Binary Mixtures Of Lennard-Jones Fluids Research Articles

Choice of reference, influence of non-additivity, and present challenges in thermodynamic perturbation theory for mixtures.

This work revisits the fundamentals of thermodynamic perturbation theory for fluid mixtures. The choice of reference and governing assumptions can profoundly influence the accuracy of the perturbation theory. The statistical associating fluid theory for variable range interactions of the generic Mie form equation of state is used as a basis to evaluate three choices of hard-sphere reference fluids: single component, additive mixture, and non-additive mixture. Binary mixtures of Lennard-Jones fluids are investigated, where the ratios of σ (the distance where the potential is zero) and the ratios of ϵ (the well depth) are varied. By comparing with Monte Carlo simulations and results from the literature, we gauge the accuracy of different theories. A perturbation theory with a single-component reference gives inaccurate predictions when the σ-ratio differs significantly from unity but is otherwise applicable. Non-additivity becomes relevant in phase-equilibrium calculations for fluids with high ϵ-ratios or when the mixing rule of σ incorporates non-additivity through an adjustable parameter. This can be handled in three ways: by using a non-additive hard-sphere reference, by incorporating an extra term in the additive hard-sphere reference, or with a single-component reference when the σ-ratio is close to unity. For σ- and ϵ-ratios that differ significantly from unity, the perturbation theories overpredict the phase-equilibrium pressures regardless of reference. This is particularly pronounced in the vicinity of the critical region for mixtures with high ϵ-ratios. By comparing with Monte Carlo simulations where we compute the terms in the perturbation theory directly, we find that the shortcomings of the perturbation theory stem from an inaccurate representation of the second- and third-order perturbation terms, a2 and a3. As mixtures with molecules that differ significantly in size and depths of their interaction potentials are often encountered in industrial and natural applications, further development of the perturbation theory based on these results is an important future work.

Transition from single-file to Fickian diffusion for binary mixtures in single-walled carbon nanotubes

The transition from single-file diffusion to Fickian diffusion in narrow cylindrical pores is investigated for systems of rigid single-walled armchair carbon nanotubes, solvated with binary mixtures of Lennard-Jones fluids (Ar/Ne, Ar/Kr, and Ar/Xe). A range of effects is examined including the mixture concentration, the size ratio of the two components, and the nanotube diameter. The transition from single-file to Fickian diffusion in varying carbon nanotube diameters is analyzed in terms of the Fickian self-diffusivity and the single-file mobility of the mixture components. It is found that the single-file to Fickian carbon nanotube transition diameter is a unique property of the individual molecule's diameter and remains unchanged regardless of the mixture composition. In applications of binary mixtures, each component may crossover from single-file to Fickian diffusion in a different carbon nanotube diameter, giving rise to bimodal diffusion in some nanotubes. This transition allows for one species to diffuse in single-file while the other diffuses by a Fickian mechanism, yielding orders of magnitude difference between the self-diffusional rates of the two molecules. This phenomenon might be further extended to alter the diffusional motion of molecules in nanoporous materials.

Phase equilibria of binary mixtures by molecular simulation and cubic equations of state

Molecular simulation data were used to study the performance of equations of state (EoS) and combining rules usually employed in thermodynamic property calculations. The Monte Carlo method and the Gibbs ensemble technique were used for determining composition and densities of vapor and liquid phases in equilibrium for binary mixtures of Lennard-Jones fluids. Simulation results are compared to data in the literature and to those calculated by the t-PR-LJ EoS. The use of adequate combining rules has been shown to be very important for the satisfactory representation of molecular simulation data.

Second-order Percus Yevick theory for mixtures of Lennard-Jones fluids

The second-order integral equation formalism of Attard, applied recently, with good results, to one-component hard spheres and Lennard-Jones fluids, is applied to some binary mixtures of Lennard-Jones fluids. Comparison with molecular dynamic simulations of the pair correlation functions shows that this method is also quite accurate for mixtures. This is true not only when the Lorentz–Berthelot mixing rules are obeyed but also when there are substantial deviations from these rules.

Integral equation theory for Lennard-Jones fluids: The bridge function and applications to pure fluids and mixtures

The pure Lennard-Jones fluid and various binary mixtures of Lennard-Jones fluids are studied by both molecular dynamics simulation and with a new integral equation which is based on that proposed by Duh and Haymet recently [J. Chem. Phys. 103, 2625 (1995)]. The structural and thermodynamic properties calculated from this integral equation show excellent agreement with simulations for both pure fluids and mixtures under the conditions which we have studied. For mixtures, the effect of deviations from the Lorentz-Berthelot (LB) mixing rules for the interaction parameters between unlike species is studied. Positive deviations from the nonadditivity of the molecular cores leads to an entropy driven tendency for the species to separate. This tendency persists even in the presence of a deviation from the LB rule for the energy parameter which enhances the attraction of the unlike species. On the other hand, in the case of negative deviations from nonadditivity, the tendency for association may be either energy or entropy driven, depending on the size ratio.

A simple expression for radial distribution functions of pure fluids and mixtures

A simple expression for the radial distribution function (RDF) of pure fluids and mixtures is presented. It satisfies the limiting conditions of zero density and infinite distance imposed by statistical thermodynamics. The equation contains seven adjustable parameters; they have been fitted to extensive literature data of RDF’s for a Lennard-Jones fluid at different values of temperature and density. These in turn have been expressed as functions of reduced temperature and density, thus allowing a complete parametrization with respect to these variables using 21 parameters altogether with fairly good accuracy. The values of the reduced pressure and internal energy calculated by numerical integration of the completely parametrized equation compare fairly with literature molecular dynamics simulation results. The capability of the expression to fit to RDF’s of mixtures has been checked against some of the extensive RDF simulation data of binary mixtures of Lennard-Jones fluids with different diameters available in the literature. Data pertaining to different molar fractions as well as to different εAA/εBB ratios have been considered, and the agreement between calculated and simulation curves has resulted satisfactory. The proposed expression can be used to calculate by integration related quantities such as compressibility, internal energy, pressure and, using the Kirkwood–Buff theory, the chemical potentials and partial molar volumes of the components of mixtures for which RDF data are available.

A direct method for determination of chemical potential with molecular dynamics simulations

A new direct method for the determination of chemical potentials from molecular dynamics simulations is proposed. This paper focuses on development and testing of the method for binary mixtures of Lennard-Jones fluids. The proposed method uses a semipermeable membrane to mimic an osmotic experiment. The excess chemical potential is obtained directly from the osmotic pressure that develops across the membrane and the equilibrium mole fraction of the component to which the membrane is permeable. The method is capable of accurate determination of the chemical potential of either component in the mole fraction range 0·2 < xi < 1. The Gibbs-Duhem equation can be used in conjunction with the individual component simulations in the above range to obtain the chemical potentials and the excess free energy over the entire composition range. The new method was tested for Lennard-Jones mixtures of various size and energy ratios by direct comparison of chemical potentials and excess free energies obtained from the osm...

Computer simulation results for thermodynamic excess properties in fluid mixtures II. Effects of energy parameter differences in simple binary mixtures

This paper reports results from isothermal-isobaric molecular dynamics simulations of binary mixtures of Lennard-Jones fluids. The simulations were performed for size-parameter ratios in the range 1ˇ-σ BB /σ AA ˇ-1·5 and energy-parameter ratios 1ˇ-e BB /e AA ˇ-2. The principal results are excess Gibbs free energies, excess enthalpies, and excess volumes, which are used to test a first-order perturbation theory based on hard sphere mixtures.

Computer simulation results for thermodynamic excess properties in fluid mixtures

This paper reports results from isothermal-isobaric molecular dynamics simulations of binary mixtures of Lennard-Jones fluids. The simulations were performed at several component size ratios in the range 1 ˇ- σ BB /σ AA ˇ- 2 and at three pressures. The principal results reported here are excess Gibbs free energies g E, excess volumes v E, and excess enthalpies h E. These new results do not coincide with previous Lennard-Jones simulations because of the extensive size and pressure ranges studied and because of the accuracy attained in the values for g E. The simulation data are used to test a recent revision of thermodynamic perturbation theory based on hard-sphere mixtures.

Molecular-dynamics studies of binary mixtures of Lennard-Jones fluids with differing component sizes

Molecular-dynamics calculations have been carried out for six pure liquids and three binary mixtures of Lennard-Jones fluids with differing component sizes and attractive interactions. Internal energies, radial-distribution functions, velocity autocorrelation functions and self-diffusion coefficients have been calculated and are discussed together with our previous results. The three mixtures obey the Lorentz-Berthelot rules and show endothermic mixing. The excess internal energy Δ U E of mixtures with equal-sized components is symmetrical with respect to the mole fraction, but those for mixtures of different-sized components become asymmetrical. A comparison is made between the present Δ U E data and those for real mixtures.

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.

The chemical potential in non-ideal liquid mixtures

We report Monte Carlo calculations for two non-ideal binary mixtures of Lennard-Jones fluids A and B. In the first the molecules have the same diameter but different well depths, eAA = 2eBB . In the second the well depths are the same but the diameters differ, (σ AA /σ BB )3=2·144. The chemical potentials of both components are obtained over the entire range of compositions, using a modified test particle method called f-g sampling. The simulation data are used to test a variety of mixture theories based on both the n-fluid idea and on a perturbation expansion about a mixture of hard spheres. Of the n-fluid theories the van der Waals 1- and 2-fluid theories are best in general. However, none of the n-fluid theories give good results when the molecular size ratio parameter (σ AB /σ BB )3 differs from unity by more than about 30 or 40 per cent. When the molecules are appreciably different in size the Leonard-Henderson-Barker (LHB) and Lee-Levesque (LL) forms of hard sphere perturbation theory are both much ...

The structure and surface tension of the liquid-vapour interface near the upper critical end point of a binary mixture of Lennard-Jones fluids

We present the results of calculations of the density profiles, relative adsorption and surface tension of the liquid-vapour interface of a binary mixture of Lennard-Jones fluids on a path of constant temperature and varying composition which passes through the consolute point for liquid-liquid separation but lies entirely in the two phase region. Our calculations are based on a square gradient approximation to the free energy functional of the inhomogeneous fluid. For bulk liquid concentrations x 1≲0·5 the density profile of species 1, the more volatile component, exhibits a maximum in the interface indicating pronounced surface segregation. The relative adsorption Г1,2 is positive for x 1≲0·66 and negative for larger x 1, i.e. the system exhibits an aneotrope. Our analysis suggests that it may be more useful to focus attention on the ratio Г1,2/x 1 than Г1,2 itself. We comment on recent attempts to measure Г1,2 for such interfaces. Our results for the surface tension in the vicinity of the critical end ...

The structure and surface tension of the liquid-vapour interface near the upper critical end point of a binary mixture of Lennard-Jones fluids

We present the results of calculations of the density profiles, relative adsorption and surface tension of the liquid-vapour and liquid-liquid interfaces of a binary mixture of Lennard-Jones fluids for a second path through the critical end point. This path consists of the triple point line in the three phase region and a path of constant critical composition and varying temperature in the two phase region. In the three phase region the mixture exhibits a first order Cahn wetting transition at a temperature T w which is a few degrees below the critical end point, T c. For temperatures T<T w the density profiles for the two liquid-vapour interfaces, αβ and αγ, are qualitatively different and the relative adsorption Г1,2 is positive at the αγ interface and negative for the αβ interface. At T = T w, where the intermediate liquid phase, β, completely wets the αγ interface, Г1,2 changes discontinuously for αγ but varies continuously for the αβ and the liquid-liquid (βγ) interfaces. The temperature derivative of the surface tension of the αγ interface is discontinuous at the wetting transition. At the critical end point the αγ and αβ surface tensions merge smoothly into the α, βγ surface tension in agreement with Widom's predictions. By analysing our results in terms of number-concentration variables we show that concentration fluctuations are important in determining the behaviour of the liquid-vapour surface tension as well as the liquid-liquid surface tension. We find that T c - T w depends rather sensitively on the parameters and mixing rule which characterize the intermolecular potentials.

Surface segregation and surface tension at the liquid–vapour interface of a binary mixture of Lennard-Jones fluids

We have calculated the surface segregation C(z) and the surface tension for the planar liquid–vapour interface of a binary mixture of Lennard-Jones fluids at various concentrations and temperatures. Calculations are based on the square-gradient approximation for the Helmholtz free-energy functional. For parameters appropriate to argon and krypton “argon” is preferentially adsorbed at all concentrations and the adsorption is particularly pronounced for small “argon” concentrations and at low temperatures. The magnitude and concentration dependence of the surface tension γ is only weakly dependent on C(z); γ depends rather on a contribution γNN which involves the total density profile N(z). By approximating γNN we derive the Bhatia–March relation which relates the surface tension to the isothermal compressibility of the bulk liquid mixture. We also derive a formula for (∂γ/∂x)x= 0, where x is the concentration of one of the species, which should provide insight into the factors which determine adsorption in dilute mixtures.

Theory of the liquid-vapour interface of a binary mixture of Lennard-Jones fluids

We present results of calculations of the equilibrium surface tension and density profiles for the liquid-vapour interface of a binary mixture of Lennard-Jones 12-6 fluids. The calculations are based on a density-functional theory for the Helmholtz free energy of the inhomogeneous mixture. This is a ‘microscopic’ generalization of the van der Waals-Cahn-Hilliard theory for the interface of a binary mixture. Our calculations cover the full range of liquid-vapour coexistence and the whole range of concentration. We find a correlation between the excess surface tension of the mixture and the surface segregation (adsorption) of the species with the lower surface tension. The ways in which segregation and excess surface tension depend on the Lennard-Jones parameters of the pure components are briefly discussed. Our results for the excess surface tension of mixtures of Ar and N2 and Ar and CH4 are compared with experiment; the agreement is reasonable.

Equation of state of mixtures of simple fluids at high pressures

Recently Lee and Levesque have extended the Weeks-Chandler-Andersen pure fluid perturbation theory to mixtures and have compared the results to the Leonard-Henderson-Barker mixture theory. The results seem to favour the Leonard-Henderson-Barker theory. This and other previous comparisons of mixture theories have been mostly confined to the study of ‘zero pressure’ thermodynamic properties. In this paper we compare the Lee-Levesque, Leonard-Henderson-Barker and the van der Waals one-fluid theories to high pressure equation of state data for helium-xenon mixtures. This system is modelled by a binary mixture of Lennard-Jones fluids and the hard sphere reference system is characterized by the Grundke-Henderson hard sphere mixture radial distribution function. The Lee-Levesque theory compares favourably with experimental equation of state data up to pressures of 2000 atmospheres. The Leonard-Henderson-Barker and van der Waals one theories are satisfactory. Although the van der Waals one theory yields the poorest results, it does offer the advantage of having the greatest ease of computation. Previous theoretical and Monte Carlo calculations of mixture properties have assumed the geometric mean rule for the mixed interaction energy parameter, ε 12, with consequent disagreement with experimental results. We point out that ε 12 can be determined from mixed second virial coefficient data and use such improved determinations of ε 12. We show that this method yields significantly improved theoretical predictions.