The Free Energy of a Diffuse Double Layer

The calculation involved here is conceptually a complex one, and for the necessarily detailed discussion needed to do it justice, the reader is referred to Verwey and Overbeek [5] and Kruyt [6] or to Hamed and Owen [10]. Qualitatively, what must be done is to calculate the reversible electrostatic work for the process  

Charged surface plus diffuse double layer of ions —  

One way of doing this makes use of the Gibbs equation (Eq. III-81) in the form (see also Section V-7A) 

the only surface adsorption is taken to be that of the charge balancing the double-layer charge, and the electrochemical potential change is equated to a change in o- Integration then gives 

The ordinary Debye-Huckel interionic attraction effects have been neglected and are of second-order importance. 

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