Binary Lennard-Jones Mixture Research Articles

Application of the SLV-EoS for representing phase equilibria of binary Lennard–Jones mixtures including solid phases

In 2003, Yokozeki proposed an equation of state capable of representing solid, liquid, and vapor phases. This equation represents an innovative approach of including solid in phase diagrams. The capability of this equation of state, named SLV-EoS, of giving a qualitative correct representation of phase diagrams for binary mixtures of Lennard–Jones spheres has been tested in this work. The SLV-EoS has been used for producing the phase diagrams of binary Lennard–Jones mixtures with diameter ratio σ11/σ22 ranging from 0.85 to 1, and well-depth ratio ɛ11/ɛ22 ranging from 0.625 to 1.6 at reduced pressure P*=Pσ113/ε11=0.002. The obtained phase diagrams have been compared with literature data obtained by Monte-Carlo simulation. The comparison shows the incapability of the SLV-EoS with null binary interaction parameters of predicting solid–liquid azeotrope and eutectic in the investigated range of σ11/σ22 and ɛ11/ɛ22. Binary interaction parameters have been regressed to allow the SLV-EoS giving a qualitative representation of the three types of phase diagrams: solid solution, solid azeotrope and simple eutectic. Binary interaction parameters are shown being smoothed functions of σ11/σ22 and ɛ11/ɛ22, allowing the prediction of the phase behavior for other Lennard–Jones mixtures or real mixtures of simple fluids.

Demixing in liquids: approaches based on simple equations of state

The demixing transition in partially miscible liquid mixtures is investigated within the framework of the simple van der Waals (vdW)-type equations of state (EOS) approaches. Two approximations for the excluded volume free energy have been considered. One is a modified vdW expression (denoted as vdW here). The other is the well known Mansoori–Carnahan–Starling–Leland (MCSL) excess free energy for hard sphere fluid mixtures (MCSL). In order to adopt an universal representation, we suggest to rescale the physical quantities such as the temperature, pressure and density by the critical parameters of the liquid–vapour (L–V) transition of the monodisperse fluid. We compare phase diagrams from the two theories and the theoretical predictions with available simulation results of binary Lennard–Jones mixtures. For the systems studied, the two theoretical approaches give qualitatively similar L–V and liquid–liquid (L–L) phase diagrams. The MCSL EOS is able to predict in a semi-quantitative way the L–L phase diagram.

Diffusive Dynamics of Binary Lennard-Jones Liquid in the Presence of Gold Nanoparticle: A Mode Coupling Theory Analysis

Molecular dynamics simulation has been performed to analyze the effect of the presence of gold nanoparticle on dynamics of Kob-Anderson binary Lennard-Jones mixture upon supercooling within the framework of the mode coupling theory of the dynamic glass transition. The presence of gold nanoparticle has a direct effect on the liquid structure and causes the peaks of the radial distribution functions to become shorter with respect to the bulk binary Lennard-Jones liquid. It is found that the dynamics of the liquid at a given density is consistent with the mode coupling theory (MCT) predictions. In accordance with the idealized MCT, the diffusion constants D(T) show power-law behavior at low temperatures for both types of binary Lennard-Jones (BLJ) particles as well as the 13 gold atoms comprising the nanoparticle. The mode coupling crossover temperature Tc is the same for all particle types, however, Tc = 0.4 is reduced with respect to that of the bulk BLJ liquid and the exponent is found to depend on the particle type. The existence of the nanoparticle causes the short-time β-relaxation regime to shorten and the range of validity of the MCT shrink with respect to the bulk BLJ. It is also found that the behavior of intermediate scattering function (ISF) is in agreement with MCT prediction and in spite of the presence of gold nanoparticle the time temperature superposition principle at intermediate and low temperatures is still valid and the curves of ISF vs. t/ (T) fall onto a master curve.

Heterogeneous relaxation dynamics in amorphous materials under cyclic loading

Molecular dynamics simulations are performed to investigate heterogeneous dynamics in amorphous glassy materials under oscillatory shear strain. We consider three-dimensional binary Lennard-Jones mixture well below the glass transition temperature. The structural relaxation and dynamical heterogeneity are quantified by means of the self-overlap order parameter and the dynamic susceptibility. We found that at sufficiently small strain amplitudes, the mean square displacement exhibits a broad subdiffusive plateau and the system undergoes nearly reversible deformation over about 10(4) cycles. Upon increasing strain amplitude, the transition to the diffusive regime occurs at shorter time intervals and the relaxation process involves intermittent bursts of large particle displacements. The detailed analysis of particle hopping dynamics and the dynamic susceptibility indicates that mobile particles aggregate into clusters whose sizes increase at larger strain amplitudes. Finally, the correlation between particle mobilities in consecutive time intervals demonstrates that dynamic facilitation becomes increasingly pronounced at larger strain amplitudes.

Static triplet correlations in glass-forming liquids: A molecular dynamics study

We present a numerical evaluation of the three-point static correlations functions of the Kob-Andersen Lennard-Jones binary mixture and of its purely repulsive, Weeks-Chandler-Andersen variant. In the glassy regime, the two models possess a similar pair structure, yet their dynamics differ markedly. The static triplet correlation functions S(3) indicate that the local ordering is more pronounced in the Lennard-Jones model, an observation consistent with its slower dynamics. A comparison of the direct triplet correlation functions c(3) reveals that these structural differences are due, to a good extent, to an amplification of the small discrepancies observed at the pair level. We demonstrate the existence of a broad, positive peak at small wave-vectors and angles in c(3). In this portion of k-space, slight, systematic differences between the models are observed, revealing "genuine" three-body contributions to the triplet structure. The possible role of the low-k features of c(3) and the implications of our results for dynamic theories of the glass transition are discussed.

Effect of gold nanoparticles on structure and dynamics of binary Lennard-Jones liquid: Direct space analysis

We investigate the static structure and diffusive dynamics of binary Lennard-Jones mixture upon supercooling in the presence of gold nanoparticle within the framework of the mode-coupling theory of the dynamic glass transition in the direct space by means of constant-NVT molecular dynamics simulations. It is found that the presence of gold nanoparticle causes the energy per particle and the pressure of this system to decrease with respect to the bulk binary Lennard-Jones mixture. Furthermore, the presence of nanoparticle has a direct effect on the liquid structure and causes the peaks of the radial distribution functions to become shorter with respect to the bulk binary Lennard-Jones liquid. The dynamics of the liquid at a given density is found to be consistent with the mode-coupling theory (MCT) predictions in a certain range at low temperatures. In accordance with the idealized MCT, the diffusion constants D(T) show a power-law behavior at low temperatures for both types of binary Lennard-Jones (BLJ) particles as well as the gold atoms comprising the nanoparticle. The mode-coupling crossover temperature T(c) is the same for all particle types; however, T(c)=0.4 is reduced with respect to that of the bulk BLJ liquid, and the γ exponent is found to depend on the particle type. The existence of the nanoparticle causes the short-time β-relaxation regime to shorten and the range of validity of the MCT shrinks with respect to the bulk BLJ. It is also found that at intermediate and low temperatures the curves of the mean-squared displacements (MSDs) versus tD(T) fall onto a master curve. The MSDs follow the master curve in an identical time range with the long-time α-relaxation regime of the mode-coupling theory. By obtaining the viscosity, it is observed that the Stokes-Einstein relation remains valid at high and intermediate temperatures but breaks down as the temperatures approach T(c) as a result of the cooperative motion or activated processes.

Anomalous Diffusion of Driven Particles in Supercooled Liquids

We perform nonequilibrium dynamics simulations of a binary Lennard-Jones mixture in which an external force is applied on a single tagged particle. For the diffusive properties of this particle parallel to the force, superdiffusive behavior at intermediate times as well as giant long-time diffusivity is observed. A quantitative description of this nontrivial behavior is given by a continuous time random walk analysis of the system in configuration space. We further demonstrate that the same physical properties which are responsible for the superdiffusivity in nonequilibrium systems also determine the non-Gaussian parameter in equilibrium systems.

Slippage of binary fluid mixtures in a nanopore

This work focuses on the slip phenomenon at the fluid–solid interface accompanying Poiseuille flow of simple binary miscible fluids in a slit nanopore. To explore such flows, molecular dynamics simulations are used on Lennard–Jones binary mixtures composed of species of varying affinities with the walls. The results have shown that the apparent slip magnitude at the fluid–solid interface depends largely on the species that is dominant in contact with the walls. In addition, it has been shown that the velocity profiles of each species (of different “wettability”) does not superpose with the velocity profile of the mixture and such a result points out the limitations of the classical approaches based on a single momentum conservation equation to deal with mixtures flow in nanochannels.

Relaxation of surface tension in the free-surface boundary layer of simple Lennard-Jones liquids

In this paper we use molecular dynamics to answer a classical question: how does the surface tension on a liquid/gas interface appear? After defining surface tension from the first principles and performing several consistency checks, we perform a dynamic experiment with a single simple liquid nanodroplet. At time zero, we remove all molecules of the interfacial layer, creating a fresh bare interface with the bulk arrangement of molecules. After that the system evolves towards equilibrium, and the expected surface tension is re-established. We found that the system relaxation consists of three distinct stages. First, the mechanical balance is quickly re-established. During this process the notion of surface tension is meaningless. In the second stage, the surface tension equilibrates, and the density profile broadens to a value which we call "intrinsic" interfacial width. During the third stage, the density profile continues to broaden due to capillary wave excitations, which does not however affect the surface tension. We have observed this scenario for monatomic Lennard-Jones (LJ) liquid as well as for binary LJ mixtures at different temperatures, monitoring a wide range of physical observables.

Nonlinear response and crowding effects in microrheology

The mobility of tagged particles in a microrheological setup has been investigated via molecular dynamics simulations of a three-dimensional Lennard-Jones binary mixture. After coupling a small number of particles to a constant external driving force, the drift velocity and other observables of the dragged probe particles are reported in the linear and nonlinear response regime. In the nonlinear regime significant crowding effects are observed, thereby creating stringlike structures. Formation of the strings further enhances the nonlinear effects. A systematic study of these effects' dependence on temperature and total number of driven probe atoms is presented.

Representation of Solid, Liquid, and Vapor phases of Binary Lennard Jones Mixtures using the SLV-EoS

The capability of the SLV-EoS, recently proposed by A. Yokozeki [1], of representing the phase diagrams for binary mixtures of Lennard-Jones (LJ) fluids has been investigated in this work. The SLV-EoS has been used for producing the phase diagrams of binary Lennard-Jones mixtures with diameter ratio σ11 /σ22 ranging from 0.85 and 0.95, and well-depth ratio ɛ11 /ɛ22 ranging from 0.625 and 1.6 at reduced pressure P * =P σ11 3 /ɛ11 =0.002. The obtained phase diagrams have been compared with the corresponding results obtained by Monte-Carlo (MC) simulation [2-5].

Lifetimes and lengthscales of structural motifs in a model glassformer

We use a newly-developed method to identify local structural motifs in a popular model glassformer, the Kob-Andersen binary Lennard-Jones mixture. By measuring the lifetimes of a zoo of clusters, we find that 11-membered bicapped square antiprisms, denoted as 11A, have longer lifetimes on average than other structures considered. Other long-lived clusters are similar in structure to the 11A cluster. These clusters group into ramified networks that are correlated with slow particles and act to retard the motion of neighbouring particles. The structural lengthscale associated with these networks does not grow as fast as the dynamical lengthscale xi(4) as the system is cooled, in the range of temperatures our molecular dynamics simulations access. Thus we find a strong, but indirect, correlation between static structural ordering and slow dynamics.

Scaling of viscous dynamics in simple liquids: theory, simulation and experiment

Supercooled liquids are characterized by relaxation times that increase dramatically by cooling or compression. From a single assumption follows a scaling law according to which the relaxation time is a function of h(ρ) over temperature, where ρ is the density and the function h(ρ) depends on the liquid in question. This scaling is demonstrated to work well for simulations of the Kob–Andersen binary Lennard-Jones mixture and two molecular models, as well as for the experimental results for two van der Waals liquids, dibutyl phthalate and decahydroisoquinoline. The often used power-law density scaling, h(ρ)∝ργ, is an approximation to the more general form of scaling discussed here. A thermodynamic derivation was previously given for an explicit expression for h(ρ) for liquids of particles interacting via the generalized Lennard-Jones potential. Here a statistical mechanics derivation is given, and the prediction is shown to agree very well with simulations over large density changes. Our findings effectively reduce the problem of understanding the viscous slowing down from being a quest for a function of two variables to a search for a single-variable function.

Molecular simulation of the phase behavior of fluids and fluid mixtures using the synthetic method

A new molecular simulation procedure is reported for determining the phase behavior of fluids and fluid mixtures, which closely follows the experimental synthetic method. The simulation procedure can be implemented using Monte Calro or molecular dynamics in either the microcanonical or canonical statistical ensembles. Microcanonical molecular dynamics simulations are reported for the phase behavior of both the pure Lennard-Jones fluid and a Lennard-Jones mixture. The vapor pressures for the pure fluid are in good agreement with Monte Carlo Gibbs ensemble and Gibbs-Duhem calculations. The Lennard-Jones mixture is composed of equal size particles, with dissimilar energy parameters (ε(2)/ε(1) = 1/2, ε(12)/ε(1) = 1/√2). The binary Lennard-Jones mixture exhibits liquid-liquid equilibria at high pressures and the simulation procedure allows us to estimate the coordinates of the high-pressure branch of the critical curve.

AZEOTROPE PREDICTION BY MONTE CARLO MOLECULAR SIMULATION

This article presents a methodology for checking the existence of the azeotrope and computing its composition, density, and pressure at a given temperature by integrating chemical engineering insights with molecular simulation principles. Liquid-vapor equilibrium points are computed by molecular simulations using the Gibbs ensemble Monte Carlo (GEMC) method at constant volume. The appearance of the azeotropic point is marked by a shift of the equilibrium constant from one side of the unity to the other. After each GEMC simulation, an identity change move is derived in the grand canonical ensemble to progress towards the azeotrope along the equilibrium curve. The effectiveness of the proposed methodology is successfully tested for several binary Lennard-Jones mixtures reported in the literature.

A new method of semigrand canonical ensemble to calculate first-order phase transitions for binary mixtures

First-order phase transitions of binary mixtures at the given pressure (P) and temperature (T) are studied by taking into account the composition fluctuations. Isothermal-isobaric semigrand canonical ensemble is adopted to find the relations among the total number of molecules, the composition fluctuations and Gibbs free energy density. By combining two identical subsystems of mixtures successively, the free energy density is transformed until being stable and its linear segments represent phase transitions. A new method is developed to calculate the phase equilibriums of binary mixtures. The method handles multiple types and number of phase equilibriums at single time and its solutions are physically justified. One example is shown for calculating the phase diagram of binary Lennard-Jones mixture. It demonstrates that the fluctuations of the total number of molecules in mixtures are fundamental behind phase transitions and the van der Waals loops in Gibbs free energy are reasonable.

Universal Critical Behavior of Curvature-Dependent Interfacial Tension

From the analysis of Monte Carlo simulations of a binary Lennard-Jones mixture in the coexistence region, we provide evidence that the curvature dependence of the interfacial tension can be described by a simple theoretical function σ(R)ξ(2)=C(1)/[1+C(2)(ξ/R)(2)], where ξ is the correlation length and R is the droplet radius. The universal constants C(1) and C(2) are estimated. In the model, a Tolman length is strictly absent, but, since its critical behavior is believed to be much weaker than ξ, we argue that it only provides a correction to scaling and does not affect the leading critical behavior, which should be described by the above function for any system in the Ising universality class. The large value of C(2)≃32 implies that conventional nucleation theory becomes inaccurate even for a significantly large droplet radius.

Lumping analysis for the prediction of long-time dynamics: From monomolecular reaction systems to inherent structure dynamics of glassy materials

In this work we develop, test, and implement a methodology that is able to perform, in an automated manner, "lumping" of a high-dimensional, discrete dynamical system onto a lower-dimensional space. Our aim is to develop an algorithm which, without any assumption about the nature of the system's slow dynamics, is able to reproduce accurately the long-time dynamics with minimal loss of information. Both the original and the lumped systems conform to master equations, related via the "lumping" analysis introduced by Wei and Kuo [Ind. Eng. Chem. Fundam. 8, 114 (1969)], and have the same limiting equilibrium probability distribution. The proposed method can be used in a variety of processes that can be modeled via a first order kinetic reaction scheme. Lumping affords great savings in the computational cost and reveals the characteristic times governing the slow dynamics of the system. Our goal is to approach the best lumping scheme with respect to three criteria, in order for the lumped system to be able to fully describe the long-time dynamics of the original system. The criteria used are: (a) the lumping error arising from the reduction process; (b) a measure of the magnitude of singular values associated with long-time evolution of the lumped system; and (c) the size of the lumped system. The search for the optimum lumping proceeds via Monte Carlo simulation based on the Wang-Landau scheme, which enables us to overcome entrapment in local minima in the above criteria and therefore increases the probability of encountering the global optimum. The developed algorithm is implemented to reproduce the long-time dynamics of a glassy binary Lennard-Jones mixture based on the idea of "inherent structures," where the rate constants for transitions between inherent structures have been evaluated via hazard plot analysis of a properly designed ensemble of molecular dynamics trajectories.

Construction of a disorder variable from Steinhardt order parameters in binary mixtures at high densities in three dimensions

Using molecular dynamics simulation, we investigate the structural disorder in crystal, polycrystal, and glass in a Lennard-Jones binary mixture composed of N(1) + N(2) = 4096 particles at a low temperature in three dimensions. The size ratio σ(2)/σ(1) between the large and small particles is either 1.2 or 1.4. The crossovers among these states occur, as the composition of the large particles c = N(2)/(N(1) + N(2)) is varied. We define a disorder variable D(j) for each particle j in terms of local bond order parameters based on spherical harmonics (Steinhardt order parameters). Stacking faults and grain boundaries in fcc polycrystal and mesoscopic structural heterogeneity in glass are then visualized. At small c, disturbances of large particles is stronger for larger σ(2)/σ(1). At large c, the transition between glass and polycrystal occurs nearly discontinuously at c = c(c) ~ 0.8. At σ(2)/σ(1) = 1.4, microphase separation occurs in polycrystal states with c > c(c), where fcc crystal grains comprising the large particles are enclosed by amorphous layers composed of the two particle species.

Role of the first coordination shell in determining the equilibrium structure and dynamics of simple liquids

The traditional view that the physical properties of a simple liquid are determined primarily by its repulsive forces was recently challenged by Berthier and Tarjus, who showed that in some cases ignoring the attractions leads to large errors in the dynamics [L. Berthier and G. Tarjus, Phys. Rev. Lett. 103, 170601 (2009); J. Chem. Phys. 134, 214503 (2011)]. We present simulations of the standard Lennard-Jones liquid at several condensed-fluid state points, including a fairly low density state and a very high density state, as well as simulations of the Kob-Andersen binary Lennard-Jones mixture. By varying the range of the forces via a shifted-forces cutoff, results for the thermodynamics, dynamics, and structure show that the determining factor for getting the correct statics and dynamics is not whether or not the attractive forces per se are included in the simulations. What matters is whether or not interactions are included from all particles within the first coordination shell - the attractive forces can thus be ignored, but only at extremely high densities. The recognition of the importance of a local shell in condensed fluids goes back to van der Waals; our results confirm this idea and thereby the basic picture of the old hole and cell theories for simple condensed fluids.