Modeling of the Electrochemical Impedance Spectroscopy of a Porous Electrode Composed of Micro-sized Particles Embedded by a Nano Layer
Abstract
Electrochemical impedance spectroscopy (EIS) is a powerful technique for characterizing an
electrochemical system and is widely used in the battery field. The comprehensive
interpretation of EIS spectra obtained on Li-ion batteries can however be tedious because these
systems are composed of porous electrodes and a complex electrolyte. Moreover side reactions,
such as the formation of an insulating layer around the particles of the porous electrodes can
occur during the battery operation, thus modifying the impedance response. Additionally, it is
often difficult to measure the impedance of a half-cell during battery cycle-life, and the resulting
EIS response consists in the impedance of the whole battery measured without reference
electrode.
A way to improve the interpretation of impedance data of Li-ion systems is to use modeling.
Most of the time, the modeling of EIS is limited to the use of electrical equivalent circuits (EEC)
but the link between EEC and the physical processes accounting for the system is hard to
establish. However, in the 60s, Newman et al. [1] developed a model for porous battery
electrodes. Their model describes the whole battery system with equations that are directly
related to the physical phenomena occurring in the composite electrodes. This model is still
widely used in the battery field to simulate galvanostatic charge and discharge. Based on their
work, and inspiring by works already done on the modeling of EIS [2], it is possible to devise
a model for electrochemical impedance spectroscopy by linearizing all the equations [3]. The
model obtained will then be directly connected to the physical phenomena occurring inside the
porous electrodes which will greatly help to interpret impedance spectra.
In our work, we developed an analytical solution of EIS for a porous electrode composed of
particles with insertion reactions considering the kinetics of the electron transfer reactions, the
diffusion processes in both solid and liquid phases. We then studied the influence of an
insulating film forming around the particles on the EIS spectra. The model presented here
allows not only to predict the impedance of a porous electrode depending on its state of charge
but it is also valid for the whole intercalation rate with the same set of parameters.
References
(1) Newman, J.S.; Tobias, C.W. Journal of the Electrochemical Society 1962, 109(12),
page 1183-1191.
(2) Meyers, J.P. et al. ; Journal of the Electrochemical Society 2000, 147(8), page 2930-
2940.
(3) Huang, J.; Zhang, J.B. Journal of the Electrochemical Society 2016, 163(9), page
A1983-A2000.