Gay-Berne Potential Research Articles

Two-stage assembly of patchy ellipses: From bent-core particles to liquid crystal analogs.

We investigate the two-dimensional behavior of colloidal patchy ellipsoids specifically designed to follow a two-step assembly process from the monomer state to mesoscopic liquid-crystal phases via the formation of the so-called bent-core units at the intermediate stage. Our model comprises a binary mixture of ellipses interacting via the Gay-Berne potential and decorated by surface patches, with the binary components being mirror-image variants of each other-referred to as left-handed and right-handed ellipses according to the position of their patches. The surface patches are designed so as in the first stage of the assembly the monomers form bent-cores units, i.e., V-shaped dimers with a specific bent angle. The Gay-Berne interactions, which act between the ellipses, drive the dimers to subsequently form the characteristic phase observed in bent-core liquid crystals. We numerically investigate-by means of both Molecular Dynamics and Monte Carlo simulations-the described two-step process: we first optimize a target bent-core unit and then fully characterize its state diagram in temperature and density, defining the regions where the different liquid crystalline phases dominate.

Boltzmann's H-function for molecules with orientational degrees of freedom: Emergence of unique features.

Boltzmann's H-function H(t), often regarded as an analog of time-dependent entropy, holds a venerable place in the history of science. However, accurate numerical evaluation of H(t) for particles other than atoms is rare. To remove this lacuna, we generalize Boltzmann's H-function to a gas of molecules with orientational degrees of freedom and evaluate H(t) from the time-dependent joint probability distribution function f(p, L, t) for linear (p) and angular (L) momenta, evolving from an initial nonequilibrium state, by molecular dynamics simulations. We consider both prolate- and oblate-shaped particles, interacting via the well-known Gay-Berne potential and obtain the relaxation of the generalized molecular H(t) from initial (t = 0) nonequilibrium states. In the long-time limit, the H function saturates to its exact equilibrium value, which is the sum of translational and rotational contributions to the respective entropies. Both the translational and rotational components of H(t) decay nearly exponentially with time; the rotational component is more sensitive to the molecular shape that enters through the aspect ratio. A remarkable rapid decrease in the rotational relaxation time is observed as the spherical limit is approached, in a way tantalizingly reminiscent of Hu-Zwanzig hydrodynamic prediction with the slip boundary condition. In addition, we obtain H(t) analytically by solving the appropriate translational and rotational Fokker-Planck equation and obtain a modest agreement with simulations. We observe a remarkable signature of translation-rotation coupling as a function of molecular shape, captured through a physically meaningful differential term that quantifies the magnitude of translation-rotation coupling.

Composite ellipsoids to model charge anisotropy in particle-scale simulations of kaolinite

This paper outlines a new approach to use coarse-grained molecular dynamics (CGMD) and the Gay–Berne (GB) potential to simulate the compression of kaolinite saturated with water at an acidic pH ( = 4) in a low (1 mM) ion concentration solution. To overcome the limitations of the standard GB potential and capture the charge heterogeneity on the surface of kaolinite particles under acidic pH conditions, each clay platelet is modelled using a two-ellipsoid composite particle. The molecular dynamics software Large-scale Atomic/Molecular Massively Parallel Software was employed to generate virtual monodisperse samples containing 1000 composite particles and to simulate isotropic compression at 100 kPa. The observed macro-scale response in void ratio–effective stress space lay above the response obtained in a simulation that used an equivalent CGMD model developed to simulate alkaline (pH = 8) pore water conditions. This is in qualitative agreement with available experimental data for one-dimensional compression. A post-compression qualitative observation of two virtual samples revealed a book-house-type fabric in the sample with acidic pore fluid, whereas a turbostatic-type fabric was observed when an alkaline pore fluid was simulated. These observations are also in qualitative agreement with scanning electron microscopy data reported in the literature.

Evaluation and improvement of Gay-Berne interaction potential to simulate 3D DLVO interaction of clay particles

This paper first presents a set of DLVO-based energy-separation functions for a pair of finite uniformly charged square platelets of infinitesimal thickness in three elementary configurations: face-to-face, edge-to-edge, and edge-to-face. The novel dataset was generated by summing the electrostatic interaction energy computed numerically by solving the non-linear 3D Poisson-Boltzmann equation and the van der Waals interaction energy calculated analytically. The dataset aims to inform qualitatively and quantitatively the energy/force separation functions used in the Discrete Element Method (DEM) and Coarse-Grained Molecular Dynamics (CGMD) modelling of clays. The same dataset was then used to calibrate and evaluate two Gay-Berne (GB)-type potentials: i) a DLVO-adapted Gay-Berne potential, where the Born-van der Waals branches of the underlying Lennard-Jones (LJ) potential are replaced with van der Waals-Columbic branches to represent DLVO interactions; ii) the Mie potential, where the exponents of the two energy terms are ‘unlocked’ instead of being set equal to 12 and 6 as per the original LJ potential. It is shown that the orientation parameter, µ, and the anisotropy parameter, ν, need to be different from µ = 2 and ν = 1 as adopted in CGMD clay modelling to capture the progression of the shape of the pair energy-separation function from face-to-face to edge-to-face and edge-to-edge configuration. It is also shown that the MIE potential (with exponents m = 3 and n = 1.5) better captures the slow decay of the electrostatic repulsive energy component of the DLVO potential energy Coulombic branch of the interaction potential compared to the DLVO-adapted GB potential, which embeds the Lennard-Jones (LJ) exponents m = 12 and n = 6.

Isotropic compression simulation of kaolinite using coarse-grained molecular dynamics

It is now viable to use coarse-grained molecular dynamics (CGMD) to model interacting clay particles in simulations of soil mechanics element tests. In CGMD, particle interactions are described by the Gay-Berne (GB) potential, which can approximate the potential energy between clay particles as a function of their separation and relative orientations; however, a previous study identified a significant shortcoming of the GB potential, which is that it lacks a local maximum called the “energy barrier” that the true interaction possesses at very close range. In this study, we propose a modified GB potential which can capture the energy barrier at and we use this new potential function to simulate the clay mineral kaolinite under isotropic compression. Our simulations show that the energy barrier is a crucial ingredient required to reproduce the elastoplastic behaviour observed in laboratory tests upon unloading from an isotropic normally consolidated state. Our data show that the difference in mechanical behaviour between normally consolidated clay and overconsolidated clay can be explained by the fact that, during the initial loading, some pairs of interacting particles surmount the energy barrier so that they then experience a large attractive force. Effectively, these particles become bounded and do not separate when the stress applied to the sample is released. The response of overconsolidated clay to applied stress is stiffer than that of normally consolidated clay because a larger proportion of the clay particle interactions exist in this bonded state.

Migration and division in cell monolayers on substrates with topological defects

Collective movement and organization of cell monolayers are important for wound healing and tissue development. Recent experiments highlighted the importance of liquid crystal order within these layers, suggesting that +1 topological defects have a role in organizing tissue morphogenesis. We study fibroblast organization, motion, and proliferation on a substrate with micron-sized ridges that induce +1 and -1 topological defects using simulation and experiment. We model cells as self-propelled deformable ellipses that interact via a Gay-Berne potential. Unlike earlier work on other cell types, we see that density variation near defects is not explained by collective migration. We propose instead that fibroblasts have different division rates depending on their area and aspect ratio. This model captures key features of our previous experiments: the alignment quality worsens at high cell density and, at the center of the +1 defects, cells can adopt either highly anisotropic or primarily isotropic morphologies. Experiments performed with different ridge heights confirm a prediction of this model: Suppressing migration across ridges promotes higher cell density at the +1 defect. Our work enables a mechanism for tissue patterning using topological defects without relying on cell migration.

Orientational transition in nanobridges of nematic liquid crystals in slit pores

ABSTRACTIn this work, the morphology of nematic capillary nanobridges in slit pores separated by a vertical distance D will be characterised by Monte Carlo simulations for oblate molecules nematogen modelled by the Gay-Berne potential. Previous studies on droplets show that the molecules are arranged homeotropically at the nematic-vapour interface and form spherical droplets with an annular disclination located in their equatorial plane. In the presence of pores with attractive substrates that favour homeotropic anchoring, the formation of nanobridges characterised by anchoring angles that decrease with increasing particle-substrate interaction intensity is observed. When the orientational field in the nanobridge is analysed, the formation of an annular disclination of topological charge+1/2 located in the plane perpendicular to the z-axis that passes through the centre of mass of the nanobridge is observed for small D. However, when considering higher values of D, a change to a biaxial orientational profile within the nanobridge is observed, where now the annular disclination is arranged in a plane perpendicular to one direction of the xy plane. These results are indicative of the existence of an orientational phase transition for an intermediate D value between a uniaxial and a biaxial orientational configuration in the capillary nanobridge.

Mesoscale modeling to study isolated asphaltene agglomerates

The mesoscopic behavior of asphaltene plays a significant role in the formation of microstructures and agglomerates. In this study, a new coarse-grained model is developed to investigate the formation of aggregated microstructures in asphaltene. Disk-like building block is adopted as the basic unit in the coarse-grained model. The forcefield parameters based on Gay-Berne potential are derived from the full atomistic simulations and applied in the coarse-grained simulations. The results show that randomly orientated asphaltene disks gradually adjust their positions and orientations during equilibrium process, and reach the jammed state with different columnar structures containing packed asphaltene disks. The packing fraction and the microstructures of agglomerates are affected by the aspect ratio of asphaltene disks, temperature and pressure. The developed coarse-grained model can characterize the evolution of asphaltene microstructures and help understand the formation mechanism of asphaltene agglomerates. The in-depth analysis reveals the influencing factors on asphaltene agglomerates, which can enlighten the solutions to aggregation problems of asphaltene system.

Potential of Mean Force for Face-Face Interactions between Pairs of 2:1 Clay Mineral Platelets.

Bottom-up modeling of clay behavior from the molecular scale requires a detailed understanding of the free energy between pairs of clay platelets. We investigate the potential of mean force (PMF) for hydrated clays in face-to-face interactions with free energy perturbation (FEP) methods through molecular dynamics simulations using simple overlap sampling (SOS). We show that PMF results for open systems with one finite in-plane dimension are affected by migration of counterions from within the interlayer space compared with fully confined closed system conditions. We compare PMFs for two common 2:1 clay sheet minerals Illite (IMt-1) and Na-smectite. The PMFs for the open illite systems exhibit a strong attractive energy well at a basal layer separation, d = 11 Å and interlayer water content, wIL = ∼0.4% while the attractive minimum for the closed system occurs at d = 12 Å, wIL = 3.5%. In contrast, net repulsion occurs between pairs of Na-smectite platelets for both open and closed systems (for d < 15-16 Å). The free energy is closely related to the distribution of counterions; while K+ ions are bound closely to the surfaces of the illite platelets, Na+ ions are more spatially disperse. This PMF results contradict prior findings for Na-smectite and prompted further comparisons with other published results. We find that most of the published results do not represent accurately the free energy for face-face interactions between pairs of clay platelets that are effectively infinite (with width/thickness O[104]). The PMF results presented in this paper form a reliable basis for mesoscale, coarse-grained modeling of illite and smectite particle assemblies. We show that the Gay-Berne potential provides a reasonable first-order model for upscaling, while the solvation potential proposed by Masoumi enables a more accurate representation of the computed PMFs.

Effect of anisotropy on the formation of active particle films.

Active colloids belong to a class of nonequilibrium systems where energy uptake, conversion, and dissipation occur at the level of individual colloidal particles, which can lead to particles' self-propelled motion and surprising collective behavior. Examples include coexistence of vapor- and liquid-like steady states for active particles with repulsive interactions only, phenomena known as motility-induced phase transitions. Similarly to motile unicellular organisms, active colloids tend to accumulate at confining surfaces forming dense adsorbed films. In this work, we study the structure and dynamics of aggregates of self-propelled particles near confining solid surfaces, focusing on the effects of the particle anisotropic interactions. We performed Langevin dynamics simulations of two complementary models for active particles: ellipsoidal particles interacting through the Gay-Berne potential and rodlike particles composed of several repulsive Lennard-Jones beads. We observe a nonmonotonic behavior of the structure of clusters formed along the confining surface as a function of the particle aspect ratio, with a film spreading when particles are near-spherical, compact clusters with hedgehog-like particle orientation for more elongated active particles, and a complex dynamical behavior for an intermediate aspect ratio. The stabilization time of cluster formation along the confining surface also displays a nonmonotonic dependence on the aspect ratio, with a local minimum at intermediate values. Additionally, we demonstrate that the hedgehog-like aggregates formed by Gay-Berne ellipsoids exhibit higher structural stability as compared to the ones formed by purely repulsive active rods, which are stable due to the particle activity only.

Novel smectic phases and orientational order switching in two-dimensional liquid crystalline system

ABSTRACT Liquid crystalline (LC) materials are ubiquitous in our modern life. Most of the applications where LC materials find their use depend on maintaining the orientation of the constituent LC particles. In this article, we report a recipe to control the molecular orientation. We have done a computer simulation study of a two-dimensional (2D) liquid crystalline material consisting of soft ellipses. The pair interaction is modelled by using the Gay–Berne potential. The 2D LC material is set to interact with an underlying substrate which varies periodically in one-dimension (1D) only. By controlling the substrate parameters like periodicity and strength, we showed that a nematic phase LC material transitions into different novel phases. We finally show that by applying a substrate with large periodicity, the substrate strength can be used as a control parameter to steer the LC director.

Anisotropic Electrostatic Interactions in Coarse-Grained Water Models to Enhance the Accuracy and Speed-Up Factor of Mesoscopic Simulations.

Water models with realistic physical–chemical properties are essential to study a variety of biomedical processes or engineering technologies involving molecules or nanomaterials. Atomistic models of water are constrained by the feasible computational capacity, but calibrated coarse-grained (CG) ones can go beyond these limits. Here, we compare three popular atomistic water models with their corresponding CG model built using finite-size particles such as ellipsoids. Differently from previous approaches, short-range interactions are accounted for with the generalized Gay–Berne potential, while electrostatic and long-range interactions are computed from virtual charges inside the ellipsoids. Such an approach leads to a quantitative agreement between the original atomistic models and their CG counterparts. Results show that a timestep of up to 10 fs can be achieved to integrate the equations of motion without significant degradation of the physical observables extracted from the computed trajectories, thus unlocking a significant acceleration of water-based mesoscopic simulations at a given accuracy.

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.

Self-Assembly of an Equimolar Mixture of Liquid Crystals and Magnetic Nanoparticles

We studied the equilibrium self-assembly of an equimolar mixture of uniaxial liquid crystals (LCs) and magnetic nanoparticles (MNPs) using molecular dynamics simulations. The LCs are modeled by ellipsoids interacting via Gay–Berne potential, and MNPs are represented by dipolar soft spheres (DSS). We found that the LCs show isotropic, nematic, and smectic phases when the mixture is compressed at a fixed temperature. The DSS form chain-like structures, which remain randomly oriented at low densities where the LCs are in the isotropic phase. At intermediate and high densities, the DSS chains align along the nematic and smectic directors of LCs. We found that the DSS inside a chain follow a ferromagnetic ordering. However, the mixture does not show a significant macroscopic magnetization. The extent of nematic order in the DSS remains very similar to the LCs in intermediate densities. At high densities, the DSS have a lower extent of nematic order than the LCs. The structure of the LC–DSS mixture was further analyzed via projected pair correlation functions for distances parallel and perpendicular to directors in the nematic and smectic phases.

Coarse-grained molecular dynamics simulations of clay compression

This paper outlines a framework for using molecular dynamics to simulate the compression of kaolinite saturated at alkaline pH (=8) in a low (1 mM) concentration solution. The particles are modelled as flat (3D) ellipsoids and their interactions are described by a modified form of the Gay-Berne potential, calibrated against DLVO theory. The LAMMPS software was used to generate monodisperse and slightly polydisperse samples, and to simulate isotropic compression to 100 kPa. The influences of sample size and strain rate on the void ratio and the arrangement of particles within the samples were investigated via parametric studies. It is useful to consider the extent to which the system temperature (a measure of the average kinetic energy) is controlled when assessing whether the applied strain rate is appropriate. It is found that the number of particles that can be considered a representative element volume is orders of magnitude larger than the number simulated in earlier studies and that larger number of particles are required in polydisperse samples than in the monodisperse case. A comparison between the results obtained and those of published experimental studies show that the methodology proposed can deliver sensible results for the material considered.

Anisotropic numerical potentials for coarse-grained modeling from high-speed multidimensional lookup table and interpolation algorithms.

A high-speed numerical potential delivering computational performance comparable with complex coarse-grained analytic potentials makes available models that have greater degrees of physical and chemical accuracy. This opens the possibility of increased accuracy in classical molecular dynamics simulations of anisotropic systems. In this work, we report the development of a high-speed lookup table (LUT) of four-dimensional gridded data, that uses cubic B-spline interpolations to derive off grid values and their associated partial derivatives that are located between the known grid data points. The accuracy of the coarse-grained numerical potential using a LUT from uniaxial Gay-Berne (GB) potential produced array of values is within a 3% and a 5% margin of error respectively for the interpolation of the uniaxial GB potential and its partial derivatives. The numerical potential model and partial derivatives speedup is made competitive with the analytical potential by exploiting graphics processing units on board functionality. The capability of the numerical potential is demonstrated by comparing minimizations of a box of 500 naphthalene molecules. The minimizations using a full atomistic (NAMD/CHARMM force field), a biaxial GB and a numerical potential from a LUT using data from the CHARMM pair potential was done. The numerical potential model is significantly more accurate in its approximation of the atomistic local minimum configuration than is the biaxial GB analytical potential function. This demonstrates that using a numerical potential founded on a direct lookup of the atomistic potential landscape significantly improves coarse grain (CG) modeling of complex molecules, possibly paving the way for accurate anisotropic system CG modeling.

Pressure-tensor method evaluation of the interfacial tension between Gay-Berne isotropic fluid and a smooth repulsive wall.

The interfacial properties of a confined thermotropic liquid crystalline material are investigated using a molecular dynamics simulation technique. The pairwise interaction among the soft ellipsoidal particles is modeled by the Gay-Berne (GB) potential. The GB ellipsoids are confined by two soft, smooth, repulsive walls defined by the Weeks-Chandler-Andersen (WCA) potential. The aperiodic confinement due to walls makes the system mechanically anisotropic. Hence using the pressure-tensor method, the interfacial tension of an interface between the bulk isotropic (I) phase and WCA wall at various number densities (ρ) is calculated. From the pressure tensor and orientational order profiles, the arrangement of ellipsoids in the bulk and the vicinity of the wall is determined. The effect of system size and the wall-particle interaction strength (εW) on is also analyzed by varying the system size and εW.

Structure and rheology of soft hybrid systems of magnetic nanoparticles in liquid-crystalline matrices: results from particle-resolved computer simulations

Abstract Hybrid mixtures composed of magnetic nanoparticles (MNP) in liquid crystalline (LC) matrices are a fascinating class of soft materials with intriguing physical properties and a wide range of potential applications, e.g., as stimuli-responsive and adaptive materials. Already in the absence of an external stimulus, these systems can display various types of orientationally disordered and ordered phases, which are enriched by self-assembled structures formed by the MNPs. In the presence of external fields, one typically observes highly nonlinear macroscopic behavior. However, an understanding of the structure and dynamics of such systems on the particle level has, so far, remained elusive. In the present paper we review recent computer simulation studies targeting the structure, equilibrium dynamics and rheology of LC-MNP systems, in which the particle sizes of the two components are comparable. As a numerically tractable model system we consider mixtures of soft spherical or elongated particles with a permanent magnetic dipole moment and ellipsoidal non-magnetic particles interacting via a Gay-Berne potential. We address, first, equilibrium aspects such as structural organization and self-assembly (cluster formation) of the MNPs in dependence of the orientational state of the matrix, the role of the size ratio, the impact of an external magnetic field, and the translational and orientational diffusion of the two components. Second, we discuss the non-equilibrium dynamics of LC-MNP mixtures under planar shear flow, considering both, spherical and non-spherical MNPs. Our results contribute to a detailed understanding of these intriguing hybrid materials, and they may serve as a guide for future experiments.

Extraction a formalism for fluids with non-spherical molecules based on the cluster expansion of the energy functional

In this work, based on the cluster expansion of the energy functional, we have extracted a formalism for calculation of the thermodynamic properties of fluids with non-spherical molecules. The salient feature of the extracted formalism is that it has no restrictions on the type of interaction. In fact our formalism can be employed for all types of realistic inter-particle interactions. Here, for the interaction of two anisotropic molecules, we have applied the Gay-Berne potential. Finally, we have applied this formalism to calculate some thermodynamic properties of fluid H2 which shows some expected results.

From scalar to polar active matter: Connecting simulations with mean-field theory.

We study numerically the phase behavior of self-propelled elliptical particles interacting through the "hard" repulsive Gay-Berne potential at infinite Péclet number. Changing a single parameter, the aspect ratio, allows us to continuously go from discoid active Brownian particles to elongated polar rods. Discoids show phase separation, which changes to a cluster state of polar domains, which then form polar bands as the aspect ratio is increased. From the simulations, we identify and extract the two effective parameters entering the mean-field description: the force imbalance coefficient and the effective coupling to the local polarization. These two coefficients are sufficient to obtain a complete and consistent picture, unifying the paradigms of scalar and polar active matter.