Breakdown of the Nernst-Einstein relation in carbon nanotube porins

For over 100 years, the Nernst-Einstein relation has linked a charged particle's electrophoretic mobility and diffusion coefficient. Here we report experimental measurements of diffusion and electromigration of K⁺ ions in narrow 0.8-nm-diameter single-walled carbon nanotube porins (CNTPs) and demonstrate that the Nernst-Einstein relation in these channels breaks down by more than three orders of magnitude. Molecular dynamics simulations using polarizable force fields show that K⁺ ion diffusion in CNTPs in the presence of a single-file water chain is three orders of magnitude slower than bulk diffusion. Intriguingly, the simulations also reveal a disintegration of the water chain upon application of electric fields, resulting in the formation of distinct K⁺-water clusters, which then traverse the CNTP at high velocity. Finally, we show that although individual ion-water clusters still obey the Nernst-Einstein relation, the overall relation breaks down because of two distinct mechanisms for ion diffusion and electromigration.