Pore Network Modelling of a Lithium Ion Battery Cathode as a Tool for Microstructure Optimization
Authors: McKague Michael Gilmour , Sadeghi Mohammad Amin , Gostick Jeff 
Published: August 2024

Lithium ion batteries (LIBs) have become the battery of choice, owning almost 90% of the energy storage market [1]. They boast excellent power and energy density, but performance decreases at high discharge rates limiting their use in large scale applications [2]. With the availability of graphite and silicon materials as anode, the anode in a lithium-ion battery is already well optimized and research has focused primarily on the development of cathode materials with high rate-capacity. A LIB cathode is a porous material comprised of electrolyte, active material, and carbon binder phases. The electrolyte facilitates the migration and diffusion of lithium ions from the anode, through a porous separator, and to the active material where lithium ions intercalate, and electronic current is produced as the battery discharges. A carbon binder phase is also dispersed to enhance the electrical conductivity of the cathode and may even contain micropores that can increase current density [3]. The porous microstructure of a LIB cathode thereby plays an important role in controlling the movement of lithium ions and accessibility of active material effecting both discharge rate and capacity of LIBs. Therefore, tailoring the cathode microstructure provides a route for LIB cathode optimization. Pore scale models that resolve the electrolyte, active material, and carbon binder phases in a cathode can be used for this purpose. Pore scale models offer unique advantages compared to experimental studies in that they can test a wide variety of microstructures, even ones that are not yet realized, in a relatively short time frame. Typical battery models are continuum models that do not resolve the pore space and instead use effective properties determined from experiment. Pore scale models do not use effective properties saving experimental effort but are disadvantageous in that they are computationally very expensive requiring a fine mesh on a highly resolved volumetric image. Of the pore-scale modeling options, pore network modelling (PNM) is an especially efficient approach that discretizes the microstructure into pores and throats where pores are the computational nodes and throats are constrictions connecting pores [4]. In the literature, there is only one known pore network model of a LIB cathode, but it is an isothermal model that does not consider the effect of heat generation from electrochemical reactions [5]. While this model was effective at predicting discharge performance at low currents, predicting the voltage for galvanostatic discharge at high currents proved to be difficult, possibly because of assumed isothermal behaviour. Therefore, this work is focused on the development of a non-isothermal pore network model of a LIB cathode undergoing galvanostatic discharge. The complete set of partial differential equations and their discretization’s for modelling lithium transport, ionic or electronic charge transport, as well as heat transfer in all three phases of a LIB cathode is presented along with the numerical framework used for solving the coupled physics. This framework and discretized set of equations are demonstrated on a pore network extracted from an X-ray tomography image of a NMC532 cathode. Post-processing of the extracted network is done to apply novel interphase nodes between active material and electrolyte phases to provide sites for lithium intercalation to occur. The pore network model is written in Python using OpenPNM, an open-source pore network modelling package [6].
[1] S. Zavahir et al., “A review on lithium recovery using electrochemical capturing systems,” Desalination, vol. 500, Mar. 2021, doi: 10.1016/j.desal.2020.114883.
[2] R. Wagner, N. Preschitschek, S. Passerini, J. Leker, and M. Winter, “Current research trends and prospects among the various materials and designs used in lithium-based batteries,” J Appl Electrochem, vol. 43, no. 5, pp. 481–496, May 2013, doi: 10.1007/S10800-013-0533-6/FIGURES/10.
[3] Z. A. Khan et al., “Probing the Structure-Performance Relationship of Lithium-Ion Battery Cathodes Using Pore-Networks Extracted from Three-Phase Tomograms,” J Electrochem Soc, 2020, doi: 10.1149/1945-7111/ab7bd8.
[4] M. McKague, H. Fathiannasab, M. Agnaou, M. A. Sadeghi, and J. Gostick, “Extending pore network models to include electrical double layer effects in micropores for studying capacitive deionization,” Desalination, vol. 535, 2022, doi: 10.1016/j.desal.2022.115784.
[5] Z. A. Khan, M. Agnaou, M. A. Sadeghi, A. Elkamel, and J. T. Gostick, “Pore Network Modelling of Galvanostatic Discharge Behaviour of Lithium-Ion Battery Cathodes,” J Electrochem Soc, vol. 168, no. 7, Jul. 2021, doi: 10.1149/1945-7111/ac120c.
[6] J. Gostick et al., “OpenPNM: A Pore Network Modeling Package,” Comput Sci Eng, vol. 18, no. 4, pp. 60–74, Jul. 2016, doi: 10.1109/MCSE.2016.49.

Figure 1