Modeling of surface vs. bulk ionic conductivity in fixed charge membranes

Abstract

A two-region model for describing the conductivity of porous fixed charge membranes is proposed. In the surface region, the conductivity is due to the mobile positive ions (counterions) around the negative fixed charges. In the pore center region, the conductive properties resemble those of the external electrolyte solution because the fixed charges are assumed to be effectively neutralized by the counterions in the surface region. Activation energies and surface diffusion coefficients are estimated by assuming that the counterion jump from a fixed charge group is the rate limiting process for surface transport. The barrier energy for this jump is calculated using a simple electrostatic model with two microscopic parameters, the sum of the counterion and fixed charge hydration radii and the local dielectric constant. The bulk conductivity is obtained from experimental data. The total membrane conductivity and the counterion transport number are then calculated as functions of the external solution concentration for several pore radii and membrane fixed charge concentrations. The results are compared with those given by the Donnan model for homogeneous membranes and by the numerical solution of a continuous model based on the Poisson-Boltzmann equation extended to finite size ions. The study of the membrane conductivity for a series of electrolytes allows to distinguish clearly between the mechanism characteristic of the bulk ionic conductivity and that of surface conductivity. The surface conductivity is found to be significant for narrow pores at low external solution concentrations.

Incorporating ionic size in the transport equations for charged nanopores

“…Experimentally, the G vs. c s curves are sometimes concave downwards in the high concentrations range. This is related to a reduction in the effective values for the ionic concentrations and diffusion coefficients inside the pore due to electrostatic interactions between the mobile ions and the pore fixed charges (Mafé et al 2003 and references therein).…”

Proton Conductivity Study of a Fuel Cell Membrane with Nanoscale Resolution

“…Perhaps the measured values represent the proton mobility in "bulk water" in the center of a pore which was predicted to be higher than near the pore walls where it is diminished by proton trapping at SO 3 À groups. [22] Depending upon the radial distribution of protons in Nafion pores the conductivity can vary by more than two orders of magnitude as the RH is increased from dry conditions to saturation. [23] For I DC = 0.2 nA through the single pore under an applied potential of 0.5 V the local resistance R of the membrane amounts to 2.5 10 9 W, and for a membrane thickness of d = 50 mm and an assumed conducting pore radius r = 10 nm this leads to a conductivity…”

Protein diffusion through charged nanopores with different radii at low ionic strength

“…4 is an activated process relatively slow compared with the bulk diffusion in the pore center. 19 As a first approximation, we assume that protein surface diffusion involves two processes that should occur sequentially. The protein has to enter first the surface region (in) from the central region and has to leave then the surface region (out) to the central region (Fig.…”

“…The charges on the pore surface act as effective barriers for these processes. 2,19 If the charges s (pore) and z (protein) have the same sign, the electrostatic repulsion makes it difficult the first process (in) because of the protein exclusion from the pore surface. On the contrary, if z and s have different signs, the protein may be adsorbed to the pore surface and the second process (out) is now inhibited.…”