Impedance of Battery Primary Particles with a Solid–Electrolyte Interphase: Physical Models and Electrical Circuit Analogs

Single-particle impedance measurements (SPIMs) have emerged as powerful tools for probing fundamental electrode processes in lithium-ion batteries. However, electrical circuit models used to interpret impedance data are often vague in their physical meaning. In this paper, we develop a physics-based impedance model for primary intercalation particles with the absence or the existence of the solid–electrolyte interphase (SEI). The model considers multiple physicochemical processes, including solid-phase diffusion, interfacial transfer, double-layer charging, and ion transport in a solid-electrolyte interphase and electrolyte solution. Electrical double-layer effects on the interfacial transfer kinetics are considered. Analytical expressions for the impedance are derived and approximated into two equivalent circuits with each element mapped to a specific physical process. Our study shows that two coupled semicircles emerge when the ratio of the ion-transfer time constant to the SEI-transport time constant exceeds a critical threshold. The high-frequency semicircle should be attributed to interfacial transfer and the mid- to high-frequency semicircle to ion transport within the compact layer of SEI. When the ratio of two time constants is lower than the threshold, a semicardicircle extending partially into the second quadrant appears, consistent with recent experimental observations. We introduce a time-constant space framework to explain the result, which enables the clear assignment of individual semicircles to their governing processes. Finally, a comparison with experimental SPIM data validates the model.