The interaction of ions in an ionic medium

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Abstract
The energy of interaction, W12(R), of two ions at separation R in an ionic medium is considered using Debye–Hückel (DH) theory for spheres of diameter a0. The ions are treated as spheres of dielectric constant D’ which may differ from that of the medium, say D; they have radii b and carry equal or opposite point charges. The electrostatic potential φ(r) in the ionic medium satisfies the DH equation ∇2φ=κ2φ. An exact, closed‐form expression is obtained for W12(R). In the limit of zero ionic strength (κ2→0) previous asymptotic results for R→∞, indicating Φ4/R4 +Φ6/R6+Φ7/R7+... corrections to Coulomb’s law, are reproduced; by contrast for κb≳0 the leading interaction term when R→∞ varies, as expected, like e−κR/DR but the first correction decays as κ2e−2κR/DR2, i.e., with a squared screening factor, and can be stated for two ions differing in charge, radii, etc. The same calculations show that, within DH theory, modeling the ions with D’≠D has no effects on the predicted thermodynamics.