Electrostatic Funneling in Ionic Transport Through Solid Porous Membranes*

Advancements in membrane fabrication techniques allowing precise control over pore size distribution, density, and surface chemistry, together with the development of higher resolution characterization methods, have renewed interest in studying ionic conduction in solid pores.

Recently, it has been shown that ionic concentration polarization (ICP) fundamentally hinders ionic transport through charged pores and impedes the scaling from the conduction efficiency of a single pore to a multiple pore membrane, which renders osmotic power extraction inviable. 

In this work, we revise the classical understanding of ICP in light of a concept termed "Electrostatic Funneling" (EF). EF is an out-of-equilibrium phenomenon originating from a mismatch between the ionic concentration inside and outside charged membranes. This effect is driven by the dual imperatives of maintaining near-electroneutrality within the pore while ensuring current continuity. 

Utilizing state-of-the-art all-atom Molecular Dynamics (MD) simulations with explicit water and Poisson-Nernst-Planck (PNP) modeling, we establish that EF is essentially the root cause of ICP. 

Our findings elucidate the conditions under which EF either impedes or enhances ionic transport, thereby offering a pathway for the rational design and optimization of membrane performance in various applications.