LJ Particles Research Articles

Scaling towards the critical point in the combined reaction/Gibbs ensemble

We explore the impact of force field parameters and reaction equilibrium on the scaling behavior towards the critical point in reactive binary systems, focusing on NO2/N2O4. This system can be considered as a special single-component system since NO2 and N2O4 are in chemical equilibrium via the chemical reaction 2NO2⇌N2O4. We simplify the system by representing both components as single LJ particles, achieving excellent agreement with densities computed using molecular simulations in which all-atom force fields were used. We investigate the effect of force field parameters (ɛ and σ) on phase behavior and show that the critical exponent β remains constant, which means that intermolecular interactions do not affect the scaling to the critical point when the chemical reaction takes place. We also investigate the sensitivity of the reaction equilibrium constant and show that even small changes in isolated molecule partition functions lead to large differences in chemical equilibria. We show that the critical exponent β is different for systems with different reaction equilibrium constants, so a careful parameterization of β is needed for an accurate computation of critical temperatures of reactive mixtures. We perform a screening of reactive binary mixtures for a wide range of ideal gas reaction equilibrium constants, revealing key insights into the thermodynamic behavior and critical properties. Thereby we facilitate the efficient screening of reactive binary mixtures for various applications. Our results emphasize the importance of accurately parameterizing β and provide valuable insights into the critical scaling behavior of complex reactive systems.

Phase behaviour of mixtures of charged soft disks and spheres.

We have investigated the phase behaviour of mixtures of soft disks (Gay-Berne oblate ellipsoids, GB) and soft spheres (Lennard-Jones, LJ) with opposite charge as a model of ionic liquid crystals and colloidal suspensions. We have used constant volume Molecular Dynamics simulations and fixed the stoichiometry of the mixture in order to have electroneutrality; three systems have been selected GB : LJ = 1 : 2, GB : LJ = 1 : 1 and GB : LJ = 2 : 1. For each system we have selected three values of the scaled point charge q* of the GB particles, namely 0.5, 1.0 and 2.0 (and a corresponding negative scaled charge of the LJ particles that depends on the stoichiometric ratio). We have found a very rich mesomorphism with the formation, as a function of the scaled temperature, of the isotropic phase, the discotic nematic phase, the hexagonal columnar phase and crystal phases. While the structure of the high temperature phases was similar in all systems, the hexagonal columnar phases exhibited a highly variable morphology depending on the scaled charge and stoichiometry. On the one hand, GB : LJ = 1 : 2 systems form lamellar structures, akin to smectic phases, with an alternation of layers of disks (exhibiting an hexagonal columnar phase) and layers of LJ particles (in the isotropic phase). On the other hand, for the 2 : 1 stoichiometry we observe the formation of a frustrated hexagonal columnar phase with an alternating tilt direction of the molecular axis. We rationalize these findings based on the structure of the neutral ion pair dominating the behaviour at low temperature and high charge.

Phase behavior of Lennard-Jones particles in two dimensions

The phase diagram of the prototypical two-dimensional Lennard-Jones (LJ) system, while extensively investigated, is still debated. In particular, there are controversial results in the literature with regard to the existence of the hexatic phase and the melting scenario. Here we study the phase behavior of two-dimensional range-limited LJ particles via large-scale numerical simulations. We demonstrate that at a high temperature, when the attraction in the potential plays a minor role, melting occurs via a continuous solid-hexatic transition followed by a first-order hexatic-fluid transition. The hexatic phase occurs in a density range that vanishes as the temperature decreases so that at low-temperature melting occurs via a first-order liquid-solid transition. The temperature where the hexatic phase disappears is well above the liquid-gas critical temperature. The evolution of the density of topological defects confirms this scenario.

Transport Properties of the Simple Lennard-Jones/Spline Fluid I: Binary Scattering and High-Accuracy Low-Density Transport Coefficients

Inspired by recent work on the thermodynamic properties of the Lennard-Jones/spline (LJ/s) fluid, we have considered the transport properties of the simple LJ/s fluid. The binary scattering problem for LJ/s particles was solved numerically, and results were compared to the untruncated LJ fluid. The scattering dynamics are affected both by the restricted range of the LJ/s potential, and the stronger attraction between LJ/s particles at distances between the inflection point of the potential and the cutoff range. At small relative kinetic energies, it was found that the scattering cross section of the LJ/s particles is much smaller than that of the LJ particles. The shear viscosity, thermal conductivity, and the self-diffusion coefficient were calculated from the scattering cross sections by the Chapman-Enskog method, and a six-parameter equation with a worst case accuracy of roughly 1 % over the temperature interval [0.1,1000] in LJ units is provided. The smaller scattering cross section at low kinetic energies leads to transport coefficients of the LJ/s fluid to be greater than those of the LJ fluid at low temperatures, and were all found to be roughly 50 % greater at T = 0.1, which is the lowest temperature considered.

Diffusion and Friction Dynamics of Probe Molecules in Liquid n-Alkane Systems: A Molecular Dynamics Simulation Study

We present a molecular dynamics simulation study of the probe diffusion and friction dynamics of Lennard-Jones particles in a series of liquid n-alkane systems from C12 up to C400 at 318 K, 418 K, 518 K, and 618 K, to investigate the power law dependence of self-diffusion of polymer liquids on their molecular weights. Two LJ particles MY1 with a mass of 114 g/mol and MY2 with a mass of 225 g/mol are used as probes to model methyl yellow. We observed that a clear transition in the power law dependence of n-alkane self-diffusion on the molecular weight (M) of n-alkane, Dself∼M−γ, occurs in the range C120∼C160 at temperatures of 318 K, 418 K, and 518 K, corresponding to a crossover from the “oligomer” to the “Rouse” regime. We also observed that a clear transition in the power law dependence of the diffusion coefficient DMY2 on the molecular weight (M) of n-alkane, DMY2∼M−γ, occurs at low temperatures. The exponent γ for DMY2 shows a sharp transition from 1.21 to 0.52 near C36 at 418 K and from 1.54 to 0.60 near C36 at 318 K. However, no such transition is found for the probe molecule MY2 at temperatures of 518 K and 618 K and for MY1 probe at temperatures of 418 K, 518 K, and 618 K, but the power law exponent γ for MY1 at 318 K shows instead a linear or a rather slow transition. The dependence of the probe diffusion (DMY2) on the matrix molecular weight (M) reflects a significant change of the matrix dynamics associated with the probe diffusion: a crossover from the “solvent-like” to the “oligomer” regime. As the molecular weight of n-alkane increases, the ratio of Dself/DMY2 becomes less than 1 and the probe molecules encounter, in turn, two different microscopic frictions depending on MMY/Mmatrix and the temperature. It is believed that a reduction in the microscopic friction on the probe molecules that diffuse at a rate faster than the solvent fluctuations leads to large deviations of slope from the linear dependence of the friction of MY2 on the chain length of the n-alkane at 318 K and 418 K.

Scalar activity induced phase separation and liquid-solid transition in a Lennard-Jones system.

We report scalar activity induced phase separation and crystallization in a system of 3-d Lennard-Jones particles taken at state points spanning from the gas to the liquid regime using molecular dynamics simulation (MD). Scalar activity was introduced by increasing the temperature of half of the particles (labeled 'hot') while keeping the temperature of the other half constant at a lower value (labeled 'cold'). The relative temperature difference between the two subsystems is considered as a measure of the activity. From our simulations we observe that the two species tend to phase separate at sufficiently high activity ratio. The extent of separation is quantified by the defined order parameter and the entropy production during this process is determined by employing the two-phase thermodynamic (2PT) model and the standard modified Benedict-Webb-Rubin (MBWR) equation of state for a LJ fluid. We observe that the extent of the phase separation and entropy production increases with the density of the system. From a cluster analysis, we obtain the mean number of clusters ncl, and the mean size of the largest cluster n0 in the system, complementing each other. Bond orientation order parameters reveal that the so formed largest cluster also develops solid-like order consisting of both FCC and HCP packing. The presence of such crystalline order is also supported by a common neighbor analysis.

Modeling of Bulk Kerogen Porosity: Methods for Control and Characterization

Shale gas is an unconventional source of energy, which has attracted a lot of attention during the last years. Kerogen is a prime constituent of shale formations and plays a crucial role in shale gas technology. Significant experimental effort in the study of shales and kerogen has produced a broad diversity of experimentally determined structural and thermodynamic properties even for samples of the same well. Moreover, proposed methods reported in the literature for constructing realistic bulk kerogen configurations have not been thoroughly investigated. One of the most important characteristics of kerogens is their porosity, due to its direct connection with their transport properties and its potential as discriminating and classifying metric between samples. In this study, molecular dynamics (MD) simulations are used to study the porosity of model kerogens. The porosity is controlled effectively with systematic variations of the number and the size of dummy LJ particles that are used during the constru...

A Local Order Parameter-Based Method for Simulation of Free Energy Barriers in Crystal Nucleation

While global order parameters have been widely used as reaction coordinates in nucleation and crystallization studies, their use in nucleation studies is claimed to have a serious drawback. In this work, a local order parameter is introduced as a local reaction coordinate to drive the simulation from the liquid phase to the solid phase and vice versa. This local order parameter holds information regarding the order in the first- and second-shell neighbors of a particle and has different well-defined values for local crystallites and disordered neighborhoods but is insensitive to the type of the crystal structure. The order parameter is employed in metadynamics simulations to calculate the solid-liquid phase equilibria and free energy barrier to nucleation. Our results for repulsive soft spheres and the Lennard-Jones potential, LJ(12-6), reveal better-resolved solid and liquid basins compared with the case in which a global order parameter is used. It is also shown that the configuration space is sampled more efficiently in the present method, allowing a more accurate calculation of the free energy barrier and the solid-liquid interfacial free energy. Another feature of the present local order parameter-based method is that it is possible to apply the bias potential to regions of interest in the order parameter space, for example, on the largest nucleus in the case of nucleation studies. In the present scheme for metadynamics simulation of the nucleation in supercooled LJ(12-6) particles, unlike the cases in which global order parameters are employed, there is no need to have an estimate of the size of the critical nucleus and to refine the results with the results of umbrella sampling simulations. The barrier heights and the nucleation pathway obtained from this method agree very well with the results of former umbrella sampling simulations.

Computation of thermodynamic properties in the continuous fractional component Monte Carlo Gibbs ensemble

It is shown that ensemble averages computed in the Gibbs Ensemble with Continuous Fractional Component Monte Carlo (CFCMC GE) are different from those computed in the conventional Gibbs Ensemble (GE). However, it is possible to compute averages corresponding to the conventional GE while performing simulations in the CFCMC GE. In this way, one can benefit from the nice features of CFCMC GE (e.g. more efficient particle exchange) and at the same time compute the ensemble averages that correspond to the conventional GE. As a case study, the equilibrium pressure and densities of the systems of 256 and 512 LJ particles at different reduced temperatures () are computed in the conventional GE and CFCMC GE. The validity of the expressions derived for computation of the thermodynamic pressure and densities corresponding to the conventional GE and computed in the CFCMC GE is examined numerically. The thermodynamic pressure in the conventional GE and CFCMC GE typically differs by at most 4%. It is shown that a very good estimate of the average pressure and densities corresponding to the conventional GE can be obtained by performing simulation in CFCMC GE and ignoring the contributions of the fractional molecule. It is also shown that the fractional molecule does not have an influence on the structure of the liquid, even for very small system sizes (e.g. 40 particles). The approach used here to compute the equilibrium pressure and densities of the conventional GE using the CFCMC GE can be easily extended to other thermodynamic properties and other ensembles.

Fourier Correlation Method for Simulating Mutual Diffusion Coefficients in Condensed Systems at Equilibrium

We introduce here the Fourier correlation (FC) method for obtaining bulk diffusion coefficients in simulations of condensed, nonideal mixtures. The method in particular allows a Fickian mutual diffusion coefficient to be calculated directly in a molecular dynamics simulation and provides for a correction of errors due to finite system sizes. It is an equilibrium method that may be performed at the same time as standard thermodynamic computations. The method is tested by simulating a binary system of LJ particles meant to approximate a nonideal liquid mixture of methane and carbon tetrafluoride. Results are validated by comparison to Green–Kubo and nonequilibrium methods and simulation at multiple system sizes.

Crossover from normal diffusion to single-file diffusion of particles in a one-dimensional channel: LJ particles in zeolite zsm-22

The crossover from normal Fickian diffusion, where mean-squared displacement goes as t to single-file diffusion, where <z2> t 0.5 is studied as function of particle size confined in zeolite zsm-22 using molecular dynamics simulations. The simulation results indicate that the crossover is smooth as the particle size increases and the diffusion reaches single file through a series of subdiffusion processes. A small number of mutual passage of particles can destroy the correlated single-file diffusion. The density dependence on single-file mobility obtained from molecular dynamics simulations are in very good agreement with theoretical predictions.

Phase diagram of Lennard-Jones fluid confined in slit pores

We performed molecular dynamics simulations of Lennard-Jones particles confined in a parallel slit pore. When a slit width h was 2 σ - 6 σ , the frozen LJ particles had an hcp structure and two different axes of an fcc structure depending on the slit width. We estimated the freezing/melting point when the LJ fluid was cooled/heated, and observed an abnormality in the freezing/melting point corresponding to the difference in the crystal structure for the first time, which agreed with the results of the Clausius–Clapeyron equation. We found new crystal structures and proposed the complex h - T phase diagram.

Non-equilibrium molecular dynamics simulation study on permeation phenomena of LJ particles in slit-shaped membranes with periodic belt-like heterogeneous surfaces

In order to make clear the relationship between the pore structure and the diffusivity, we have carried out permeation simulations of pure gases through simple model membranes by using the external-field non-equilibrium molecular dynamics method. As the membrane, we model slit-shaped pores with periodic belt-like heterogeneous pore surfaces which are caused by the upheaval of surface atoms. Applying simulation results for membranes with several upheaval interval distances to Maxwell–Stefan (MS) theory, we calculate the effects of the molecular loading of permeating molecules in the pores on MS diffusivity ( D MS). In addition, the permeation potential barrier is estimated as the difference between the maximum and minimum permeation potential energies. The effect of the molecular loading on the permeation potential barrier and the D MS are in inverse proportion. It is noted that, when the width of the adsorption area in the permeation direction is not common multiples of the molecular diameter, the permeation potential barrier decreases with the increase in the molecular loading. This is because the positive force against the permeation direction is caused to the permeating molecules by interactions with permeating molecules in the adsorpton area between adjacent upheavals. Therefore, we could suggest that the key factor for controlling diffusion property is the structural relationship between the adsorption area and the permeating molecules.

Extending the simple weighted density approximation for a hard-sphere fluid to a Lennard–Jones fluid: II. Application

A simple weighted density approximation (SWDA) was extended to nonuniform Lennard–Jones fluids by following the spirit of a partitioned density function theory [S. Zhou, Phys. Rev. E 68 (2003) 061201] and mapping the hard-core part onto an effective hard-sphere fluid whose higher order terms beyond the second order of the functional perturbation expansion are treated by the SWDA. The resultant DFT formalism performs well for Lennard–Jones fluids under the influence of diverse external fields. With the present DFT formalism, we investigate in detail the structure and adsorption properties of a low-density LJ gas in a spherical cavity with a wall consisting of hard-sphere or LJ particles. It was found that when the cavity wall exerts an attractive external potential on the LJ particles in the cavity, the excess adsorption decreases as the temperature increases, while when the cavity wall exerts a hard repulsive external potential on the LJ particles in the cavity, the excess adsorption increases as the temperature increases.

Condensable vapor permeation through miroporous silica membranes studied with molecular dynamics simulation

Abstract Molecular dynamics (MD) simulations of condensable vapor permeation through sub-nano scale pores were conducted for a virtual amorphous silica membrane, prepared by melt–quench procedures. The simulated permeance of C 2 H 6 ( T C =305 K)-like LJ particles through an 8 A in diameter pore showed a surface diffusion-like temperature dependency in the relatively high temperature region (400–800 K), while at around 300 K, the permeance decreased with decreasing temperature. That is, a maximum was observed in the temperature dependency curve for permeance. The critical temperature, T C of the permeating condensable vapor could be a contributing factor in the permeation properties through the micropore. The simulated permeance of C 2 H 6 at 260 K decreased with increasing mean pressure. At low pressure, where micropore filling would not be expected to occur, an almost gas like permeation was observed even at temperatures below the T C , while under micrpore filling conditions at a relatively high pressure, the permeance abruptly decreased. Adsorption simulations were also conducted on the same unit cell, and the mobility of the adsorbed molecules in the micropore filling phase were smaller than those in the lower density phase. Through this investigation of temperature and pressure dependency of permeance, it can be concluded that the development of the micropore filling phase led to a decrease in permeance, and transport as the condensed filling phase through the micropore was an activated process.

Molecular dynamics studies on gas permeation properties through microporous silica membranes

Gas permeation mechanisms through a micropore of a vitreous silica (v-SiO 2 ) membrane were studied using a molecular dynamics (MD) simulation. Virtual v-SiO 2 membranes were prepared by the melt-quench methods using the modified Born–Mayer–Huggins pair potential and Stillinger–Waber three-body interactions. The particle-generating non-equilibrium MD technique was employed in order to simulate gas permeation phenomena, where permeating molecules were modeled as Lennard–Jones particles. This simulation method accommodates a change in the number of particles in a unit cell and, hence, an accurate simulation of the steady-state process of permeation can be achieved. The dependencies of permeance on temperature and pressure were discussed. For cylindrical pores of about 5 Å in diameter, the calculated temperature dependencies of the permeance of He-like LJ particles were similar to those predicted by the normal Knudsen permeation mechanism, while, for CO 2 permeation, a temperature dependency larger than He and a significant deviation from the Knudsen's could be observed. In the relatively high-temperature region (400–800 K), the simulated permeance of CO 2 was nearly independent of the upstream pressure, while at the temperature below 300 K, a pressure dependency of permeance was observed. Simulations of adsorption conducted on the same unit cell yielded a Henry-type isotherm at 400 K and a Langmuir-type isotherm at 260 K. These results indicate that gas-like permeation occurred in the higher-temperature region, where the permeation flux is proportional to the pressure drop across the pore. However, at lower temperatures, the transports of molecules as some type of adsorption phase might be dominant in such a small pore. A simple gas permeation model, considering the effect of the pore wall potential field and Langmuir type adsorption within a micropore explained those permeation properties of CO 2 well.

Molecular Dynamics Simulation of the Maxwell-Stefan Diffusion Coefficients in Lennard-Jones Liquid Mixtures

Maxwell-Stefan (MS) diffusion coefficients in multicomponent liquids have been determined by the equilibrium molecular dynamics calculation of the appropriate Green-Kubo equation. Simulations were performed for systems of 300 LJ particles at various compositions. The unary system was divided into three components by attaching a colour label to the particles, which plays no role in the dynamics. The binary system argon + krypton was divided into three species by attaching a colour label to the particles of argon. The ternary system consisted of argon, krypton and neon. The results of the calculation of the MS diffusion coefficients in the unary and binary systems agreed well with the literature values. The MS diffusion coefficients of the unary system did not differ significantly from the self-diffusion coefficient. The MS diffusion coefficients of the ternary system behaved as expected from other physical properties.

Fragmentation of hot drops

We analyze the process of fragment formation in small aggregates of LJ particles. Particular emphasis is put on the determination of the time scales of fragment formation and fragment emission. We find that some degree of thermalization takes place at these times, allowing us to calculate the caloric curve T(E) in the fragmentation regime.

Hybrid MC/RISM technique for simulation of polymer solutions: Monte Carlo+ RISM integral equations

A new (hybrid) method is reported for modelling complex macromolecular systems. The approach combines the traditional atomistic Monte Carlo (MC) computer simulation of flexible polymer chains with the numerical solution of the site-site Ornstein-Zernike-like (RISM) integral equations. The method is used for calculating properties of a linear polymer in dilute solution. Since the condensed-phase environment of a flexible macromolecule affects the equilibrium configuration probability distribution of the macromolecule, the site-site intramolecular correlation function and the intramolecular potential field are treated in a self-consistent manner. Briefly, the MC method is applied to generate the configurations of a single chain molecule. Using the coordinates of chain beads, the averaged intrapolymer correlation function is obtained. Then, solving the coupled RISM equations for a given density of solvent particles, we find the polymer-solvent correlation functions. This yields the medium-induced intrapolymer potential and the corresponding effective intramolecular energies, which are used in the standard Metropolis MC procedure. The structural properties of the polymer chain are computed by averaging over the statistically representative set of configurations. As a result of many such iterations, the intramolecular structure is determined self-consistently. Using the hybrid MC/RISM method, extensive studies have been made of static properties of flexible polymer chains surrounded by LJ particles with purely repulsive interactions between the particles and chain beads. Also, direct molecular dynamics simulations have been carried out and have demonstrated that the hybrid MC/RISM approach gives a quite accurate prediction for condensed-phase effects.

Capillary condensation model within nano-scale pores studied with molecular dynamics simulation.

A new capillary condensation model for nano-scale pores is proposed. The effect of the pore wall potential on the condensation phenomenon was considered in the model. The critical relative pressure at which the condensation phase is formed can be related to the pore size by the model. The curvature dependency of the surface tension was also taken into account. This is a new model based on hydrostatic analysis, and its feature is non-uniformity of the condensation phase caused by the potential field exerted by the pore walls. We carried out adsorption simulations within slit-like pores in the range of 2-4 nm in width by using a Molecular Dynamics (MD) method. In the simulations, equilibrium vapor pressure for an adsorbed state was able to be calculated by counting the number of adsorbate particles which desorbed from the pore and reached a border plane with imaginary vapor phase. We used argon-like LJ particles as the adsorbate and the adsorbent consisted of LJ carbon-like walls. For various pore widths, we simulated the adsorption phenomena to obtain the adsorption equilibrium relation, from the state of the surface adsorption on a pore wall under a low relative pressure to the state of the condensation under a high relative pressure. Consequently, significant discrepancy in the critical relative pressure for capillary condensation from the value predicted by the Kelvin model was reaffirmed, while the proposed model predicted well the critical relative pressure for condensation in nano-scale pores. The validity of the proposed model was examined also from the aspects of the shape of gas-condensate interface and pressure distribution in the condensed phase, and gave fairly good agreement.