Thickness of electrical double layer. Effect of ion size

The thickness of a single flat electrical double layer is considered. The electrostatic mean field and the excluded volume effect are taken into account. A simple statistical mechanical approach is used, where the particles in the solution are distributed over a lattice with an adjustable lattice constant. Different sizes of ions are described by different values of the lattice constant. Two measures are introduced that describe an effective thickness of the electrical double layer: a distance where the density of the number of counterions drops to a chosen fraction of its maximal value, and a distance defining a region that contains a chosen fraction of the excess of the counterions. It is shown that the effective thickness of the electrical double layer increases with increasing counterion size and with decreasing bulk concentration of ions, whereas increasing the surface charge may cause either a decrease or an increase of the effective thickness. It is shown that the description of the effective thickness of the electrical double layer by the Debye length differs qualitatively from the description presented for low bulk concentrations of ions