title: Theoretical Treatment and Numerical Simulation of Potential and Concentration Profiles in Extremely Thin Non-Electroneutral Membranes Used for Ion-Selective Electrodes.
abstract: The applicability of extremely thin non-electroneutral membranes for ion-selective electrodes (ISEs) is investigated. A theoretical treatment of potential and concentration profiles in space-charge membranes of << 1 μm thickness is presented. The theory is based on the Nernst-Planck equation for ion fluxes, which reduces to Boltzmann's formula at equilibrium, and on the Poisson relationship between space-charge density and electric field gradient. A general solution in integral form is obtained for the potential function and the corresponding ion profiles at equilibrium. A series of explicit sub-solutions is derived for particular cases. Membrane systems with up to three different ion species are discussed, including trapped ionic sites and co-extracted ions. Solid-contacted thin membranes (without formation of aqueous films at the inner interface) are shown to exhibit a sub-Nernstian response. The theoretical results are confirmed by numerical simulations using a simplified finite-difference procedure based on the Nernst-Planck-Poisson model, which are shown to be in excellent agreement.
authors.affiliation: Institute of Microengineering (IMT), SAMLAB, Federal Institute of Technology (EPFL STI), CH-2000 Neuchâtel, Switzerland.
authors.forename: W E
authors.initials: WE
authors.lastname: Morf
authors.forename: E
authors.initials: E
authors.lastname: Pretsch
authors.forename: N F
authors.initials: NF
authors.lastname: De Rooij