Gases Lennard-Jones, thermodynamic

The temperature-dependent second and third virial coefficient describe the increasing two- and three-particle collisions between the gas molecules and their accompanying increase in gas density. The virial coefficients are calculated using a suitable intermolecular por-tential model (usually a 12-6 Lennard-Jones Potential) from rudimentary statistical thermodynamics. 

The interface between the droplet and the gas is not discontinuous the average molecular density decreases over a narrow region from the liquid side to the vapor. When the size of the droplet becomes sufhctently small compared with the thickness of the transition layer, the use of classical thermodynamics and the bulk surface tension become inaccurate the Kelvin relation and Laplace formula no longer apply. This effect has been studied by molecular dynamics calculations of the behavior of liquid droplets composed of 41 to 2(X)4 molecules that interact through a Lennard-Jones (LI) intermolecular potential (Thomp.son et al., 1984). The results of this analysis are shown in Fig. 9.5, in which the nondimensional pressure difference between the drop interior and the surrounding vapor (Pd — p)rr / ij is... 

The thermodynamic functions of the solubilities of many gases in molecular liquids at room temperature have been tabulated [22]. The enthalpy of sorption is negative (exothermic) if the sorption energy exceeds the energy needed to make a hole of molecular size in the polymer or molecular liquid, and positive (endothermic) otherwise. In rough empirical correlations [21], S and AHS are usually related to the boiling temperature, critical temperature, or Lennard-Jones 6-12 potential energy parameter of the gas molecule. AHS can also be modeled atomistically [23-25], and by statistical thermodynamic equation-of-state theories (Section 3.E and Ref. [26]). 

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... 

An interesting question is, at what size nanosystems have properties like those of their macroscopic counterparts, i.e., when is the thermodynamic limit reached. The answer may depend on the property that is being considered. One property is the structure. Polak studied clusters for which the Lennard-Jones potential was used to model the interatomic interactions. This system is a realistic model for rare-gas clusters and for those, experiments have predicted that the crystalline face-centered cubic structure occurs for clusters with between some few 100s and some few 1000s of atoms (see ref. 15). On the other hand, calculations have predicted that the transition to a crystalline structure should not occur before the cluster size has reached at least several 10000s of atoms. 

Modern use of perturbation theory stems from the quantitative success of Barker and Henderson in 1967 in calculating ffie structure and thermodynamic properties of a homogeneous Lennard-Jones fluid. A few years later Toxvaerd" extended this work to the liquid-gas surface. It is based, not on (7.7), but on the division u(r) = Uo(r) + Ui(r) where... 

One of the simplest quantitative models was proposed by Horvath and Kawazoe (ref. 12) developed for adsorption in active carbons. It is employed in these studies to compare different zeolites, but, recognizing the differences between active carbons and zeolites, it is only a qualitative measure of pore dimensions. This method (denoted "H-K ) is based on statistical thermodynamics of the adsorbed gas molecules on surfaces. They use a 10-6 Lennard-Jones potential model to relate the free energy of a sorbed gas molecule to the distance between the gas molecule and solid surface. The smallest pore size is constrained by the diameter of the sorbent molecule (e.g., for nitrogen 3.65 A). Sensitivity increases with decreasing pore size. The comparison between the pore size predicted by the Kelvin and H-K theories is shown below in figure 1. 

An ab initio potential for the methane-water bimolecular system has been developed for use in modeling methane hydrates and in order to evaluate currently used statistical thermodynamic models. In this paper, an introduction to gas hydrates is first given, and the problem with the Lennard-Jones and Devonshire (LJD) approximation, typically used for modeling hydrates, is described. Second, the methodologies for generating the ab initio potential energy surface are described and results discussed. Third,... 

The most important test of our bimolecular potential is its use in statistical thermodynamic models for the prediction of phase equilibria. Monovariant, three-phase pressure-temperature measurements and invariant point determinations of various gas hydrates are available and are typically used to fit parameters in molecular computations. The key component needed for phase equilibrium calculations is a model of the intermolecular potential between guest and host molecules for use in the configurational integral. Lennard-Jones and Kihara potentials are usually selected to fit the experimental dissociation pressure-temperature data using the LJD approximation (2,4,6), Although this approach is able to reproduce the experimental data well, the fitted parameters do not have any physical connection to the properties of the molecules involved. 

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