Density functional theory Lennard-Jones solid

Molecular dynamics and density functional theory studies (see Section IX-2) of the Lennard-Jones 6-12 system determine the interfacial tension for the solid-liquid and solid-vapor interfaces [47-49]. The dimensionless interfacial tension ya /kT, where a is the Lennard-Jones molecular size, increases from about 0.83 for the solid-liquid interface to 2.38 for the solid-vapor at the triple point [49], reflecting the large energy associated with a solid-vapor interface. 

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 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). 

Statistical mechanical theory and computer simulations provide a link between the equation of state and the interatomic potential energy functions. A fluid-solid transition at high density has been inferred from computer simulations of hard spheres. A vapour-liquid phase transition also appears when an attractive component is present in the interatomic potential (e g. atoms interacting through a Lennard-Jones potential) provided the temperature lies below T, the critical temperature for this transition. This is illustrated in figure A2.3.2 where the critical point is a point of inflexion of the critical isotherm in the / - F plane. 

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