A New Model for the Electrical Double Layer Interaction between Two Surfaces in Aqueous Solutions

A new theoretical model is developed to evaluate the total potential energy of interaction between two charged flat plates in aqueous solutions. Instead of using the Boltzmann distribution to predict the ionic concentrations of counterion and coion, which is not correct for small confined spaces, this modified model determines the ionic concentrations of counterion and coion based on the Poisson equation, the Nernst equation, and the mass conservation condition. Instead of the approximations used in the traditional model, the osmotic pressure is directly evaluated based on the ionic concentration distributions predicted by this new model. Finally, the total interaction energy is examined and compared with that predicted by the traditional model. It has been found that for high ionic concentration solutions, the traditional model tends to overestimate the total interaction energy due to the approximations employed in simplifying the osmotic pressure. However, for dilute solutions, the traditional model tends to underestimate the total interaction energy at small separation distance due to the misuse of the Boltzmann distribution in calculating the ionic concentration.