A PERCOLATION THEORY OF IONIC CLUSTERING IN ELECTROLYTES

We use the methods of continuum percolation theory to develop a consis tent, essentially analytic theory for the properties of the restricted primitive model (RPM) of electrolytes. Contributions to the thermodyn amic properties of this system are divided into two types; those from pairs of ions in the same cluster, and those from pairs in different c lusters (we call these IN and OUT contributions, respectively, for bre vity). We give exact expressions for the IN contributions as weighted integrals over the ionic pair connectedness functions. We give an exac t analytic solution for these functions in the generalized mean-spheri cal approximation. The OUT contributions are calculated by replacing t he system of ionic clusters by a system of charged hard spheres having the same statistics, and using the analytic results available for the latter system. Because the method requires no input from simulations, it can be readily adapted to treat many different electrolyte systems . Our method closely models simulation data for the thermodynamic quan tities of the RPM. An earlier note [J. Chem. Phys. 96, 9233 (1992)] sk etched our theory and compared our results to electrolyte data. Here w e present in detail the analytic basis for our method. In future paper s we expect to present detailed numerical results. (C) 1997 American I nstitute of Physics.