On the chemical free energy of the electrical double layer

The free energy of interaction between colloidal particles due to the overlap of their double layers was traditionally calculated either for systems of arbitrary geometry interacting at constant surface potential or at constant surface charge or for parallel plates interacting under arbitrary surface conditions. An expression is obtained for the change in the chemical contribution to the free energy of the double layers during a general interaction, which allows the calculation (within the Poisson-Boltzmann formalism) of the interaction free energy for systems of arbitrary geometry and surface conditions. The change in chemical free energy depends not only on the values of the surface charge and potential at the final state but also on their values at each distance between infinity and the final state. A simple approximate expression for the change in the chemical free energy contribution is also proposed, which involves only the states at infinite and final distances. Its accuracy is tested for planar and parallel surfaces, with charges generated via the dissociation of surface groups.