Saddle-node bifurcation in interfacial morphology selects battery degradation phase

TL;DR

This paper models interfacial morphology in batteries using a nonlinear ODE that exhibits a saddle-node bifurcation, predicting stability limits and phase transitions relevant to battery degradation.

Contribution

It introduces a minimal nonlinear closure model capturing bifurcation behavior in battery interfaces, linking morphology to operational stability.

Findings

Identifies a saddle-node bifurcation separating stable and unstable phases.

Maps different battery configurations onto the model, showing proximity to the bifurcation point.

Predicts critical operational parameters consistent with available data.

Abstract

We propose a minimal nonlinear closure ODE for the dynamic active-area factor of a battery interface and show that it exhibits a saddle-node bifurcation when the smoothing rate saturates with surface roughness. The closure is the simplest physically motivated extension of a recently introduced single-fixed-point closure [C. Bae, in preparation (2026)]: u = K - u/(1 + alphau^2), where u = xi - 1 is the dimensionless excess active area, K the dimensionless drive, and alpha a single saturation parameter. The bifurcation occurs at K_c = 1/(2sqrt(alpha)), separating a smooth passivating phase from a morphologically unstable phase. Mapping four canonical anode configurations -- graphite, silicon composite, lithium metal, and anode-free Li/Cu -- onto the closure via end-of-cycling steady-state xi extracted from publicly available long-cycle data populates the stable branch with monotonically increasing K/K_c ratios: graphite (~0.01), silicon composite (~0.24), lithium metal (~0.73), and anode-free (~0.95). The anode-free configuration sits within 5% of the saddle-node threshold, predicting a vanishingly small operational stability window in current density, temperature, and electrolyte composition. We test three falsifiable predictions of the framework -- a critical current density, a critical temperature shift, and a mean-field critical-slowing-down exponent -- and find them broadly consistent with publicly available data. We argue that this near-critical position is universal to nucleation-controlled deposition on non-passivating substrates.