Binary Lennard-Jones Mixture Research Articles

Mass transfer through vapour–liquid interfaces: a molecular dynamics simulation study

ABSTRACT A quasi-stationary molecular dynamics simulation method for studying mass transfer through vapour–liquid interfaces of mixtures driven by gradients of the chemical potential based on the dual control volume (DCV) method is described and tested. The rectangular simulation volume contains three bulk domains: a liquid domain in the middle with vapour on each side such that there are two vapour–liquid interfaces. The mass flux is generated by prescribing the chemical potential in control volumes in the vapour domains close to the outer boundary of the simulation volume. The simulation method was applied for studies of two binary Lennard-Jones mixtures: one in which a strong enrichment of the low-boiling component at the vapour–liquid interface is observed and another in which there is practically no enrichment. The two mixtures differ only in the dispersive interactions; their bulk diffusion coefficients are similar. Furthermore, the prescribed chemical potential difference was the same in all simulations. Nevertheless, important differences in the mass flux of the low-boiling component were observed for the two mixtures at all studied temperatures which might be related to the enrichment at the interfaces.

Flow heterogeneities in supercooled liquids and glasses under shear.

Using extensive nonequilibrium molecular dynamics simulations, we investigate a glass-forming binary Lennard-Jones mixture under shear. Both supercooled liquids and glasses are considered. Our focus is on the characterization of inhomogeneous flow patterns such as shear bands that appear as a transient response to the external shear. For the supercooled liquids, we analyze the crossover from Newtonian to non-Newtonian behavior with increasing shear rate γ[over ̇]. Above a critical shear rate γ[over ̇]_{c} where a non-Newtonian response sets in, the transient dynamics are associated with the occurrence of short-lived vertical shear bands, i.e., bands of high mobility that form perpendicular to the flow direction. In the glass states, long-lived horizontal shear bands, i.e., bands of high mobility parallel to the flow direction, are observed in addition to vertical ones. The systems with shear bands are characterized in terms of mobility maps, stress-strain relations, mean-squared displacements, and (local) potential energies. The initial formation of a horizontal shear band provides an efficient stress release, corresponds to a local minimum of the potential energy, and is followed by a slow broadening of the band towards the homogeneously flowing fluid in the steady state. Whether a horizontal or a vertical shear band forms cannot be predicted from the initial undeformed sample. Furthermore, we show that with increasing system size, the probability for the occurrence of horizontal shear bands increases.

Solid-like mean-square displacement in glass-forming liquids.

It was recently shown that the real part of the frequency-dependent fluidity for several glass-forming liquids of different chemistry conforms to the prediction of the random barrier model (RBM) devised for ac electrical conduction in disordered solids [Bierwirth et al., Phys. Rev. Lett. 119, 248001 (2017)]. Inspired by these results, we introduce a crystallization-resistant modification of the Kob-Andersen binary Lennard-Jones mixture for which the results of extensive graphics-processing-unit-based molecular-dynamics simulations are presented. We find that the low-temperature mean-square displacement is fitted well by the RBM prediction, which involves no shape parameters. This finding highlights the challenge of explaining why a simple model based on hopping of non-interacting particles in a fixed random energy landscape with identical minima can reproduce the complex and highly cooperative dynamics of glass-forming liquids.

Plastic instabilities and yielding in amorphous solids under pure shear

The nature of mechanical yielding in amorphous materials under external loading is investigated using computer simulation. We study the plastic instabilities and yielding transition in a model amorphous solid of a binary Lennard-Jones mixture under pure shear deformation. We carefully examine the plastic instabilities in the pre- and post-yield regime and find that these occur via the so-called saddle-node bifurcation mechanism in the athermal quasistatic limit. To quantify the yielding transition, we use the overlap order parameter Q12, which has been successfully used in various glassy models. Our results show that the yielding transition is accompanied by a dramatic change in the structure of the material. We identify this as a first-order phase transition with a significant difference in the yielding transition point compared to the simple shear protocol.

Response of glassy liquids to thermal gradients.

The Soret effect, i.e., the flow of matter caused by a temperature gradient, is studied in a glass-forming binary Lennard-Jones (LJ) mixture, using nonequilibrium molecular dynamics computer simulation. The transport processes associated with this effect are thermal diffusion and interdiffusion. While interdiffusion processes exhibit a drastic slowing down when approaching the glass transition, thermal diffusion appears to be a fast process even in the glass. We show that the Soret effect becomes more pronounced in the vicinity of the glass transition, due to the decoupling between thermal diffusion and interdiffusion as well as the chemical ordering in the considered LJ mixture. This is reflected in the occurrence of large concentration gradients, nonlinear concentration profiles, and long-lived nonstationary structures.

Influence of dispersive long-range interactions on properties of vapour–liquid equilibria and interfaces of binary Lennard-Jones mixtures

The influence of dispersive long-range interactions on properties of vapour–liquid equilibria and interfaces of six binary Lennard-Jones (LJ) mixtures was studied by molecular dynamics (MD) simulations and density gradient theory (DGT). The mixtures were investigated at a constant temperature T, at which the low-boiling component, which is the same in all mixtures, is subcritical. Two different high-boiling components were considered: one is subcritical, the other is supercritical at T. Furthermore, the unlike dispersive interaction was varied such that mixtures with three different types of phase behaviour were obtained: ideal, low-boiling azeotrope, and high-boiling azeotrope. In a first series of simulations, the full LJ potential was used to describe these mixtures. To assess the influence of the long-range interactions, these results were compared with simulations carried out with the LJ truncated and shifted (LJTS) potential applying the corresponding states principle. The dispersive long-range interactions have a significant influence on the surface tension and the interfacial thickness of the studied mixtures, whereas the relative adsorption and the enrichment are hardly affected. Furthermore, the influence of the long-range interactions on Henry's law constants and the phase envelopes of the vapour–liquid equilibrium was investigated. The long-range interactions have practically no influence on the composition dependency of the investigated mixture properties.

Metabasin dynamics of supercooled polymer melt**Project supported by the National Natural Science Foundation of China (Grant No. 11804085) and the Doctoral Foundation of Heze University, China (Grant No. XY18BS13).

We employ molecular dynamic simulation to investigate metabasin dynamics for supercooled polymer melt. We find that, in a small system, the α-relaxation process is composed of a few crossing events that the monomers hops from one metabasin to another. Each crossing event is very rapid and involves a democratic movement of many particles, whereas such collective motion is not string-like. Evaluation on the contributions of metabasin exploration and democratic movement shows that the structural relaxation is mostly governed by the latter. Our calculated results show that the metabasin–metabasin transitions are not the main reason of spatially dynamical heterogeneity. It is different from the binary Lennard–Jones mixture model in which the metabasin–metabasin transitions are relevant for the spatially dynamical heterogeneity.

Molecular Dynamics Simulation of the Capillary Leveling of a Glass-Forming Liquid.

Motivated by recent experimental studies probing (i) the existence of a mobile layer at the free surface of glasses and (ii) the capillary leveling of polymer nanofilms, we study the evolution of square-wave patterns at the free surface of a generic glass-forming binary Lennard-Jones mixture over a wide temperature range, by means of molecular dynamics simulations. The pattern's amplitude is monitored, and the associated decay rate is extracted. The evolution of the latter as a function of temperature exhibits a crossover between two distinct behaviors, over a temperature range typically bounded by the glass-transition temperature and the mode-coupling critical temperature. Layer-resolved analysis of the film particles' mean-squared displacements further shows that diffusion at the surface is considerably faster than in the bulk, below the glass-transition temperature. The diffusion coefficient of the surface particles is larger than its bulk counterpart by a factor that reaches 105 at the lowest temperature studied. This factor decreases upon heating, in agreement with recent experimental studies.

Study of nanoconfined mixtures of decane and water: Structure and dynamic

In the last years, the phase behaviour of multi-component hydrocarbon systems in shale reservoirs has received significant attention. The main complexities in modelling the phase behaviour is the confinement. It is presented in this work, the results obtained by molecular dynamics simulation in the NPT ensemble of n-decane/water liquid mixture confined in an amorphous hydrophobic nanometric tube. Nanotube walls are made up of a Lennard-Jones binary mixture similar to a Kob-Andersen system. As it happens in a macroscopic flow of biphasic fluid, a transition from drop to a thread is observed in this confined system when increasing water molar fraction. Different values of the water tetrahedral bond distribution, water density profiles, and the mean square-displacement of water were found for a drop to a thread transition. The calculated quantities, substantially differ from those corresponding to the bulk system.

Tuning the glass-forming ability of metallic glasses through energetic frustration

The design of multi-functional BMGs is limited by the lack of a quantitative understanding of the variables that control the glass-forming ability (GFA) of alloys. Both geometric frustration (e.g. differences in atomic radii) and energetic frustration (e.g. differences in the cohesive energies of the atomic species) contribute to the GFA. We perform molecular dynamics simulations of binary Lennard-Jones mixtures with only energetic frustration. We show that there is little correlation between the heat of mixing and critical cooling rate $R_c$, below which the system crystallizes, except that $\Delta H_{\rm mix} < 0$. By removing the effects of geometric frustration, we show strong correlations between $R_c$ and the variables $\epsilon_- = (\epsilon_{BB}-\epsilon_{AA})/(\epsilon_{AA}+\epsilon_{BB})$ and ${\overline \epsilon}_{AB} = 2\epsilon_{AB}/(\epsilon_{AA}+\epsilon_{BB})$, where $\epsilon_{AA}$ and $\epsilon_{BB}$ are the cohesive energies of atoms $A$ and $B$ and $\epsilon_{AB}$ is the pair interaction between $A$ and $B$ atoms. We identify a particular $f_B$-dependent combination of $\epsilon_-$ and ${\overline \epsilon}_{AB}$ that collapses the data for $R_c$ over nearly $4$ orders of magnitude in cooling rate.

Molecular Simulation of Pervaporation of a Lennard-Jones Mixture Using a Crystalline Membrane

Numeric simulation of the pervaporation process is carried out using molecular dynamics. Various conditions of the separation of an ideal binary Lennard-Jones mixture using a crystalline membrane are considered. Components of separated mixtures differ in regards to the energy of interaction with molecules of the membrane. As a result of simulation, fields of concentrations and densities along the cell, as well as flux values of components, are obtained. In addition, coefficients of the diffusion of components in the membrane are computed. It is shown that the correspondence of numeric simulation data to macroscopic mass transfer equations are observed in all cases. It can be concluded that the behavior of molecules in a nonequilibrium system with a scale of several dozens of molecule diameters corresponds to transfer equations of linear nonequilibrium thermodynamics. Results of numeric simulation show the selectivity of a membrane in regard to the component with a larger interaction energy. It is shown that molecular simulation is able to predict the main characteristics of membrane separation (fluxes, selectivity, adsorption, and diffusion coefficients).

Interfacial properties of binary Lennard-Jones mixtures by molecular simulation and density gradient theory.

A systematic study of interfacial properties of binary mixtures of simple fluids was carried out by molecular dynamics (MD) simulation and density gradient theory (DGT). The fluids are described by the Lennard-Jones truncated and shifted (LJTS) potential with truncation radius of 2.5 diameters. The following interfacial properties were studied: surface tension, relative adsorption, enrichment, and interfacial thickness. A recently developed equation of state for the LJTS fluid, the Perturbed Lennard-Jones truncated and shifted equation of state (PeTS EOS) was used as the basis for DGT. Six binary mixtures (components 1 + 2) were studied at a constant temperature, which was chosen such that the high-boiling component 1 is subcritical, while the low-boiling component 2 is either subcritical or supercritical. Furthermore, a parameter ξ in the combination rule for the unlike dispersive interaction was varied such that the resulting mixtures showed three types of behavior: high-boiling azeotrope, ideal, and low-boiling azeotrope. The parameters of the LJTS potential, including ξ, were also used in the PeTS EOS without any adjustment. Despite this simple approach, excellent agreement between the results of the PeTS EOS and the MD results for the phase equilibrium and the interfacial properties is observed. Enrichment at the interface is only found for the low-boiling component 2. The enrichment increases with decreasing concentration of component 2 and is favored by high boiling point differences of the pure components 1 and 2 and positive deviations from Raoult's law for the mixture 1 + 2.

Linear viscoelasticity of a two-dimensional glass-former by stress-fluctuation formalism

Viscoelastic properties of dense colloids are investigated using the stress-fluctuation formalism and equilibrium molecular dynamics simulations. The focus is on a two-dimensional (2D) non-additive Lennard-Jones binary mixture, which is a glass-former. Its behaviour is compared with that of a one-component Lennard-Jones system, which forms a 2D crystal with triangular lattice at low temperatures. The systems are under fixed pressure and temperature conditions. The effects of the mixing, the temperature and the pressure are studied. Calculated functions include the shear modulus relaxation function, the dynamic moduli (storage modulus and loss modulus), the complex compliance and the dynamic viscosity. Both the liquid and the solid (crystal and glass) states are investigated. Qualitative aspects are discussed in the light of simple rheological models.

Polytetrahedral structure and glass-forming ability of simulated Ni-Zr alloys.

Binary Cu-Zr system is a representative bulk glassformer demonstrating high glass-forming ability (GFA). From the first glance, the Ni-Zr system is the most natural object to expect the same behavior because nickel and copper are neighbors in the periodic table and have similar physicochemical properties. However, it is known that the Ni-Zr system has worse GFA than the Cu-Zr one. To understand the underlying physics, we investigate the Ni α Zr1-α system in whole concentration range α ∈ [0, 1]. Doing molecular dynamic simulations with a reliable embedded atom model potential, we show that the simulated Ni-Zr system also has relatively low GFA, which is comparable to that for an additive binary Lennard-Jones mixture without any chemical interaction. Icosahedral local ordering in Ni-Zr alloys is known to be less pronounced than that in the Cu-Zr ones; we see that as well. However, the icosahedron is not the only structural motif responsible for GFA. We find that the local structure of glassy Ni α Zr1-α alloys at 0.3 < α < 0.65 can be described in terms of Z11-Z16 Kasper polyhedra with high density of topological defects including icosahedra as a part of this family. Concentration of topologically perfect Kasper polyhedra appears to be several times smaller than that in Cu-Zr. This is the reason for relatively poor GFA of the Ni-Zr system.

Viscosity of Lennard-Jones mixtures: A systematic study and empirical law.

A systematic study of the viscosity of the binary Lennard-Jones (LJ) mixtures is carried out by equilibrium molecular dynamics simulations via the Green-Kubo relation. The effects of mass, size, and energy-parameter asymmetries on the viscosity and the self-diffusion coefficients are examined separately, both in equimolar mixtures and by varying the molar fractions. The systems are mapped into an effective one-component model according to the van der Waals one-fluid (vdW1) model. Furthermore, using an empirical law for pure LJ liquids, similar to the one proposed recently for liquid sodium, it is shown that the viscosity of the mixtures studied here are well-predicted by the combination of vdW1 fluid and empirical law. The Stokes-Einstein relation in the mixtures has also been investigated. A possible simple extension of this relation, from pure liquids to mixtures, has been proposed and tested.

Thermodynamic analysis of Lennard-Jones binary mixtures using Kirkwood-Buff theory

The ability to extract thermodynamic properties of mixtures from molecular geometry and interactions is one of the major advantages of atomistic simulations, but, at the same time, can be a great challenge, especially for statistical properties such as the Gibbs energy of mixing (ΔmixG). This challenge becomes even greater in the case of mixtures of complicated molecules or macromolecules. Kirkwood-Buff theory offers a promising avenue for estimating ΔmixG from atomistic simulation of binary mixtures. In this work we perform molecular dynamics simulations of both ideal and real binary Lennard-Jones mixtures at various mole fractions. We estimate the Kirkwood-Buff integrals by two different methods and identify the most efficient one. Then we validate our methodology by comparing several thermodynamic properties of the ideal mixtures against the theoretical expressions of thermodynamics. Finally, we calculate the mixing thermodynamic properties for the real mixtures, namely the enthalpy, Gibbs energy, volume, and entropy of mixing, as well as their excess parts relative to an ideal solution. We compare our results against the predictions of the well-known modified Benedict-Webb-Rubin equation of state for Lennard-Jones systems and find good agreement.

Gibbs ensemble Monte Carlo with solvent repacking: phase coexistence of size–asymmetrical binary Lennard-Jones mixtures

We describe a Monte Carlo method for simulation of vapour–liquid phase coexistence in size-asymmetrical Lennard–Jones (LJ) binary mixtures. The method incorporates the Solvent Repacking Monte Carlo (SRMC) approach, which offers efficient trial moves for the exchange of a large particle for several small particles, into the Gibbs Ensemble Monte Carlo (GEMC) method. SRMC yields a significant efficiency improvement in simulation of dilute large species mixtures at low temperature compared to the original GEMC method with identity exchange moves. Vapor–liquid phase diagrams are reported for LJ mixtures with a diameter ratio of 1:2 with well depth ratios and 2, producing spindle-type, azeotrope and closed loop types of phase diagram, respectively.

Enhanced Crystal Growth in Binary Lennard-Jones Mixtures.

We study the crystal growth in binary Lennard-Jones mixtures by molecular dynamics simulations. Growth dynamics, the structure of the liquid-solid interfaces as well as droplet incorporation into the crystal vary with solution properties. For demixed systems we observe a strongly enhanced crystal growth at the cost of enclosed impurities. Furthermore, we find different interface morphologies depending on solubility. We relate our observations to growth mechanisms based on the Gibbs-Thomson effect as well as to predictions of the Kardar-Parisi-Zhang theory in 2+1 dimensions.

Velocity autocorrelation function in supercooled liquids: Long-time tails and anomalous shear-wave propagation.

Molecular dynamic simulations are performed to reveal the long-time behavior of the velocity autocorrelation function (VAF) by utilizing the finite-size effect in a Lennard-Jones binary mixture. Whereas in normal liquids the classical positive t^{-3/2} long-time tail is observed, we find in supercooled liquids a negative tail. It is strongly influenced by the transfer of the transverse current wave across the period boundary. The t^{-5/2} decay of the negative long-time tail is confirmed in the spectrum of VAF. Modeling the long-time transverse current within a generalized Maxwell model, we reproduce the negative long-time tail of the VAF, but with a slower algebraic t^{-2} decay.

Decoupled length scales for diffusivity and viscosity in glass-forming liquids.

The growth of the characteristic length scales both for diffusion and viscosity is investigated by molecular dynamics utilizing the finite-size effect in a binary Lennard-Jones mixture. For those quantities relevant to the diffusion process (e.g., the hydrodynamic value and the spatial correlation function), a strong system-size dependence is found. In contrast, it is weak or absent for the shear relaxation process. Correlation lengths are estimated from the decay of the spatial correlation functions. We find the length scale for viscosity decouples from the one of diffusivity, featured by a saturated length even in high supercooling. This temperature-independent behavior of the length scale is reminiscent of the unapparent structure change upon supercooling, implying the manifestation of configuration entropy. Whereas for the diffusion process, it is manifested by relaxation dynamics and dynamic heterogeneity. The Stokes-Einstein relation is found to break down at the temperature where the decoupling of these lengths happens.