Integral equations Lennard-Jones fluid model

An example drawn from Deitrick s work (Fig. 2) shows the chemical potential and the pressure of a Lennard-Jones fluid computed from molecular dynamics. The variance about the computed mean values is indicated in the figure by the small dots in the circles, which serve only to locate the dots. A test of the thermodynamic goodness of the molecular dynamics result is to compute the chemical potential from the simulated pressure by integrating the Gibbs-Duhem equation. The results of the test are also shown in Fig. 2. The point of the example is that accurate and affordable molecular simulations of thermodynamic, dynamic, and transport behavior of dense fluids can now be done. Currently, one can simulate realistic water, electrolytic solutions, and small polyatomic molecular fluids. Even some of the properties of micellar solutions and liquid crystals can be captured by idealized models [4, 5]. 

Wc saw in 5.5-5.7 that the potential distribution theorem was a valuable route to p(z) for a simple model for which p and p were known. It has not yet been used for the liquid-gas surface of a Lennard-Jones fluid. An older and less useful definition of p,(z) is in terms of the function g(ri2, z, Zj a) where a is a coupling parameter which turns on the interaction between molecules 1 and 2. By integrating from a = Otoa = litis possible to obtain a formally exact expression for p(z) but one which has the great disadvantage that g is not known as a function of a. Plesner and Platz used this route, with some simple approximation for g and for the equation of state of the liquid, to obtain profiles that are again similar to those of Figs 7.1 and 7.2. 

We propose the study of Lennard-Jones (LJ) mixtures that simulate the carbon dioxide-naphthalene system. The LJ fluid is used only as a model, as real CO2 and CioHg are far from LJ particles. The rationale is that supercritical solubility enhancement is common to all fluids exhibiting critical behavior, irrespective of their specific intermolecular forces. Study of simpler models will bring out the salient features without the complications of details. The accurate HMSA integral equation (Ifl) is employed to calculate the pair correlation functions at various conditions characteristic of supercritical solutions. In closely related work reported elsewhere (Pfund, D. M. Lee, L. L. Cochran, H. D. Int. J. Thermophvs. in press and Fluid Phase Equilib. in preparation) we have explored methods of determining chemical potentials in solutions from molecular distribution functions. 

Application of the GDI method to the coexistence lines requires establishment of a coexistence datum on each. A point on the vapor-liquid line can be determined by a GE simulation. At high temperature the model behaves as a system of hard spheres, and the liquid-solid coexistence line approaches the fluid-solid transition for hard spheres, which is known [76,77]. Integration of liquid-solid coexistence from the hard-sphere transition proceeds much as described in Section III.C.l for the Lennard-Jones example. The limiting behavior (fi - 0) finds that /IP is well behaved and smoothly approaches the hard-sphere value [76,77] of 11.686 at f = 0 (unlike the LJ case, we need not work with j81/2). Thus the appropriate governing equation for the GDI procedure is... 

---