Phase equilibria of systems considered in supercritical fluid extraction determined from perturbation theory

The residual chemical potential of a solute, which is the main characteristic of the phase equilibrium at conditions of supercritical fluid extraction of solids, is determined from the second-order perturbation expansion proposed for mixtures of non-spherical polar molecules. Intermolecular forces are described via the generalized Kihara pair potential with a permanent point dipole or quadrupole embedded in the centre of the hard core ascribed to each molecule. General expressions for ternary systems are given first. The average and molecular distribution functions are determined on the basis of the radial distribution functions (RDFs) of the hard sphere multicomponent system; the recently proposed method for determining RDFs in the hard sphere mixture is employed. In the case of the contribution of dispersion forces, the Barker-Henderson approximation is considered for the second-order term, whereas the second-order electrostatic contributions are approximated by employing the Gaussian overlap model. Values of the calculated residual chemical potential of a solute are compared with the simulation data for the infinitely diluted binary Lennard-Jones system and infinitely diluted ternary systems; fair agreement is found. When employing parameters of the Kihara polar molecules (adjusted to experimental orthobaric data) an increase in values of the residual chemical potential is found in comparison with those for Lennard-Jones systems.