Ternary Lennard-Jones Research Articles

Shear Viscosity Computed from the Finite-Size Effects of Self-Diffusivity in Equilibrium Molecular Dynamics.

A method is proposed for calculating the shear viscosity of a liquid from finite-size effects of self-diffusion coefficients in Molecular Dynamics simulations. This method uses the difference in the self-diffusivities, computed from at least two system sizes, and an analytic equation to calculate the shear viscosity. To enable the efficient use of this method, a set of guidelines is developed. The most efficient number of system sizes is two and the large system is at least four times the small system. The number of independent simulations for each system size should be assigned in such a way that 50%–70% of the total available computational resources are allocated to the large system. We verified the method for 250 binary and 26 ternary Lennard-Jones systems, pure water, and an ionic liquid ([Bmim][Tf2N]). The computed shear viscosities are in good agreement with viscosities obtained from equilibrium Molecular Dynamics simulations for all liquid systems far from the critical point. Our results indicate that the proposed method is suitable for multicomponent mixtures and highly viscous liquids. This may enable the systematic screening of the viscosities of ionic liquids and deep eutectic solvents.

Theoretical Study of Structural Symmetry in Ternary Clusters

The geometrical symmetry presents an intriguing theoretical problem in many kinds of clusters. The diversity of geometrical structures is associated with cluster sizes, different model functions and potential parameters, and ternary clusters are investigated to study the relationship between geometrical symmetry and homotopic symmetry. Ternary Lennard-Jones model potential is studied with different parameters, and the putative global minimum structures of A13B30C12 clusters are optimized using an adaptive immune optimization algorithm. The results show that there mainly exist five geometrical symmetry structures, i.e., Mackay icosahedral, fivefold partial Mackay icosahedral, sixfold pancake, partial double Mackay icosahedral, and amorphous structures. Furthermore, the number of bonds is used to distinguish the geometrical symmetry. The importance of geometrical symmetry and homotopic symmetry determined by potential parameters is discussed. It was found that in the optimization it is more important to generate geometrical symmetry than to optimize homotopic symmetry.

On the phase and interface behavior along the three-phase line of ternary Lennard-Jones mixtures: a collaborative approach based on square gradient theory and molecular dynamics simulations.

This work focuses on the application of a two-way approach, where Molecular Dynamics (MD) simulations and the Square Gradient Theory (SGT) have been used for describing the phase and interface behavior of binary and ternary Lennard-Jones (LJ) mixtures, along a condition of three-phase equilibrium. The unequivocal correspondence between MD and SGT has been achieved by using the global phase diagram of binary mixtures composed by equally sized Lennard-Jones molecules, from which representative molecular parameters for Type-I, Type-II, and Type-III systems have been determined. The so selected binaries have been used then to scale the behavior of a ternary mixture characterized by complex phase equilibrium patterns. For the case of the theoretical SGT approach applied to the Lennard-Jones equation of state was used for predicting phase equilibrium and interfacial properties. In addition the corresponding MD simulations of these macroscopic properties have been conducted for the LJ potential by using equivalent molecular parameters and conditions than in the theoretical approach. Excellent agreement has been observed between the predictions obtained from theory and simulations. Particularly, our results concerning the characterization of the three phase line of a binary Type-III mixture indicate that the bulk liquid (α) and the bulk gas (G) regions are sharply separated by a bulk liquid region (β) for all the explored temperature, pressure, and concentration conditions. The structural analysis of these bulk phases reveals that a secondary liquid phase (β) perfectly wets the liquid-gas interface (α-G), as previously found for Type-II mixture [A. Mejía and L. F. Vega, J. Chem. Phys. 124, 244505 (2006)]. The exploration along the three-phase line for the ternary mixture shows good agreement between SGT and MD. Particularly, we observed the specific influence of a third component in the phase and interface behavior. From all the previous results, we conclude that the SGT applied to an EoS with appropriate mixing rules produces reliable predictions of the properties of ternary mixtures.

Structural transitions in mixed ternary noble gas clusters

The properties of noble gas systems can be greatly extended by heterogeneous mixtures of elements. The geometrical structures and energies of mixed Ar-Kr-Xe clusters were investigated using ternary Lennard-Jones (TLJ) potential. For the Ar19Kr n Xe19, Ar19Kr19Xe n , and Ar n Kr19Xe19 (n = 0-17) clusters investigated, the results show that only two minimum energy configurations exist, i.e., polytetrahedron and six-fold pancake. The inner core of all these clusters is composed mainly of Ar atoms, and Kr and Xe atoms are distributed on the surface with well mixed pattern for polytetrahedral and segregate pattern for six-fold pancake configurations. The relative stability property of Ar-Kr-Xe clusters with a certain composition is discussed. Moreover, the role of heterogeneity on the strain was investigated, and reduced strain energies in Ar-Kr-Xe clusters were studied to find possible ways of reducing strain. The results showed that the strain energies were affected mainly by Ar-Ar, Ar-Kr, and Xe-Xe bonds.

Structural distribution in mixed ternary noble gas and Lennard-Jones clusters

The geometrical structures and energies of mixed 38- and 55-atom Ar–Kr–Xe clusters are investigated. The interaction is described by ternary Lennard-Jones (TLJ) potential. The stable structures are optimized by adaptive immune optimization algorithm. Results show that in Ar12KrmXen (m+n=26) clusters, there exist amorphous and polytetrahedral configurations, and in Ar13KrmXen (m+n=42) clusters, structures are categorized into four classes, i.e., 8 Mackay icosahedra, 19 amorphous structures, 4 sixfold pancake structures, and 10 ring-like structures. Furthermore, strain energies in Ar–Kr–Xe clusters are studied to propose the possible ways of reducing strain. To investigate the potential energy surface of Ar–Kr–Xe clusters in TLJ model potential, the bond numbers of the Ar12Kr13Xe13 cluster and A12B13C13 TLJ model potential are compared, and the case of the former one is studied in the bond number phase diagram of the latter one.

Parametric Effects of the Potential Energy Function on the Geometrical Features of Ternary Lennard-Jones Clusters

The impact of parameters in potential function for describing atomic or molecular clusters is complex due to the complicated potential energy surface. Ternary Lennard-Jones (TLJ) A(l)B(m)C(n) clusters with two-body potential are investigated to study the effect of parameters. In the potential, the size parameter (σ(AA)) of A atoms is fixed, and corresponding parameters of B and C atoms (relative to A atoms), i.e., σ(BB)/σ(AA) and σ(CC)/σ(AA) > 1.00, are used to control the atomic interaction among A, B, and C atoms in TLJ clusters. The minimum energy configurations of A(l)B(m)C(n) clusters with different species are optimized by adaptive immune optimization algorithm. Ternary cluster structures, bonds, and energies of the putative minima are studied. The results show that two different structures based on double-icosahedra are found in 30-atom TLJ clusters. Furthermore, with increasing potential size parameters of B and C atoms, A atoms tend to be more compact for the increasing numbers of A-A bonds, but the short-range attractive part in TLJ clusters becomes weaker. To lower the potential energy, B and C atoms grow around the A atoms in pursuit of a compact configuration. The results are also approved in A(l)B(m)C(n) (l + m + n = 9-55) clusters and A(l)B(m)C(n) (l = 13, m + n = 42) clusters.

Accurate Simulation Estimates of Phase Behavior in Ternary Mixtures with Prescribed Composition

This paper describes an isobaric semi-grand canonical ensemble Monte Carlo scheme for the accurate study of phase behaviour in ternary fluid mixtures under the experimentally relevant conditions of prescribed pressure, temperature and overall composition. It is shown how to tune the relative chemical potentials of the individual components to target some requisite overall composition and how, in regions of phase coexistence, to extract accurate estimates for the compositions and phase fractions of individual coexisting phases. The method is illustrated by tracking a path through the composition space of a model ternary Lennard-Jones mixture.

Dynamics of ternary liquid mixtures: Generalized collective modes analysis

A parameter-free generalized collective modes (GCM) approach is applied to the study of longitudinal and transverse dynamics in a ternary Lennard-Jones liquid mixture. Spectra of collective excitations are calculated in a wide range of wavenumbers starting from the hydrodynamic region and up to the range of molecular regime. Several simplified dynamical models are used in order to estimate the origin of branches in the spectra of collective excitations. This analysis permits to establish a crossover from a “coherent” to “partial” type of collective dynamics in the dispersion laws of propagating collective modes. The ”coherent” type of collective dynamics is observed in the hydrodynamic region and is represented by sound modes (in the transverse case – shear waves) and propagating optic-like excitations, while in the range of “partial” dynamics (intermediate and large wavenumbers) the dynamical properties are mainly determined by correlated “partial” motions of particles of each species. Within the GCM scheme used the number of propagating optic-like modes, identified in this study, is simply related to the number of components in a multi-component mixture, and this has a close analogy in the dynamics of solids.

Direct evaluation of multicomponent phase equilibria using flat-histogram methods

We present a method for directly locating density-driven phase transitions in multicomponent systems. Phase coexistence conditions are determined through manipulation of a total density probability distribution evaluated over a density range that includes both coexisting phases. Saturation quantities are determined through appropriate averaging of density-dependent mean values of a given property of interest. We discuss how to implement the method in both the grand-canonical and isothermal-isobaric semigrand ensembles. Calculations can be conducted using any of the recently introduced flat-histogram techniques. Here, we combine the general algorithm with a transition-matrix approach to produce an efficient self-adaptive technique for determining multicomponent phase equilibrium properties. To assess the performance of the new method, we generate phase diagrams for a number of binary and ternary Lennard-Jones mixtures.

Preferential solvation in supercritical fluids: An integral equation study

A statistical mechanical study of preferential solvation in supercritical fluids is presented. The study is focused on attractive mixtures, which are characterized by local density and composition enhancement in the vicinity of the solute molecule. The solute–solvent radial distribution functions are obtained from two versions of the integral equation formalism, both of which are designed for treating inhomogeneous systems. Model calculations are performed for a ternary Lennard-Jones mixture composed of a dilute solute and two solvent species, which are identical except for their interaction strength with the solute. It is shown that theoretical results agree well with Monte Carlo simulations in reproducing local solvent density and composition augmentation induced by the solute.

Phase equilibria in ternary Lennard-Jones systems

Gibbs ensemble Monte Carlo simulations are used to test the ability of the van der Waals one-fluid theory to predict phase equilibria for ternary systems of particles interacting with Lennard-Jones potentials. Simulation results for asymmetric systems are compared to theoretical results for mixtures that obey the Lorentz-Berthelot combining rules. Good agreement is found between theory and simulation far form the plait point. The theory is found to overestimate the plait point, as expected from previous studies of binary systems. Liquid-liquid equilibria in a symmetric ternary system with energy parameters deviating from the geometric mean (Berthelot) rule are also investigated at three different pressures. A three-phase region is found at high pressures. The agreement between theory and simulation is excellent for the symmetric systems studied here.

Monte carlo simulation of ternary Lennard-Jones dense fluids with different molecular sizes and interaction energies

Wang W.-C. and Liang H., 1991. Monte Carlo simulation of ternary Lennard-Jones dense fluids with different molecular sizes and interaction energies. Fluid Phase Equilibria, 67: 15-30. Three-component Lennard-Jones dense fluids have been simulated by the Monte Carlo method. Computer simulation covering different molecular sizes, interaction energies and bulk compositions have been done and the results are compared with those for square-well model fluid mixtures. Though the coordination numbers for the two model fluids differ significantly, the local compositions are similar, and are correlated with good accuracy using a model proposed by the authors.

Molecular theory of ternary supercritical solutions. 1. Theory and methods of calculation

Experiments have shown that added third components can have important effects on the solubility of a solute in a supercritical solvent. Added co-solvents and entrainers have been used to enhance solubility or selectivity and added secondary solutes have been found to influence the solubility of a primary solute. We present a rigorous fundamental equation, derived from Kirkwood-Buff solution theory, which provides a molecular basis for understanding these effects. Key quantities in this equation are the Kirkwood fluctuation integrals — spatial integrals of the total pair correlation functions. We present a method for calculating correlation functions and fluctuation integrals for ternary Lennard-Jones mixtures with the Percus-Yevick integral equation theory by using Baxter's Wiener-Hopf factorization of the Ornstein-Zernike relation. The fundamental solubility equation leads to expressions for solubility in the presence of an added co-solvent or second solute which can be integrated numerically using the results from the Percus-Yevick calculations. The method we present is capable of general application and could be used to guide process research and development for practical systems.

Local composition in ternary Lennard-Jones liquid mixtures: molecular dynamics simulation and a simple correlation

Molecular dynamics calculations have been carried out for binary and ternary Lennard-Jones liquid mixtures. Local compositions (LC) within the first peak of radial distribution function (RDF) have been evaluated. These mixtures show rather smaller deviation from ideality than with previously used models and the dependence of the LC on attractive interaction is the reverse of that of the peak height of RDF. A simple correlation is derived between LC and the peak height, based on a Wilson type equation.