Numerical Modeling of Transport Properties in Battery Electrodes

Abstract

Analysis and optimization of transport properties such as the effective diffusion coefficient have a strong impact on the development of advanced batteries. Since electrodes of all batteries, from lithium-ion batteries to fuel cells, used in various applications have different porous structures, there is a need to evaluate their transport property dependence on the microstructure of the electrodes.Among the calculation methods of effective diffusion coefficient, the methods based on the simulation of the tortuosity have been gaining attraction of many scientists. Kishimoto et al. [1] evaluated the tortuosity of SOFC anode for its microstructure optimization applying a random walk method. Iwai et al. [2] studies on tortuosity factor evaluation showed less than 3% differences between random walk and lattice Boltzmann methods (LBM). Tjaden et al. [3] compared the tortuosities calculated using the fast marching image-based method with those obtained by using the diffusion cell experimental measurements. Semeykina et al. [4] developed a tortuosity-based calculation method of diffusion coefficient for optimization of catalyst texture used to macromolecule conversions applying Voronoi radical tessellation. Our study is concentrated to uncover the relationship between Voronoi parameters and transport properties since a detailed analysis of the porous structure of powder compact via Voronoi tessellation will provide the opportunity to anticipate optimal decisions for many parameters such as particle shape, size distribution, and composition.In the present research, three electrode structures were generated using CFDEM®WORKBENCH software based on the discrete element method (DEM) [5] as ternary powder compact with different size ratios. Periodic boundary conditions were set along x- and y-axes and fixed one along z-axis. Due to periodic boundaries the wall effect during particle compaction is reduced. The generation of the packing structure was carried out under gravity. Each of three compacts consists of small, medium and large spherical particles with volume fractions equal to 25 %, 25 % and 50 %, respectively, having the ratios of their diameters equal to 1:2:4 for the first compact, and 1:2:6 and 1:2:8 for the second and third compacts, respectively. The number of particles varied from roughly twenty thousand to thirty thousand. Then, the Voronoi radical tessellation was applied to the compacts to simulate the Voronoi diagram representing the pathway network of the void spaces among grains. The tesselation was carried out using the open-source software package voro++ which also output Voronoi cell parameters, i.e. cell volume, total surface area, number of faces, etc. as described by Akhmetov et al. [6]. Finally, the tortuosity was calculated using the Dijkstra algorithm on the Voronoi diagram. The Dijkstra algorithm calculates the shortest path between two specified points. Here it was applied to every pair of vertices lying on the opposite faces of the domain separately in x, y and z directions. The path length was calculated by summing the Voronoi cell edge lengths along the path. This methodology is summarized in Figure 1.The packing densities of particle compacts generated by DEM were measured as 0.651, 0.677 and 0.690 for the first, second and third compact, respectively. Voronoi tessellation provided information about the length of every cell edges and their connectivity, necessary for tortuosity calculation. Results of tortuosity simulations demonstrate that there is no significant difference between tortuosity values of three compacts in the x and y directions, while the well and medium packed compacts give higher tortuosities (approximately 1.27) than the loosely packed ones in the z-direction (1.17 in average). It can be attributed to the periodic boundary conditions along the x- and y-directions and gravity applied in the z-direction. Since the Voronoi cell metric properties such as volume and surface area vary significantly with the particle size ratio, the lengths of the cell edges will also vary in the same way. Therefore, there is a positive correlation between the Voronoi cell metric properties and the effective diffusivity in the powder compact.