Gay-Berne Research Articles

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.

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.

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.

Effect of the varying repulsive core of Gay–Berne pair potential on the structure and freezing transition in a two-dimensional system of soft ellipses

ABSTRACT We have investigated the effect of the strength of repulsive core of Gay–Berne (GB) ( n − 6 ) pair potential on the pair correlations and isotropic-nematic ( I − N ) freezing transition in a system of soft ellipses confined to a two-dimensional plane. The power n has been varied in the range 8 ≤ n ≤ 16 at an interval of two. Percus–Yevick (PY) integral equation theory (IET) has been solved to calculate the pair correlations of the isotropic fluid, which has been then used in the density functional theory to determine the isotropic-nematic transition parameters. The pair correlations obtained by PY theory have been compared with those obtained by NVT Monte-Carlo (MC) simulation. We observe a better agreement between PY and MC correlations at lower n -values of the interaction potential. An increase in the values of n results in more intricate structures manifested in both the radial distribution part and the higher order correlations. The I − N transition parameters are found to be sensitive to the value of the exponent n . The transition density is found to decrease, whereas the corresponding orientational order parameter is found to increase with the increase in n for a given temperature. At a given temperature, we observe a cut-off of n , below which the nematic does not stabilise. The smaller value of change in density at the transition indicates that the I − N transition is of weakly first order.

A Mori–Zwanzig Dissipative Particle Dynamics Approach for Anisotropic Coarse Grained Molecular Dynamics

Coarse grained (CG) molecular dynamics simulations are widely used to accelerate atomistic simulations but generally lack a formalism to preserve the dynamics of the system. For spherical particles, the Mori-Zwanzig approach, while computationally complex, has ameliorated this problem. Here we present an anisotropic dissipative particle dynamics (ADPD) model as an extension of this approach, which accounts for the anisotropy for both conservative and nonconservative interactions. For a simple anisotropic system we parametrize the coarse grained force field representing ellipsoidal CG particles from the full-atomistic simulation. To represent the anisotropy of the system, both the conservative and dissipative terms are approximated using the Gay-Berne (GB) functional forms via a force-matching approach. We compare our model with other CG models and demonstrate that it yields better results in both static and dynamical properties. The inclusion of the anisotropic nonconservative force preserves the microscopic dynamical details, and hence the dynamical properties, such as diffusivity, can be better reproduced by the aspherical model. By generalizing the isotropic DPD model, this framework is effective and promising for the development of the CG model for polymers, macromolecules, and biological systems.

Equilibrium phases and domain growth kinetics of calamitic liquid crystals.

The anisotropic shape of calamitic liquid crystal (LC) particles results in distinct values of energy when the nematogens are placed side by side or end to end. This anisotropy in energy which is governed by a parameter κ^{'} has deep consequences on equilibrium and nonequilibrium properties. Using the Gay-Berne (GB) model, which exhibits the nematic (Nm) as well as the low-temperature smectic (Sm) order, we undertake large-scale Monte Carlo and molecular dynamics simulations to probe the effect of κ^{'} on the equilibrium phase diagram and the nonequilibrium domain growth following a quench in the temperature T or coarsening. There are two transitions in the GB model: (i) isotropic to Nm at T_{c}^{1} and (ii) Nm to Sm at T_{c}^{2}<T_{c}^{1}. κ^{'} decreases T_{c}^{1} significantly but has relatively little effect on T_{c}^{2}. Domain growth in the Nm phase exhibits the well-known Lifshitz-Allen-Cahn (LAC) law, L(t)∼t^{1/2} and the evolution is via annihilation of string defects. The system exhibits dynamical scaling that is also robust with respect to κ^{'}. We find that the Sm phase at the quench temperatures T (T>T_{c}^{1}→T<T_{c}^{2}) that we consider has SmB order with a hexatic arrangement of the LC molecules in the layers (SmB-H phase). Coarsening in this phase exhibits a striking two-timescale scenario: First, the LC molecules align and develop orientational order (or nematicity), followed by the emergence of the characteristic layering (or smecticity) along with the hexatic bond-orientational-order within the layers. Consequently, the growth follows the LAC law L(t)∼t^{1/2} at early times and then shows a sharp crossover to a slower growth regime at later times. Our observations strongly suggest that L(t)∼t^{1/4} in this regime. Interestingly, the correlation function shows dynamical scaling in both the regimes and the scaling function is universal. The dynamics is also robust with respect to changes in κ^{'}, but the smecticity is more pronounced at larger values. Further, the early-time dynamics is governed by string defects, while the late-time evolution is dictated by interfacial defects. We believe this scenario is generic to the Sm phase even with other kinds of local order within the Sm layers.

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.

Interfacial stiffness of nematic-smectic B interface in Gay-Berne liquid crystals using capillary wave theory.

The interfacial stiffness for nematic-smectic B (nm-smB) interface in a liquid crystalline (LC) material is calculated using Capillary Wave Theory (CWT) and molecular dynamics simulations. The Gay-Berne (GB) pair potential with parameters κ, κ',μ, and ν equal to 3, 5, 2, and 1 is used to model the LC material. Using a smart three-step recipe, we have obtained an nm-smB phase coexistence in our simulations where the nm and smB directors are nearly parallel to each other and perpendicular to the interface normal. The density profiles are used to compute the nm-smB coexisting density range, the interfacial width, and its position. The smectic phase is differentiated from the nematic phase by using the local bond order parameter (q6q6), which has helped us to demonstrate that the interface is indeed rough. Finally, the interfacial stiffness of the nm-smB interface is computed by following the CWT analysis and is found to be γ̃nm-smB=0.39861kBT/σee 2=0.04429/σss 2, where σee and σss are the length and diameter of the GB LC particles.

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.

Chiral Gay–Berne model for molecular dynamics computer simulations

We have extended the chiral Gay–Berne (GB) pair potential of Memmer and co–workers [Liq. Cryst. (15), 345 (1993)] to the general case of biaxial ellipsoids, and we provide explicit expressions for the gradient and the torques to be used in molecular dynamics (MD) codes. To test our results against published results we have performed MD simulations of samples formed by N = 1024 uniaxial GB ellipsoids with constant volume, and we have studied how the thermotropic behavior is affected by particle chirality. We have run temperature scans starting from isotropic samples and found clear signatures of the spontaneous formation of both lower temperature blue and cholesteric phases.

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.

An evaluation of contact models for particle-scale simulation of clay

Geotechnical engineers are well aware that the particle surface chemistry and the pore fluid composition can significantly influence the mechanical behaviour of clay. Reference is often made to the Derjaguin-Landau-Vervey-Overbeek (DLVO) theory, which enables the electrochemical interactions between charged particles to be estimated. Hitherto, the absence of an effective framework for particle-scale simulation of clay has inhibited a direct link between these electrochemical interactions and clay behaviour (e.g. load:deformation response) or fabric (i.e. the development of a disperse or flocculated fabric). Ebrahimi [1] demonstrated the viability of using molecular dynamics simulations where the clay grains are simulated as ellipsoidal particles whose interactions are described by an analytical expression called the Gay-Berne (GB) potential. While promising when compared to other approaches documented in the literature, Ebrahimi's work considered only a single clay mineralogy and did not explicitly account for the pore fluid composition. This paper considers the use of the Gay-Berne potential in particle-scale modelling of clay from a more general perspective. Calibration of the GB model parameters to predict kaolinite particle interactions reveals a lack of generality in Ebrahimi's approach. The Gay-Berne potential cannot simulate situations in which attractive and repulsive interactions co-exist, which lead to the classical “cardhouse” fabric, as is the case of kaolinite particles interacting via an acidic pore fluid.

Toward Transferable Coarse‐Grained Potentials for Poly‐Aromatic Hydrocarbons: A Force Matching Approach

AbstractPoly‐aromatic hydrocarbons (PAHs) have been the subject of numerous experimental investigations for their multitude of existence, from particulate soot to the vast cosmos. Given the structural peculiarity of PAHs, where aromatic moieties serve as the basic building blocks, a generalized coarse‐grained (CG) description befits and holds immense potential to investigate large‐scale PAH systems and their derivatives via CG simulation. Toward this, a minimal CG mapping scheme is proposed where a set of PAHs are modeled as planar molecules made up of oblate ellipsoids, which interact via uniaxial Gay–Berne (GB) potential. A force‐based systematic coarse‐graining approach is followed to extract the CG force field parameters. The resulting GB parameters are found to be either comparable or show definite trends as a function of molecular size. CG simulation is shown to retain the qualitative structural features of the underlying atomistic systems with multi‐fold decrease in computational cost. Accelerated equilibration of atomistic systems is shown to be achievable by MC simulations of CG systems followed by back‐mapping, where the atomistic structure is exactly reproduced.

Comparison of the Mesomorphic Behaviour of 1:1 and 1:2 Mixtures of Charged Gay-Berne GB(4.4,20.0,1,1) and Lennard-Jones Particles

We present a Molecular Dynamics study of mixtures of charged Gay-Berne (GB) ellipsoids and spherical Lennard-Jones (LJ) particles as models of ionic liquids and ionic liquid crystals. The GB system is highly anisotropic (GB(4.4,20.0,1,1)) and we observe a rich mesomorphism, with ionic nematic and smectic phases in addition to the isotropic mixed phase and crystalline phases with honeycomb structure. The systems have been investigated by analyzing the orientational and translational order parameters, as well as radial distribution functions. We have directly compared 1:1 mixtures, where the GB and LJ particles have a charge equal in magnitude and opposite in sign, and 1:2 mixtures where the number of LJ particles is twice as large compared to the GB and their charge half in magnitude. The results highlight the role of the long-range isotropic electrostatic interaction compared to the short-range van der Waals anisotropic contribution, and the effect of the stoichiometry on the stability of ionic mesophases.

Can off-centre mesogen dipoles extend the biaxial nematic range?

We have investigated the possibility of extending the stability range of the biaxial nematic phase by adding an off-centre dipole of various strengths and orientations to elongated biaxial Gay-Berne (GB) mesogens yielding a relatively narrow biaxial nematic (Nbx) phase, and a smectic (Sbx) phase when dipole-less. The effect of dipoles is not easy to predict, and our previous investigations have shown the limited benefits of having a central dipole. Here we show, employing molecular dynamics (MD) simulations, that a not too strong off-centre dipole positioned along the longest axis of the nematogen can extend the temperature range of stability of the biaxial nematic phase, also shifting it towards lower temperatures.

Orientational ordering in a modified Gay–Berne fluid: a density-functional approach

ABSTRACTWe present a density-functional approach to describe the orientational ordering in a modified Gay–Berne (GB) potential proposed by Qi et al. [Polymer. 2012;53:634–639]. In this potential, an attractive parameter is introduced for describing the strength of attractive force relative to its repulsive counterpart between large particles. The first-order density-functional theory is tested for GB molecules with axial ratio , and the set of parameters , concentrating on the effect of varying temperature. It is observed that as the strength of attractive parameter increases, the isotropic–nematic (I–N) phase coexistence densities and pressure are seen to be shifted towards high densities with increase in temperature. The theory is found to be in good agreement with existing simulation data for the study of I–N phase transition.

Mesoscale simulation of clay aggregate formation and mechanical properties

This paper proposes a novel methodology for understanding the meso-scale aggregation of clay platelets in water. We use Molecular Dynamics simulations using the CLAYFF force fields to represent the interactions between two layers of Wyoming montmorillonite (Na-smectite) in bulk water. The analyses are used to establish the potential of mean force at different spacings between the layers for edge-to-edge and face-to-face interactions. This is accomplished by finding the change in free energy as a function of the separation distance between the platelets using thermodynamic perturbation theory with a simple overlap sampling method. These nanoscale results are then used to calibrate the Gay–Berne (GB) potential that represents each platelet as a single-site ellipsoidal body. A coarse-graining upscaling approach then uses the GB potentials and molecular dynamics to represent the meso-scale aggregation of clay platelets (at submicron length scale). Results from meso-scale simulations obtain the equilibrium/jamming configurations for mono-disperse clay platelets. The results show aggregation for a range of clay platelets dimensions and pressures with mean stack size ranging from 3 to 8 platelets. The particle assemblies become more ordered and exhibit more pronounced elastic anisotropy at higher confining pressures. The results are in good agreement with previously measured nano-indentation moduli over a wide range of clay packing densities.