Gay-Berne Particles Research Articles

Noether invariance theory for the equilibrium force structure of soft matter

We give details and derivations for the Noether invariance theory that characterizes the spatial equilibrium structure of inhomogeneous classical many-body systems, as recently proposed and investigated for bulk systems (Sammüller et al 2023 Phys. Rev. Lett. 130 268203). Thereby an intrinsic thermal symmetry against a local shifting transformation on phase space is exploited on the basis of the Noether theorem for invariant variations. We consider the consequences of the shifting that emerge at second order in the displacement field that parameterizes the transformation. In a natural way the standard two-body density distribution is generated. Its second spatial derivative is thereby balanced by two further and different two-body correlation functions, which respectively introduce thermally averaged force correlations and force gradients in a systematic and microscopically sharp way into the framework. Separate exact self and distinct sum rules express this balance. We exemplify the validity of the theory on the basis of computer simulations for the Lennard–Jones gas, liquid, and crystal, the Weeks–Chandler–Andersen fluid, monatomic Molinero–Moore water at ambient conditions, a three-body-interacting colloidal gel former, the Yukawa and soft-sphere dipolar fluids, and for isotropic and nematic phases of Gay–Berne particles. We describe explicitly the derivation of the sum rules based on Noether’s theorem and also give more elementary proofs based on partial phase space integration following Yvon’s theorem.

Deviation from the prediction of the Maier-Saupe theory of mixtures of charged discotic Gay-Berne and Lennard-Jones particles

ABSTRACT We report an analysis of the orientational order and orientational distribution functions of mixtures of discotic charged Gay-Berne (GB) and Lennard-Jones (LJ) particles as models of ionic liquid crystals and colloidal suspensions. We have studied three different stoichiometries (GB:LJ of 1:2, 1:1 and 2:1), with the opposite charges on the two particles selected to guarantee electroneutrality. We have found that for relatively low values of the scaled charge the dependence of the fourth-rank orientational order parameter, <P 4>, on the second-rank orientational order parameter, <P 2>, is in very good agreement with the prediction of the Maier-Saupe theory. In contrast, for relatively high values of the charge a deviation is observed which is in opposite directions for mixtures with an excess for GB particles and mixtures with an excess of LJ particles.

On the Effects of Different trans and cis Populations in Azobenzene Liquid Crystal Elastomers: A Monte Carlo Investigation.

We investigate main-chain liquid crystal elastomers (LCEs) formed by photoresponsive azobenzene units with different populations of trans and cis conformers (from fully trans to fully cis). We study their macroscopic properties as well as their molecular organization using extensive Monte Carlo simulations of a simple coarse-grained model where the trans and cis conformers are represented by soft-core biaxial Gay-Berne particles with size and interaction energy parameters obtained by fitting a bare bone azobenzene moiety represented at atomistic level. We find that increasing the fraction of cis conformers, as could be obtained by near-UV irradiation, shifts the nematic-isotropic transition to a lower temperature, consistently with experiment, while generating internal stress in a clamped sample. An analysis of pair distributions shows that the immediate surroundings of a bent cis molecule are slightly less dense and more orientationally disordered in comparison with that of a trans conformer. Comparing nematic and smectic LCEs, actuation in the smectic phase proved less effective, disrupting the smectic layers to some extent but preserving orientational order of the azobenzene moieties.

Structures, thermodynamics and dynamics of topological defects in Gay-Berne nematic liquid crystals.

Topological defects are a ubiquitous phenomenon across different physical systems. A better understanding of defects can be helpful in elucidating the physical behaviors of many real materials systems. In nematic liquid crystals, defects exhibit unique optical signatures and can segregate impurities, showing their promise as molecular carriers and nano-reactors. Continuum theory and simulations have been successfully applied to link static and dynamical behaviors of topological defects to the material constants of the underlying nematic. However, further evidence and molecular details are still lacking. Here we perform molecular dynamics simulations of Gay-Berne particles, a model nematic, to examine the molecular structures and dynamics of +1/2 defects in a thin-film nematic. Specifically, we measure the bend-to-splay ratio K3/K1 using two independent, indirect measurements, showing good agreement. Next, we study the annihilation event of a pair of ±1/2 defects, of which the trajectories are consistent with experiments and hydrodynamic simulations. We further examine the thermodynamics of defect annihilation in an NVE ensemble, leading us to correctly estimate the elastic modulus by using the energy conservation law. Finally, we explore effects of defect annihilation in regions of nonuniform temperature within these coarse-grained molecular models which cannot be analysed by existing continuum level simulations. We find that +1/2 defects tend to move toward hotter areas and their change of speed in a temperature gradient can be quantitatively understood through a term derived from the temperature dependence of the elastic modulus. As such, our work has provided molecular insights into structures and dynamics of topological defects, presented unique and accessible methods to measure elastic constants by inspecting defects, and proposed an alternative control parameter of defects using temperature gradient.

Substrate induced freezing, melting and depinning transitions in two-dimensional liquid crystalline systems.

We use molecular dynamics simulations to investigate the ordering phenomena in two-dimensional (2D) liquid crystals over the one-dimensional periodic substrate (1DPS). We have used Gay-Berne (GB) potential to model the interaction between a pair of liquid crystalline (LC) particles. The underlying substrate potential with which the GB particles interact varies sinusoidally in one direction only. At a given temperature and density of the GB system, we varied the substrate's periodicity (as) but fixed the substrate strength. We observed that with a small value of as, an underlying substrate helps to stabilize a disordered LC nematic phase to a 2D solid phase. However, for an intermediate range of as, the system melts and transitions to a modulate-smectic. Finally, with a further increase in as, the system undergoes a structural depinning transition and returns to an LC nematic phase like a free system with no substrate. We argue that a three-way interplay of the energies arising from orientation-dependent particle-particle and particle-substrate interaction makes it possible for the system to undergo substrate-periodicity-dependent multiple phase transitions in the GB LC system.

Mixtures of discotic and spherical soft particles: de-mixing, liquid crystal behaviour and relative solubility

Liquid crystals (LC) mixtures are ubiquitous in all real-life applications of LCs. This is due to the need of modulating the macroscopic properties of the LC phase used in specific devices. However, mixing particles of different shapes, not to mention different strength of interaction, often results in de-mixing (phase separation) with the formation of one phase rich in one type of particles separated from the other phase. In this work we investigate the phase behaviour of mixtures of discotic Gay-Berne (GB) particles with spherical Lennard-Jones (LJ) particles using molecular dynamics (MD) simulations. We have considered compositions ranging from the pure GB system up to a GB mole fraction of 0.1 and we have studied the systems at constant volume as a function of the temperature keeping all systems at the same packing fraction. We observe an interesting behaviour where GB-rich systems undergo a nematic-to-isotropic transition, with decreasing transition temperature as the fraction of LJ solutes is increased, keeping a single phase with a relatively large amount of LJ particles dissolved. Lowering the temperature eventually results in a phase separated hexagonal columnar in coexistence with an isotropic phase. In contrast, for LJ-rich systems the de-mixing occurs together with the transition to the nematic phase and the transition point raises again close to the values observed for the pure GB. A clear correlation is also observed between the orientational order parameter of the LC phase and the solubility of LJ particles within the LC phase itself.

A coarse-grained model of ionic liquid crystals: the effect of stoichiometry on the stability of the ionic nematic phase.

We have investigated, by means of molecular dynamics simulations, the phase behaviour of mixtures of charged ellipsoidal Gay-Berne (GB) particles and spherical Lennard-Jones (LJ) particles, as a coarse-grained model of ionic liquid crystals (ILCs). The anisotropic GB particles represent cations usually found in ILCs, for example, pyridinium or bipyridinium salts, while the spherical LJ particles are taken as a model of anions like common halides, hexafluorophosphate and tetrafluoroborate. Here we have focused our attention on the effect of the stoichiometry of the system (that is, the GB : LJ ratio n : m in the salt formula [GB]n[LJ]m) on the stability and thermal range of the ionic liquid crystal phases formed, with special attention to the ionic nematic phase. To isolate the stoichiometry effect, a comparison of four different systems with GB : LJ ratios of 1 : 3, 1 : 2, 1 : 1 and 2 : 1 is made by keeping the packing fraction and the charge of the minor component fixed. Our results suggest a way to improve the stability of the ionic nematic phase by enhancing the anisotropic van der Waals interaction compared to the Coulomb interaction, and by increasing the proportion of anisotropic particles in the mixture.

Molecular organizations of conical mesogenic fullerenes.

We have studied liquid crystal phases formed by fullerenes functionalized with mesogenic groups yielding a cone-shaped molecular structure. We have modelled these shuttlecock-like molecules with a set of Gay-Berne particles grafted with flexible springs to a spherical core and we have studied, using Monte Carlo simulations, their phase organization, also with a view to examining their possible use as candidate organic photovoltaic materials. We have found that, upon cooling from the isotropic phase, the system forms a columnar phase, like in the experimental work of Kato and coworkers [T. Kato et al., Nature, 2002, 419, 702]. However the phase is made of polar stacks extending not more than about ten molecules, which could limit their usefulness in enhancing and directing charge transport for possible photovoltaic applications.

MD simulations of mixtures of charged Gay-Berne and Lennard-Jones particles as models of ionic liquid crystals

ABSTRACTWe use a simple model of Ionic Liquid Crystals represented by mixtures of positively charged ellipsoidal Gay-Berne particles and negatively charged spherical Lennard-Jones particles. This system will model common ionic liquid crystals, for example those based on symmetrically substituted imidazolium halide salts. The system has been studied using Molecular Dynamics simulations for three different values of the scaled charge (0.0, 0.5, 2.0) at two different number densities (0.30, 0.36) in the NVT ensemble. Radial distribution functions and orientational order parameters have been calculated in order to get more insights on the phase segregation and organization of domains together with a comparison of the van der Waals and coulombic terms of the total interaction energy.

Density functional theory of freezing of a system of conjugated oligomers parameterised via Gay–Berne potential

ABSTRACTDensity functional theory (DFT) of freezing is used to study the isotropic–nematic, isotropic–smectic A and nematic–smectic A phase transitions in a system of large, semi-flexible conjugated oligomers parameterised within Gay–Berne (GB) potential. The pair correlation functions of the isotropic fluid, used as structural inputs in the DFT, are calculated by solving the Percus–Yevick integral equation theory. Large number of spherical harmonic coefficients of each orientation-dependent functions has been considered to ensure the numerical accuracy at different densities and temperatures for the system of these model GB ellipsoids having large aspect ratio (length-to-breadth ratio). We found that the system of GB ellipsoids parameterised for conjugated oligomers shows stable isotropic, nematic and smectic A phases. At low temperatures, on increasing the density, isotropic fluid makes a direct transition to smectic A phase. Nematic phase get stabilised in between the isotropic and smectic A phases on increasing the temperature. Using the transition parameter obtained through the DFT, we have plotted the temperature–density and pressure–temperature phase diagrams which are found to be qualitatively similar to the one obtained in simulations for the systems with low aspect ratio GB particles.

SOLVATION FORCE OF ELLIPSE-SHAPED MOLECULES MOVING IN ONE DIMENSION AND CONFINED BETWEEN TWO PARALLEL PLANAR WALLS

The model fluids containing hard ellipses (HEs) and Gay-Berne (GB) particles where their center is moving in one dimension and confined between two parallel walls with different interactions are investigated using Monte Carlo simulation, NVT ensemble. The dependency of fluid pressure with respect to the wall distances is studied. The oscillatory behaviors are seen in this quantity against wall separations. The total average number density profile of particles is calculated using the angular number density. For both HE and GB particles confined between hard walls the total average number density at the wall shows a similar oscillatory behavior. We also related the pressure of these systems to the relevant solvation force between two colloidal particles. We have investigated the dependency of this quantity to the packing fraction, temperature, structure of the walls confining the particles and the interaction between ellipses of the fluid. Finally it is possible to reach the required solvation forces by changing the thermodynamic or structural properties.

Carrier transport simulation in a model liquid crystalline system with the biaxial Gay–Berne potential

In this paper, we performed carrier transport simulation to understand the unusual temperature dependence of the carrier mobility observed in nematic liquid crystals. For this purpose, we made a model liquid crystalline system consisting of biaxial Gay-Berne particles, and then we simulated hopping transport between these particles. The hopping rate was formulated suitably for the biaxial Gay-Berne particles based on the investigation of the electronic overlaps between actual aromatic molecules. The carrier transport simulation was performed by master equation method on the model system prepared by N-P-T ensemble Monte Carlo simulation. We reproduced gradual mobility increase in the nematic phase as a result of the change in the short range molecular order.

Liquid crystal nanodroplets in solution

The aggregation of liquid crystal nanodroplets from a homogeneous solution is studied by molecular dynamics simulations. The liquid crystal particles are modeled as elongated ellipsoidal Gay-Berne particles while the solvent is modeled as spherical Lennard-Jones particles. Extending previous studies of Berardi et al. [J. Chem. Phys. 126, 044905 (2007)], we find that liquid crystal nanodroplets are not stable and that after sufficiently long times the nanodroplets always aggregate into a single large droplet. Results describing the droplet shape and orientation for different temperatures and shear rates are presented. The implementation of the Gay-Berne potential for biaxial ellipsoidal particles in a parallel molecular dynamics code is also briefly discussed.

Cell size dependence of orientational order of uniaxial liquid crystals in flat slit

In order to investigate the ordered structure of nematic liquid crystal molecules confined in a nanoslit, we carried out a classical molecular dynamics simulation of uniaxial prolate Gay–Berne particles in a flat, structureless slit at several temperatures. When the slit gap is so small that the system is not assumed as the bulk, particles in the slit possess orientationally ordered structures different from ones in the bulk. The weak spacial orientational correlation existed when the temperature corresponded to the isotropic phase in the bulk system. The first order isotropic–nematic phase transition was not clearly observed and the transitional phenomenon of the creation and annihilation of the uniaxial domains were observed. These results revealed that the ordered structure depends on the number of particles, in other words, cell size, and that the system with 100,000 or more particles gives reasonable results of an infinitely wide slit. The number of particles is converted into up to 220 particles of the length of the base.

Molecular Dynamics Study of Flexo-Electric Effect in the Banana-Shaped Gay-Berne System

To study flexo-electric effect of nematic liquid crystalline phase, molecular dynamics simulation of a system composed of banana-shaped molecules consisting of a couple of Gay-Berne particles is carried out. A fan-shaped simulation cell together with an external field is utilized to obtain equilibrium nematic phase with bend deformation. An order of the second axis of molecules is shown to be induced by bend deformation of the principal axis of the order. The flexo-electric coefficient is obtained for some bend angles of constituent molecule, which exhibits systematic temperature dependence.

Hydrophobic solvation of Gay–Berne particles in modified water models

The solvation of large hydrophobic solutes, modeled as repulsive and attractive Gay-Berne oblate ellipsoids, is characterized in several modified water liquids using the SPC/E model as the reference water fluid. We find that small amounts of attraction between the Gay-Berne particle and any model fluid result in wetting of the hydrophobic surface. However, significant differences are found among the modified and SPC/E water models and the critical distances in which they dewet the hydrophobic surfaces of pairs of repulsive Gay-Berne particles. We find that the dewetting trends for repulsive Gay-Berne particles in the various model liquids correlate directly with their surface tensions, the widths of the interfaces they form, and the openness of their network structure. The largest critical separations are found in liquids with the smallest surface tensions and the broadest interfaces as measured by the Egelstaff-Widom length.

Field response and switching times in biaxial nematics

We study by means of virtual molecular dynamics computer experiments the response of a bulk biaxial nematic to an applied external field and, in particular, the relative speed of reorientation of the principal director axis and of the secondary one, typical of these new materials, upon a pi2 field switch. We perform the simulations setting up and integrating the equations of motion for biaxial Gay-Berne particles using quaternions and a suitable time reversible symplectic integrator. We find that switching of the secondary axis is up to an order of magnitude faster than that of the principal axis, and that under fields above a certain strength a reorganization of local domains, temporarily disrupting the nematic and biaxial ordering, rather than a collective concerted reorientation occurs.

Simulations of the Elastic Bent-Core Molecules

An influence of thermal fluctuations in opening angle was studied for a model of bent-core molecules using MC NPT computer simulation. The elastic bent-core shape was modeled by joining two Gay-Berne particles through the harmonic bond. Results for two stiff bananas with fixed opening angles of φ = 120° and φ = 140° were compared with their elastic counterparts. For all systems studied we found that with the varying opening angle the melting point moves towards lower temperatures. We did not discover any new phase as compared to the stiff cases.

Characteristic behavior of short-term dynamics in reorientation for Gay-Berne particles near the nematic-isotropic phase transition temperature

A specific transition behavior was found in the tumbling motion near the nematic-isotropic phase boundary using molecular dynamics simulations of the Gay-Berne mesogenic model under isobaric conditions at a reduced pressure P* of 2.0. The relaxation time for the motion obtained from the second-rank orientational time correlation function and the rotational diffusion coefficient showed a clear jump at the nematic-isotropic phase transition temperature. Regardless of the temperature dependence of the relaxation time, the change in the rotational diffusion coefficient evaluated from the orientational order parameters and the relaxation time agreed qualitatively with that of real mesogens. The rotational viscosity coefficients gamma(1) and gamma(2) were obtained from the simulation data for the relaxation time for the short-term dynamics and for the rotational diffusion coefficients. gamma(1) was proportional to <P2>(2), where <P2> is the second-rank orientational parameter. Furthermore, the rotational behavior of the model was compared with that of the Debye approximation in the isotropic phase.

A134 液晶を模擬した異方的粒子の分子動力学シミュレーション : 微小空隙に閉じ込めた場合(マイクロ・ナノスケール3)

Molecular dynamics simulation of Gay-Berne particles confined between two smooth walls parallel to each other was carried out to study the ordering and transport properties of confined liquid crystals. The equilibration process and ordering were investigated with NhP_<xx>T ensemble (N is the number of particles, h is the distance between two walls, P_<xx> is the element of pressure tensor parallel to walls and T is the temperature) and diffusion coefficients were calculated with NhAE ensemble (A is the area parallel to walls and E is the total energy). There were two kinds of parts: the center part, where the physical properties coincided ones of bulk system and the parts near walls, where liquid crystals possessed higher ordering than center part. The difference of spatial constrain from ordering caused transport properties of two kinds of narts.