Testing a modified model of the Poisson–Boltzmann theory that includes ion size effects through Monte Carlo simulations

Abstract

In this work we test the validity of a recent modified Poisson–Boltzmann (MPB) theory that includes ion size effects through a Langmuir-type correction. In particular, we will focus on an analytic charge–potential relationship accounting for such effects. Previous electric double layer (EDL) surveys have demonstrated that the inclusion of ions size in classical EDL theories, based on the Poisson–Boltzmann (PB) equation, can yield considerable improvements. In this sense, the theory we analyze assumes that, as a result of the excluded volume, the ion concentration close to the charged surface cannot exceed a fixed value determined by the close packing fraction. This leads to predictions of counterion concentrations (in this region) smaller than the corresponding PB values. In our opinion, it is worthwhile to test the validity of this novel theory. To this end, computer simulations appear as a useful tool for this kind of task. Our results prove that the above-mentioned analytical expression works fairly well for 1 : 1 electrolytes and large ions, and its predictions can be considerably improved with certain corrections in the estimation of some key parameters. However, it fails for multivalent electrolytes.