Comparison of exclusion volume corrections to the Poisson-Boltzmann equation for inhomogeneous electrolytes.

Comparisons are made of exclusion volume corrections to the Poisson-Boltzmann equation for the electric double layer next to a charged electrode. The exclusion volume terms treated are based mainly on (i) Langmuir type theories and (ii) the Bogoliubov-Born-Green-Yvon integral equations. The Langmuir type theories are modified to incorporate a distance of closest approach to the charged surface for comparison purposes. The theories are applied to the spherical electric double layer around a large macroion and the planar electric double layer. At high surface charge steric effects dominate when the Langmuir theories predict saturation in the counterion profile at and near contact, while the Bogoliubov-Born-Green-Yvon based theories predict layering in the same profile.