APPLICATION OF THE KIRKWOOD-BUFF SOLUTION FORMALISM AND THE HARD-SPHERE EXPANSION METHOD WITH THE MODIFIED MEAN DENSITY APPROXIMATION TO PREDICT SOLUBILITY OF SOLUTES IN SUPERCRITICAL FLUIDS

The Kirkwood-Buff solution theory to give the relations between macros copic thermodynamic properties and the fluctuation integrals (G(ij)) w as utilized to predict solubility of solutes in supercritical fluids. The solvent-solute fluctuation integral (G(21)) in the derivation for solubility of solute is expressed in terms of the solvent-solvent fluc tuation integral (G(11)) using the hard sphere expansion (HSE) conform al solution method with the modified mean density approximation (MMDA) where the scaling factor (R-12) represents the ratio of the first pea k heights of the radial distribution functions for the mixture and the reference fluid having the mean density determined from the mean dens ity approximation (MDA). The values of R-12 were evaluated by consider ing it as an adjustable parameter and solving the Ornstein-Zernike equ ation with the hypernetted chain (HNC) closure, and were compared. It is shown that solubility can be evaluated with an equation of state fo r pure supercritical fluid, three molecular parameters, and the scalin g factor (R-12) without knowledge of critical properties of solutes, w hich can not be measured precisely for some organic solids. This model based on the molecular theory leads to better results in solubility c alculations than both the Peng-Robinson equation of state with the cla ssical mixing rule and the previous method with the original MDA inste ad of the MA IDA. It might be due to the superiority of the MMDA over the original MDA.