Ion transport in charged membranes with heterogeneous fixed charge densities  

A. Szymczyk1, B. Balannec1, A. Ghoufi2
1 Univ Rennes, Ecole Nationale Supérieure de Chimie de Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes) – UMR 6226, F-35000 Rennes, France
2 Univ Rennes, CNRS, IPR (Institut de Physique de Rennes) – UMR 6251, F-35000 Rennes, France

Nanopores are characterized by a high surface-to-volume ratio and dimensions comparable with the Debye length of the surrounding electrolyte solution, thus leading to surface-charge-governed ion transport with direct implications on the nanopore performance (conductance, selectivity, efficiency in electrokinetic energy conversion…).

In this work, we will focus on the specific transport properties of nanoporous membranes exhibiting heterogeneous fixed charge densities. Various examples will be considered including bipolar membranes, membranes with conical or hourglass-shaped nanopores (in this case the non-uniform pore geometry leads to a spatially inhomogeneous distribution of the volume charge density), etc.

A mechanistic picture will be provided within the scope of the Poisson / Nernst-Planck theory (combined with the Navier-Stokes equation in order to account for the electro-osmosis phenomenon) to explain the improved separation performance of such membranes compared with their homogeneously charged counterparts. For instance, we will show that membranes with hourglass-shaped nanopores can break the detrimental trade-off between solvent permeability and solute rejection and that membranes with a bipolar charge distribution can exhibit similar selectivities towards multivalent cations and anions when transport through the membrane is mainly controlled by diffusion.