Electrochemical contribution to the interaction between semi-infinite charged plates

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Abstract
A general method of obtaining the electrochemical contribution to the free energy of interaction of dissimilar charged plates in an electrolyte solution is developed. This method is applicable to real systems in which there are specific adsorption effects. If for each interface there is a surface s, on the solution side of which the Poisson-Boltzmann equation holds, the information required is the way in which the charge on the solid side of s and the potential at s varies with the plate separation. This information can be found from the corresponding quantities for isolated surfaces in equilibrium with bulk solutions in which the concentrations of all species found in significant amounts on both sides of s satisfy the expression νjΔ log nb* i=νiΔ log nb* j where vi and nb i are the valence and bulk concentration of species i and Δ log nb* i is the value of log nb i for the solution concerned minus that for the solution in which the interactions take place. When the potential at s for an isolated surface can be identified with the zeta potential, the necessary information for such surfaces can be found from electrokinetic data. Alternatively it may be obtainable from titration data. An explicit expression is derived for the free energy of interaction ΔGE. Alternatively, this quantity can be found via integration of the force. The treatment requires hardly any knowledge of the nature of the inner regions of the double layer. The calculations required to apply it are no harder than those needed to calculate either constant-charge or constant-potential interactions.

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