The Gibbs Energy of an Electrical Double Layer

As the electrical double layer is formed spontaneously AG°(total) 0. 

The electric term AG°(el) equals, at constant p and T, the reversible woric of charging the surface against its potential  

The two terms at the right-hand side of Equation 9.20 may be taken in one term 

Because Oq and tpi have the same signs AG°(total) 0, as it should be for the spontaneous formation of the electrical double layer upon exposing the surface to the (aqueous) solution. 

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As depicted in Fig. 5, both the protein molecule and the sorbent surface are electrically charged. In an aqueous environment, they are surrounded by counterions, which, together with the surface charge, form the so-called electrical double layer. The Gibbs energy of an electrical double layer, may be calculated as the isothermal, isobaric reversible work required to invoke the charge distribution in the double layer... 

To calculate the electrostatic force, we first derive an expression for the Gibbs energy of an electric double layer. The energy of an electric double layer plays a central role in colloid science, for instance, to describe the properties of charged polymers (polyelectrolytes) or the interaction between colloidal particles. Here, we only give results for diffuse layers because it is simpler and in most applications only the diffuse layer is relevant. The formalism is, however, applicable to other double layers as well. 

The Gibbs energy of an electric double layer is negative because it forms spontaneously. Roughly, it increases in proportion to the square of the surface potential. 

The chemical energy of this ion is — Qi)),). Hence, the Gibbs energy per unit area for the formation of an electric double layer is -otpo. 

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