Lennard-Jones Liquid Mixtures Research Articles

Molecular size and shape effects: Tracer diffusion and the Stokes-Einstein relation

Molecular size and shape effects are evaluated on the Stokes–Einstein (SE) relation from the viewpoint of molecular differences between the solute and solvent. To this end, dilute solutions of both an n-alkane in Ar and Ar in an n-alkane were simulated using the molecular dynamics method. The molecular-based SE relation derived for the Lennard-Jones liquid mixtures was found to be applicable to both systems, which shows that the effects of the differences in the size and interaction energy are predominant but that those in the shape are negligible in these systems.

Structure and dynamics of binary liquid mixtures near their continuous demixing transitions

The dynamic and static critical behavior of a family of binary Lennard-Jones liquid mixtures, close to their continuous demixing points (belonging to the so-called model H' dynamic universality class), are studied computationally by combining semi-grand canonical Monte Carlo simulations and large-scale molecular dynamics (MD) simulations, accelerated by graphic processing units (GPU). The symmetric binary liquid mixtures considered cover a variety of densities, a wide range of compressibilities, and various interactions between the unlike particles. The static quantities studied here encompass the bulk phase diagram (including both the binodal and the λ-line), the correlation length, and the concentration susceptibility, of the finite-sized systems above the bulk critical temperature Tc, the compressibility and the pressure at Tc. Concerning the collective transport properties, we focus on the Onsager coefficient and the shear viscosity. The critical power-law singularities of these quantities are analyzed in the mixed phase (above Tc) and non-universal critical amplitudes are extracted. Two universal amplitude ratios are calculated. The first one involves static amplitudes only and agrees well with the expectations for the three-dimensional Ising universality class. The second ratio includes also dynamic critical amplitudes and is related to the Einstein-Kawasaki relation for the interdiffusion constant. Precise estimates of this amplitude ratio are difficult to obtain from MD simulations, but within the error bars our results are compatible with theoretical predictions and experimental values for model H'. Evidence is reported for an inverse proportionality of the pressure and the isothermal compressibility at the demixing transition, upon varying either the number density or the repulsion strength between unlike particles.

Explicit expressions of self-diffusion coefficient, shear viscosity, and the Stokes-Einstein relation for binary mixtures of Lennard-Jones liquids.

Explicit expressions of the self-diffusion coefficient, D(i), and shear viscosity, η(sv), are presented for Lennard-Jones (LJ) binary mixtures in the liquid states along the saturated vapor line. The variables necessary for the expressions were derived from dimensional analysis of the properties: atomic mass, number density, packing fraction, temperature, and the size and energy parameters used in the LJ potential. The unknown dependence of the properties on each variable was determined by molecular dynamics (MD) calculations for an equimolar mixture of Ar and Kr at the temperature of 140 K and density of 1676 kg m(-3). The scaling equations obtained by multiplying all the single-variable dependences can well express D(i) and η(sv) evaluated by the MD simulation for a whole range of compositions and temperatures without any significant coupling between the variables. The equation for Di can also explain the dual atomic-mass dependence, i.e., the average-mass and the individual-mass dependence; the latter accounts for the "isotope effect" on Di. The Stokes-Einstein (SE) relation obtained from these equations is fully consistent with the SE relation for pure LJ liquids and that for infinitely dilute solutions. The main differences from the original SE relation are the presence of dependence on the individual mass and on the individual energy parameter. In addition, the packing-fraction dependence turned out to bridge another gap between the present and original SE relations as well as unifying the SE relation between pure liquids and infinitely dilute solutions.

Scaling Analysis of Dynamic Heterogeneity in a Supercooled Lennard-Jones Liquid

We have performed molecular dynamics computer simulations of a dense Lennard-Jones liquid mixture to study dynamic heterogeneity from normal liquid temperatures down to a supercooled temperature 15% above the previously identified mode-coupling temperature Tc of the model. A temperature-dependent correlation length associated with the correlation function of mobility fluctuations is calculated. The results are used to test two sets of scaling hypotheses for the dynamic heterogeneity. The results are in close agreement with the inhomogeneous mode-coupling theory of Biroli et al. [Phys. Rev. Lett. 97, 195701 (2006)] for both the alpha and beta relaxation regimes. Comparison with results for kinetically constrained models suggest that the Lennard-Jones mixture studied is more similar to models of fragile liquids than models of very strong liquids.

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.

Development of a model for the Description of Intra-diffusion in Homogeneous Liquid Lennard–Jones Mixtures

A model for calculation of intra-diffusion coefficients of homogeneous liquid 1-centre Lennard–Jones (LJ) mixtures is proposed. As starting point for deriving this model we have chosen the model of Liu et al. [Chem. Eng. Sci. 53, (1998), 2403–2422] suggested for calculation of the self-diffusion coefficients of pure LJ model fluids. This model was extended to liquid mixtures by introducing suitable combining and mixing rules for description of different characteristics of the mixture components. The five parameters of the model were determined from data obtained by molecular-dynamics (MD) simulations performed in this work. To generate a database for intra-diffusion coefficients the method of optimal experiment design is employed. This method is applied to plan simulations in such a way as to obtain optimal estimates of the model parameters. The parameters were determined based on the range of temperatures 90 < T<350 K and mass densities 200 < ρ M<2580 kg/m3 with the total average absolute deviation of 5.56%. The suggested model was tested on the data available in literature concerning intra-diffusivities of 1-centre LJ liquid mixtures. The prediction accuracy of 42 data points is 13.08%. Further work will be directed at further optimisation of model structure and model parameters.

Determination of the critical consolution point of a Lennard-Jones mixture through a thermodynamically self-consistent structural theory

We show that a structural theory of fluids embodying a thermodynamic consistency constraint can be solved up to extremely near the “critical” consolution point of a Lennard-Jones liquid mixture. The predicted thermodynamic quantities are in close agreement with molecular dynamics (MD) simulation data. The MD experiments also signal incipient segregation of the mixture in the thermodynamic region where the theoretically estimated concentration fluctuation correlations tend to diverge; the “critical” temperature is then accurately determined from the theory. Comparison with other structural liquid state theories, and a preliminary determination of the critical exponent γ, are also reported.

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.

Monte carlo simulation of continuous Lennard-Jones mixtures

We report our simulation results for continuous mixtures of Lennard-Jones liquids, with parameters chosen to represent the paraffinic series of hydrocarbons. A novel, “semi-grand” ensemble is used, where each molecule is allowed to adopt all species identities during the simulation, thus modeling a truly polydisperse mixture. This approach also facilitates evaluation of the entire activity distribution, not easily determined using more conventional techniques. We have examined in detail the effect of the width of the composition distribution, from the very narrow to the very wide case.

Nonadditivity effects in generalized Langevin dynamics simulation of interacting particles

An analysis of the generalized Langevin dynamics simulation method is carried out. Simple Lennard-Jones liquid mixtures with identical solute and solvent particles have been considered. The mean force potential and the memory function are obtained from a suitable molecular dynamics simulation at infinite dilution. Radial distribution functions, velocity autocorrelation functions, and self-diffusion coefficients of the solute at different concentrations are calculated. The comparison with the results obtained from molecular dynamics simulations of the full systems allows an analysis of the reliability of generalized Langevin dynamics as a function of the solute concentration.

Static and dynamic cross correlation in thermodynamically stable and unstable mixtures

‘Lennard-Jones liquid mixtures’ of various potential parameters for the unlike interaction have been investigated by molecular dynamics calculations. Systems of (μ = σ22/σ11 = σ12/σ11 = 1; v = ϵ22/ϵ11 = 2; v 12 = ϵ12/ϵ12/av) were considered. A variation of the 1–2 potential function has been studied in terms of the quotient v 12 = ϵ12/ϵ12/av with ϵ12/av = 1/2(ϵ11 + ϵ22) for the interval 0·5 ˇ v 12 ˇ 1>·2. Both the static and the dynamic cross correlations show a characteristic behaviour indicating ranges of thermodynamically stable and unstable systems. The corresponding cross correlation functions display a characteristic long-range tail for the unstable mixtures. Generally the dynamic cross correlation depends more strongly on the changes of the 1–2 interaction than the static one. However, both quantities agree in indicating the transition to unstable mixtures. Our value v 12/(lim) = 0·81 for the transition boundary is in excellent accordance with the estimates of recent Monte Carlo simulations of Naka...

Local composition in binary mixtures of Lennard-Jones fluids with differing sizes of components

Three Lennard-Jones binary liquid mixture systems obeying Lorentz-Berthelot rules, but having differing component sizes and energy parameters, have been used to calculate the local fractions of the two components around each type of central particle over the entire composition range from molecular-dynamics data. It is found that well-defined local fractions can be determined even in the case where the size difference between the particles is large. The results obtained are compared with values predicted by the Wilson and NRTL equations. It is confirmed that the NRTL equation gives satisfactory agreement only in the case of mixtures of components having the same size parameters. A new correlation is proposed by a modification of the NRTL equation. This correlation can predict reasonably well local-fraction data for all the Lennard-Jones liquid mixtures studied so far.

Molecular dynamics studies on the local composition in Lennard-Jones liquid mixtures and mixtures of nonspherical molecules

Molecular dynamics calculations have been carried out both for various kinds of mixtures of spherical molecules interacting pairwisely with Lennard-Jones(LJ) potential and for mixtures of diatomic molecules having two centers of LJ-type interaction. Radial distribution function(RDF) and internal energy have been calculated. The local composition(LC) around each kind of central molecule has been evaluated from RDF data. The effect of attractive interaction on LC and the validity of the Wilson and related equations for LC have been discussed.

Free energy of mixing, phase stability, and local composition in Lennard-Jones liquid mixtures

By the use of umbrella-sampling technique in the Monte Carlo method proposed by Torrie and Valleau, reliable data have been established for the Helmoholtz free energy of mixing in some selected models of Lennard-Jones liquid mixtures. The variational method in perturbation theory is found to account for these Monte Carlo data. Validity of some representative semiempirical theories is discussed and it is found that none of them can reproduce the present Monte Carlo results reasonably well. Finally the phase stability of the present models is discussed in terms of both the free energy of mixing and local composition values recently obtained from our molecular dynamics calculations.

Molecular dynamics simulation of the mutual and self diffusion coefficients in Lennard-Jones liquid mixtures

A molecular dynamics calculation has been attempted for the mutual diffusion coefficient in a Lennard-Jones liquid mixture utilizing about 200 000 timesteps and incorporating the contribution for the thermodynamic factor. The precision of the result is about 8 per cent, excluding errors arising from the N dependence of the coefficient. For the same mixture, a number of calculations have been made for the self diffusion coefficients D 1 and D 2 varying the total number of particles. A significant apparent N dependence is noted for D 1 and D 2 individually but the ration D 1/D 2 is constant.

Molecular dynamics studies of Lennard-Jones liquid mixtures. VI. Temperature, density, and unlike interaction dependencies in static and dynamic properties of binary equimolar mixtures

Molecular dynamics calculations have been made for pure fluids and binary equimolar mixtures each containing 108 Lennard-Jones particles. The purpose of the calculations is threefold. First, the effect of the attractive term on the dynamic properties of liquids has been examined at fixed temperature and number density with equimolar mixtures of three models in which different combining rules for the energy parameter are assumed. Next the temperature and density dependences in static and dynamic properties of Lorentz–Berthelot mixture have been investigated. The variation of the velocity autocorrelation function with temperature and number density has been examined in detail. The activation energy for self-diffusion at constant number density is almost independent of the strength of interparticle interaction and is estimated to be 0.35 kcal mol−1, which is comparable with that for argon. In spite of remarkable change in the pattern of velocity autocorrelation function in the density range studied, self-diffusion coefficient changes linearly with density. Finally, a preliminary calculation on the microscopic process of mixing has been described.

Molecular dynamics studies of Lennard-Jones liquid mixtures. V. Local composition in several kinds of equimolar mixtures with different combining rule

Local fractions of two components around each kind of central particle have been calculated for the purpose of obtaining detailed structural information on binary model mixtures from molecular dynamics data for three equimolar mixtures of Lennard-Jones fluids with different combining rules for the energy parameter. It was found that well-defined local fractions can be determined in each case and that they are different from the overall mole fractions in nonideal mixtures. The validity of empirical formulations for local compositions has been tested against the present results and it was suggested that the Boltzmann factor relation between local and overall compositions may be inadequate to describe relative configuration of two components around a central particle.

Molecular dynamics studies of Lennard-Jones liquid mixtures. IV. Further calculation on the behavior of one different particle as a model of real fluid systems

Molecular dynamics calculation has been made on Lennard-Jones liquid mixtures containing 107 solvents and one solute, the attractive term, size, and mass of which are all different from those of solvent for the purpose of simulating real fluid system. The results were compared with those of our previous studies to discuss which factor is effective in determining static and dynamic properties. It was found that, although the position of the first peak of the solvent–solute radial distribution function g12 is primarily dependent on the size of the solute, its height is much influenced by the strength of the attractive term. The attractive term and mass have also a small but nonnegligible effect on the velocity autocorrelation function and diffusion coefficient. A comparison of the present results with the diffusivity in real fluid systems has also been made.

Molecular dynamics studies of Lennard-Jones liquid mixtures. II. Mass and size dependence in the behavior of one different particle

Molecular dynamics calculations have been made for Lennard-Jones liquid mixtures consisting of 107 solvents and one solute. In order to examine the effects of mass and size of solute on the solvent structure around the solute and on the motion of solute, the mass or σ value of the Lennard-Jones potential assigned for a solute was chosen as either twice or half that for solvent, while the ε value for all solutes was assumed to be the same as that for solvent. Thermodynamic quantities, radial distribution functions, velocity autocorrelation functions, and self-diffusion coefficients were obtained. They were compared with those for the corresponding hard sphere system calculated by Alder et al. In some respects, characteristic behaviors of LJ solute were found to be different from those of the hard sphere. In contrast with the case of the hard sphere, the first peak of g12 becomes higher as the size of the solute decreases. The rate of increase in the self-diffusion of LJ solute with decrease in the size of the solute is not so large as that of hard sphere solute.

Molecular dynamics studies of Lennard-Jones liquid mixtures. I. Role of attractive term in the behavior of one different particle

Molecular dynamics calculations have been made for three kinds of fluid systems each containing 108 Lennard-Jones particles. In the first reference system, the values of the potential parameters for all the particles were assumed to be those of argon. In order to examine the effect of the attractive term, each particle (referred to as the solute) in the other two systems was assumed to have different values for the energy parameter of the potential, ε12. The ε12 value assigned was either twice or half that of the ε11 value for all the other particles (referred to as the solvent), while the σ value was common to all the particles. Both equilibrium and transport properties, as well as cooperative and relaxation phenomena, were calculated and discussed. Among others, the following important results were obtained. The position and height of the first peak of the solute–solvent radial distribution function change appreciably and systematically with ε12. The self-diffusion coefficient of the solute becomes larger as ε12 decreases, and in contrast to the somewhat gaslike motion of the 0.5ε solute, the oscillatory nature of the motion of the 2.0ε solute was clearly seen from the velocity autocorrelation function for each solute. The time dependence of the pair correlation functions and the correlation between solute and neighboring solvents were also investigated. The correlations of the motion of neighboring solvents with that of the central solute, especially of 2.0ε solute, were found to be unexpectedly large for the first neighbors as compared with those for the particles outside them.