As shown in Fig. 1, typical porous electrodes (in this case for a Li-ion anode) clearly have heterogeneity on the µm and smaller length scales. In addition, it has been shown that there is heterogeneity on mm length scale for even commercial quality electrodes [1]. This heterogeneity is a consequence of the particle-based manufacturing processes [2]. Furthermore, this heterogeneity is undesirable as it essentially requires that the electrodes be overdesigned to achieve adequate minimum performance.

The commonly accepted Newman-type model of the full-cell sandwich essentially averages over local heterogeneities in porous electrodes in order to make the system “macrohomogeneous.” The resulting model allows for uniform pathways for electrons and ions. Homogenization of the microstructure greatly decreases the computational cost of the model while retaining the essential physics of transport and reaction within the electrodes.

In this presentation I will discuss how one can measure heterogeneities as well as average values of electronic and ionic conductivities [1,3]. These can be compared to empirical correlations such as the Bruggeman equation. Our group has considerable experience in this area.

With respect to modeling, I will discuss strategies for dealing with heterogeneities in the context of Newman-type models. This can include using multiple particle types [4] as well as effective medium theories that allow one to average local values of physical properties to generate an overall or effective medium property. Lastly, I will discuss what effect such averaging has on predictions of the battery model.

This work was supported by the U.S. Department of Energy through the BMR program.

[1] Lanterman et al., J. Electrochem. Soc. 162, A2145 (2015).

[2] Forouzan et al., J. Power Sources 312, 172 (2016).

[3] Zacharias et al., J. Electrochem. Soc. 160, A306 (2013).

[4] Thorat et al., J. Electrochem. Soc. 158, A1185 (2011).

Fig. 1 SEM/FIB cross section of Li-ion anode showing local heterogeneity.