Effect of finite ion sizes in an electrostatic potential distribution for a charged soft surface in contact with an electrolyte solution

Abstract

We provide a theory to analyze the impact of finite ion sizes (or steric effect) in electrostatic potential distribution for a charged soft surface in contact with an electrolyte solution. The theory is based on a free energy model that appropriately accounts for the contribution of finite ion sizes as well as the structural characteristics of a soft interface, represented by a combination of a rigid surface and a fixed charge layer (FCL), with the FCL being in contact with an electrolyte solution forming an electric double layer (EDL). This FCL contains a particular kind of ion which is impermeable to the electrolyte solution, and this impermeability is quantified in terms of the corresponding Donnan potential of the "membrane" represented by the FCL-electrolyte interface. We find that consideration of the finite ion size increases the magnitude of this Donnan potential, with the extent of increase being dictated by three length scales, namely, the thickness of the FCL, the thickness of the electrolyte EDL, and the thickness of an equivalent EDL within the FCL. Such regulation of the Donnan potential strongly affects the distribution of the permeable electrolyte ions within the FCL, which in turn will have significant implications in several processes involving "soft" biological membranes.