THE INTERACTION OF IONS IN AN IONIC MEDIUM

The energy of interaction, W-12(R), of two ions at separation R in an ionic medium is considered using Debye-Huckel (DH) theory for spheres of diameter a(0). The ions are treated as spheres of dielectric consta nt D' which may differ from that of the medium, say D; they have radii b and carry equal or opposite point charges. The electrostatic potent ial phi(r) in the ionic medium satisfies the DH equation del(2) phi=ka ppa(2) phi. An exact, closed-form expression is obtained for W-12(R). In the limit of zero ionic strength (kappa(2)-->0) previous asymptotic results for R-->infinity, indicating Phi(4)/R(4) +Phi(6)/R(6)+Phi(7)/ R(7)+... corrections to Coulomb's law, are reproduced; by contrast for kappa b>0 the leading interaction term when R-->infinity varies, as e xpected, like e(-kappa R)/DR but the first correction decays as kappa( 2)e(-2 kappa R)/DR(2), i.e., with a squared screening factor, and can be stated for two ions differing in charge, radii, etc. The same calcu lations show that, within DH theory, modeling the ions with D' not equ al D has no effects on the predicted thermodynamics.