L3.6 - Ionic-charge fluctuations

Summary

Because they have so many unexpected features and because they are kind of a hybrid with electrostatic double-layer forces, ionic-charge-fluctuation forces deserve separate consideration.

In the language of dielectric response, how is one to regard the movement of mobile ions?

First, through conductivity. An applied electric field creates an electric current in a salt solution. Formally, a conductivity σ appears in the form that varies with frequency as ∼ {iσ /[ω (1 − iωτ)]} in the dielectric permittivity ɛ(ω). In the limit of low frequency, ωτ → 0, this diverges as ∼ (iσ/ω). In that limit, a conducting material begins to appear as an infinitely polarizable medium, its mobile charges able to move indefinitely long distances.

In real life, we know this is not necessarily so. An electric field applied to a conducting medium can be maintained only as long as reactions or transfers of charges occur at the walls. The electrical outlet delivers and removes electrons; the electrodes react to remove or to produce ions. In real life we must recognize what goes on at the walls bounding a conducting medium. In the ideal “bad-electrode” limit there is no removing or producing a reaction at the walls. In that limit, under the action of a constant applied electric field, the charges pile up to create electrostatic double layers. When oscillating fields settle down at ω → 0 there is a spatially varying electric field across the space between the bounding walls.