Experimental Validation of Newman Model Analysis for Modern Li-Ion Battery Cathode Materials
Authors: Nham Marlene Andersen , Morasch Robert , Landesfeind Johannes 
Published: February 2024

The Butler-Volmer equation is a fundamental equation extensively used to describe electrochemical kinetics and relates the reaction current at an electrode interface to the voltage. Newman and coworkers suggested an equation (Fig. 1a) for the exchange current density, which includes the state of charge (SoC) dependence of Li-ion batteries as well as theory-based anodic and cathodic transfer coefficients. This description of interface kinetics, part of the commonly used Newman model, is widely used for battery modeling.1,2 Because of the lack of experimental data, several assumptions were made in the derivations,3 such as assuming the intercalation reaction to be a first order reaction, and assuming the transfer coefficients to be 0.5. As new battery materials emerge, it is important to validate whether these assumptions are applicable, or whether the model needs to be extended.
In this work, we compare experimentally obtained interface resistances from different cathode materials with the theoretical behavior of the interface kinetics predicted from the Newman model as well as experimental characterizations published in the research literature. The experimental data for the interface resistance is determined using electrochemical impedance spectroscopy,4 where the electrodes are built into a three-electrode cell setup, using a gold wire reference electrode, which allows studying the cathode impedance separately.5 As anode, we use graphite that is prelithiated to ~20% to make sure there is enough lithium in the cell to be able to relithiate the cathode completely. The loading of the electrodes is low to ensure negligible pore resistance contributions, so that the semicircle in the Nyquist-plot originates from kinetics only. The obtained charge transfer resistance is analyzed as a function of Li-content to show how the kinetics of the cathode depend on the degree of lithiation.
From the Newman model, it is expected that the interface resistance shows a U-shape over the degree of lithiation with a minimum at 50% SoC with a drastic increase in charge transfer resistance for the first and last 10%. This is because the kinetics are slower when the cathode is completely empty and completely full, which can be seen from the equation in Fig. 1a. When c=c
max or c=0, i
0 becomes 0. Fig. 1b. shows the theoretical behavior based on the Newman model, the experimental results found in this study, and experimental results found in the literature for NMC1116.
Figure 1: a) Exchange current density suggested by Newman and coworkers. i
0 is the exchange current density, F is the Faraday constant, k
a and k
c are reaction rate constants for the anodic and cathodic reactions, α
a and α
c are the anodic and cathodic transfer coefficients, c
max is the maximum lithium concentration in the material, c is the lithium concentration in the material, and c
l is the salt concentration in the electrolyte. b) Charge transfer resistance vs. Li-content for ~0.5 mAh/cm² NMC111 (Gelon Lib) with prelithiated graphite (Sigma Aldrich) anode, gold wire reference electrode with a core diameter of 50 µm coated with a 7 µm polyimide insulation (Goodfellow), 80 µl 1 M LiPF6 in EC:EMC (3:7) (Gotion), two glass fiber separators (260 µm, VWR) at 25 °C determined from semi-circle width of cathode impedance (100 kHz to 10 mHz, 10 mV amplitude) using a potentiostat (VMP3, BioLogic) recorded in three electrode Swagelok cell (average of 3 measurements) is represented by dark grey points. The red points show theory according to Eq. 1 with, and the light brown points show NMC111 from Ref. 6. The lines between the points are drawn to enhance the features of the figure.
Comparison of experimental data and the theoretical framework shows pronounced discrepancies, which cannot be resolved if the transfer coefficients are kept at 0.5. Similar measurements are conducted for a wide range of active materials and changed environmental conditions to further elaborate validity and/or necessity to modify the commonly used description of the interface kinetics relation. This will help to better understand interface resistance in battery cells and thereby allow optimization of material properties by, e.g., surface modification.

References

M. Ecker et al., J. Electrochem. Soc., 162, A1836 (2015).

T. F. Fuller, M. Doyle, and J. Newman, J. Electrochem. Soc., 141, 1–10 (1994).

M. Doyle, T. F. Fuller, and J. Newman, J. Electrochem. Soc., 140, 1526–1533 (1993).

A. Lasia, in Electrochemical Impedance Spectroscopy and its Applications, A. Lasia, Editor, p. 203–250, Springer, New York, NY (2014).

S. Solchenbach, D. Pritzl, E. J. Y. Kong, J. Landesfeind, and H. A. Gasteiger, J. Electrochem.
Soc., 163, A2265–A2272 (2016).

R. Morasch, H. A. Gasteiger, and B. Suthar, J. Electrochem. Soc., 170, 080522 (2023).

Figure 1