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.