Exact results and theorems

There are a number of exact sum rules that the density profiles neqr electrodes have to satisfy. One set of these rules is due to the special long range nature of the Coulomb forces, which give rise to the screening of the charges in conducting media. The second set of sur mles originates from force balance requirements, and are the dynamic sum mles. 

The screening sum mles, are specific to Coulomb forces. Because of the very long range of the electrostatic forces, the stability of the system requires that all charges surround themselves with a neutralizing cloud. The surface charge satisfies the electroneutrality eondition 

Carnie and Chan [54] have shown that this normalization condition is also valid for the inhomogeneous systems of charged particles. 

For flat hard electrode surfaces there are number of other sum rules. A relevant sum rule for the calculation of density profiles in the electric double layer is the dipole rule [55] 

We integrate the force balance equation in the volume of a prism of the same section S but smaller height i, L, summing over all ionic and neutral species /, For central forces in the average over the surface S the pair interactions are cancelled out exactly. At the plane L these forces will contribute to the bulk pressure P. The statement of dynamic balance is that 

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