A PRACTICAL APPROACH TO SOLVING THE DOUBLE-LAYER PROBLEM THAT INCLUDES EFFECTS OF ION SIZE AND CORRELATION

We consider the hypernetted chain approximation to the interaction fre e energy between charged walls in a monovalent electrolyte, emphasizin g the practical advantage of using the mean spherical approximation fo r the bulk ion correlation functions (the MSA theory). The decay rate of the interaction potential is largely determined by the bulk ion clo sure assumed, and in comparison with other closures, the asymptotic de cay of the MSA theory is more rapid than given by the classical Debye length, agreeing well with the decay in the hypernetted chain (HNC) an d the improved HNC (including bridge functions) models and with exact calculations. Common to both the MSA and HNC theories, the magnitude o f the asymptotic interaction potential is underestimated, due to the i naccuracy in the hypernetted chain wall-ion closure approximation. Bec ause of the semianalytical nature of the MSA closure, the MSA is numer ically more appealing for practical implementation in an analysis of e xperimental data. For such purposes the Poisson-Boltzmann theory and t he MSA theory provide lower and upper estimates, respectively, of the surface charge. By using both in comparison, one obtains a far better appreciation of the true value of the surface charge operating in real circumstances.