System Of Lennard-Jones Particles Research Articles

Complex Networks and Interacting Particle Systems.

Complex networks is a growing discipline aimed at understanding large interacting systems. One of its goals is to establish a relation between the interactions of a system and the networks structure that emerges. Taking a Lennard-Jones particle system as an example, we show that when interactions are governed by a potential, the notion of structure given by the physical arrangement of the interacting particles can be interpreted as a binary approximation to the interaction potential. This approximation simplifies the calculation of the partition function of the system and allows to study the stability of the interaction structure. We compare simulated results with those from the approximated partition function and show how the network and system perspective complement each other. With this, we draw a direct connection between the interactions of a molecular system and the network structure it forms and assess the degree to which it describes the system. We conclude by discussing the advantages and limitations of this method for weighted networks, as well as how this concept might be extended to more general systems.

Kinetic singularities at transition points from equilibrium to metastable states of the Lennard-Jones particle system

The equilibrium and metastable states of the Lennard-Jones vapor, liquid, and crystal, are studied in the vicinity of the phase transition points. Vapor-liquid, liquid-vapor, liquid-crystal, and crystal-liquid transitions are modeled within the molecular dynamics method. As a research tool, a four-point correlation function is used for the qualitative detection of collective motions of atoms in the equilibrium and metastable states. We use its modification, a correlation coefficient, and find singularities at the transition from equilibrium to metastable states. The nature of these changes, as precursors of nucleation, is discussed.

Local free energies for the coarse-graining of adsorption phenomena: The interacting pair approximation.

We investigate the coarse-graining of host-guest systems under the perspective of the local distribution of pore occupancies, along with the physical meaning and actual computability of the coarse-interaction terms. We show that the widely accepted approach, in which the contributions to the free energy given by the molecules located in two neighboring pores are estimated through Monte Carlo simulations where the two pores are kept separated from the rest of the system, leads to inaccurate results at high sorbate densities. In the coarse-graining strategy that we propose, which is based on the Bethe-Peierls approximation, density-independent interaction terms are instead computed according to local effective potentials that take into account the correlations between the pore pair and its surroundings by means of mean-field correction terms without the need for simulating the pore pair separately. Use of the interaction parameters obtained this way allows the coarse-grained system to reproduce more closely the equilibrium properties of the original one. Results are shown for lattice-gases where the local free energy can be computed exactly and for a system of Lennard-Jones particles under the effect of a static confining field.

SEED CONCENTRATION EFFECT ON HETEROGENEOUS NUCLEATION BY MOLECULAR DYNAMICS

Heterogeneous nucleation on a system with multiple seeds were conducted by molecular dynamics to understand how seed concentrations can affect the phase transition process. A constant particle number, volume, and temperature ensemble was applied to multiple systems of Lennard-Jones particles with a carrier gas that acts as a thermal reservoir. A different number of seeds were inserted into systems that have been previously found to have no spontaneous nucleation due to low supersaturation ratios. The addition of the seeds activated nucleation, but the increase in the nucleation rate was not perpetual because the system size was finite. A clear understanding of how the number of seeds decreasing the free energy barrier is presented along with the kinetic attachment and detachment rate variations. The decrease in the free energy barrier has a limit similarly to the aforementioned nucleation rate increase. The seed concentration results coincide with the predictions from the classical nucleation theory.

The potential energy landscape for crystallisation of a Lennard-Jones fluid

Crystallisation pathways are explored by direct analysis of the potential energy landscape for a system of Lennard-Jones particles with periodic boundary conditions. A database of minima and transition states linking liquid and crystalline states is constructed using discrete path sampling and the entire potential energy landscape from liquid to crystal is visualised. We demonstrate that there is a strong negative correlation between the number of atoms in the largest crystalline cluster and the potential energy. In common with previous results we find a strong bias towards the growth of FCC rather than HCP clusters, despite a very small potential energy difference. We characterise three types of perfect crystals with very similar energies: pure FCC, pure HCP, and combinations of FCC and HCP layers. There are also many slightly defective crystalline structures. The effect of the simulation box is analysed for a supercell containing 864 atoms. There are low barriers between some of the different crystalline structures via pathways involving sliding layers, and many different defective structures with FCC layers stacked at an angle to the periodic box. Finally, we compare a binary Lennard-Jones system and visualise the potential energy landscape from supercooled liquid to crystal.

Improving the acceptance in Monte Carlo simulations: Sampling through intermediate states

In this paper we discuss a variation of the multiple-proposal approach to Markov chain-based Monte Carlo methods. We show that by means of intermediate states, used as pivots between the departure configuration and a number of possible arrival configurations, detailed balance is maintained and the acceptance of trial moves is significantly improved with respect to the standard Metropolis Monte Carlo approach. When applied to the case of a particle in a one-dimensional rough potential, this method results in an improved accuracy in the sampling of the distribution function. For all densities of a three-dimensional bulk system of Lennard-Jones particles, it requires less Monte Carlo steps to reach equilibrium and it allows for using wider displacement steps than Metropolis Monte Carlo. In particular, for low-intermediate densities the maximum displacement step can be set to exceptionally large values. We show how biases can be introduced to further reduce the number of operations necessary to construct the trial states while still fulfilling the detailed balance requirement. Although this method is more computationally demanding than (standard) single-proposal Monte Carlo, it samples the configuration space faster. Moreover, its multiple-proposal nature makes it amenable to parallel implementation, while requiring about half the number of operations required by multiple-try Monte Carlo.

A Quadratically-Converging Nudged Elastic Band Optimizer.

Nudged elastic band (NEB) is a well established chain-of-states method to locate the minimum energy path in configuration space. Unfortunately, existing search algorithms suffer from slow convergence. We provide an analytic derivative of the nudged elastic band force, enabling a full Newton-Raphson optimization. For molecular systems, the components of the step belonging to translations and rotations are removed with an efficient algorithm. Minimization of the NEB force is ensured by reversing components for which the Newton-Raphson step would increase the force. We achieve quadratic convergence of this optimizer when applied to simple test cases where analytic Hessians are available: one analytic two-dimensional potential and a system of Lennard-Jones particles.

Communication: Phase transitions, criticality, and three-phase coexistence in constrained cell models

In simulation studies of fluid-solid transitions, the solid phase is usually modeled as a constrained system in which each particle is confined to move in a single Wigner-Seitz cell. The constrained cell model has been used in the determination of fluid-solid coexistence via thermodynamic integration and other techniques. In the present work, the phase diagram of such a constrained system of Lennard-Jones particles is determined from constant-pressure simulations. The pressure-density isotherms exhibit inflection points which are interpreted as the mechanical stability limit of the solid phase. The phase diagram of the constrained system contains a critical and a triple point. The temperature and pressure at the critical and the triple point are both higher than those of the unconstrained system due to the reduction in the entropy caused by the single occupancy constraint.

Rejection-free Monte Carlo sampling for general potentials

A Monte Carlo method to sample the classical configurational canonical ensemble is introduced. In contrast to the Metropolis algorithm, where trial moves can be rejected, in this approach collisions take place. The implementation is event-driven; i.e., at scheduled times the collisions occur. A unique feature of the new method is that smooth potentials (instead of only step-wise changing ones) can be used. In addition to an event-driven approach, where all particles move simultaneously, we introduce a straight event-chain implementation. As proof of principle, a system of Lennard-Jones particles is simulated.

On the existence of a third-order phase transition beyond the Andrews critical point: A molecular dynamics study

The possibility of the existence of a gas-liquid third order phase transition for fluids is becoming a subject of growing interest. Experimental work suggests its existence for specific systems while recent theoretical models claim its universality. In this work, we employ Molecular Dynamics and investigate the third-order phase transition beyond the Andrews critical point by treating a system of Lennard-Jones particles along three isotherms. Two partial derivatives of the Gibbs free energy are measured, namely the molar constant pressure heat capacity and isothermal compressibility. The convergence of these simulations with respect to the system size as well as the cut-off radius is carefully checked. The obtained results show that partial derivatives certainly do not present sharp cusp singularities at the maxima, and actually suggest that there are no singularities at all. On these basis we then conclude that a third-order phase transition in the considered temperature region: T∗ ≥ 1.36 may indeed not exist.

Precise simulation of the freezing transition of supercritical Lennard-Jones

The fluid-solid transition of the Lennard-Jones model is analyzed along a supercritical isotherm. The analysis is implemented via a simulation method which is based on a modification of the constrained cell model of Hoover and Ree. In the context of hard-sphere freezing, Hoover and Ree simulated the solid phase using a constrained cell model in which each particle is confined within its own Wigner-Seitz cell. Hoover and Ree also proposed a modified cell model by considering the effect of an external field of variable strength. High-field values favor configurations with a single particle per Wigner-Seitz cell and thus stabilize the solid phase. In previous work, a simulation method for freezing transitions, based on constant-pressure simulations of the modified cell model, was developed and tested on a system of hard spheres. In the present work, this method is used to determine the freezing transition of a Lennard-Jones model system on a supercritical isotherm at a reduced temperature of 2. As in the case of hard spheres, constant-pressure simulations of the fully occupied constrained cell model of a system of Lennard-Jones particles indicate a point of mechanical instability at a density which is approximately 70% of the density at close packing. Furthermore, constant-pressure simulations of the modified cell model indicate that as the strength of the field is reduced, the transition from the solid to the fluid is continuous below the mechanical instability point and discontinuous above. The fluid-solid transition of the Lennard-Jones system is obtained by analyzing the field-induced fluid-solid transition of the modified cell model in the high-pressure, zero-field limit. The simulations are implemented under constant pressure using tempering and histogram reweighting techniques. The coexistence pressure and densities are determined through finite-size scaling techniques for first-order phase transitions which are based on analyzing the size-dependent behavior of susceptibilities and dimensionless moment ratios of the order parameter.

Scaling relation and regime map of explosive gas–liquid flow of binary Lennard-Jones particle system

We study explosive gas–liquid flows caused by rapid depressurization using a molecular dynamics model of Lennard-Jones particle systems. A unique feature of our model is that it consists of two types of particles: liquid particles, which tend to form liquid droplets, and gas particles, which remain supercritical gaseous states under the depressurization realized by simulations. The system has a pipe-like structure similar to the model of a shock tube. We observed physical quantities and flow regimes in systems with various combinations of initial particle number densities and initial temperatures. It is observed that a physical quantity Q, such as pressure, at position z measured along a pipe-like system at time t follows a scaling relation Q(z,t)=Q̃(z/t) with a scaling function Q̃(ζ). A similar scaling relation holds for time evolution of flow regimes in a system. These scaling relations lead to a regime map of explosive flows in parameter spaces of local physical quantities. The validity of the scaling relations of physical quantities means that physics of equilibrium systems, such as an equation of state, is applicable to explosive flows in our simulations, though the explosive flows involve highly nonequilibrium processes. In other words, if the breaking of the scaling relations is observed, it means that the explosive flows cannot be fully described by physics of equilibrium systems. We show the possibility of breaking of the scaling relations and discuss its implications in the last section.

Spray flow-network flow transition of binary Lennard-Jones particle system

We simulate gas–liquid flows caused by rapid depressurization using a molecular dynamics model. The model consists of two types of Lennard-Jones particles, which we call liquid particles and gas particles. These two types of particles are distinguished by their mass and strength of interaction: a liquid particle has heavier mass and stronger interaction than a gas particle. By simulations with various initial number densities of these particles, we found that there is a transition from a spray flow to a network flow with an increase of the number density of the liquid particles. At the transition point, the size of the liquid droplets follows a power-law distribution, while it follows an exponential distribution when the number density of the liquid particles is lower than the critical value. The comparison between the transition of the model and that of models of percolation is discussed. The change of the average droplet size with the initial number density of the gas particles is also presented.

Interfacial Excess Free Energies of Solid–Liquid Interfaces by Molecular Dynamics Simulation and Thermodynamic Integration

A method to compute the interfacial excess free energy of systems where a liquid phase is interacting with a solid phase is presented. The calculations are carried out by means of molecular dynamics simulations. The algorithm is based on a thermodynamic integration scheme that reversibly turns a flexible atomistically detailed solid surface that interacts with a liquid phase into a flat surface and allows the calculation of the variation in Gibbs free energy. The approach is probed by applying it to a model system of Lennard-Jones particles and comparing to previous calculations on similar systems.

Energy Transport in Lennard-Jones Particle System

Energy Transport in Lennard-Jones Particle System

TRILLION-ATOM MOLECULAR DYNAMICS BECOMES A REALITY

By utilizing the molecular dynamics code SPaSM on Livermore's BlueGene/L architecture, consisting of 212 992 IBM PowerPC440 700 MHz processors, a molecular dynamics simulation was run with one trillion atoms. To demonstrate the practicality and future potential of such ultra large-scale simulations, the onset of the mechanical shear instability occurring in a system of Lennard-Jones particles arranged in a simple cubic lattice was simulated. The evolution of the instability was analyzed on-the-fly using the in-house developed massively parallel graphical object-rendering code MD_render.

A novel algorithm for creating coarse-grained, density dependent implicit solvent models

Implicit solvent simulations are those in which solvent molecules are not explicitly simulated, and the solute-solute interaction potential is modified to compensate for the implicit solvent effect. Implicit solvation is well known in Brownian dynamics of dilute solutions but offers promise to speed up many other types of molecular simulations as well, including studies of proteins and colloids where the local density can vary considerably. This work examines implicit solvent potentials within a more general coarse-graining framework. While a pairwise potential between solute sites is relatively simple and ubiquitous, an additional parametrization based on the local solute concentration has the possibility to increase the accuracy of the simulations with only a marginal increase in computational cost. We describe here a method in which the radial distribution function and excess chemical potential of solute insertion for a system of Lennard-Jones particles are first measured in a fully explicit, all-particle simulation, and then reproduced across a range of solute particle densities in an implicit solvent simulation.

Formation of double helical and filamentous structures in models of physical and chemical gels.

This discusses two recent models, one that captures physical network formation starting from the molecular architecture of its constituents and another that contains the basic features of phase separation in cross-linked polymer gels: A) the Janus chain (multibead bead-spring type) model exhibiting semiflexibility and induced curvature and B) a stretched elastic network of Lennard-Jones particles. The length scales and related structures predicted by the two generic models are different. Model B, a generic soft solid model, exhibits hysteresis and the formation of filamentous structures in two dimensions. The Janus chain model A is able to describe the process of the formation of double helical superstructures, will be operated in three dimensions, and its internal parameters are directly deduced from atomistic simulation. Both models rely on classical ingredients which have been separately studied extensively: i) the Lennard-Jones particle system, ii) the elastic solid, and iii) the FENE-B model for semiflexible, finitely extendable nonlinear elastic (FENE) polymer chains. While model A combines i) and iii), model B combines i) and ii). This aspect of technical simplicity, however, is contrasted by the rich phenomenology observed for these models. The Janus model even resolves structure formation on the molecular scale. Intriguingly, the coarse dynamical models capture a wide range of superstructures known for polymeric networks and therefore clearly serve to understand their underlying physical mechanisms.

Singular Point of a System of Lennard-Jones Particles at Negative Pressures

The method of molecular dynamics is used in a system of 2048 Lennard-Jones particles to determine the spinodal of a stretched liquid and crystal and the lines of their phase equilibrium at negative pressures. It is shown that a metastable extension of the melting line does not reach the zero isotherm, and ends on the spinodal of a stretched liquid. The point of termination of metastable liquid-crystal phase equilibrium is the singular point at a thermodynamic surface of states.

Heat Conduction of Lennard-Jones Particle System in Supercritical Fluid Phase

The heat conduction of the three-dimensional Lennard-Jones particle system is studied using nonequilibrium molecular dynamics simulation. The geometry of the system is a rectangular parallelepiped box of L x × L y × L z dimensions. Two Nose–Hoover heat baths with different temperatures are attached to the regions near both ends of the x -direction. The density of the system and temperature of heat bath are selected so that the system is in the supercritical fluid phase. It is observed that the nonequilibrium steady state with a constant temperature gradient d T /d x and a energy (heat) flux J is realized after relaxation process from its initial configuration. The ratio of J to d T /d x denoted by κ which corresponds to the heat conductivity in the macroscopic limit is estimated for various system sizes L x . It is confirmed that κ( L x ) shows a size dependence as expressed \(\kappa_{0} + a/\sqrt{L_{x}}\) and this dependence is consistent with the so-called long-time tail behavior. This κ 0 is regarded ...