Argon, Lennard-Jones potential

A comparison of the pairwise contribution to the Barker-Fisher-Watts potential with the Lennard-Jones potential for argon is shown in Figure 4.38. 

For two argon atoms interacting via the Lennard-Jones potential, find ... 

The Lennard-Jones potential (so-called 6-12 equation) commonly holds for nonpolar molecules having no permanent dipole moment such as helium, argon, and methane [39-41]. Nevertheless, this potential can be expected to give an accurate description of long-range forces only for sufficiently long distance between two bodies [27,42]. 

We adopted a microcanonical ensemble MD method. The Lennard-Jones potential was used for the molecular interaction in the argon, OPLS potentials for methanol and water. We make a liquid slab with thickness of about 10 molecules at the center of the rectangular unit cell with periodic boundary conditions for all three dimentions. Figure 1 is a snapshot of a typical molecular configuration. Both sides of the slab are free liquid surfaces, on which molecules can evaporate and condense. The cell size along the surface normal is typically 100 A. and the surface area is -50 A x.50 A. The number of molecules is 1200 for argon, 864 for methanol, and 1024 for water. Other technical details are described elsewhere. ... 

After ealeulating discrete values of frequency and relaxation time for the polarization mode and different wave veetors, a continuous function for the relaxation time and dispersion relations can be established for eaeh mode. The results shown in Fig. 3 are obtained with the Lennard-Jones potential for Argon. An approach similar to that described above can be applied with the Stillinger-Weber potential for silieon. 

In the dense phase the intermolecular potential consists mainly of a two-body term to which small three-body contributions should be added. This problem is poorly documented for molecular systems, and the classic example remains that of argon where an effective two-body Lennard-Jones potential accounts fairly well for the thermodynamic data simply as a result of cancellation of errors. For vibrational energy relaxation one is not directly concerned with the whole intermolecular potential, but rather by its vibrationally dependent part. As mentioned earlier, three-body effects are not usually observable and may be masked by inadequate knowledge of the true potential. Nevertheless one can expect some simply observable solvent effects describable by changes of either the intermolecular or the vibrational potentials. 

When one adds the attractive van der Waals potential terms to the repulsive term, one obtains the Lennard-Jones expression for the intermolecular potential energy for a simple fluid such as an inert gas like argon. On the basis of the above, the Lennard-Jones potential function may be written... 

The following table gives the distribution function g r) for liquid argon at 85 K. The Lennard-Jones parameters for argon are a = 350 pm and = 118K. Estimate the Lennard-Jones potential at each value of r, and then use the Percus-Yevick equation to calculate the direct correlation function c(r) (equation (2.6.5)). Plot g(r) and c(r) against r. 

Figure 4 Time-dependence of temperature, uniaxial stress in the shock propagation direction, and volume calculated for an elastic-plastic shock in the [111] direction of a perfect Lennard-Jones crystal. After initial elastic compression, pltistic deformation occurs around 2 picoseconds into the simulation. Lennard-Jones potential parameters have been chosen for Argon. See text for details.

The differential cross sections of argon and neon have been measured by using refinements of the modulated molecular-beam technique. From these measurements the intermolecular potentials were found. These potentials differ significantly from the Lennard-Jones potential. The neon and argon potentials have different shapes and are not related by any simple scaling factor. The macroscopic properties have been calculated and are in reasonable agreement with experiment. The face-centered cubic structure was found to be the most stable crystal lattice for neon. The effect of the argon potential on the critical properties and saturation pressures is also discussed. 

Fig. 7. The second virial coefficient of argon. The results calculated from the scattering potential of Fig. 4 are indicated by the solid line and those of the Lennard-Jones potential, by the dashed curve. The experimental data are represented by squares, open circles, triangles, and solid circles. ... 

In the case of pure liquids numerical computations for the transport coefficients in argon, krypton, and xenon have been carried out by Palyvos et al. using a modified Lennard-Jones potential and the radial distribution function of Kirkwood, Lewinson, and Alder. The results, for instance for argon, represent percentages betw een 60 and 90% of the experimental values in a wide range of temperatures and densities. Besides, they agree with experiment better than the results derived from the Kirkwood of Rice-AIInatt types of theories. 

Figure A2.3.7 The radial distribution function g(r) of a Lennard-Jones fluid representing argon at 7 = 0.72 and p = 0.844 determined by computer simulations using the Lennard-Jones potential.

F. Characteristics of RDX Detonation Products. Volk (Ref 105) measured the fumes produced by the deton of RDX by gas chromatographic and chemiluminescence techniques. He identi-fiedHj, Nj, CO2, CO, HjO, CH4, CjHg C2H4 (chromatography) as well as NO and NO2 (chemiluminescence) in the products. Shots were made in air and in argon. As little as 4% air in Ar markedly increased the NO content of the products Kuznetsov et al (Ref 68) used Lennard-Jones potentials to compute the thermodynamic functions for most deton products over the range of 1500—4500°K for RDX at po of 0.1 to 1 g /cc... 

Figure 3.1. (a) Simulation box of argon atoms (interacting with each other via the Lennard-Jones potential) extracted from their trajectories. The position of an argon atom is depicted as it executes its natural motion in the liquid state at temp = 183 K. (b) This shows the trajectory of one tagged argon atom. 

Example 1.5 (SimpleN-Body Molecular System) We can now describe a molecular system consisting of N neutral atoms with pairwise Lennard-Jones potentials this could be used to model liquid argon or a similar inert system it is one of the first important simulations performed using a smooth classical potential [306, 387], The Lennard-Jones potential is... 

The Lennard-Jones potential includes a strongly repelling term proportional to which represents the excluded volume by an atom, and a long attractive tail of the form — l/rif, which models the effect of attractive interactions between induced dipoles due to fluctuating charge distributions. This potential provides reasonable simulation results for the properties of liquid argon. The parameters dij and Sij, the effective diameter and the depth of the potential well between different atoms, can be calculated by using the combination rules since... 

Early molecular dynamics simulations focused on spherically shaped particles in zeolites. These particles were either noble gases, such as argon, krypton, and xenon, or small molecules like methane. For these simulations, the sorbates were treated as soft spheres interacting with the zeolite lattice via a Lennard-Jones potential. Usually the aluminum and silicon atoms in the framework were considered to be shielded by the surrounding oxygen atoms, and no aluminum and silicon interactions with the sorbates were included. The majority of those studies have concentrated on commercially important zeolites such as zeolites A and Y and silicalite (all-silica ZSM-5), for which there is a wealth of experimental information for comparison with computed properties. 

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