A microscopic origin for the breakdown of the Stokes Einstein relation in ion transport

Abstract

Ion transport underlies the operation of biological ion channels and governs the performance of electrochemical energy-storage devices. A long-standing anomaly is that smaller alkali metal ions, such as Li$^+$, migrate more slowly in water than larger ions, in apparent violation of the Stokes-Einstein relation. This breakdown is conventionally attributed to dielectric friction, a collective drag force arising from electrostatic interactions between a drifting ion and its surrounding solvent. Here, combining nanopore transport measurements over electric fields spanning several orders of magnitude with molecular dynamics simulations, we show that the time-averaged electrostatic force on a migrating ion is not a drag force but a net driving force. By contrasting charged ions with neutral particles, we reveal that ionic charge introduces additional Lorentzian peaks in the frequency-dependent friction coefficient. These peaks originate predominantly from short-range Lennard-Jones (LJ) interactions within the first hydration layer and represent additional channels for energy dissipation, strongest for Li$^+$ and progressively weaker for Na$^+$ and K$^+$. Our results demonstrate that electrostatic interactions primarily act to tighten the local hydration structure, thereby amplifying short-range LJ interactions rather than directly opposing ion motion. This microscopic mechanism provides a unified physical explanation for the breakdown of the Stokes-Einstein relation in aqueous ion transport.