Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics

TL;DR

This paper develops a comprehensive nonequilibrium thermodynamics framework for chemical kinetics, unifying classical and phase transformation reactions, and extends models for electrochemical systems like Li-ion batteries.

Contribution

It introduces a general nonlinear reaction rate theory based on thermodynamic potentials, unifies phase boundary kinetics with classical models, and applies to battery materials.

Findings

Unified treatment of Cahn-Hilliard and Allen-Cahn equations

Generalized Marcus and Butler-Volmer kinetics for concentrated solutions

Applied theory to intercalation dynamics in LiFePO4 batteries

Abstract

Classical theories of chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations. In condensed matter, strong interactions alter chemical activities and create inhomogeneities that can dramatically affect the reaction rate. The extreme case is that of a reaction coupled to a phase transformation, whose kinetics must depend on the order parameter -- and its gradients, at phase boundaries. This Account presents a general theory of chemical kinetics based on nonequilibrium thermodynamics. The reaction rate is a nonlinear function of the thermodynamic driving force (free energy of reaction) expressed in terms of variational chemical potentials. The Cahn-Hilliard and Allen-Cahn equations are unified and extended via a master equation for non-equilibrium chemical thermodynamics. For electrochemistry, both Marcus and Butler-Volmer kinetics are generalized for concentrated solutions and ionic solids. The theory is applied to intercalation dynamics in the phase separating Li-ion battery material Li$_x$FePO$_4$.