A novel differential equation approach to modeling ion size effects in the diffuse double layer

A new differential equation for the diffuse double layer is derived from the integral form of the hypernetted chain approximation (HNCA). Using the mean-spherical approximation for ion–ion interactions in the bulk, the resulting theory is found to be in excellent agreement with results obtained by the traditional solution of the HNCA integral equation for 1:1 electrolytes, provided the product of the Debye–Hückel reciprocal length and the ionic diameter is less than 1.5. The new theory is much easier to implement than the traditional method, and provides a rapid route to the estimates of the ion–wall correlation functions, diffuse layer potential profiles, differential capacities, and ionic surface excesses for a restricted electrolyte in a primitive solvent.