Lennard-Jones System Research Articles

Hybrid Monte Carlo with non-uniform step size.

The Hybrid Monte Carlo method offers a rigorous and potentially efficient approach to the simulation of dense systems, by combining numerical integration of Newton's equations of motion with a Metropolis accept-or-reject step. The Metropolis step corrects for sampling errors caused by the discretization of the equations of motion. The integration is usually performed using a uniform step size. Here, we present simulations of the Lennard-Jones system showing that the use of smaller time steps in the tails of each integration trajectory can reduce errors in energy. The acceptance rate is 10-15 percentage points higher in these runs, compared to simulations with the same trajectory length and the same number of integration steps but a uniform step size. We observe similar effects for the harmonic oscillator and a coarse-grained peptide model, indicating generality of the approach.

Direct molecular simulation of the Grüneisen parameter and density scaling exponent in fluid systems

Direct molecular-simulation results of the thermodynamic Grüneisen parameter, γG, and the density scaling exponent, γ, are reported for the Lennard-Jones and the Gaussian core model potential in extended fluid-phase regions, and are compared with results calculated from equations of state. The direct molecular simulation method is based on the calculation of so-called phase-space functions and allows, in principle, the investigation of any thermodynamic property without any restrictive approximation. The Grüneisen parameter and the density scaling exponent are key quantities in the theory of strongly correlating liquids. Therefore, we paid special attention on the relationship between γG and γ for the Lennard-Jones system as a strongly correlating fluid. Because the Grüneisen parameter can be related to experimentally accessible thermodynamic properties, we analysed in detail the decomposition of γG into the thermal expansion coefficient, the isothermal compressibility, the isochoric heat capacity, and the thermal pressure coefficient. Moreover, we show that a predicted effective density scaling exponent of γ≈6 for the Lennard-Jones fluid can be found close to the triple point of the system. The investigation of γG for the Gaussian core model, which is not a strongly correlating fluid, revealed anomalous behaviour at higher densities with negative values of γG.

Variational evolution of one-dimensional Lennard-Jones systems

We analyze Lennard-Jonessystems from the standpoint of variational principles beyond the staticframework.In a one-dimensional setting such systems have already been shown to beequivalent toenergies of Fracture Mechanics. Here we show that this equivalence can alsobe given indynamical terms using the notion of minimizing movements.

Phase Diagram of a Lennard-Jones System by Molecular Dynamics Simulations

Phase Diagram of a Lennard-Jones System by Molecular Dynamics Simulations

Phase Diagram for a Lennard-Jones System Obtained through Constant-Pressure Molecular Dynamics Simulations

The phase diagram for a Lennard-Jones system was estimated using conventional NPH molecular dynamics (MD) simulations. Standard periodic boundaries were assumed for unit cells containing 1000 molecules. An elongated unit cell with both solid and vacuum sections was found to be suitable for the NPH MD simulations when calculating both the melting and vapor pressure curves under pressures lower than the critical one. Under high pressures, a unit cell with both solid and liquid sections was used as the initial configuration to obtain the melting temperature. The results of these simulations were compared with the phase transition point given by the reported equations of state.

Investigating isomorphs with the topological cluster classification

Isomorphs are lines in the density-temperature plane of certain "strongly correlating" or "Roskilde simple" liquids where two-point structure and dynamics have been shown to be close to identical up to a scale transformation. Here we consider such a liquid, a Lennard-Jones glass former, and investigate the behavior along isomorphs of higher-order structural and dynamical correlations. We then consider an inverse power law reference system mapped to the Lennard-Jones system [Pedersen et al., Phys. Rev. Lett. 105, 157801 (2010)]. Using the topological cluster classification to identify higher-order structures, in both systems we find bicapped square antiprisms, which are known to be a locally favored structure in the Lennard-Jones glass former. The population of these locally favored structures is up to 80% higher in the Lennard-Jones system than the equivalent inverse power law system. The structural relaxation time of the two systems, on the other hand, is almost identical, and the four-point dynamical susceptibility is marginally higher in the inverse power law system. Upon cooling, the lifetime of the locally favored structures in the Lennard-Jones system is up to 40% higher relative to the reference system.

Surface induced nucleation of a Lennard-Jones system on an implicit surface at sub-freezing temperatures: A comparison with the classical nucleation theory

The aggregation-volume-bias Monte Carlo method was employed to study surface-induced nucleation of Lennard-Jonesium on an implicit surface below the melting point. It was found that surfaces catalyze not only the formation of the droplets (where the nucleation free energy barriers were shown to decrease with increasing surface interaction strength), but also the transition of these droplets into crystal structures due to the surface-induced layering effects. However, this only occurs under suitable interaction strength. When surface attraction is too strong, crystallization is actually inhibited due to the spread of the particles across the surface and corresponding formation of two-dimensional clusters. The simulation results were also used to examine the bulk-droplet based classical nucleation theory for surface-induced nucleation, particularly the additional contact angle term used to describe both the nucleation free energy barrier heights and the critical cluster sizes compared to its homogeneous nucleation formalism. Similar to what has been found previously for homogeneous nucleation, the theory does poorly toward the high-supersaturation region when the critical clusters are small and fractal, but the theoretical predictions on both barrier heights and critical cluster sizes improve rapidly with the decrease of the supersaturation.

On the behavior of indicators of melting: Lennard-Jones system in the vicinity of the phase transition

Various indicators of melting for a system of particles whose pair interaction is described by the Lennard-Jones potential have been considered. The behavior of the radial distribution function g(r) and the associated criteria of melting, modified Lindemann criterion, and criteria based on the properties of short-range orientational order (rotational invariants ql and wl of various orders l) has been analyzed in detail in the vicinity of the melting phase transition. A parameter based on the loss of the nearest neighbors of an atom/particle has been proposed to characterize the melting transition. All considered indicators of melting for the Lennard-Jones system have been compared. It has been shown that the indicators of melting derived from the properties of the short-range orientational order are much more sensitive to the melting phase transition and can be used to construct new phenomenological criteria of melting similar to the Lindemann criterion. An additional important advantage of such indicators is the relatively small number of configurations of the system necessary for their calculation.

Neural networks for local structure detection in polymorphic systems

The accurate identification and classification of local ordered and disordered structures is an important task in atomistic computer simulations. Here, we demonstrate that properly trained artificial neural networks can be used for this purpose. Based on a neural network approach recently developed for the calculation of energies and forces, the proposed method recognizes local atomic arrangements from a set of symmetry functions that characterize the environment around a given atom. The algorithm is simple and flexible and it does not rely on the definition of a reference frame. Using the Lennard-Jones system as well as liquid water and ice as illustrative examples, we show that the neural networks developed here detect amorphous and crystalline structures with high accuracy even in the case of complex atomic arrangements, for which conventional structure detection approaches are unreliable.

How to quantify solid–liquid phase transition: Lennard–Jones system case study

AbstractIn this paper we analyzed different measures, characterizing the melting of Lennard–Jones solid, and associated with the properties of both the translational and the orientational local order. It has been shown that the most sensitive indicator of melting is the cumulant of the probability distribution function over w6 bond-order parameter. The criterion of melting based on the indicator is proposed; the criterion can be used for any solids, having fcc/hcp types of symmetry.

Bottom-up construction of interaction models of non-Markovian dissipative particle dynamics

We derive the equation of motion for non-Markovian dissipative particle dynamics (NMDPD) by introducing the history effects on the time evolution of the system. Our formulation is based on the generalized Langevin equation, which describes the motions of the centers of mass of clusters comprising microscopic particles. The mean, friction, and fluctuating forces in the NMDPD model are directly constructed from an underlying molecular dynamics (MD) system without any scaling procedure. For the validation of our formulation, we construct NMDPD models from high-density Lennard-Jones systems, in which the typical time scales of the coarse-grained particle motions and the fluctuating forces are not fully separable. The NMDPD models reproduce the temperatures, diffusion coefficients, and viscosities of the corresponding MD systems more accurately than the dissipative particle dynamics models based on a Markovian approximation. Our results suggest that the NMDPD method is a promising alternative for simulating mesoscale flows where a Markovian approximation is not valid.

Do Transport Properties of Entangled Linear Polymers Scale with Excess Entropy?

We analyze the range of validity of the empirical excess entropy scalings proposed independently by Rosenfeld and Dzugutov for the viscosity and the diffusion coefficient of monodisperse Lennard-Jones chains. They are long enough to be considered as entangled. Thus, the influence of entanglements on entropy scalings can be quantified. We make use of thermodynamic integration to determine the exact excess entropy. Different ways of approximating the excess entropy either based on conformational information or by employing the self-associating fluid theory (SAFT) are explored. The correlations between the various excess entropy estimates are investigated in detail. The conformational route appears to be the most suitable way for the studied Lennard-Jones systems. Its prediction is in qualitative agreement with those obtained by thermodynamic integration, which is computationally more demanding. The SAFT results are not always consistent with the simulation data. The main qualitative feature of both the Rosenfeld and Dzugutov scaling is the coexistence of two linear regimes in the correlation of different entropy expressions. The sharpness of the transition regime depends on the way the excess entropy is approximated. The Dzugutov scaling for the viscosity seems to have certain advantages in comparison to the Rosenfeld one. The influence of the chain length on the parameters appearing in the excess entropy scaling relationships is examined. Despite the pronounced chain length dependence of the scaling parameters, a master curve relating the diffusion coefficient to the excess entropy is derived when performing a suitable renormalization. The relation between the scaling parameters of the viscosity and the diffusion coefficient are—with one exception—in line with the predictions of the Stokes–Einstein law.

Thermodynamic curvature for attractive and repulsive intermolecular forces

The thermodynamic curvature scalar R for the Lennard-Jones system is evaluated in phase space, including vapor, liquid, and solid state. We paid special attention to the investigation of R along vapor-liquid, liquid-solid, and vapor-solid equilibria. Because R is a measure of interaction strength, we traced out the line R=0 dividing the phase space into regions with effectively attractive (R<0) or repulsive (R>0) interactions. Furthermore, we analyzed the dependence of R on the strength of attraction applying a perturbation ansatz proposed by Weeks-Chandler-Anderson. Our results show clearly a transition from R>0 (for poorly repulsive interaction) to R<0 when loading attraction in the intermolecular potential.

Lennard-Jones systems near solid walls: Computing interfacial free energies from molecular simulation methods

Different computational techniques in combination with molecular dynamics computer simulation are used to determine the wall-liquid and the wall-crystal interfacial free energies of a modified Lennard-Jones (LJ) system in contact with a solid wall. Two different kinds of solid walls are considered: a flat structureless wall and a structured wall consisting of an ideal crystal with the particles rigidly attached to fcc lattice sites. Interfacial free energies are determined by a thermodynamic integration scheme, the anisotropy of the pressure tensor, the non-equilibrium work method based on Bennett acceptance criteria, and a method using Cahn's adsorption equations based on the interfacial thermodynamics of Gibbs. For the flat wall, interfacial free energies as a function of different densities of the LJ liquid and as a function of temperature along the coexistence curve are calculated. In the case of a structured wall, the interaction strength between the wall and the LJ system and the lattice constant of the structured wall are varied. Using the values of the wall-liquid and wall-crystal interfacial energies along with the value for the crystal-liquid interfacial free energy determined previously for the same system by the "cleaving potential method," we obtain the contact angle as a function of various parameters; in particular, the conditions are found under which partial wetting occurs.

Understanding wetting of immiscible liquids near a solid surface using molecular simulation

We introduce Monte Carlo simulation methods for determining interfacial properties of fluids that exhibit bulk liquid-liquid immiscibility. An interface-potential-based approach, in which the interfacial properties of a system are related to the surface excess free energy of a thin fluid film in contact with a surface, is utilized to deduce the wetting characteristics of these systems. We present a framework for implementing this general method within both the grand canonical and semigrand isobaric-isothermal ensembles. Tracking the evolution of interfacial properties along various thermodynamic paths is also examined. This task is accomplished by implementing variants of the expanded ensemble technique, which enables one to obtain components of the interface potential along a path of interest. We also discuss how these concepts are employed to calculate bulk liquid-liquid coexistence properties in an efficient manner. The computational strategies introduced here are applied to three model Lennard-Jones systems. For each system, we compile the evolution of the liquid-liquid surface tension and contact angle with temperature or pressure. For one of the model systems we compare our results with literature data. We also examine how interfacial properties evolve upon variation of the relative affinity of the fluid components for the substrate. Overall, we find that the approach pursued here is generally applicable and provides an efficient and precise means to calculate the bulk and interfacial properties of fluids that exhibit liquid-liquid immiscibility.

Elastic Signature of Flow Events in Supercooled Liquids Under Shear

Using numerical simulation of a 2D Lennard-Jones system, we study the crossover from shear thinning to Newtonian flow. We find that the short-time elastic response of our system essentially does not change through this crossover, and show that, in the Newtonian regime, thermal activation triggers shear transformations, i.e., local irreversible shear events that produce Eshelby (long-ranged, anisotropic) deformation fields as previously seen in low-T glasses. Quite surprisingly, these Eshelby fields are found to persist much beyond the α-relaxation time, and shear thinning to coincide with the emergence of correlations between shear relaxation centers.

Solid-liquid transition in polydisperse Lennard-Jones systems

We study melting of a face-centered crystalline solid consisting of polydisperse Lennard-Jones spheres with Gaussian polydispersity in size. The phase diagram reproduces the existence of a nearly temperature invariant terminal polydispersity (δ(t) =/~ 0.11), with no signature of reentrant melting. The absence of reentrant melting can be attributed to the influence of the attractive part of the potential upon melting. We find that at terminal polydispersity the fractional density change approaches zero, which seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction the system undergoes a sharp transition from crystalline solid to the disordered amorphous or fluid state with increasing polydispersity. This has been quantified by second- and third-order rotational invariant bond orientational order, as well as by the average inherent structure energy. The translational order parameter also indicates a similar sharp structural change at δ =/~ 0.09 in case of T(*) = 1.0, φ = 0.58. The free energy calculation further supports the sharp nature of the transition. The third-order rotationally invariant bond order shows that with increasing polydispersity, the local cluster favors a more icosahedral arrangement and the system loses its local crystalline symmetry. Interestingly, the value of structure factor S(k) of the amorphous phase at δ =/~ 0.10 (just beyond the solid-liquid transition density at T(*) = 1) becomes 2.75, which is below the value of 2.85 required for freezing given by the empirical Hansen-Verlet rule of crystallization, well known in the theory of freezing.

Regarding the Universality of Some Consequences of the van der Waals Equation in the Supercritical Domain

We show that some of the thermodynamic regularities, following from the van der Waals (VDW) equation, are valid for the real substances and models described by completely different equations of state. These regularities relate to lines of ideal enthalpy, enthalpy minima, and isothermal compressibility maxima. The first one appears to be the straight line on the density-temperature plane, while for the two others there are universal relations, which are the same for various substances and models (argon and Lennard-Jones system as examples). The model systems were studied by Monte Carlo simulations (NVT MC), while experimental data were analyzed for the real substances. Our numerical calculations and the analysis of experimental data have shown that for the considered systems these curves are similar to the VDW ones.

Three new branched chain equations of state based on Wertheim's perturbation theory

In this work, we present three new branched chain equations of state (EOS) based on Wertheim's perturbation theory. The first represents a slightly approximate general branched chain solution of Wertheim's second order perturbation theory (TPT2) for athermal hard chains, and the second represents the extension of first order perturbation theory with a dimer reference fluid (TPT1-D) to branched athermal hard chain molecules. Each athermal branched chain EOS was shown to give improved results over their linear counterparts when compared to simulation data for branched chain molecules with the branched TPT1-D EOS being the most accurate. Further, it is shown that the branched TPT1-D EOS can be extended to a Lennard-Jones dimer reference system to obtain an equation of state for branched Lennard-Jones chains. The theory is shown to accurately predict the change in phase diagram and vapor pressure which results from branching as compared to experimental data for n-octane and corresponding branched isomers.

Structural features of a Lennard-Jones system at melting and crystallization

The structural features of the crystallization and melting of a system of particles whose pair interaction is described by the Lennard-Jones potential have been considered. The bond order parameter method is used to quantitatively describe the orientational short-range order. The rotational invariants of the second (ql) and third (wl) orders are calculated for each particle of the system. These calculations require only information on the snapshot of atom positions, which is quite easily obtained in experiments, and provide the distribution functions of particles in ql and wl (where l is the rank of an invariant; the results for l = 4, 6 are presented), which are important characteristics of the phase state of the system. It has been shown that the cumulant of the distribution of particles in w6 is very sensitive to the destruction/formation of the short-range orientational order in the Lennard-Jones system and, correspondingly, can be used as a criterion of the melting and crystallization of this system.