Influence of Membrane Permittivity on Charge Regulation of Weak Polyelectrolytes End-Tethered in Nanopores

Artificial nanopores functionalized with weak polyelectrolytes are an interesting and important class of stimuli-responsive nanofluidic devices. So far, the effects of the dielectric properties of the supporting nanopore surface on the behavior of the nanopore are largely unexplored. Here, we theoretically investigate the influence that the dielectric mismatch between solvent and nanopore surface has on the charge regulation of weak polyelectrolyte brushes inside the nanopore. Our approach is based on a molecular theory that explicitly incorporates the coupling between molecular organization, physical interactions, and chemical equilibrium. It is further extended to consider both the dielectric properties of the supporting surface of the nanopore as well as those of the nanopore solvent and polymer layer. We find that the surface polarization plays a crucial role in modulating the charge and structure of the weak polyelectrolytes that are end-tethered to the inner wall of the nanopore. Likewise, the surface polarization influences the nanoscale transport through the nanopore. We demonstrate that different dielectric properties of the nanopore membrane can result in large changes in the local ion distribution and electrostatic potential around the ionizable groups of the weak polyelectrolytes, which simultaneously alter the charge and structure of the polyelectrolyte layer inside the nanopore. Our quantitative approach systematically reveals how various intrinsic and external factors such as bulk salt concentration, polymer grafting density, and polymer length influence the surface polarization and its effects on properties such as the charge of the polyelectrolyte layer. For specific conditions, we report a high sensitivity of translocating cargoes to the changes in the dielectric properties of the polyelectrolyte-coated nanopore surface.