On the interaction of highly charged plates in an electrolyte: a correction

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Abstract
It is shown that the treatment of the interaction of electric double layers, as given by I. S. Sogami, T. Shinohara and M. V. Smalley (Molec. Phys., 1990, 71, 1251; 1992, 74, 599; 76, 1) contains errors and leads to incorrect results. These authors consider the interaction of parallel, identically charged plates with a surface potential that is independent of the distance between the plates. Surface charges are considered to be smeared out, and the electric field in the solution obeys the Poisson-Boltzmann equation. A weak attraction is found at large distances, and a strong repulsion at short distances. The authors stress that these results are in fundamental disagreement with results obtained in DLVO theory. Two types of error are described. When the plates are brought closer together at constant surface potential, the absolute value of the surface charge decreases. The non-electric (chemical) part of the effect of this decrease on the free energy of the system is not taken into account and this omission results in the calculated attraction. Furthermore, in the calculation of the free energy of the system, the ions are considered to make a non-electric contribution to the free energy of the order of -20kT per ion in 0·001 M solution. Unfortunately, the authors count fewer ions when the plates are close together, than when they are far apart, and this results in a wholly artificial calculated repulsion. When these errors are eliminated, the treatment as set up by the three authors reproduces the classical results, in particular a repulsion for all distances.