Mesoscale Transport in Magnetite Electrodes for Lithium-Ion Batteries
Authors: Knehr Kevin William , Brady Nicholas W , Lininger Christianna Naomi , Cama Christina A , Bock David C , Lin Zhou , Marschilok Amy C , Takeuchi Kenneth J , Takeuchi Esther S , West Alan C 
Published: February 2020

In recent years, magnetite (Fe3O4) has shown promise as a lithium-ion electrode material due to its low cost, safety (non-toxic), and high theoretical capacity (926 mAh/g) [1]. The high theoretical capacity results from the close-packing, inverse spinel structure of the material. This structure also hinders rapid ion transfer, which causes the experimental capacity to deviate significantly from the theoretical value [2]. To address this issue, several authors have synthesized Fe3O4nano-crystals in attempts to minimize the path length for ion transport [3-4]. Improvements in electrochemical performance have been observed; however, the mechanisms responsible for these improvements are not well understood.
A complete understanding of the physical phenomena impacting performance has been difficult to obtain due to the complexity of the battery electrodes. The electrodes are composed of blends of Fe3O4, carbon black, and a polymer binder. Due to the synthesis and fabrication processes, the electrodes contain structures across three distinct length scales (Fig. 1). The crystalline active material and bulk electrode provide structure on the nano-scale and macro-scale, respectively. In addition, the intermediate length scale (i.e., the meso-scale) contains a third structure due to the presence of agglomerates, which form as a result of nano-particle aggregation. Behavior on all three length scales must be understood in order to properly interpret electrochemical data.
In this work, we seek to provide a deeper understanding of the physical and chemical processes occurring in Fe3O4electrodes through a combined experimental and mathematical approach. First, to identify which length scale (crystal, agglomerate, or bulk) has the biggest impact on mass transport, the time constants associated with mass transport at each length scale have been determined through a theoretical, dimensional analysis. These results have been compared to time constants obtained from voltage relaxation experiments. From this comparison, it has been determined that mass transport on the agglomerate scale is a significant factor.
Based on these findings, a one-dimensional mathematical model of a Fe­3O4agglomerate has been developed, which assumes mass transport on the crystal and bulk scales are negligible. In the model, the Butler-Volmer equation along with lithium-intercalation relations are used to simulate the charge transfer kinetics. Changes in thermodynamic potential due to changes in the degree of lithium intercalation are accounted for by fitting experimental data to a modified Nernst equation. In addition, the mesoscale transport occurring between the aggregated nano-crystals is modeled based off of electrochemical measurements and TEM images. Good agreement is observed between the simulations and experimental data for electrochemical discharge and voltage relaxation experiments (Fig. 2). These results further confirm the validity of an agglomerate-based model for this system.
Using the model, we have investigated the effects of crystallite and agglomerate size on mesoscale transport in the electrode. To facilitate these studies, the model has been expanded to account for distributions in agglomerate size, which are obtained from TEM images. The resulting simulations suggest that interpretation of electrochemical performance without an understanding of the agglomerate size distributions can lead to significant errors in the analysis.
[1] S. Zhu, A. C. Marschilok, E. S. Takeuchi, G. T. Yee, G. Wang, and K. J. Takeuchi, J. Electrochem. Soc., 157 (2010) A1158.
[2] M. C. Menard, K. J. Takeuchi, A. C. Marshilok, and E. S. Takeuchi, Phys. Chem. Chem. Phys., 15 (2013) 18539.
[3] S. Zhu, A. C. Marschilok, E. S. Takeuchi, and K. J. Takeuchi, Electrochem. Solid-State Lett., 12 (2009) A91.
[4] Z. Cui, L. Jiang, W. Song, and Y. Guo, Chem. Mat., 21 (2009) 1162.

Figure 1