Lennard-Jones models density functional theory

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.

In view of the failure of the rigid sphere model to yield the correct isochoric temperature coefficient of the viscosity, the investigation of other less approximate models of the liquid state becomes desirable. In particular, a study making use of the Lennard-Jones and Devonshire cell theory of liquids28 would be of interest because it makes use of a realistic intermolecular potential function while retaining the essential simplicity of a single particle theory. The main task is to calculate the probability density of the molecule within its cell as perturbed by the steady-state transport process. 

The first theoretical work providing information on the Debye temperature (Go) of intermetallic clathrates dates back to the year 1999 [33]. Molecular dynamics calculations for the carbon-framework of type-I and type-II clathrates used a Lennard-Jones potential (later on also for Si-based clathrates [34]). 0d for Ci36 [35] and for Siiae [34] were estimated from the calculated elastic constant Cn applying the empirical relation Qd = —11.3964 + 0.3475 x C — 1.6150 x 10 X Cj 1. Moriguchi et al. [36] used an empirical bond-order potential developed by Tersofif for the calculation of several thermodynamic properties, including the heat capacity, for the type-I and type-II Si networks. From the heat capacity data in the temperature range from 0 to 150 K 6d was extracted applying the Debye-model. The heat capacity, Cy, was calculated by the density functional theory (DFT),... 

The use of nonlocal density functional theory (NLDFT) for modeling adsorption isotherms of Lennard-Jones (LJ) fluids in porous materials is now well-established [1-5], and is central to modem characterization of nanoporous carbons as well as a variety of other adsorbent materials [1-3]. The principal concept here is that in confined spaces the potential energy is related to the size of the pore [6], thereby permitting a pore size distribution (PSD) to be extracted by fitting adsorption isotherm data. For carbons the slit pore model is now well established, and known to be applicable to a variety of nanoporous carbon forms, where the underlying micro structure comprises a disordered aggregate of crystallites. Such slit width distributions are then useful in predicting the equilibrium [1-5] and transport behavior [7,8] of other fluids in the same carbon. 

We present simulation results for the packing for single center Lennard Jones models of adsorbed fluids such as methane, carbon thoxide and carbon tetrachloride at high pressure in carbon slit pores. These show a series of packing transitions that are well described by a lattice density functional theory model developed in our laboratory. By contrast, simulations show that these transitions are absent for a three-center model, whidi provides a more adequate representation of carbon dioxide. Analysis of the simulation results shows that alternations of flat lying molecules and rotated molecules can occur in this case as the pore widfli is increased. The presence or absence of quadrupoles has negligible effect on fliese hi -density structures. 

The droplet shape is obtained by solving the augmented Young equation with an appropriate anal5d ical form of derived from density functional theory with intermolecular interactions modeled by pairwise Lennard-Jones potentials (see Fig. 6.10b). Because > scales as for thick films, theory predicts the height of droplets to scale with the width according to a power law with exponent 1 /2 at saturation, as found in the experiments. Moreover, the model describes accurately the droplet shape off-coexistence (solid lines in Fig. 6.10a). 

Talanquer, V. Oxtoby, D. W. Nucleation in molecular and dipolar fluids interaction site model, J. Chem. Phys. 1995,103, 3686-3695. The phenomenological density functional theory is applied in conjunction with a simulation model including spherical objects interacting by Lennard-Jones and coulombic potentials. 

The thermodynamic integration scheme can be appUed to different models including coarse-grained, partide-based models of amphiphihc systems and membranes [133, 134] (e.g., soft DPD-models [135-137], Lennard-Jones models [138,139], or solvent-free models [140-142] of membranes) as well as field-theoretic representations [28]. It can be implemented in Monte Carlo or molecular dynamic simulations, as well as SCMF simulations [40-42, 86], field-theoretic simulations [28], and external potential dynamics [27, 63, 64] or dynamic density functional theory [143, 144]. 

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