Thickness dependence of ion permeation in nanoscale films: fundamental trade-offs and opportunities.

Nanoscale films play a central role in biology and osmotic separations. Their water/salt selectivity is often regarded as an intrinsic property, favoring thinner membranes for faster permeation. Here, we highlight and quantify a fundamental limitation arising from the dependence of ion self-energy on film thickness, governed by its ratio to the Bjerrum length. The resulting relationship factors out this dependence from intrinsic ion permeability, which agrees well with available data and enables evaluation of the dielectric properties of ultrathin films, advancing the understanding of ion transport and the optimal design of membranes.