Lennard-Jones binary mixture

In contrast to the Gibbs ensemble discussed later in this chapter, a number of simulations are required per coexistence point, but the number can be quite small, especially for vapor-liquid equilibrium calculations away from the critical point. For example, for a one-component system near the triple point, the density of the dense liquid can be obtained from a single NPT simulation at zero pressure. The chemical potential of the liquid, in turn, determines the density of the (near-ideal) vapor phase so that only one simulation is required. The method has been extended to mixtures [12, 13]. Significantly lower statistical uncertainties were obtained in [13] compared to earlier Gibbs ensemble calculations of the same Lennard-Jones binary mixtures, but the NPT + test particle method calculations were based on longer simulations. 

Liquid-Glass Transition in a Lennard-Jones Binary Mixture. 

Lennard-Jones binary mixture of particles is a prototypical model that describes glass-forming liquids [52,53,158,162-165]. The temperature and the density dependence of diffusivity D(T, p) have been obtained by computer simulations for the Lennard-Jones binary mixture in the supercooled state. To relate fragility of binary Lennard-Jones mixture to thermodynamic properties necessitates determination of the configurational entropy SC(T, p) as well as the vibration entropy Sv,h(T, p) at a given temperature and density. 

The enthalpy, internal energy and their excess quantities of the Lennard-Jones binary mixture have been determined using the PY approximation. The values obtained are in good agreement with the results of MC calculation. The enthalpy and isobaric heat capacity are calculated using the extended expression of the thermodynamic quantities in terms of pair correlation functions. 

In somewhat earlier work, Vlot et al. [229,230] made calculations of Lennard-Jones binary mixtures in which the pure components are identical but in which the unlike interactions have departures from the Lorentz-Berthelot combining rules. They use this as a model of mixtures of enantiomers. A variety of solid-fluid phase behavior can be obtained from the model. Both substitutionally ordered and substitutionally disordered solid solutions were found to occur. 

Das SK, Puri S, Horbach J, Binder K (2006) Spinodal decomposition in thin films molecular dynamics simulations of a binary Lennard-Jones fluid mixture. Phys Rev 73(031604) 1-15... 

Binary Mixtures—Low Pressure—Polar Components The Brokaw correlation was based on the Chapman-Enskog equation, but 0 g and were evaluated with a modified Stockmayer potential for polar molecules. Hence, slightly different symbols are used. That potential model reduces to the Lennard-Jones 6-12 potential for interactions between nonpolar molecules. As a result, the method should yield accurate predictions for polar as well as nonpolar gas mixtures. Brokaw presented data for 9 relatively polar pairs along with the prediction. The agreement was good an average absolute error of 6.4 percent, considering the complexity of some of... 

Similar calculations have been carried out for an equimolar binary mixture of associating Lennard-Jones particles with spherically symmetric associative potential [173]. The interaction between similar species is given by Eq. (87), whereas the interaction between different species is chosen in the form... 

Adsorption of hard sphere fluid mixtures in disordered hard sphere matrices has not been studied profoundly and the accuracy of the ROZ-type theory in the description of the structure and thermodynamics of simple mixtures is difficult to discuss. Adsorption of mixtures consisting of argon with ethane and methane in a matrix mimicking silica xerogel has been simulated by Kaminsky and Monson [42,43] in the framework of the Lennard-Jones model. A comparison with experimentally measured properties has also been performed. However, we are not aware of similar studies for simpler hard sphere mixtures, but the work from our laboratory has focused on a two-dimensional partly quenched model of hard discs [44]. That makes it impossible to judge the accuracy of theoretical approaches even for simple binary mixtures in disordered microporous media. 

From the quantitative point of view, the success of the cell model of solutions was more limited. For example, a detailed analysis of the excess functions of seven binary mixtures by Prigogine and Bellemans5 only showed a very rough agreement between theory and experiment. One should of course realize here that besides the use of the cell model itself, several supplementary assumptions had to be made in order to obtain numerical estimates of the excess functions. For example, it was assumed that two molecules of species and fi interact following the 6-12 potential of Lennard-Jones ... 

Figure 14 Master curve generated from mean-square displacements at different temperatures, plotting them against the diffusion coefficient at that temperature times time. Shown are only the envelopes of this procedure for the monomer displacement in the bead-spring model and for the atom displacement in a binary Lennard-Jones mixture. Also indicated are the long-time Fickian diffusion limit, the Rouse-like subdiffusive regime for the bead-spring model ( ° 63), the MCT von Schweidler description of the plateau regime, and typical length scales R2 and R2e of the bead-spring model.

Figure 18. (a) Response versus the dynamical structure factor for the binary mixture Lennard-Jones particles system in a quench from the initial temperature Ti = 0.8 to a final temperature T( = 0.25 and two waiting times t = 1024 (square) and = 16384 (circle). Dashed lines have slope l/Tf while thick hues have slope l/T (t ). (From Ref. 182.) (b) Integrated response function as a function of IS correlation, that is the correlation between different IS configurations for the ROM. The dashed fine has slope Tf = 5.0, where Tf is the final quench temperature, whereas the full lines are the prediction from Eq. (205) andF = F (T ) Teff(2") 0.694, Teff(2 ) 0.634, and 7 eff(2 ) 0.608. The dot-dash line is for t , = 2" drawn for comparison. (From Ref. 178.)... 

The concept of the ring effect has recently been applied to the diffusion of a binary mixture of Lennard-Jones particles in zeolite NaY (57). The first particle was varied in size while the second was held fixed. The results suggest that when the diameter of the larger sorbate is close to that of the 12-ring window in zeolite NaY, the larger sorbate will diffuse faster than the smaller one. 

Although there has not been much theoretical work other than a quantitative study by Hynes et al [58], there are some computer simulation studies of the mass dependence of diffusion which provide valuable insight to this problem (see Refs. 96-105). Alder et al. [96, 97] have studied the mass dependence of a solute diffusion at an infinite solute dilution in binary isotopic hard-sphere mixtures. The mass effect and its influence on the concentration dependence of the self-diffusion coefficient in a binary isotopic Lennard-Jones mixture up to solute-solvent mass ratio 5 was studied by Ebbsjo et al. [98]. Later on, Bearman and Jolly [99, 100] studied the mass dependence of diffusion in binary mixtures by varying the solute-solvent mass ratio from 1 to 16, and recently Kerl and Willeke [101] have reported a study for binary and ternary isotopic mixtures. Also, by varying the size of the tagged molecule the mass dependence of diffusion for a binary Lennard-Jones mixture has been studied by Ould-Kaddour and Barrat by performing MD simulations [102]. There have also been some experimental studies of mass diffusion [106-109]. 

The principal tools have been density functional theory and computer simulation, especially grand canonical Monte Carlo and molecular dynamics [17-19]. Typical phase diagrams for a simple Lennard-Jones fluid and for a binary mixture of Lennard-Jones fluids confined within cylindrical pores of various diameters are shown in Figs. 9 and 10, respectively. Also shown in Fig. 10 is the vapor-liquid phase diagram for the bulk fluid (i.e., a pore of infinite radius). In these examples, the walls are inert and exert only weak forces on the molecules, which themselves interact weakly. Nevertheless,... 

Throop, G. J., and R. J. Bearman Radial Distribution Functions for Binary Fluid Mixtures of Lennard-Jones Molecules Calculated from the Percus-Yevick Equation. J. Chem. Phys. 44, 1423—1444 (1966). 

It was shown by us J. Phys. Chem. B, 2006, 110, 12707) that the excess (deficit) of any species i around a central molecule j in a binary mixture is not provided by c,Gy (where c, is the molar concentration of species i in the mixture and Gy are the Kirkwood-Buff integrals) as usually considered and that an additional term, involving a volume F which is inaccessible to molecules of species i because of the presence of the central molecule j, must be included. In this paper, the new expression is applied to various binary mixtures and used to establish a simple criterion for preferential solvation in a binary system. First, it is applied to binary Lennard-Jones fluids. The conventional expression for the excess (deficit) in binary mixtures, c,Gy, provides always deficits around any central molecule in such fluids. In contrast, the new expression provides excess for one species and deficit for the other one. In addition, two kinds of binary mixtures involving weak (argon/krypton) and strong (alcohols/water) mtermolecular interactions were considered. 

The Gibbs technique has been used to predict vapor>liquid, liquid-liquid and osmotic equilibria for binary Lennard-Jones mixtures (2) phase transitions for fluids in pores (U), and phase equilibria for quadrupolar systems (Stapleton et al., Mol, Simulation, in press). 

A comparison of mesoscopic simulation methods with MD simulations has been performed by Denniston and Robbins.423 They study a binary mixture of simple Lennard-Jones fluids and map out the required parameters of the mesoscopic model from their MD simulation data. Their mapping scheme is more complete than those of previous workers because in addition to accounting for the interfacial order parameter and density profiles, they also consider the stress. Their mapping consists of using MD simulations to parameterise the popular mesoscale Lattice Boltzmann simulation technique and find that a... 

One important point we should stress, in conjunction with our current interest, is that similar slow relaxation as liquid water is observed in much simpler model systems The binary mixture of Lennard-Jones liquids, which consist of two species of particles, is now studied extensively as a toy model of glass-forming liquids. It is simulated after careful preparation of simulation conditions to avoid crystallization. Also, the modified Lennard-Jones model glass, in which a many-body interaction potential is added to the standard pairwise Lennard-Jones potential, is also studied as a model system satisfying desired features. 

Figure 1. Radial distribution functions calculated for a Lennard-Jones KrAr binary mixture (left) and molten LiF alloy (right).

About the type of local structure in the two simulated binary fluids one may judge from the shape of the partial radial distribution functions, shown in Fig. 1. Attractive and repulsive character of interactions between different and similar particles in LiF creates the situation when the A-B structure becomes dominant. This results in a well-pronounced peak in the Li-F distribution function that is located at a smaller distance than the corresponding peaks in the Li-Li and F-F radial distribution functions. In liquid KrAr mixture the local structure is completely different the sequence of partial radial distribution functions in the left frame of Fig. 1 reflects the difference in the Lennard-Jones parameter a in interatomic potentials. 

Figure 3. Generalized thermodynamic quantities calculated for a Lennard-Jones KrAr binary mixture (left) and molten LiF alloy (right) the generalized dilatation 6(k) the generalized linear thermal expansion coefficient ckt (fc) the generalized specific heat at constant volume Cy (fc) (the filled boxes at k = 0 correspond to the values obtained directly in MD simulations) and the generalized ratio of specific heats 7(k).

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