A Deterministic Limit for Electrochemical Double-Layer Collapse: Deriving the Critical Steric Radius via Ionic Diffusion

The prediction of catastrophic cell degradation during extreme fast charging (XFC) of solid-state batteries and supercapacitors relies heavily on bulk Electrochemical Impedance Spectroscopy (EIS) and empirical C-rate charging profiles. While these macroscopic thermodynamic frameworks estimate internal resistance and state-of-health, they fail to deterministically define the spatial boundary where localized steric hindrance triggers an irreversible collapse of the Helmholtz double-layer. This paper introduces a continuum framework for solid-state electrochemistry. By modeling the electrode-electrolyte interface as a dynamic balance between ionic diffusion and electrostatic ion crowding (steric accumulation), we derive a universal critical steric radius (Rsteric). We show that catastrophic failure is not a probabilistic degradation but an exact limit where ion crowding overpowers the electrolyte's ionic diffusion capacity. We propose a blueprint for Active Charge Telemetry (ACT) to safely unlock maximum theoretical charge rates without triggering dendrite nucleation or dielectric collapse.