Methods—Understanding Porous Electrode Impedance and the Implications for the Impedance Analysis of Li-Ion Battery Electrodes

Abstract

Two of the main factors influencing the performance of Li-ion battery (LIB) electrodes are the kinetic losses due to the charge transfer resistance of the active material ( R ct ) and the ionic transport resistance in the electrolyte phase within the electrode pores ( R ion ). Seeking to increase the energy density of LIBs, ever higher active material loadings are applied, resulting in thicker electrodes for which R ion becomes dominant. As electrochemical impedance spectroscopy is commonly used to quantify R ct of electrodes, understanding the impact of R ion on the impedance response of thick electrodes is crucial. By use of a simplified transmission line model (TLM), we simulate the impedance response of electrodes as a function of electrode loading. This will be compared to the impedance of graphite anodes (obtained using a micro-reference electrode), demonstrating that their impedance response varies from purely kinetically limited at 0.6 mAh cm−2 to purely transport limited at 7.5 mAh cm−2. We then introduce a simple method with which R ct and R ion can be determined from the electrode impedance, even under transport limited conditions. Finally, we show how the initially homogenous ionic current distribution across porous electrodes under kinetically limited conditions becomes severely inhomogeneous under transport limited conditions.

Mathematical model based on staircase structure for porous electrode impedance

“…Therefore, the calculation results and practical example indicate that R ct > R ion /3, which indicates at least the condition of unlimited ion transport, should be satisfied for a power capable electrode design in any energy conversion and storage devices involving charge-transfer reactions. This investigation using the staircase model is not only in good agreement with previous reports, 27 but also provides a detailed boundary for the separation of resistive components that reflects the rate-limiting step changes in the electrochemical process at porous electrodes.…”

“…6,25 In contrast, when R ion is sufficiently larger than R ct , Z re,f converging to zero shows the following relationship, which is ion transport limited. 26,27 …”

“…One of the advantages of impedance analysis for porous electrodes is the separation of resistive components using the relations in eqn ( 9) and ( 10), but the specific boundaries of these relations have not been clear. 27 Assuming that eqn (12) and ( 14) obtained in the staircase model are valid in eqn (10) when R ion is sufficiently larger than R ct (R ct { R ion ), Z re,f converging to zero is derived as the following equation. Hence, we attempted to clarify the boundaries of eqn ( 13) and ( 15) for accurate resistive component separation using the proposed staircase model.…”

Which Exchange Current Densities Can Be Achieved in Composite Cathodes of Bulk-Type All-Solid-State Batteries? A Comparative Case Study

“…Consequently, we carried out simulations of TLM impedance spectra and compared these spectra to the experimental spectra. We found that for improving the agreement between experimental spectra and simulated TLM spectra, two modifications of the TLM were necessary: In eq , the double layer admittance iωC DL had to be replaced by a constant phase element (CPE) expression ( iω ) β Q DL with β < 1, resulting in Such a nonideal capacitive behavior of double layers in composite electrodes has been reported in the literature. , In eq , the factor a v l SE describes the CAM | SE interfacial area normalized by the nominal area of the cathode. However, the appearance of the ionic tortuosity in the factor a v l SE = a v τ Li + d is caused by mapping the 3D morphology of the composite electrode on 1D pores with tortuosities >1.…”

“…In a number of studies on lithium-ion batteries, TLMs have been used for analyzing the impedance of composite electrodes with pores filled by the liquid electrolyte. , In this way, charge transfer resistances R CT have been determined and used to calculate exchange current densities j 0 of Li + at the active material | electrolyte interface. − Morasch et al examined graphite anodes with variable thickness and determined charge transfer resistances. These charge transfer resistances correspond to exchange current densities in the range 1–6 A m –2 .…”