Modified Poisson–Boltzmann equation in electric double layer theory based on the Bogoliubov–Born–Green–Yvon integral equations

Abstract

The lowest order equation of the Bogoliubov–Born–Green–Yvon system of integral equations is applied to the electric double layer to obtain a modified Poisson-Boltzmann equation. Charge oscillations are predicted for κ₀a > 1.720 (κ₀ bulk Debye–Hückel constant, a ionic diameter) and this critical value of κ₀a is shown to be related to that derived by Martuynov. Comparison is also made with the modified Poisson–Boltzmann equation based on the Kirkwood integral equation.