Lennard-Jones Mixture Research Articles

Liquidus curve of a Lennard-Jones mixture.

The temperature below which the homogeneous liquid state of a mixture is not thermodynamically stable is called the liquidus temperature. This temperature varies with composition, and its composition dependence is represented by the liquidus curve. This curve provides fundamental reference points on the composition-temperature plane for characterizing the behavior of liquids, glasses, and crystals. In this paper, using molecular dynamics simulations, we determine the liquidus curve of the Wahnström mixture, which consists of large and small atoms interacting via the Lennard-Jones potential. Since this system is one of the standard models used to study the behavior of liquids and glasses, the liquidus curve presented in this work will contribute to a deeper understanding of disordered materials in general.

Deviation from the prediction of the Maier-Saupe theory of mixtures of charged discotic Gay-Berne and Lennard-Jones particles

ABSTRACT We report an analysis of the orientational order and orientational distribution functions of mixtures of discotic charged Gay-Berne (GB) and Lennard-Jones (LJ) particles as models of ionic liquid crystals and colloidal suspensions. We have studied three different stoichiometries (GB:LJ of 1:2, 1:1 and 2:1), with the opposite charges on the two particles selected to guarantee electroneutrality. We have found that for relatively low values of the scaled charge the dependence of the fourth-rank orientational order parameter, <P 4>, on the second-rank orientational order parameter, <P 2>, is in very good agreement with the prediction of the Maier-Saupe theory. In contrast, for relatively high values of the charge a deviation is observed which is in opposite directions for mixtures with an excess for GB particles and mixtures with an excess of LJ particles.

Crystal nucleation in a vapor deposited Lennard-Jones mixture

Understanding the pathways to crystallization during the deposition of a vapor phase on a cold solid substrate is of great interest in industry, e.g., for the realization of electronic devices made of crystallites-free glassy materials, as well as in the atmospheric science in relation to ice nucleation and growth in clouds. Here we numerically investigate the nucleation process during the deposition of a glassformer by using a Lennard-Jones mixture, and compare the properties of this nucleation process with both its quenched counterpart and the bulk system. We find that all three systems homogeneously nucleate crystals in a narrow range of temperatures. However, the deposited layer shows a peculiar formation of ordered domains, promoted by the faster relaxation dynamics toward the free surface even in an as-deposited state. In contrast, the formation of such domains in the other systems occurs only when the structures are fully relaxed by quenching. Furthermore, the nucleus initially grows in an isotropic symmetrical manner, but eventually shows sub-3D growth due to its preference to grow along the basal plane, irrespective of the layer production procedure.

Revised Enskog theory for Mie fluids: Prediction of diffusion coefficients, thermal diffusion coefficients, viscosities, and thermal conductivities.

Since the 1920s, the Enskog solutions to the Boltzmann equation have provided a route to predicting the transport properties of dilute gas mixtures. At higher densities, predictions have been limited to gases of hard spheres. In this work, we present a revised Enskog theory for multicomponent mixtures of Mie fluids, where the Barker-Henderson perturbation theory is used to calculate the radial distribution function at contact. With parameters of the Mie-potentials regressed to equilibrium properties, the theory is fully predictive for transport properties. The presented framework offers a link between the Mie potential and transport properties at elevated densities, giving accurate predictions for real fluids. For mixtures of noble gases, diffusion coefficients from experiments are reproduced within ±4%. For hydrogen, the predicted self-diffusion coefficient is within 10% of experimental data up to 200 MPa and at temperatures above 171K. Binary diffusion coefficients of the CO2/CH4 mixture from simulations are reproduced within 20% at pressures up to 14.7 MPa. Except for xenon in the vicinity of the critical point, the thermal conductivity of noble gases and their mixtures is reproduced within 10% of the experimental data. For other molecules than noble gases, the temperature dependence of the thermal conductivity is under-predicted, while the density dependence appears to be correctly predicted. Predictions of the viscosity are within ±10% of the experimental data for methane, nitrogen, and argon up to 300bar, for temperatures ranging from 233 to 523K. At pressures up to 500bar and temperatures from 200 to 800K, the predictions are within ±15% of the most accurate correlation for the viscosity of air. Comparing the theory to an extensive set of measurements of thermal diffusion ratios, we find that 49% of the model predictions are within ±20% of the reported measurements. The predicted thermal diffusion factor differs by less than 15% from the simulation results of Lennard-Jones mixtures, even at densities well exceeding the critical density.

Equilibrium thermodynamic properties of Lennard–Jones fluid mixtures from a single-component effective fluid model

ABSTRACT The equilibrium thermodynamic properties of binary Lennard–Jones mixtures are determined by means of a Monte Carlo-based perturbation theory for an effective single-component fluid. The results for the equation of state and the excess energy are compared with simulation data obtained for two equimolar binary Lennard–Jones fluid mixtures at different temperatures along a wide range of densities. The satisfactory accuracy achieved seems to suggest that this approach might be a useful tool to deal with mixtures with a wide variety of intermolecular interactions including mixtures of real fluids.

Relationship between Diffusion Coefficients in Nonideal Binary Lennard-Jones Mixtures and Entropy

Relationship between Diffusion Coefficients in Nonideal Binary Lennard-Jones Mixtures and Entropy

Estimation of bubble cavitation rates in a symmetrical Lennard-Jones mixture by NVT seeding simulations.

The liquid-vapor transition starts with the formation of a sufficiently large bubble in the metastable liquid to trigger the phase transition. Understanding this process is of fundamental and practical interest, but its study is challenging because it occurs over timescales that are too short for experiments but too long for simulations. The seeding method estimates cavitation rates by simulating a liquid in which a bubble is inserted, thus avoiding the long times needed for its formation. In one-component systems, in the NpT ensemble, the bubble grows or redissolves depending on whether its size is larger or smaller than the critical size, whereas in the NVT ensemble (i.e., at constant number of particles, volume, and temperature), the critical bubble can remain in equilibrium. Provided that a good criterion is used to determine the bubble size, this method, combined with the Classical Nucleation Theory (CNT), gives cavitation rates consistent with those obtained by methods independent of the CNT. In this work, the applicability of NVT seeding to homogeneous cavitation in mixtures is demonstrated, focusing on a partially miscible symmetrical binary Lennard-Jones (LJ) liquid at a temperature within the mixing regime. At the same stretching pressure, cavitation rates are higher in the binary mixture than in the pure liquid due to the lower interfacial free energy of the mixture. Curiously, the cost of creating a bubble is similar in the pure and binary LJ liquids at the same metastability, Δμ/Δμspin, with Δμ being the difference in chemical potential between the metastable liquid and coexistence, and Δμspin between the spinodal and coexistence.

Mass Transfer through Vapor–Liquid Interfaces Studied by Non-Stationary Molecular Dynamics Simulations

Molecular dynamics (MD) simulations are highly attractive for studying the influence of interfacial effects, such as the enrichment of components, on the mass transfer through the interface. In a recent work, we have presented a steady-state MD simulation method for investigating this phenomenon and tested it using model mixtures with and without interfacial enrichment. The present study extends this work by introducing a non-stationary MD simulation method. A rectangular simulation box that contains a mixture of two components 1 + 2 with a vapor phase in the middle and two liquid phases on both sides is used. Starting from a vapor-liquid equilibrium state, a non-stationary molar flux of component 2 is induced by inserting particles of component 2 into the center of the vapor phase in a pulse-like manner. During the isothermal relaxation process, particles of component 2 pass through the vapor phase, cross the vapor-liquid interface, and enter the liquid phase. The system thereby relaxes into a new vapor-liquid equilibrium state. During the relaxation process, spatially resolved responses for the component densities, fluxes, and pressure are sampled. To reduce the noise and provide measures for the uncertainty of the observables, a set of replicas of simulations is carried out. The new simulation method was applied to study mass transfer in two binary Lennard-Jones mixtures: one that exhibits a strong enrichment of the low-boiling component 2 at the vapor-liquid interface and one that shows no enrichment. Even though both mixtures have similar transport coefficients in the bulk phases, the results for mass transfer differ significantly, indicating that the interfacial enrichment influences the mass transfer.

Continuous fractional component Gibbs ensemble Monte Carlo

A continuous fractional component (CFC) approach increases the probability of particle swaps in the context of vapor-liquid equilibrium simulations using the Gibbs ensemble Monte Carlo algorithm. Two variants of the CFC approach are compared for simulations of pure Lennard-Jones (LJ) fluids and binary LJ mixtures as examples. The details of an exemplary CFC implementation are presented. Recommendations are provided to reduce the effort required for the suggested problems.

Phase equilibria of symmetric Lennard-Jones mixtures and a look at the transport properties near the upper critical solution temperature.

This study investigates phase equilibria and transport properties of five symmetric binary Lennard-Jones mixtures using molecular simulation and equation of state models. The mixtures are selected for their representation of different types of phase behavior and the research contributes to the development of simulation techniques, mixture theories and understanding of thermophysical mixture properties. A novel method is introduced for determining the critical end point (CEP) and critical azeotropic end point (CAEP) by molecular simulation. The van der Waals one-fluid theory is assessed for its performance in conjunction with Lennard-Jones equation of state models, while addressing different phase equilibrium types simultaneously. An empirical correlation is introduced to account for deviations between the equation of state and simulation that arise when using the same binary interaction parameter. This study also investigates the influence of the liquid-liquid critical point on thermophysical properties, which are found to exhibit no significant anomalies or singularities. System-size effects of diffusion coefficients are addressed by extrapolating simulation data to the thermodynamic limit and applying analytical finite-size corrections.

Predicting Scaling Properties from a Single Fluid Configuration.

Time-dependent dynamical properties of a fluid cannot be estimated directly from a single configuration without performing a simulation. Here, however, we present a method that predicts the scaling properties of both structure and dynamics from a single configuration. The method is demonstrated to work well for the Lennard-Jones fluid as well as the viscous Kob-Andersen Lennard-Jones mixture, both in and out of equilibrium. The method is conceptually simple and easy to implement and, thus, should become a standard tool in the study of scaling properties of fluids and liquids.

Gas-liquid interface of a Lennard-Jones binary mixture controlled by differential activity: phase transition and interfacial stability.

We perform molecular dynamics simulations of a two-dimensional binary mixture of Lennard-Jones particles, characterized by some degree of "activity" inside. Starting from a base state that features a gas-liquid interface and a completely segregated system at thermodynamic equilibrium, we introduce differential scalar activity between the two species by prescribing two different effective temperatures. The differential activity is measured as the ratio of the two temperatures. Previous studies showed segregation in a homogeneously mixed system induced by high activity. In this study, we investigate the effect of activity on a pre-existing gas-liquid interface between two separated species. Whereas a high activity ratio induces the formation of new interfaces, we show that a low activity ratio destabilizes existing ones. Moreover, the combination of a pre-existent interface with differential activity leads to partial crystallization and thus to triple phase coexistence (solid, liquid and gas), which is observed over a wide range of moderate differential activities. Findings from this idealized system can guide our understanding of interfacial behaviors in certain biological systems.

Interfacial properties of binary azeotropic mixtures of simple fluids: Molecular dynamics simulation and density gradient theory.

Interfacial properties of binary azeotropic mixtures of Lennard-Jones truncated and shifted fluids were studied by molecular dynamics (MD) simulation and density gradient theory (DGT) in combination with an equation of state. Three binary mixtures were investigated, which differ in the energetic cross interaction parameter that yields different types of azeotropic behavior. This study covers a wide temperature and composition range. Mixture A exhibits a heteroazeotrope at low temperatures, which changes to a low-boiling azeotrope at high temperatures, mixture B exhibits a low-boiling azeotrope, and mixture C exhibits a high-boiling azeotrope. The phase behavior and fluid interfacial properties as well as their relation were studied. Vapor-liquid, liquid-liquid, and vapor-liquid-liquid equilibria and interfaces were considered. Density profiles, the surface tension, the interfacial thickness, as well as the relative adsorption and enrichment of the components at the interface were studied. The results obtained from the two independent methods (MD and DGT) are overall in good agreement. The results provide insights into the relation of the phase behavior, particularly the azeotropic behavior, of simple fluid mixtures and the corresponding interfacial properties. Strong enrichment was found for the mixture with a heteroazeotrope in the vicinity of the three-phase equilibrium, which is related to a wetting transition.

Transport properties of binary Lennard-Jones mixtures: Insights from entropy scaling and conformal solution theory

The relation of transport properties and the molecular interactions in binary mixtures was studied. The self-diffusion coefficient, Maxwell–Stefan as well as Fickian mutual diffusion coefficient, shear viscosity, and thermal conductivity of liquid binary simple mixtures were therefore sampled using molecular dynamics simulations. The mixtures were described by the Lennard-Jones potential. The molecular interaction parameters were chosen such that a large variety of mixture behavior was covered. The two components had the same size parameter in all cases, but different dispersion energies. Moreover, the cross-interaction parameter used in the modified Lorentz-Berthelot combination rule was varied such that the resulting mixtures showed different types of phase behavior: ideal, high- and low-boiling azeotrope. The results are discussed using conformal solution theory as a link between the molecular interactions in the mixtures and the macroscopic properties. Moreover, the applicability of Rosenfeld’s entropy scaling is tested. Despite the important differences of the studied mixtures regarding their molecular interactions and the large pressure, temperature, and composition range considered, a practically monovariate relation of these properties with respect to the configurational entropy is observed. Yet, the quality of the approximation differs for the studied properties.

Importance of feature construction in machine learning for phase transitions.

Machine learning is an important tool in the study of the phase behavior from molecular simulations. In this work, we use un-supervised machine learning methods to study the phase behavior of two off-lattice models, a binary Lennard-Jones (LJ) mixture and the Widom-Rowlinson (WR) non-additive hard-sphere mixture. The majority of previous work has focused on lattice models, such as the 2D Ising model, where the values of the spins are used as the feature vector that is input into the machine learning algorithm, with considerable success. For these two off-lattice models, we find that the choice of the feature vector is crucial to the ability of the algorithm to predict a phase transition, and this depends on the particular model system being studied. We consider two feature vectors, one where the elements are distances of the particles of a given species from a probe (distance-based feature) and one where the elements are +1 if there is an excess of particles of the same species within a cut-off distance and -1 otherwise (affinity-based feature). We use principal component analysis and t-distributed stochastic neighbor embedding to investigate the phase behavior at a critical composition. We find that the choice of the feature vector is the key to the success of the unsupervised machine learning algorithm in predicting the phase behavior, and the sophistication of the machine learning algorithm is of secondary importance. In the case of the LJ mixture, both feature vectors are adequate to accurately predict the critical point, but in the case of the WR mixture, the affinity-based feature vector provides accurate estimates of the critical point, but the distance-based feature vector does not provide a clear signature of the phase transition. The study suggests that physical insight into the choice of input features is an important aspect for implementing machine learning methods.

Molecular simulations and hydrodynamic theory of nonlocal shear-stress correlations in supercooled fluids.

A supercooled fluid close to the glass transition develops nonlocal shear-stress correlations that anticipate the emergence of elasticity. We performed molecular dynamics simulations of a binary Lennard-Jones mixture at different temperatures and investigated the spatiotemporal autocorrelation function of the shear stress for different wavevectors, q, from a locally measured and Fourier-transformed stress tensor. Anisotropic correlations are observed at non-zero wavevectors, exhibiting strongly damped oscillations with a characteristic frequency ω(q). A comparison with a recently developed hydrodynamic theory [Maier et al., Phys. Rev. Lett. 119, 265701 (2017)] shows a remarkably good quantitative agreement between particle-based simulations and theoretical predictions.

Detecting temporal correlations in hopping dynamics in Lennard–Jones liquids

Lennard–Jones mixtures represent one of the popular systems for the study of glass-forming liquids. Spatio/temporal heterogeneity and rare (activated) events are at the heart of the slow dynamics typical of these systems. Such slow dynamics is characterised by the development of a plateau in the mean-squared displacement (MSD) at intermediate times, accompanied by a non-Gaussianity in the displacement distribution identified by exponential tails. As pointed out by some recent works, the non-Gaussianity persists at times beyond the MSD plateau, leading to a Brownian yet non-Gaussian regime and thus highlighting once again the relevance of rare events in such systems. Single-particle motion of glass-forming liquids is usually interpreted as an alternation of rattling within the local cage and cage-escape motion and therefore can be described as a sequence of waiting times and jumps. In this work, by using a simple yet robust algorithm, we extract jumps and waiting times from single-particle trajectories obtained via molecular dynamics simulations. We investigate the presence of correlations between waiting times and find negative correlations, which becomes more and more pronounced when lowering the temperature.

Glass-forming ability of binary Lennard-Jones systems

The glass-forming ability (GFA) of alloys, colloidal dispersions, and other particulate materials, as measured by the critical cooling rate $R_c$, can span more than ten orders of magnitude. Even after numerous previous studies, the physical features that control the GFA are still not well understood. For example, it is well-known that mixtures are better glass-formers than monodisperse systems and that particle size and cohesive energy differences among constituents improve the GFA, but it is not currently known how particle size differences couple to cohesive energy differences to determine the GFA. We perform molecular dynamics simulations to determine the GFA of equimolar, binary Lennard-Jones (LJ) mixtures versus the normalized cohesive energy difference $\epsilon_\_$ and mixing energy $\bar \epsilon_{AB}$ between particles A and B. We find several important results. First, the $\log_{10} R_c$ contours in the $\bar \epsilon_{AB}$-$\epsilon_\_$ plane are ellipsoidal for all diameter ratios, and thus $R_c$ is determined by the Mahalanobis distance $d_M$ from a given point in the $\bar \epsilon_{AB}$-$\epsilon_\_$ plane to the center of the ellipsoidal contours. Second, LJ systems for which the larger particles have larger cohesive energy are generally better glass formers than those for which the larger particles have smaller cohesive energy. Third, $d_M(\epsilon_\_,\bar \epsilon_{AB})$ is determined by the relative Voronoi volume difference between particles and local chemical order $S_{AB}$, which gives the average fraction of nearest-neighbor B particles surrounding an A particle and vice-versa. In particular, the shifted Mahalanobis distance $d_M - d^0_M$ versus the shifted chemical order $S_{AB}-S_{AB}^0$ collapses onto a hyperbolic master curve for all diameter ratios.

Entropy Scaling for Viscosity of Pure Lennard-Jones Fluids and Their Binary Mixtures

In this work, entropy scaling approaches for viscosity of pure Lennard-Jones (LJ) fluids and their mixtures have been investigated. To do so, we have employed reliable viscosity database available in literature for the pure LJ fluids, and performed the molecular dynamics simulation to generate viscosity database over a wide range of thermodynamic condition for the LJ mixture fluids. It has shown that for the pure LJ fluid, the entropy scaling approaches using the macroscopic properties for the reduction of viscosity yield noticeably better collapse of data than the one using the zero-density viscosity in the dense fluid region. In addition, we have developed viscosity correlations based on these approaches. It has been obtained that the correlations of macroscopic properties approaches predict the pure LJ fluid viscosity with average absolute deviation of around 4% more coming from the low-density states, whereas it is of around 8.50% more coming from the dense states for the other one. Finally, the viscosity correlations have been applied to the LJ mixtures. Interestingly, the correlations of macroscopic properties approaches are able to provide good estimations for all mixtures studied. However, it deteriorates for the viscosity of dense mixtures when the other employed.

Mass effect on viscosity of mixtures in entropy scaling framework: Application to Lennard-Jones mixtures

Entropy scaling has proved to be an appealing framework to connect transport properties to microscopic structure for many pure fluids. Its extension to mixtures is not fully straightforward in particular because it requires the definition of an effective molecular mass equivalent to that of the mixture from the transport properties point of view. However, the exact definition of such an effective molecular mass, thanks to a mixing rule, is unknown theoretically apart from the zero-density regime. Thus, in this work, various mixing rules that express the effective molecular mass as a function of molar fractions and molecular masses of the components of the mixture, have been investigated by performing molecular simulations on mixtures of Lennard-Jones fluids at various thermodynamic conditions ranging from low- to high-density states. It has been found that the best results are obtained by decomposing the viscosity into zero-density and residual contributions, the latter being described by a correlation based on the entropy scaling. More precisely, good estimates of the viscosity of mixtures of Lennard-Jones fluids are achieved by using a combination of a van der Waals one fluid-Chapman-Enskog approximation for the zero-density viscosity with a mixing rule derived from the Grunberg-Nissan equation for the residual viscosity. It is even possible to improve these results at high density, using an empirical modification to the Grunberg-Nissan derived mixing rule.