Gouy-Chapman theory of the diffuse electrical double-layer

Appendix 102 Gouy-Chapman theory of the diffuse electrical double-layer 

The French scientist Gouy and the British one Chapman developed, about 100 years ago, a rather complex but accurate theory for the diffuse doublelayer, which is a solution of the Poisson-Boltzmann 

These assumptions are rather severe but they do not seem to affect significantly the accuracy of the theory. The second assumption implies that ions have no volumes although they do have a radii which, moreover, increases with hydration. The last assumption is definitely not correct for water. The relative permittivity decreases much nearer the surface in addition, ions may dehydrate on a surface. 

Through the Gouy-Chapman theory, we can arrive to expressions for the electrostatic potential and ion concentration as a function of distance from a charged surface and finally - what is most important for applications - the expressions for the potential energy interaction between two double layers as a function of distance between the particles or surfaces. 

These are the potential electrostatic interactions due to the overlap of the diffuse double layers. 

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According to the Gouy-Chapman theory of the diffuse electric double layer (chapter 3 of [18]), for a uni-univalent electrolyte,... 

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