Extraction of Electrochemical Impedance Spectra from Physical Models

Abstract

Electrochemical impedance spectroscopy (EIS) is used widely to assist the understanding and interpretation of electrochemical cells, including batteries, fuel cells, electrolyzers, etc. The measured spectra, often illustrated in terms of Nyquist plots, are typically interpreted in terms of equivalent-circuit models. The present approach is to interpret EIS using physical models. In principle, virtually any physical model that represents physics and chemistry in terms of conservation equations can be written abstractly as Eqs. 1-2, where x is the state vector, u is the actuation vector, yis the observable vector, and p is the physical param eter vector. The model can be represented in locally linear state-space form as Eqs. 3-4, where the Jacobian matrices A, B, C, and Dcan be established from local linearization as Eq. 5. The present paper compares two approaches to determine the state-space matrices. Assuming one has access to the physical model’s source code, the matrices can be evaluated by direct computational differentiation. Alternatively, the matrices can be evaluated using Pseudo Random Binary Sequence (PRBS) perturbations. With these matrices in hand, using the Laplace transform between actuation to observable, the complex impedance (i.e., real and imaginary parts of the impedance at frequency ω) can be evaluated as Eq. 6, where I is the identity matrix. By extracting the EIS from a physical model, the relationships between measurable parameters, such as cell dimensions, ion mobilities, etc., and the complex impedance can be established. These relationships are much more physically meaningful than those that can be inferred from equivalent-circuit models. The presentation includes examples of EIS derived from pseudo-two-dimensional (P2D) Li-ion battery models. Figure 1