An Ionic Wagner Number Predicts Reaction-Zone Localization in Thick Lithium-Ion Cathodes

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Abstract
Peukert exponents are widely used to summarize battery rate capability, yet they obscure the transition from nearly uniform intercalation across a porous cathode to strongly nonuniform through-plane current distribution. Here we derive an analytical Wagner-number criterion for this transition from a one-dimensional conduction-kinetics model. The ionic Wagner number governs the spatial current distribution, yielding a closed-form second-moment utilization factor and a mechanistic relation between Peukert response and cathode utilization. In its predictive form, the criterion is evaluated before field-resolved simulation from applied areal current density, cathode thickness, effective ionic conductivity, and the Tafel slope parameter; the specific interfacial area cancels from the mean-field expression. The framework establishes a single-mechanism conduction-Tafel ceiling of 1.5 for the Peukert exponent. Isothermal Doyle-Fuller-Newman simulations of a 75.6 µm NMC811 cathode show nearly uniform utilization through 2C discharge, with 93.5% capacity retention, followed by entry into reaction-zone localization as the predicted Wagner number approaches unity near 3C, where electrolyte depletion drives retention down to 45.5%. Balanced thickness scaling and literature data support the predicted Wagner number as an onset criterion for rate-dependent cathode underutilization.
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