Lennard-Jones Spheres Research Articles

Molecular dynamics simulations of the dielectric constants of salt-free and salt-doped polar solvents.

We develop a Stockmayer fluid model that accounts for the dielectric responses of polar solvents (water, MeOH, EtOH, acetone, 1-propanol, DMSO, and DMF) and NaCl solutions. These solvent molecules are represented by Lennard-Jones (LJ) spheres with permanent dipole moments and the ions by charged LJ spheres. The simulated dielectric constants of these liquids are comparable to experimental values, including the substantial decrease in the dielectric constant of water upon the addition of NaCl. Moreover, the simulations predict an increase in the dielectric constant when considering the influence of ion translations in addition to the orientation of permanent dipoles.

Influence of Lennard-Jones Parameters in the Temperature Dependence of Real Gases Diffusion through Nanochannels.

Umbrella Sampling Molecular Dynamics has been used to determine transition energies for different guest molecules through hydroquinone β-clathrate nanochannels, as well as their temperature trend. This clathrate has been shown to successfully enclathrate different types of small gases with remarkable selectivity, and thus it has been proposed as a potential gas separation and storage medium. Most of these potential guest gases can be successfully modeled as single Lennard-Jones spheres. Then, to obtain a general view of diffusion probabilities for different potential guest molecules, a comparative study for different virtual guest molecules described by different Lennard-Jones parameters has been performed. A regular temperature trend has been obtained for the transition energies for the molecular model characteristic parameter range explored. Finally, to locate the transition energy values of real gases within the space of phases explored, calculations have been repeated for molecular models of different noble gases and H2. The correlation results presented allow a wide interpolation ability for determining the transition energies of potential guest molecules stored or diffusing through the nanochannels of the studied clathrate structure.

Unified description for the temperature dependence of mobility in liquids.

The physical mechanisms governing molecular mobility in liquids remain unresolved. Whether distinct mechanisms govern mobility in the Arrhenian and super-cooled regions, and whether the mobility in these regions can be unified remain open questions. Here, molecular dynamics simulations were used to search for a structural property with a temperature dependence related by a simple functional form to the temperature dependent translational diffusion coefficient, Dtrans. The logarithm of Dtrans was found to be a two-parameter function of F2, where F2 is the mean squared-force per molecule. The relationship is demonstrated for all systems investigated: a three-bead model of ortho-terphenyl, an 80:20 binary mixture of Lennard-Jones spheres, and a system of Lennard-Jones dumbbells. For each system, the relationship holds for the entire range of temperatures under both constant pressure and constant density conditions. The same F2-based expression describes the translational diffusion coefficient in the Arrhenian, crossover, and super-Arrhenian regions.

Scaling Properties of Liquid Dynamics Predicted from a Single Configuration: Small Rigid Molecules

Isomorphs are curves in the thermodynamic phase diagram along which structure and dynamics are invariant to a good approximation. There are two main ways to trace out isomorphs, the configurational-adiabat method and the direct-isomorph-check method. Recently a new method based on the scaling properties of forces was introduced and shown to work very well for atomic systems [T. B. Schrøder, Phys. Rev. Lett. 2022, 129, 245501]. A unique feature of this method is that it only requires a single equilibrium configuration for tracing out an isomorph. We here test generalizations of this method to molecular systems and compare to simulations of three simple molecular models: the asymmetric dumbbell model of two Lennard-Jones spheres, the symmetric inverse-power-law dumbbell model, and the Lewis-Wahnström o-terphenyl model. We introduce and test two force-based and one torque-based methods, all of which require just a single configuration for tracing out an isomorph. Overall, the method based on requiring invariant center-of-mass reduced forces works best.

Diffusion-driven rotation in cholesteric liquid crystals studied using molecular dynamics simulation of a mixture of the Gay-Berne fluid and the Lennard-Jones fluid.

Diffusion-driven rotation in cholesteric liquid crystals has been studied using molecular dynamics simulation. Then a chemical potential gradient parallel to the cholesteric axis induces a torque that rotates the director at a constant rate around this axis, besides driving a mass current. An equimolar mixture of Gay-Berne ellipsoids and Lennard-Jones spheres was used as the molecular model. In order to keep the system homogeneous, the color conductivity algorithm was used to apply a color field instead of a chemical potential gradient to drive a mass current. Then the particles are given a color charge that interacts with a color field in the same way as with an electric field, but these charges do not interact with each other. This algorithm is often used to calculate the mutual diffusion coefficient. In the above liquid crystal model, it was found that the color field induces a torque that rotates the director at a constant rate around the cholesteric axis in addition to driving a mass current. The phenomenon was quantified by calculating the cross-coupling coefficient between the color field and the director angular velocity. The results were cross-checked by using a director rotation algorithm to exert a torque to rotate the director at a constant rate. Besides rotation of the director, this resulted in a mass current parallel to the cholesteric axis. The cross-coupling coefficient between the torque and the mass current was equal to the cross-coupling coefficient between the color field and the director rotation rate within a statistical uncertainty of 10 percent, thus fulfilling the Onsager reciprocity relations. As a further cross-check, these cross-coupling coupling coefficients, the color conductivity, and the twist viscosity were calculated by evaluating the corresponding Green-Kubo relations. Finally, it was noted that the orientation of the cholesteric axis parallel to the color field is the one that minimizes the irreversible energy dissipation rate. This is in accordance with a theorem stating that this quantity is minimal in the linear regime of a nonequilibrium steady state.

Toward comprehensive exploration of the physisorption space in porous pseudomaterials using an iterative mutation search algorithm.

We describe an updated algorithm for efficiently exploring structure-property spaces relating to physisorption of gases in porous materials. This algorithm uses previously described "pseudomaterials," which are crystals of randomly arranged and parameterized Lennard-Jones spheres, and combines it with a new iterative mutation exploration method. This algorithm is significantly more efficient at sampling the structure-property space than previously reported methods. For the sake of benchmarking to prior work, we apply this method to exploring methane adsorption at 35 bars (298K) and void fraction as the main structure-property combination. We demonstrate the effect and importance of the changes that were required to increase efficiency over prior methods. The most important changes were (1) using "discrete" mutations less often, (2) decreasing degrees of freedom, and (3) removing biasing from mutations on bounded parameters.

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.

Dynamic Crossover in Fluids: From Hard Spheres to Molecules.

We propose a simple and generic definition of a demarcation reconciling structural and dynamic frameworks when combined with the entropy scaling framework. This crossover line between gas- and liquid-like behaviors is defined as the curve for which an individual property, the contribution to viscosity due to molecules' translation, is exactly equal to a collective property, the contribution to viscosity due to molecular interactions. Such a definition is shown to be consistent with the one based on the minima of the kinematic viscosity. For the hard sphere, this is shown to be an exact solution. For Lennard-Jones spheres and dimers and for some simple real fluids, this relation holds very well. This crossover line passes nearby the critical point, and for all studied fluids, it is well captured by the critical excess entropy curve for atomic fluids, emphasizing the link between transport properties and local structure.

Molecular dynamics simulation of the n-octacosane-water mixture confined in hydrophilic and hydrophobic mesopores: The effect of oxygenates

Wax and water mixtures are the main products of the Gas-To-Liquids (GTL) process through the Fischer-Tropsch synthesis (FTS), along with relatively small quantities of oxygenated compounds such as alcohols. It has been established that water production in high concentrations leads to phase segregation inside the catalyst support pores. Excess water conditions are considered responsible for sintering of catalytic nanoparticles, which reduces catalyst lifetime and increases GTL operational cost. Apart from the effects of increased water concentration in wax – water FTS mixtures, the presence of oxygenates has not been studied at the molecular level. Moreover, the effect of the surface support chemistry on the wax – water mixture inside catalyst pores is essential in understanding mixture phase behavior. All these open questions are of significant interest for the petrochemical industry. The present study focuses on simulating by means of Molecular Dynamics (MD) the n-octacosane (n-C28) – water mixture inside titanium dioxide (TiO2) and silicon carbide (SiC) mesopores at low-temperature FTS conditions (473.15 K). The presence of small alcohols such as methanol and ethanol on the n-C28 – H2O mixture's phase behavior was also evaluated. The united atom TraPPE (TraPPE-UA) force field was used for n-C28 and the alcohols, while the SPC/E was used for water. Catalyst support atoms were modeled as Lennard-Jones spheres (charged or neutral) at fixed positions. Our simulations show that inside TiO2, water molecules organize into two discrete layers on the TiO2 surface, with n-C28 occupying the pore center; mixture phase separation is completely reversed inside the SiC pore. In both cases, alcohol addition does not influence either n-C28 or H2O distribution inside the pores. Furthermore, we examine the hydrogen bonds formed between water molecules and how these are influenced upon alcohol addition and confinement. Finally, through the calculation of lateral diffusion coefficients, we provide insights on the mobility of the individual n-C28 – H2O mixture components inside the pores considered.

Combined temperature and density series for fluid-phase properties. II. Lennard-Jones spheres.

In Paper I [J. R. Elliott, A. J. Schultz, and D. A. Kofke, J. Chem. Phys. 143, 114110 (2015)] of this series, a methodology was presented for computing the coefficients of a power series of the Helmholtz energy in reciprocal temperature, β, through density series based on cluster integral expansions. Previously, power series in β were evaluated by thermodynamic perturbation theory (TPT) using molecular simulation of a reference fluid. The present methodology uses cluster integrals to evaluate coefficients of the density expansion at each individual order of temperature. While Paper I [J. R. Elliott, A. J. Schultz, and D. A. Kofke, J. Chem. Phys. 143, 114110 (2015)] developed this methodology for square well (SW) spheres, the present work extends the methodology to Lennard-Jones (LJ) spheres, where the reference fluid is the Weeks-Chandler-Andersen potential. Comparisons of TPT coefficients computed from cluster integrals to those from molecular simulation show good agreement through third order in β when coefficients are expressed with effective approximants. Notably, the agreement for LJ spheres is much better than for SW spheres although fewer coefficients of the density series (B2-B5) are available than for SW spheres (B2-B6). The coefficients for Bi(β) of the reference fluid are shown to follow a simple relationship to the virial coefficients of hard sphere fluids, corrected for the temperature dependency of the equivalent hard sphere diameter. This lays the foundation for a correlation of the second virial coefficient of LJ spheres B2(β) that extrapolates to infinite order in temperature. This correlation of B2(β) provides a basis for estimating the low density limit of TPT coefficients at all orders in temperature, facilitating a recursive extrapolation formula to estimate TPT coefficients of fourth order and higher over the entire density range. The applicability of the resulting equation of state is demonstrated by computing the thermodynamic properties for LJ spheres and comparing to standard simulation results.

Dual-potential approach for coarse-grained implicit solvent models with accurate, internally consistent energetics and predictive transferability.

The dual-potential approach promises coarse-grained (CG) models that accurately reproduce both structural and energetic properties, while simultaneously providing predictive estimates for the temperature-dependence of the effective CG potentials. In this work, we examine the dual-potential approach for implicit solvent CG models that reflect large entropic effects from the eliminated solvent. Specifically, we construct implicit solvent models at various resolutions, R, by retaining a fraction 0.10 ≤ R ≤ 0.95 of the molecules from a simple fluid of Lennard-Jones spheres. We consider the dual-potential approach in both the constant volume and constant pressure ensembles across a relatively wide range of temperatures. We approximate the many-body potential of mean force for the remaining solutes with pair and volume potentials, which we determine via multiscale coarse-graining and self-consistent pressure-matching, respectively. Interestingly, with increasing temperature, the pair potentials appear increasingly attractive, while the volume potentials become increasingly repulsive. The dual-potential approach not only reproduces the atomic energetics but also quite accurately predicts this temperature-dependence. We also derive an exact relationship between the thermodynamic specific heat of an atomic model and the energetic fluctuations that are observable at the CG resolution. With this generalized fluctuation relationship, the approximate CG models quite accurately reproduce the thermodynamic specific heat of the underlying atomic model.

Directional Ostwald Ripening for Producing Aligned Arrays of Nanowires.

The remarkable electronic and mechanical properties of nanowires have great potential for fascinating applications; however, the difficulties of assembling ordered arrays of aligned nanowires over large areas prevent their integration into many practical devices. In this paper, we show that aligned VO2 nanowires form spontaneously after heating a thin V2O5 film on a grooved SiO2 surface. Nanowires grow after complete dewetting of the film, after which there is the formation of supercooled nanodroplets and subsequent Ostwald ripening and coalescence. We investigate the growth mechanism using molecular dynamics simulations of spherical Lennard-Jones particles, and the simulations help explain how the grooved surface produces aligned nanowires. Using this simple synthesis approach, we produce self-aligned, millimeter-long nanowire arrays with uniform metal-insulator transition properties; after their transfer to a polymer substrate, the nanowires act as a highly sensitive array of strain sensors with a very fast response time of several tens of milliseconds.

Configurational mapping significantly increases the efficiency of solid-solid phase coexistence calculations via molecular dynamics: Determining the FCC-HCP coexistence line of Lennard-Jones particles.

In this study, we incorporate configuration mapping between simulation ensembles into the successive interpolation of multistate reweighting (SIMR) method in order to increase phase space overlap between neighboring simulation ensembles. This significantly increases computational efficiency over the original SIMR method in many situations. We use this approach to determine the coexistence curve of face-centered cubic-hexagonal close-packed Lennard-Jones spheres using direct molecular dynamics and SIMR. As previously noted, the coexistence curve is highly sensitive to the treatment of the van der Waals cutoff. Using a cutoff treatment, the chemical potential difference between phases is moderate and SIMR quickly finds the phase equilibrium lines with good statistical uncertainty. Using a smoothed cutoff results in nonphysical errors in the phase diagram, while the use of particle mesh Ewald for the dispersion term results in a phase equilibrium curve that is comparable with previous results. The drastically closer free energy surfaces for this case test the limits of this configuration mapping approach to phase diagram prediction.

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.

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.

High-Pressure Methane Adsorption in Porous Lennard-Jones Crystals.

Decades of research have yet to yield porous adsorbents that meet the U.S. Department of Energy's methane storage targets. To better understand why, we calculated high-pressure methane adsorption in 600 000 randomly generated porous crystals, or "pseudomaterials," using atomistic grand canonical Monte Carlo (GCMC) simulations. These pseudomaterials were periodic configurations of Lennard-Jones spheres whose coordinates in space, along with corresponding well depths and radii, were all chosen at random. GCMC simulations were performed for pressures of 35 and 65 bar at a temperature of 298 K. Methane adsorption was compared for all materials against a range of other properties: average well depths and radii, number density, helium void fraction, and volumetric surface area. The results reveal structure-property relationships that resemble those previously observed for metal-organic frameworks and other porous materials. We contend that our computational methodology can be useful for discovering useful structure-property relationships related to gas adsorption without requiring experimentally accessible structural data.

Implicit Solvation Using the Superposition Approximation (IS-SPA): An Implicit Treatment of the Nonpolar Component to Solvation for Simulating Molecular Aggregation.

Nonpolar solute-solvent interactions are the driving force for aggregation in important chemical and biological phenomena including protein folding, peptide self-assembly, and oil-water emulsion formation. Currently, the most accurate and computationally efficient description of these processes requires an explicit treatment of all solvent and solute atoms. Previous computationally feasible implicit solvent models, such as solute surface area approaches, are unsuccessful at capturing aggregation features including both structural and energetic trends while more theoretically rigorous approaches, such as Reference Interaction Site Model (RISM), are accurate but extremely computationally demanding. Our approach, denoted Implicit Solvation using the Superposition Approximation (IS-SPA), builds on previous theory utilizing the Kirkwood superposition approximation to approximate the mean force of the solvent from solute parameters. We introduce and verify a parabolic first solvation shell truncation of atomic solvation, fitting water distributions around a molecule, and a Monte Carlo integration of the mean solvent force. These extensions allow this method to be implemented as an efficient nonpolar implicit solvent model for molecular simulation. The approximations in IS-SPA are first explored and justified for the homodimerization of an array of different sized Lennard-Jones spheres. The accuracy and transferability of the approach are demonstrated by its ability to capture the position and relative energies of the desolvation barrier and free energy minimum of alkane homodimers. The model is then shown to reproduce the phase separation and solubility of cyclohexane and water. These promising results, coupled with 2 orders of magnitude speed-up for dilute systems as compared to explicit solvent simulations, demonstrate that IS-SPA is an appealing approach to boost the time- and length-scale of molecular aggregation simulations.

Shape matters: The case for Ellipsoids and Ellipsoidal Water11This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form

We describe the shape potentials used for the van der Waals interactions between soft-ellipsoids used to coarse-grain molecular moieties in Metropolis Monte-Carlo simulation software. The morphologies resulting from different expressions for these van der Waals interaction potentials are discussed for the case of a prolate spheroid system with a strong dipole at the center. We also show that the calculation of ellipsoids is, at worst, only about fivefold more expensive computationally when compared to a simple Lennard-Jones sphere. Finally, as an application of the ellipsoidal shape we parametrize water from the original SPC water model and observe – just through the difference in shape alone – a significant improvement of the O-O radial distribution function when compared to experimental data.

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.

Heterogeneous nucleation from a supercooled ionic liquid on a carbon surface.

Classical molecular dynamics simulations were used to study the nucleation of the crystal phase of the ionic liquid [dmim+][Cl-] from its supercooled liquid phase, both in the bulk and in contact with a graphitic surface of D = 3 nm. By combining the string method in collective variables [Maragliano et al., J. Chem. Phys. 125, 024106 (2006)], with Markovian milestoning with Voronoi tessellations [Maragliano et al., J. Chem. Theory Comput. 5, 2589-2594 (2009)] and order parameters for molecular crystals [Santiso and Trout, J. Chem. Phys. 134, 064109 (2011)], we computed minimum free energy paths, the approximate size of the critical nucleus, the free energy barrier, and the rates involved in these nucleation processes. For homogeneous nucleation, the subcooled liquid phase has to overcome a free energy barrier of ∼85 kcal/mol to form a critical nucleus of size ∼3.6 nm, which then grows into the monoclinic crystal phase. This free energy barrier becomes about 42% smaller (∼49 kcal/mol) when the subcooled liquid phase is in contact with a graphitic disk, and the critical nucleus formed is about 17% smaller (∼3.0 nm) than the one observed for homogeneous nucleation. The crystal formed in the heterogeneous nucleation scenario has a structure that is similar to that of the bulk crystal, with the exception of the layers of ions next to the graphene surface, which have larger local density and the cations lie with their imidazolium rings parallel to the graphitic surface. The critical nucleus forms near the graphene surface separated only by these layers of ions. The heterogeneous nucleation rate (∼4.8 × 1011 cm-3 s-1) is about one order of magnitude faster than the homogeneous rate (∼6.6 × 1010 cm-3 s-1). The computed free energy barriers and nucleation rates are in reasonable agreement with experimental and simulation values obtained for the homogeneous and heterogeneous nucleation of other systems (ice, urea, Lennard-Jones spheres, and oxide glasses).