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

TL;DR

This study reveals that the breakdown of the Stokes-Einstein relation in ion transport is due to short-range Lennard-Jones interactions within hydration layers, not dielectric friction, providing a new microscopic understanding.

Contribution

It uncovers that electrostatic forces enhance LJ interactions rather than oppose ion movement, explaining the anomalous ion mobility in water.

Findings

Electrostatic forces act as net driving forces, not drag.

Short-range LJ interactions dominate energy dissipation.

LJ interactions are strongest for Li+ and weaken for larger ions.

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.