The effective direct correlation function: An approach to the theory of liquid solutions

An approach to the theory of liquid solutions based on the concept of the effective solute direct interaction is presented. The Ornstein–Zernike (OZ) matrix equation for an n-component mixture containing p solute components and q=n−p solvent components is rigorously transformed to an effective p-dimensional OZ equation explicitly involving just the solute components. Solvent effects enter the solute OZ equation through a pxp matrix of modified or effective solute direct correlation functions. The osmotic thermodynamic properties of the solution are related to the effective direct correlation function by formulas identical in structure to those which relate the corresponding thermodynamic properties of a pure fluid to the direct correlation function of the fluid. An analysis of the small wave vector k limits of several effective direct correlation functions important in the description of polar–ionic mixtures is given. The effective ion–ion direct correlation function for small k is proportional to a Coulomb potential shielded by a dielectric constant dependent on ion concentration. From the low ion density limit of this result one can recover Debye–Hückel theory. Thus the effective direct correlation function provides a convenient bridge between a first principles approach to electrolyte theory based on a molecular polar solvent and the usual continuum dielectric solvent model. From a similar analysis of the small k forms of the dipole–dipole and charge dipole effective direct correlation functions, one can demonstrate both Debye shielding and dielectric screening of the charge–dipole interactions and Debye shielding of the dipole–dipole interaction.