Ionic Interactions

E = z_i z_j/(4 pi epsilon₀r_ij)

Here epsilon₀ is the permittivity of free space. In a condensed phase, the interaction is weaker (provided r_ij is large enough so that the condensed phase can squeeze in between the two charges). This shielding is represented by a dielectric constant, which must be incorporated in the denominator of Coulomb's Law. If r_ij is very large, the macroscopic dielectric constant of the material is used. For smaller distances, the appropriate number is less clear; it may be smaller than the macroscopic dielectric constant, but larger than 1. Sometimes a distance dependent effective dielectric constant is invoked when the separation of the two charges is small.

The size of the interaction of discrete charges can be large. Furthermore, since the interaction depends on the inverse first power of the separation (rather than some higher inverse power), the interaction is of long range. For these reasons, this interaction tends to dominate the behavior of polymers (polyelectrolytes, ionomers, etc.) that bear many such charges.

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