Lennard-jones atoms

Fig. 6.11. The error in the free energy measured by several NEW implementations. Results are from Monte Carlo simulations of ion charging in water at 298 K. System 0 consists of a single Lennard-Jones atom with charge of +le and 216 SPC water molecules, and system 1 is the same but with the charge turned off. One work cycle contains 100 nonuniform steps in 7 from 0 to 1 and back. For a detailed description of the simulation, see [43]...

In what follows, we present new fluorescence spectra for pyrene in supercritical carbon dioxide. This is followed by molecular dynamics results on density augmentation in a mixture of Lennard-Jones atoms whose potential parameters were chosen so as to simulate pyrene and carbon dioxide. Finally, we compare the experimental and computational results, thereby obtaining information on the magnitude and extension of the density enhancements suggested by the experiments. 

Figure 3 Relationship between local and bulk densities at two supercritical temperatures (T7TC = 1.02, 1.145) for an infinitely dilute mixture of Lennard-Jones atoms with potential parameters chosen so as to simulate pyrene in carbon dioxide (see Table II). Molecular dynamics simulation.

The picture of a solute molecule stabilized in solution by a local environment where the solvent s concentration differs considerably from the bulk value is consistent with experiments and simulation. The encouraging agreement between the basic trends found in experiments and simulations should not obscure the fact that Lennard-Jones atoms are a pedestrian representation of the actual molecules studied in the fluorescence experiments. Caution must therefore be exercised when comparing simulations and experiments. At the same time, the very fact that such a crude model is able to capture the essential physics of the phenomenon under investigation lends further support to the notion that local density augmentations are common to all attractive supercritical systems. 

The computer simulations employed the molecular dynamics technique, in which particles are moved deterministically by integrating their equations of motion. The system size was 864 Lennard-Jones atoms, of which one was the solute (see Table II for potential parameters). There were no solute-solute interactions. Periodic boundary conditions and the minimum image criterion were used (76). The cutoff radius for binary interactions was 3.5 G (see Table II). Potentials were truncated beyond the cutoff. 

In particular, the potential functions for helium adsorbed on argon and for neon, argon, and xenon adsorbed on xenOn are shown here, and the theoretically predicted adsorption properties are compared with experiment, wherever possible. us (r ) for a Lennard-Jones atom interacting with a crystalline solid is given by the equation ... 

The conformational spaces of clusters of Lennard-Jones atoms were searched by application of the diffusion equation method for clusters of various sizes m from m = 5 to 55. For example, for m = 55, with 3m - 6 = 159 degrees of freedom, there are about 1045 local minima, and the global minimum (a MacKay icosahedron) was found in about 400 s on an IBM 3090 computer.205... 

Performance of the Diffusion Equation Method in Searches for Optimum Structures of Clusters of Lennard-Jones Atoms. 

J. Pillardy, L. Piela, Smoothing techniques of global optimization distance scaling method in searches for most stable Lennard-Jones atomic clusters, J. Comp. Chem. 19 (1998)... 

Figure 6, Profiles of the density as a fimction of z, the distance from the center of a parallel-walled slh. The vertical lines show the planes of solid that make up the pore. The density is shown for a conqjletely wet (part a) and a con letely dry (part b) surface. Both the fluid adsorbate and the solid adsorbent are made up of Lennard-Jones atoms with well-depth ratios % /% = 0.85 (part a) and 0.30 (part b). The simulations were performed under conditions such that each system was at bulk liquid-vapor coexistence for 0.7. From Ref [31], J. Stat. Phys.

Phase diagrams for strongly polar molecules in adsorbed films are still in the process of development even for the films on the basal plane of graphite [35]. These systems are made more complex because of the interplay of dipolar forces and molecular shape in determining preferred orientations relative to the surface and to neighboring molecules. A simulation of Stockmayer molecules (Lennard-Jones atoms with ideal dipoles attached) adsorbed on a featureless slit pore at low temperature [46] has shown that the dipoles tend to lie parallel to the surface in... 

The approach of Chaudhury el al,131 can in principle be combined with any of the search methods we have discussed in Section 2 (as long as the Hessian can be calculated relatively easy — this seems to be the critical point of the approach), but Chaudhury et a/.131 combined it with a genetic-algorithm search. Subsequently they demonstrated its validity for clusters of Lennard-Jones atoms. 

The first sections of this chapter are devoted to a description of the method and practical details for its implementation and utilization. Subsequent sections extend the method to the detection and simulation of double shock waves, which are ubiquitous in condensed matter. Example applications are presented for a Lennard-Jones atomic potential system (which can provide a description of solid Argon), an empirical potential model of crystalline silicon, and a tight-binding atomic potential for the chemically reactive explosive nitromethane (CH3NO2). 

Recently, two molecular dynamics simulations were published in which hexatic phases were observed for particular systems. In one [69], the phase was observed for a particular concentration in a two-component mixture of Lennard-Jones atoms, and in the other [70], the hexatic phase appeared for an inverse 12th-power potential at a particular value of the pressure. It is unclear why these special conditions should produce the hexatic phase, so extensions of these studies would appear to be necessary. 

We now proceed to more realistic models of adsorption systems. As a preliminary step, comparative simulations of various gases on various model surfaces should be mentioned. These include hard spheres at a soft repulsive wall [73] and hard spheres, soft repulsive spheres, and Lennard-Jones atoms between hard, soft repulsive, and soft attractive walls [741. For coverages greater than one monolayer, these simulations show that the local density n z) is relatively insensitive to the detailed nature of the interactions [74]. It is the repulsive cores of the adsorbed atoms that are the determining factor. This point is illustrated in Fig. 9. 

Several studies of the two-dimensional phase diagram for Lennard-Jones atoms have been reported [26,75]. In particular, the 2D liquid-vapor coexistence curve has been determined together with the critical temperature and density (/cT cr/e , - 1.316, = 0.304) (Fig. 10). These studies are relevant to mono-... 

And yet another example. A projectile hits a wall. The projectile is being composed of Lennard-Jones atoms (with some Sp and rg p, p. 287), we assume the same for the wall (for other values of the parameters, let us make the wall less... 

The graphitic surface is treated as stacked planes of Lennard-Jones atoms. The interaction energy between a fluid particle and a single graphitic surface is given by the 10-4-3 potential of Steele as ... 

The VP process is mainly affected by the behavior of the vdW interaction in the region of the well, since the VP rates are essentially determined by the overlap between a continuum wavefunction and a bound state, so that the only nonvanishing contribution originates from this region l So, a simple dumbbell model potential, consisting in a sum of Morse or Lennard-Jones atom-atom interactions is found to be adequatel" . Then, we write Vx-bc R ) (l) us... 

A model of immiscible Lennard-Jones atomic solvents has been used to study the adsorption of a diatomic solute [71]. Subsequently, studies of solute transfer have been performed for atoms interacting through Lennard-Jones potentials [69] and an ion crossing an interface between a polar and a nonpolar liquid [72]. In both cases the potential of mean force experienced by the solute was computed the results of the simulation were compared with the result from the transition state theory (TST) in the first case, and with the result from a diffusion equation in the second case. The latter comparison has led to the conclusion that the rate calculated from the molecular dynamics trajectories agreed with the rate calculated using the diffusion equation, provided the mean-force potential and the diffusion coefficient were obtained from the microscopic model. 

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