Lennard-Jones mixture

M. J. Vlot, H. E. Huitema, A. d. Vooys, J. P. v. d. Eerden. Crystal structures of symmetric Lennard-Jones mixtures. J Chem Phys 707 4345, 1997. 

Potoff, J. J. Panagiotopoulos, A. Z., Critical point and phase behavior of the pure fluid and a Lennard-Jones mixture, J. Chem. Phys. 1998,109,10914—10920... 

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.

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]. 

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. 

Figure 10. Vapor-liquid equilibria for an argon-krypton mixture (modeled as a Lennard-Jones mixture) for the bulk fluid (R = >) and for a cylindrical pore of radius R = / /Oaa = 2.5. The dotted and dashed lines are from a crude form of density functional theory (the local density approximation, LDA). The points and solid lines are molecular dynamics results for the pore. Reprinted with permission from W. L. Jorgensen and J. Tirado-Rives, J. Am. Chem. Soc.

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). 

Vogelsang, R., Hoheisel, C., Paolini, O.V., and Ciccitti, G. Soret coefficient of isotropic Lennard-Jones mixtures and Ar-Kr system as determined by equilibrium molecural dynamics simulations. Phys. Rev. A, 1987, 36, No. 8, p. 3964-3974. 

Cracknell R F, D Nicholson and N Quirke 1994 A Grand Canomcal Monte Carlo Study of Lennard-Jones Mixtures in SUt Pores 2 Mixtures of Two-Centre Ethane with Methane Molecular Simulation 13-161-175. 

Demixing, Fig. 8 Log-log plot of the length scale C(z, t) of a thin film of a binary Lennard-Jones mixture between two flat planar walls D = 20 Lennard-Jones parameters apart plotted versus time, for two different values of z. Lennard-Jones parameters were chosen ffAA = = ft = 1, Sa4 = Egg = S = 1, S B = eI2,... 

Droplets. - Liquid droplets and curved hquid surfaces in general have been the subject of some attention by MD and MC for about 30 years. A recent example of a simulation in this category was carried out by Ikoshoji et al They gradually cooled binary Lennard-Jones mixtures until they crystallised into icosahedrons or fee structures, depending on the system size. 

In this paper, we review our experimental and simulation work [5-7] and include new results on the solid - liquid phase behavior of mixtures confined in nanopores. Dielectric relaxation spectroscopy (DRS) was used to study the experimental phase diagram of CClVCaHn mixtures confined in activated carbon fibers (ACF). Grand Canonical Monte Carlo (GCMC) simulations with the parallel tempering technique were used to model the freezing of Lennard-Jones mixtures in slit pores. Mixtures having a simple solid solution or... 

Figures 3 to 5 illustrate the effects of adding a dipole-dipole or quadrupole-quadrupole interaction (Eq. (3) or (4)) to one of the components in a binary Lennard-Jones mixture. In this case the Lennard-Jones parameters are chosen so that the reference system approximates an argon-krypton mixture (24) ...

Table 1 summarizes the classes of phase behavior found for these polar/nonpolar systems, using an argon-krypton reference system, and compares it with the behavior for simple nonpolar Lennard-Jones systems. An important difference between the two types of systems is that the Lennard-Jones mixtures do not form azeotropes, and appear to exhibit class II behavior only when the components have very different vapor pressures and critical temperatures (T j /Ta > 2). In practice, the liquid ranges of the two components would not overlap in such cases, so that liquid-liquid immiscibility (and hence class II behavior) would not be observed in Lennard-Jones mixtures (the only exception to this statement seems to be when the unlike pair Interaction is improbably weak). Thus, the use of theories based on the Lennard-Jones or other Isotropic potential models cannot be expected to give good results for systems of class II, and will probably give poor results for most systems of classes III, IV and V also. 

The polar/nonpolar mixtures studied here exhibit four of the six classes of behavior shown in Figure 2. Class V is presumably present also, but is indistinguishable from class IV because the location of the solid-fluid boundary is not calculated. For polar/nonpolar mixtures in which the reference system is a weakly nonideal Lennard-Jones mixture, increasing the dipole moment of the polar molecule causes a continuous transition among the classes. 

The former corresponds effectively to a one-component compressible polymer solution, while the character of a compressible binary mixture becomes more apparent at higher pressures in the vicinity of the triple line. The composition is held constant, and the temperature is varied. From Fig. 8 (b) we conclude that the composition of the coexisting phases remains almost constant in the temperature interval 0.75 < kiTje < 0.82 for both pressures. At low pressure, the nucleation barrier decreases monotonously with temperature as expected. At higher pressure, however, the nucleation barrier exhibits a non-monotonous dependence on temperature AG exhibits both a maximum and a minimum upon increasing temperature at fixed molar fraction. The inset compares the radial density distributions of the critical bubbles and planar interfaces at ksT/e = 0.7573. In both cases the solvent density at the center of the bubble is higher than at coexistence and there is an enrichment of solvent at the interface of the bubble. However, there are no qualitative differences in the structure, in agreement with the observation of Talanquer and co-workers [196] for binary Lennard-Jones mixtures. 

Lennard-Jones mixture 53, 81 Lennard-Jones parameters 67, 74, 78 Lennard-Jones particle 95 Lennard-Jones potential 22-24, 34, 67, 69 Line tension 196 LiouvUle equation 142 Liquid crystal 243... 

Kob, W. and Andersen H. C. 1995a. Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I The van Hove correlation function. Phys. Rev. E 51 4626-4641. 

Z. Tan, F. van Swol and K.E. Gubblns, Lennard-Jones mixtures in cylindrical pores, Molec. Phys., 62, 1213 (1987). 

Mejia, A. Pamies, J.C. Duque, D. Segura, H. Vega, L.F. (2005). Phase and interface behaviors in type-I and type-V Lennard-Jones mixtures Theory and simulations, f. Chem. Phys. 123, 034505 1-10. 

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