Gay-Berne Potential Research Articles

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.

Dynamics of a binary mixture of non-spherical molecules: Test of hydrodynamic predictions.

We consider a new class of model systems to study systematically the role of molecular shape in the transport properties of dense liquids. Our model is a liquid binary mixture where both the molecules are non-spherical and characterized by a collection of parameters. Although in the real world most of the molecules are non-spherical, only a limited number of theoretical studies exist on the effects of molecular shapes and hardly any have addressed the validity of the hydrodynamic predictions of rotational and translational diffusion of these shapes in liquids. In this work, we study a model liquid consisting of a mixture of prolate and oblate (80:20 mixture) ellipsoids with interactions governed by a modified Gay-Berne potential for a particular aspect ratio (ratio of the length and diameter of the ellipsoids), at various temperature and pressure conditions. We report calculations of transport properties of this binary mixture by varying temperature over a wide range at a fixed pressure. We find that for the pressure-density conditions studied, there is no signature of any phase separation, except transitions to the crystalline phase at low temperatures and relatively low pressure (the reason we largely confined our studies to high pressure). We find that for our model binary mixture, both stick and slip hydrodynamic predictions break down in a major fashion, for both prolates and oblates and particularly so for rotation. Moreover, prolates and oblates themselves display different dynamical features in the mean square displacement and in orientational time correlation functions.

Isotropic-nematic transition of self-propelled rods in three dimensions.

Using overdamped Brownian dynamics simulations we investigate the isotropic-nematic (IN) transition of self-propelled rods in three spatial dimensions. For two well-known model systems (Gay-Berne potential and hard spherocylinders) we find that turning on activity moves to higher densities the phase boundary separating an isotropic phase from a (nonpolar) nematic phase. This active IN phase boundary is distinct from the boundary between isotropic and polar-cluster states previously reported in two-dimensional simulation studies and, unlike the latter, is not sensitive to the system size. We thus identify a generic feature of anisotropic active particles in three dimensions.

Elastocaloric effect in liquid crystal elastomers from molecular simulations

ABSTRACTLarge-scale molecular simulations of the elastocaloric effect in swollen monodomain main-chain liquid crystal elastomers are performed, following the so-called ‘indirect approach’ where the magnitude of the effect is extracted from the system’s equation of state connecting stress, strain and temperature. The presented isostress off-lattice Monte Carlo simulations are based on the soft-core Gay–Berne potential and predict an elastocaloric temperature increase that exceeds K upon applying an external engineering stress of 100 kPa, which results in an elastocaloric responsivity beyond K/MPa.

Assembled Structures of Perfluorosulfonic Acid Ionomers Investigated by Anisotropic Modeling and Simulations.

Nafion, a classic of perfluorosulfonic acid ionomers, has broad applications in proton conduction, attributed from the unique structures. However, a satisfactory structure model from theoretical calculation and simulation that can match with the well-known experimental observations is still absent. We performed GPU-accelerated molecular dynamics simulations to investigate the assembled structures of Nafion at different water contents based on an anisotropic coarse-grained model equipped with Gay-Berne potential. Accurate parameters for the coarse-grained model are collected by matching energy profiles based on density functional theory calculations. The results show that the hydrophilic phase in Nafion assemblies undergoes a crossover from isolated spherical clusters to interconnected cluster/channel networks with the increase of water content. We found the crystalline domains in polymer matrix and they are suppressed at elevated water content. These microphase-separated structures achieve quantitative agreement with existing experimental observations, including morphologies from electron microscopy and intensity profiles from scattering experiments. This work suggests that accurate consideration of the anisotropy is a key to reveal the formation of unique assembled structures of perfluorosulfonic acid ionomers at different water contents.

Solvent-free, molecular-level modeling of self-assembling amphiphiles in water.

Aggregation mesophases of self-assembling amphiphiles in water are highly important in the context of biology (biomembranes), therapy (liposomes), industry (polymer surfactants), and condensed-matter physics (lyotropic liquid crystals). Besides helping to increase fundamental understanding of collective molecular behavior, simulations of these lyotropic phases are pivotal to technological and medical developments such as smart drug carriers for gene therapy. Implicit-solvent, coarse-grained, low resolution modeling with a simple pair potential is the key to realizing the larger length and time scales associated with such mesoscopic phenomena during a computer simulation. Modeling amphiphiles by directed, soft, ellipsoidal cores interacting via a computationally simple yet tunable anisotropic pair potential, we have come to such a single-site model amphiphile that can rapidly self-assemble to give diverse lyotropic phases (such as fluid bilayers, micelles, etc.) without requiring the explicit incorporation of solvent particles. The model directly represents a tunable packing parameter that manifests in the spontaneous curvature of the amphiphile aggregates. Besides the all-important hydrophobic interaction, the hydration force is also treated implicitly. Thanks to the efficient solvent-free molecular-level coarse graining, this model is suitable for generic mesoscale studies of phenomena such as self-assembly, amphiphile mixing, domain formation, fusion, elasticity, etc., in amphiphile aggregates.

Density functional theory of freezing of a system of highly elongated ellipsoidal oligomer solutions

ABSTRACTWe have used the density functional theory of freezing to study the liquid crystalline phase behavior of a system of highly elongated ellipsoidal conjugated oligomers dispersed in three different solvents namely chloroform, toluene and their equimolar mixture. The molecules are assumed to interact via solvent-implicit coarse-grained Gay–Berne potential. Pair correlation functions needed as input in the density functional theory have been calculated using the Percus–Yevick (PY) integral equation theory. Considering the isotropic and nematic phases, we have calculated the isotropic–nematic phase transition parameters and presented the temperature–density and pressure–temperature phase diagrams. Different solvent conditions are found not only to affect the transition parameters but also determine the capability of oligomers to form nematic phase in various thermodynamic conditions. In principle, our results are verifiable through computer simulations.

Effect of Polydispersity of Clay Platelets on the Aggregation and Mechanical Properties of Clay at the Mesoscale

AbstractThe results from mesoscale simulations of the formation and evolution of microstructure for assemblies of Na-smectite particles based on assumed size distributions of individual clay platelets are presented here. The analyses predicted particle arrangements and aggregation (i.e. platelets linked in face—face configurations) and are used to link geometric properties of the microstructure and mechanical properties of the particle assemblies. Interactions between individual ellipsoidal clay platelets are represented using the Gay-Berne potential based on atomistic simulations of the free energy between two Na-smectite clay-platelets in liquid water, following a novel coarse-graining method developed previously. The current study describes the geometric (aggregate thickness, orientation, and porosity) and elastic properties in the ‘jammed states’ from the mesoscale simulations for selected ranges of clay particle sizes and confining pressures. The thickness of clay aggregates for monodisperse assemblies increases (with average stack thickness consisting of n = 3–8 platelets) with the diameter of the individualclay platelets and with the level of confining pressure. Aggregates break down at high confining pressures (50–300 atm) due to slippage between the platelets. Polydisperse simulations generate smaller aggregates (n = 2) and show much smaller effects of confining pressure. All assemblies show increased order with confining pressure, implying more anisotropic microstructure. The mesoscale simulations are also in good agreement with macroscopic compression behavior measured in conventional 1-D laboratory compression tests. The mesoscale assemblies exhibit cubic symmetry in elastic properties. The results for larger platelets (D = 1000 Å) are in good agreement with nano-indentation measurements on natural clays and shale samples.

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.

GPU-Accelerated Molecular Dynamics Simulation to Study Liquid Crystal Phase Transition Using Coarse-Grained Gay-Berne Anisotropic Potential.

Gay-Berne (GB) potential is regarded as an accurate model in the simulation of anisotropic particles, especially for liquid crystal (LC) mesogens. However, its computational complexity leads to an extremely time-consuming process for large systems. Here, we developed a GPU-accelerated molecular dynamics (MD) simulation with coarse-grained GB potential implemented in GALAMOST package to investigate the LC phase transitions for mesogens in small molecules, main-chain or side-chain polymers. For identical mesogens in three different molecules, on cooling from fully isotropic melts, the small molecules form a single-domain smectic-B phase, while the main-chain LC polymers prefer a single-domain nematic phase as a result of connective restraints in neighboring mesogens. The phase transition of side-chain LC polymers undergoes a two-step process: nucleation of nematic islands and formation of multi-domain nematic texture. The particular behavior originates in the fact that the rotational orientation of the mesogenes is hindered by the polymer backbones. Both the global distribution and the local orientation of mesogens are critical for the phase transition of anisotropic particles. Furthermore, compared with the MD simulation in LAMMPS, our GPU-accelerated code is about 4 times faster than the GPU version of LAMMPS and at least 200 times faster than the CPU version of LAMMPS. This study clearly shows that GPU-accelerated MD simulation with GB potential in GALAMOST can efficiently handle systems with anisotropic particles and interactions, and accurately explore phase differences originated from molecular structures.

Self-diffusion in the non-Newtonian regime of shearing liquid crystal model systems based on the Gay-Berne potential.

The self-diffusion coefficients of nematic phases of various model systems consisting of regular convex calamitic and discotic ellipsoids and non-convex bodies such as bent-core molecules and soft ellipsoid strings have been obtained as functions of the shear rate in a shear flow. Then the self-diffusion coefficient is a second rank tensor with three different diagonal components and two off-diagonal components. These coefficients were found to be determined by a combination of two mechanisms, which previously have been found to govern the self-diffusion of shearing isotropic liquids, namely, (i) shear alignment enhancing the diffusion in the direction parallel to the streamlines and hindering the diffusion in the perpendicular directions and (ii) the distortion of the shell structure in the liquid whereby a molecule more readily can escape from a surrounding shell of nearest neighbors, so that the mobility increases in every direction. Thus, the diffusion parallel to the streamlines always increases with the shear rate since these mechanisms cooperate in this direction. In the perpendicular directions, these mechanisms counteract each other so that the behaviour becomes less regular. In the case of the nematic phases of the calamitic and discotic ellipsoids and of the bent core molecules, mechanism (ii) prevails so that the diffusion coefficients increase. However, the diffusion coefficients of the soft ellipsoid strings decrease in the direction of the velocity gradient because the broadsides of these molecules are oriented perpendicularly to this direction due the shear alignment (i). The cross coupling coefficient relating a gradient of tracer particles in the direction of the velocity gradient and their flow in the direction of the streamlines is negative and rather large, whereas the other coupling coefficient relating a gradient in the direction of the streamlines and a flow in the direction of the velocity gradient is very small.

Coarse-Grained Modeling of Nucleic Acids Using Anisotropic Gay–Berne and Electric Multipole Potentials

In this work, we attempt to apply a coarse-grained (CG) model, which is based on anisotropic Gay-Berne and electric multipole (EMP) potentials, to the modeling of nucleic acids. First, a comparison has been made between the CG and atomistic models (AMBER point-charge model) in the modeling of DNA and RNA hairpin structures. The CG results have demonstrated a good quality in maintaining the nucleic acid hairpin structures, in reproducing the dynamics of backbone atoms of nucleic acids, and in describing the hydrogen-bonding interactions between nucleic acid base pairs. Second, the CG and atomistic AMBER models yield comparable results in modeling double-stranded DNA and RNA molecules. It is encouraging that our CG model is capable of reproducing many elastic features of nucleic acid base pairs in terms of the distributions of the interbase pair step parameters (such as shift, slide, tilt, and twist) and the intrabase pair parameters (such as buckle, propeller, shear, and stretch). Finally, The GBEMP model has shown a promising ability to predict the melting temperatures of DNA duplexes with different lengths.

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.

Elastic constants and dynamics in nematic liquid crystals

In this paper, we present molecular dynamics calculations of the Frank elastic constants, and associated time correlation functions, in nematic liquid crystals. We study two variants of the Gay–Berne potential, and use system sizes of half a million molecules, significantly larger than in previous studies of elastic behaviour. Equilibrium orientational fluctuations in reciprocal (k-) space were calculated, to determine the elastic constants by fitting at low |k|; our results indicate that small system size may be a source of inaccuracy in previous work. Furthermore, the dynamics of the Gay–Berne nematic were studied by calculating time correlation functions of components of the order tensor, together with associated components of the velocity field, for a set of wave vectors k. Confirming our earlier work, we found exponential decay for splay and twist correlations, and oscillatory exponential decay for the bend correlation. In this work, we confirm similar behaviour for the corresponding velocity components. In all cases, the decay rates, and oscillation frequencies, were found to be accurately proportional to k2 for small k, as predicted by the equations of nematodynamics. However, the observation of oscillatory bend fluctuations, and corresponding oscillatory shear flow decay, is in contradiction to the usual assumptions appearing in the literature, and in standard texts. We discuss the advantages and drawbacks of using large systems in these calculations.

Thermodynamic Scaling of Miesowicz Viscosity Coefficients via Molecular Dynamics Simulation

Thermodynamic scaling of Miesowicz viscosity coefficients was investigated via molecular dynamics simulation using the Gay–Berne potential. The Miesowicz viscosity coefficients, which were calculated using an established theoretical expression under different pressures, were rescaled onto a master curve with the scaling parameter γη. The parameter was found to be identical to the thermodynamic parameter Γ and scaling parameters reported for other dynamic properties, such as the relaxation time for flip-flop motion, the rotational diffusion constant, and the Leslie rotational viscosity coefficients.

On the calculation of the absolute grand potential of confined smectic-A phases

We determine the absolute grand potential Λ along a confined smectic-A branch of a calamitic liquid crystal system enclosed in a slit pore of transverse area A and width L, using the rod–rod Gay–Berne potential and a rod–wall potential favouring perpendicular orientation at the walls. For a confined phase with an integer number of smectic layers sandwiched between the opposite walls, we obtain the excess properties (excess grand potential Λexc, solvation force fs and adsorption Γ) with respect to the bulk phase at the same μ (chemical potential) and T (temperature) state point. While usual thermodynamic integration methods are used along the confined smectic branch to estimate the grand potential difference as μ is varied at fixed L, T, the absolute grand potential at one reference state point is obtained via the evaluation of the absolute Helmholtz free energy in the (N, L, A, T) canonical ensemble. It proceeds via a sequence of free energy difference estimations involving successively the cost of localising rods on layers and the switching on of a one-dimensional harmonic field to keep layers integrity coupled to the elimination of inter-layers and wall interactions. The absolute free energy of the resulting set of fully independent layers of interacting rods is finally estimated via the existing procedures. This work opens the way to the computer simulation study of phase transitions implying confined layered phases.

A scale-bridging modeling approach for anisotropic organic molecules at patterned semiconductor surfaces.

Hybrid systems consisting of organic molecules at inorganic semiconductor surfaces are gaining increasing importance as thin film devices for optoelectronics. The efficiency of such devices strongly depends on the collective behavior of the adsorbed molecules. In the present paper, we propose a novel, coarse-grained model addressing the condensed phases of a representative hybrid system, that is, para-sexiphenyl (6P) at zinc-oxide (ZnO). Within our model, intermolecular interactions are represented via a Gay-Berne potential (describing steric and van-der-Waals interactions) combined with the electrostatic potential between two linear quadrupoles. Similarly, the molecule-substrate interactions include a coupling between a linear molecular quadrupole to the electric field generated by the line charges characterizing ZnO(10-10). To validate our approach, we perform equilibrium Monte Carlo simulations, where the lateral positions are fixed to a 2D lattice, while the rotational degrees of freedom are continuous. We use these simulations to investigate orientational ordering in the condensed state. We reproduce various experimentally observed features such as the alignment of individual molecules with the line charges on the surface, the formation of a standing uniaxial phase with a herringbone structure, as well as the formation of a lying nematic phase.

Mesoscale modeling of cement matrix using the concept of building block

ABSTRACTCalcium silicate hydrate (C-S-H) gel is the cohesive phase in cement paste and critically controls the cement hydration. Atomistic models can reproduce reasonable structural and mechanical properties of C-S-H gel at the nano scale. However, the length and time scale of such all-atom modeling technique are restrained by limited computing power. Under this context, coarse-grained modeling technique emerges as a useful alternative for investigating cement paste at extended length and time scale. Here, we regard the building block of cement as ellipsoid and develop a coarse-grained model of cement matrix based on the Gay-Berne (GB) potential. Emphasis of the present paper is on the parameterization and interpretation of the GB potential formula.

Non-Newtonian rheological properties of shearing nematic liquid crystal model systems based on the Gay-Berne potential.

The viscosities and normal stress differences of various liquid crystal model systems based on the Gay-Berne potential have been obtained as functions of the shear rate in the non-Newtonian regime. Various molecular shapes such as regular convex calamitic and discotic ellipsoids and non-convex shapes such as bent core molecules and soft ellipsoid strings have been examined. The isotropic phases were found to be shear thinning with the shear rate dependence of the viscosity following a power law in the same way as alkanes and other non-spherical molecules. The nematic phases turned out to be shear thinning but the logarithm of the viscosity proved to be an approximately linear function of the square root of the shear rate. The normal stress differences were found to display a more or less parabolic dependence on the shear rate in the isotropic phase whereas this dependence was linear at low to intermediate shear rates in the nematic phase.

Molecular dynamics simulation of planar elongational flow in a nematic liquid crystal based on the Gay–Berne potential

Molecular dynamics simulations of planar elongational flow in a nematic liquid crystal model system based on the Gay-Berne fluid were undertaken by applying the SLLOD equations of motion with an elongational velocity field or strain rate. In order to facilitate the simulation, Kraynik-Reinelt periodic boundary conditions allowing arbitrarily long simulations were used. A Lagrangian constraint algorithm was utilized to fix the director at different angles relative to the elongation direction, so that the various pressure tensor elements could be calculated as a function of this angle. This made it possible to obtain accurate values of the shear viscosities which were found to agree with results previously obtained by shear flow simulations. The torque needed to fix the director at various angles relative to the elongation direction was evaluated in order to determine the stable orientation of the director, where this torque is equal to zero. This orientation was found to be parallel to the elongation direction. It was also noted that the irreversible entropy production was minimal when the director attained this orientation. Since the simulated system was rather large and fairly long simulation runs were undertaken it was also possible to study the cross coupling between the strain rate and the order tensor. It turned out to be very weak at low strain rates but at higher strain rates it could lead to break down of the liquid crystalline order.