The Ion-Continuum Interaction in Polar Liquids

After putting dV = 47ia2da, expanding, and integrating from a0 to °o, the result is  

As in Eqs. (19) and (20), the integration here is to oo, and so represents the infinite dilution case. In the relatively concentrated (0.1-1.0 M) solutions used in electrochemical kinetic experiments, the summation or integration should be taken over the appropriate number 

It follows that an equation of Bom type, but based on different physical principles (Eq. 56) is a good approximation for the continuum energy in dipolar liquids up to the onset of dielectric saturation at x = 3, provided it is integrated from an appropriate distance somewhat less than that of the superdipole center of the innermost solvation shell from the central ion. This corrected radius will differ from the distance from the ion to the dipole centers of the solvation shell under consideration by about 50% more than the radius of a water molecule. 

The Poisson equation should in any case not be applied where there is a gradient of E, e.g., in radial geometry121, see footnote on p. 207. 

Moelwyn-Hughes93 examined the ion-solvent interaction energy outside of the first coordination shell or Inner Sphere by a non-Born charging method using the same Inner Sphere induction term as Bemal and Fowler16 and Eley and Evans,92 i.e., -ae(EA)2/2 = with eA = 

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