Coupling Linear and Second-Harmonic Electrochemical Impedance Spectroscopy to Determine Half-Cell Physicochemical Processes from Measurements in Two-Electrode Cells

Abstract

Electrochemical impedance spectroscopy (EIS) is a widely used electroanalytical technique. A consequence of small amplitude modulation of the electrochemical interface is the linearization of inherently nonlinear processes, easing analysis, but giving up some mechanistic discriminating power. An example of this diminished discriminating power is degeneracy among linearized physics-based models [1] and even equivalent circuits [2]. The discriminating power of EIS is further degraded in situations where a two-electrode cell configuration is required, in which case, the total cell impedance is the sum of two half-cell impedances, plus an ohmic drop of the electrolyte. The summative nature of two-electrode EIS (a positive parity signal) makes the assignment of physicochemical processes to one electrode or the other extremely challenging without additional information. We have shown that second harmonic nonlinear electrochemical impedance spectroscopy (NLEIS), a natural extension of EIS achieved with somewhat larger modulations, can break model degeneracy and provide more information than EIS alone. [3,4] An added feature of second harmonic NLEIS acquired in a two-electrode cell is that the signal arises from the difference between each half-cell response (a negative parity signal). The complementary parity between EIS and second harmonic NLEIS, when analyzed with a common physics-based model, makes discriminating half-cell processes from two-electrode measurements feasible. To pave the foundation of NLEIS analysis, the first (EIS) and second harmonic (NLEIS) impedance responses of a simple electrochemical interface are considered, building from well-known Helmholtz double layer, Butler–Volmer kinetics, and solid state Fickian diffusion (to align with experimental lithium insertion chemistry). The linearized portion of this model produces a classic Randles circuit with Warburg impedance, whereas the second harmonic reveals a dependence on charge transfer symmetry and the second derivative of the open circuit voltage with insertion charge. We then adopted and extended Paasch’s macro-homogeneous porous electrode theory [5] to describe the linear and nonlinear impedance responses of a porous electrode. Half-cell models are then combined into whole-cell models to describe lithium-ion battery (LIB) systems. Experimentally, EIS and second harmonic NLEIS obtained with 1.5 Ah Samsung 18650 NMC|C cells are analyzed. Figure 1 demonstrates that our more sophisticated extended Paasch model can accurately fit the positive parity EIS and negative parity NLEIS data with a total of 15 meaningful physicochemical parameters (11 for the linear response and 4 additional for the nonlinear response). A data analysis pipeline is built based on these models to analyze a dataset that composed of 48 commercial LIBs cycled under four different aging conditions, and evaluated at 10%, 30%, and 50% state of charge (SOC). The co-evolution of EIS and NLEIS parameters from our analysis provides several insights, with perhaps the most interesting being the simultaneous increase in charge transfer resistance on the positive electrode and the breaking of charge transfer symmetry at the same time (for low SOC). These results demonstrate that the coupling of EIS and NLEIS can advance electrochemical impedance analysis with small changes from traditional EIS. Open-source software is described that leverages impedance.py to enable the easy implementation of EIS and NLEIS data analysis.