ON THE HELMHOLTZ FREE-ENERGY OF THE HIGHLY-CHARGED DOUBLE PLATES IN AN ELECTROLYTE

The theory of Sogami, Shinohara, and Smalley, concerning the interactions of highly charged parallel platelike colloidal particles, has been re-examined in the light of a recent paper by Levine and Hall. It has been shown that the calculations of Levine and Hall and Sogami et al. do not correctly deal with a simple but important term in the Helmholtz free energy. This term arises from a difference in the ''chemical part'' of the chemical potential between the plate surface and the solution. Both Sogami et al. and Levine and Hall effectively take this to be a purely kinetic term, but without considering the implication of this assumption on the surface potential, viz. the Nernst equation. When this is allowed for, the resulting Helmholtz free energy is found to satisfy a number of requirements demanded by Levine and Hall, though not satisfied by their own free energy or that of Sogami et al. In particular, the equilibrium condition that the free energy should attain its minimum value with respect to the number of adsorbed ions is shown to apply rigorously, for the free energy derived in this paper. Using our free energy, the paradox concerning different double layer forces for a constant surface charge and constant surface potential is also found to disappear. Our calculations support the view of Levine and Hall that, in accord with the classical DLVO theory, the electric double layer force is purely repulsive.