Finite-Size Charged Species Diffusion and pH Change in Nanochannels

Molecular transport through nanofluidic structures exhibits properties that are unique at the nanoscale. The high surface-to-volume ratio of nanometer-sized confined spaces renders particle interactions with the surface of central importance. The electrical double layer (EDL) at the solid-liquid interface of charged surfaces generates an enrichment of counterions and the exclusion of co-ions that lead to a change in their diffusivity. In addition, the diffusive transport is altered by steric and hydrodynamic interactions between fluid molecules and the boundaries. An extensive body of literature investigates molecular transport at the nanoscale. However, most studies account for ionic species as point charges, severely limiting the applicability of the results to "large" nanofluidic systems. Moreover, and even more importantly, the change of pH in the nanoconfined region inside nanochannels has been completely overlooked. Corroborated by experimental data, here we present an all-encompassing analysis of molecular diffusion from the micro- to the ultra-nanoscale. While accounting for finite-size ions, we compute self-consistently the pH inside the channels. Surprisingly, we found that the concentration of ions H⁺ can change by more than 2 orders of magnitude compared to the bulk, hugely affecting molecular transport. Further, we found that counterions exhibit both enrichment and exclusion, depending on the size of nanochannels. Achieving a greater understanding of the effective transport properties of fluids at the nanoscale will fill the gap in knowledge that still limits development of innovative systems for medicine and industrial applications alike.