1208.1587 (Martin Z. Bazant)

Phase-Field Theory of Ion Intercalation Kinetics    [PDF]

Martin Z. Bazant

Interest in electrochemistry is surging, driven by new applications in energy conversion, water treatment, materials processing, and biotechnology. As geometries shrink to the nanoscale, the rate-limiting step is often ion intercalation (i.e. reversible insertion) into a host solid for transport or storage. The standard phenomenological model for electrode kinetics is the Butler-Volmer equation, which fits the current-voltage relation in many situations and can be justified (in certain limits) by the Marcus theory of charge transfer. Existing theories, however, provide little guidance as to the form of the exchange-current prefactor to account for configurational entropy, elastic stress, phase transformations, and other non-idealities arising in ion intercalation. This Account describes the development of a general variational formulation of Faradaic reaction kinetics for ionic solids and concentrated solutions. The theory is based on non-equilibrium thermodynamics, consistent with Cahn-Hilliard phase-field models for the solid host. Butler-Volmer and Marcus kinetics are reformulated for concentrated solutions using activity coefficients. The theory is applied to lithium insertion in transition metal oxides. For phase-separating solids, such as LiFePO$_4$ (LFP), the intercalation rate is enhanced by concentration gradients and elastic coherency strain. This causes exposed phase boundaries to propagate as "intercalation waves" at low current. Above a small critical current, homogeneous reactions are favored, which helps to explain the high rate capability of LFP nanoparticles. The theory also predicts similar phenomena in porous electrodes with phase-separating nanoparticles. Narrow reaction fronts with mosaic instabilities at low currents become broadened and limited by electrolyte diffusion at high currents.

View original: http://arxiv.org/abs/1208.1587