A modified Poisson–Boltzmann equation in electric double layer theory for a primitive model electrolyte with size-asymmetric ions

Abstract

The modified Poisson–Boltzmann theory is extended to treat a primitive model electrolyte with unequal ionic radii in the neighborhood of a uniformly charged plane wall. The linear equation indicates that the transition from a damped exponential to a damped oscillatory asymptotic behavior in the mean electrostatic potential as the concentration is increased depends in a complicated manner on the ratio of the ionic radii, the ionic valences, and the ionic concentration. The nonlinear equation is solved numerically by a quasilinearization technique. Comparisons of the results are made with those from the Poisson–Boltzmann theory. A feature of the unequal radii model is its ability to predict a charge separation for an uncharged wall. The analysis is restricted to aj≤3ai where ai, aj are the radii of the smaller and larger ions, respectively.