Resolving a Discrepancy in Diffusion Potentials, with a Case Study for Li-Ion Batteries

Overpotentials induced by liquid-phase composition variation can be important when electrochemical devices are operated at high current. The dominant models that describe such 'diffusion potentials' are Nernst–Planck (dilute-solution) theory and Onsager–Stefan–Maxwell (concentrated-solution) theory. Nernst–Planck flux laws emerge from Onsager–Stefan–Maxwell laws in the limit of high electrolyte dilution, and the material properties involved come into agreement. The two models yield different expressions for diffusion potentials in the dilute limit, however, because of a disparity in how electric potential is defined. As applied to lithium-ion batteries, concentrated-solution theory employs a voltage measured by a reference electrode reversible to lithium cations; this provides an unambiguous connection to a measurement process, albeit hypothetical on a local scale. After the Nernst–Planck voltage is related to such a properly referenced voltage, the discrepancy in diffusion potentials vanishes. The impact of using Nernst–Planck voltages instead of measurable voltages is illustrated by simulations of a lithium-ion battery. Terminal-to-terminal voltage is relatively unaffected, but the thermal response and internal states change significantly.