilises the formation of the smectic phase which disappears altogether with high-magnitude quadrupoles. As the magnitude of the quadrupole is reduced a variety of smectic phases are formed, including smectic A, smectic C and smectic B, with the eventual formation of a crystal. The maximum magnitude of the tilt observed is 17.2°, comparable with experimentally observed magnitudes.

Viscous Behavior and Shear-Induced Structural Changes in Perfectly Oriented Liquid Crystals

The anisotropy of the viscosity and shear-induced structural changes are studied via nonequilibrium molecular dynamics (NEMD) simulations for two types of model liquid crystals which possess both isotropic and smectic phases. These models are (a) perfectly oriented Gay–Berne particles and (b) r−12-soft-spheres plus an r−6-interaction with a P2-anisotropy. Results are presented for the Miesowicz viscosity coefficients in the nematic phase. Presmectic effects are observed. Structural changes are revealed by snapshots of configurations and by the static structure factor, presented in analogy to scattering experiments. The shear-induced transition from the smectic to the nematic phase is analyzed. Similarities between magnetorheological fluids and discotic systems which can form columnar phases are discussed.

Molecular dynamics simulations of flexible liquid crystal molecules using a Gay-Berne/Lennard-Jones model

Molecular dynamics simulations are described for liquid crystal molecules composed of two Gay-Berne particles connected by an eight-site Lennard-Jones alkyl chain. Calculations have been carried out for 512 molecules in the NVE and NPT ensembles for simulation times of up to 6.4 ns. The system exhibits the sequence of phases: isotropic liquid, smectic-A, smectic-B, and the simulations demonstrate the spontaneous growth of a smectic-A liquid crystal over a period of approximately 6 ns on cooling from the isotropic liquid. Model molecules are seen to remain flexible and able to change conformation in the smectic-A phase. As temperature is reduced molecules become elongated as the number of gauche conformations drops, leading to a small increase in the spacing of smectic layers. The latter is seen through the temperature dependence of the Gay-Berne radial distribution function resolved parallel to the direction of orientational order. Results are presented which show an odd–even variation of orientational order parameters for bonds in the alkyl chain, and a change in effective torsional potentials as the system is cooled from isotropic liquid to a smectic-A phase.

Computer simulation studies of anisotropic systems. XXVII. The direct pair correlation function of the Gay–Berne discotic nematic and estimates of its elastic constants

Monte Carlo simulations have been performed for a discotic liquid crystal composed of Gay–Berne particles. On the basis of these simulations for the nematic phase, a subset of the spherical harmonic expansion coefficients of the direct pair correlation function (DPCF) were determined from the pair distribution function (PDF) by solving the Ornstein–Zernike (OZ) equation. This was achieved by generalizing the Wiener–Hopf factorization scheme for the numerical solution of the OZ equation. Only the expansion coefficients gl1,l2,l(r) (lα⩽4) of the PDF in the laboratory frame were used when solving the OZ equation; this means that the DPCF so obtained is equivalent to that for a nematic in which the director is randomly distributed. From the DPCF, the scaled Oseen–Zöcher–Frank elastic constants K11*, K22*, and K33*, as well as the surface constant K13*, have been calculated from the subset of expansion coefficients. Generally, we find that K33*<K11*<K22*, in agreement with what is expected and found for discotic nematics. These results are quantitatively but not qualitatively different from those calculated with the help of analytical approximations for the same spherical harmonic expansion coefficients of the direct pair correlation function. For example, the values of the bulk elastic constants determined via the OZ equation are about three times larger than the bulk elasticity obtained with the low density approximation.

Computer simulation studies of confined liquid-crystal films

In this paper we present results from molecular dynamics simulations performed using a system of Gay-Berne particles confined between two substrates in a slab geometry. We use a nonseparable anisotropic molecule-substrate interaction potential and investigate weak and moderate molecule-substrate coupling strengths. We find that for both coupling strengths a well-defined, tilted molecular layer forms at each wall and that the pretilt angle and layer density are only weakly dependent on temperature as the central region is cooled through isotropiclike and nematiclike regions. The orientationally ordered fluid formed at the center of the film is tilted in sympathy with the surface layers. At low temperatures, however, where the central region adopts a layered arrangement, a sharp change is observed in the pretilt angle. This transition is more marked in the weak-coupling system where the high-temperature tilted surface layers adopt an approximately planar arrangement at low temperatures and the system resembles a bookshelf-geometry smectic film. In the moderate-coupling system, the surface layers maintain some tilt in the presence of the layered central region, leading to a smectic-stripe phase arrangement.

Non-spherical molecules with spherical square-wells revisited: some possible new phase diagrams from density functional theory

A simple model fluid, in which molecules consist of hard non-spherical cores embedded in spherical square-wells, has been re-examined. Within the Gaussian approximation of Onsager–Parsons–Lee theory, for very narrow attractive square-wells, ordinary liquid–vapour coexistence is preempted by a direct transition between a low density disordered fluid phase and a nematic phase. This is consistent with recent simulation results on fluids of Gay–Berne particles, and of hard spherocylinders with generalized square-wells which probed the effect of changing the ratio of attraction range to molecular elongation. Moreover, coexistence between two nematic phases is found on further decreasing the width of square-well, analogous to the isostructural solid–solid transitions observed in fluids characterized by very short range isotropic interactions.

Non-spherical molecules with spherical square-wells revisited: some possible new phase diagrams from density functional theory

A simple model fluid, in which molecules consist of hard non-spherical cores embedded in spherical square-wells, has been re-examined. Within the Gaussian approximation of Onsager–Parsons–Lee theory, for very narrow attractive square-wells, ordinary liquid–vapour coexistence is preempted by a direct transition between a low density disordered fluid phase and a nematic phase. This is consistent with recent simulation results on fluids of Gay–Berne particles, and of hard spherocylinders with generalized square-wells which probed the effect of changing the ratio of attraction range to molecular elongation. Moreover, coexistence between two nematic phases is found on further decreasing the width of square-well, analogous to the isostructural solid–solid transitions observed in fluids characterized by very short range isotropic interactions.

Computer simulation of chiral liquid crystal phases III. A cholesteric phase formed by chiral Gay-Berne atropisomers

The relation between molecular helicity and the handedness of cholesteric phases was studied investigating a model system of chiral atropisomers using Monte Carlo simulations in the NVT ensemble. The system under investigation was given by N = 256 rigid, chiral Gay–Berne atropisomers of point symmetry group D2. The molecular chirality of the atropisomers was introduced by joining two Gay–Berne particles through a bond with a suitable fixed dihedral angle. Starting from an isotropic configuration, cholesteric phases were obtained on equilibrating the systems whereby left-handed cholesterics were formed by atropisomers with M helicity and right-handed cholesterics by atropisomers with P helicity. A11 phases have been characterized by visual representations of selected configurations, correlation functions, and sets of four local order parameters.

Computer simulation of chiral liquid crystal phases. IV. Intermolecular chirality transfer to rotamers in a cholesteric phase

Abstract Intermolecular chirality transfer was studied by investigating the conformational distribution of rotamers in a cholesteric guest-host phase using Monte Carlo (MC) simulations in the NVT ensemble. The guest-host system under investigation was given by N c = 238 rigid, chiral Gay-Berne atropisomers as host molecules and N a = 18 flexible Gay-Berne rotamers as guest molecules. The rigid, chiral Gay-Berne atropisomers of point symmetry group D2 were defined by joining two Gay-Berne particles through a bond with a suitable fixed dihedral angle. The possibility of internal rotation about the bond axis without a rotational barrier was introduced as an internal degree of freedom for the guest molecules, for convenience denoted as Gay-Berne rotamers. Starting from an isotropic configuration, cholesteric phases were obtained on equilibrating the guest-host systems, whereby left-handed and right-handed cholesterics were formed depending on the M- and P-helicity of the atropisomers, respectively. Analysing ...

Monte carlo study of Gay–Berne liquid-crystal droplets

We report results of a series of NVT Monte Carol simulations on systems of molecules interacting via a Gay–Berne (GB) potential within a spherical cavity modelling a polymer-dispersed liquid-crystal (PDLC) droplet. The cavity walls have been simulated by constructing a spherical shell of GB particles, each oriented towards the centre of the drop in an attempt to promote radial boundary conditions. The wall–fluid interactions have been modelled with a modified 1–3 GB potential (with energy exponents µ-1 and ν= 3, respectively) to favour radial alignment. We show results for the molecular organization in the droplet for a 2–1 and 1–3 fluid–fluid potential. We also show the radial order parameter as a function of temperature and droplet size. It is found that at low scaled temperatures a layer of radially aligned particles is formed, but this ordering does not propagate towards the centre of the drop unless the drop is relatively large or all the fluid–fluid interactions are modelled with the 1–3 potential. In this situation, concentric shells of aligned particles are formed, with a small smectic-like domain in the centre.

A model calculation of the surface elastic constants of a nematic liquid crystal

We have evaluated the bulk and surface elastic constants of a nematic liquid crystal composed of Gay-Berne particles, using a generalization of earlier theories by Poniewierski and Stecki, and Lipkin, Rice and Mohanty. The ratios between surface and bulk elastic constants have been plotted as a function of temperature and at nematic-isotropic coexistence. In particular, the sign of the K 13 (splay-bend) constant has been shown to depend sensitively on details of the intermolecular potential. Results have been contrasted with those obtained from a different theory.

Computer simulation studies of the dependence on density of the orientational order in nematic liquid crystals

Abstract Simulations of the temperature dependence of the nematic orientational order parameter, [Pbar] 2, at different densities have been made using the Gay-Berne potential. The results are used to calculate Γ = −(∂In T/∂ IN V) [Pbar] 2, which is a measure of the relative sensitivity of [Pbar] 2 to temperature and density. Previous experimental measurements of Γ have obtained values in the range 2–6 for real nematogens, whilst the present simulations yield Γ = 8 ± 1. Changing the Gay-Berne potential by increasing the steepness of the repulsive term increases the calculated value of Γ, whilst changing the relative well depths for side-by-side compared to end-to-end arrangements of Gay-Berne particles leaves Γ virtually unchanged. These exploratory calculations suggest that Γ is a useful parameter for testing the parametrizations of model potentials.