Using Smoothed Boundary Method for Simulating Interfacial Transport in Electrochemical Dynamics

The design of electrodes in current Li-ion batteries has long been based on experimental trial and error on electrode characteristics such as thickness, porosity, and composition [1]. Quantitative design criteria have yet to be developed due to the lack of understanding of coupled electronic-ionic transport in complex electrode structures. Physics-based modeling and simulations at electrode microstructural scale will facilitate the design process. Composite electrodes consist of tortuous channels for transport, particle with non-uniform sizes, and irregular particle-electrolyte interfaces. In addition, interfacial transport of Li and electrons along particle-particle contacts can play an important role in the electrochemical processes. Such geometric complexity makes microstructural-level electrochemical simulation a challenge in the research community.

Using a diffuse-interface description, we have previously established a framework for electrochemical simulations based on the smoothed boundary method (SBM) [2], which allows efficient simulations of electrochemical dynamics in complex electrodes [3,4]. In this presentation, we describe an extension to  the simulation tool that incorporates interfacial transport of Li and electrons on the boundaries between electrode particles or grains, which can enhance or hinder the net transport through the structure. In the SBM, an individual domain is defined by a domain parameter, which equals one inside the particle/grain and equals zero outside. The particle/grain surface is defined by the transition region where the domain parameter is between zero and one. For an agglomerate containing various particles or a polycrystalline electrode, multiple domain parameters can be employed to define individual domains. The surface Laplacian can be calculated, according to the domain parameters, to obtain the fluxes along the boundaries between the particles or grains. Using this method, bulk transport and interfacial transport can be coupled in evaluating the net transport within the electrode. A preliminary simulation of diffusion along grain boundaries of hexagonal grains is shown in Fig 1.

We will use this technique to investigate the individual and combined effects of bulk and interfacial transport. Different transport coefficients can be assigned to distinct particles/grains or particle interfaces/grain boundaries to account for the dependence of the coefficients on crystalline orientations of particles/grains. Simulations using this tool will be utilized to examine the effect of tortuosity of interfaces on Li transport in polycrystalline electrode. In the long term, this method will be incorporated into the electrochemical simulation code to examine the role of interfacial Li and electron transport in determining electrode performance, which will provide insights for design and optimization of electrode architecture.

Figure 1: SBM simulated concentration profile for grain boundary diffusion in an ideal hexagonal grain structure.

Acknowledgement: This material is based upon work supported as part of the Northeastern Center for Chemical Energy Storage, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0012583.

[1] Venkatasailanathan Ramadesigan, et al, J. Electrochem. Soc. 159, R31-R45 (2012).

[2] Hui-Chia Yu, Hsun-Yi Chen, and Katsuyo Thornton, Modelling Simul. Mater Sci. Eng. 20, 1-41 (2012). 

[3] B. Orvananos et al., Electrochimca Acta, 137 (2014) 245

[4] B. Orvananos et al.,J Electrochem Soc, 161 (2014) A535