Theory of coupled ion-electron transfer kinetics

TL;DR

This paper develops a comprehensive microscopic theory for coupled ion-electron transfer reactions, explaining their kinetics and applying it to lithium-ion batteries, notably predicting experimental behaviors without adjustable parameters.

Contribution

The paper introduces a novel theory of coupled ion-electron transfer that generalizes existing models and accurately predicts experimental data in battery systems.

Findings

Predicts curved Tafel plots with concentration-dependent reaction-limited current.

Reduces to Butler-Volmer equation for moderate overpotentials.

Accurately predicts exchange current in Li-ion batteries without adjustable parameters.

Abstract

The microscopic theory of chemical reactions is based on transition state theory, where atoms or ions transfer classically over an energy barrier, as electrons maintain their ground state. Electron transfer is fundamentally different and occurs by tunneling in response to solvent fluctuations. Here, we develop the theory of coupled ion-electron transfer, in which ions and solvent molecules fluctuate cooperatively to facilitate electron transfer. We derive a general formula of the reaction rate that depends on the overpotential, solvent properties, the electronic structure of the electron donor/acceptor, and the excess chemical potential of ions in the transition state. For Faradaic reactions, the theory predicts curved Tafel plots with a concentration-dependent reaction-limited current. For moderate overpotentials, our formula reduces to the Butler-Volmer equation and explains its relevance, not only in the well-known limit of large electron-transfer (solvent reorganization) energy, but also in the opposite limit of large ion-transfer energy. The rate formula is applied to Li-ion batteries, where reduction of the electrode host material couples with ion insertion. In the case of lithium iron phosphate, the theory accurately predicts the concentration dependence of the exchange current measured by {\it in operando} X-Ray microscopy without any adjustable parameters. These results pave the way for interfacial engineering to enhance ion intercalation rates, not only for batteries, but also for ionic separations and neuromorphic computing.