Electrokinetics of diffuse soft interfaces. 1. Limit of low Donnan potentials

The current theoretical approaches to electrokinetics of gels or polyelectrolyte layers are based on the assumption that the position of the very interface between the aqueous medium and the gel phase is well defined. Within this assumption, spatial profiles for the volume fraction of polymer segments (phi), the density of fixed charges in the porous layer (rho(fix)), and the coefficient modeling the friction to hydrodynamic flow (k) follow a step-function. In reality, the "fuzzy" nature of the charged soft layer is intrinsically incompatible with the concept of a sharp interface and therefore necessarily calls for more detailed spatial representations for phi, rho(fix) , and k. In this paper, the notion of diffuse interface is introduced. For the sake of illustration, linear spatial distributions for phi and rho(fix) are considered in the interfacial zone between the bulk of the porous charged layer and the bulk electrolyte solution. The corresponding distribution for k is inferred from the Brinkman equation, which for low phi reduces to Stokes' equation. Linear electrostatics, hydrodynamics, and electroosmosis issues are analytically solved within the context of streaming current and streaming potential of charged surface layers in a thin-layer cell. The hydrodynamic analysis clearly demonstrates the physical incorrectness of the concept of a discrete slip plane for diffuse interfaces. For moderate to low electrolyte concentrations and nanoscale spatial transition of phi from zero (bulk electrolyte) to phi(o) (bulk gel), the electrokinetic properties of the soft layer as predicted by the theory considerably deviate from those calculated on the basis of the discontinuous approximation by Ohshima.