Herein, an approach is proposed to analyze the tortuosity of porous electrodes using the radical Voronoi tessellation. For this purpose, a series of particle compacts geometrically similar to the actual porous electrode were generated using discrete element method; the radical Voronoi tessellation was constructed for each compact to characterize the structural properties; the tortuosity of compact porous structure was simulated by applying the Dijkstra’s shortest path algorithm on radical Voronoi tessellation. Finally, the relationships were established between the tortuosity and the composition of the ternary particle mixture, and between the tortuosity and the radical Voronoi cell parameters. The following correlations between tortuosity values and radical Voronoi cell parameters were found: larger faces and longer edges of radical Voronoi cell leads to the increased fraction of larger values of tortuosity in the distribution, while smaller faces and shorter edges of radical Voronoi cell contribute to the increased fraction of smaller tortuosity values, being the tortuosity values more uniform with narrower distribution. Thus, the compacts with enhanced diffusion properties are expected to be obtained by packing particle mixtures with high volume fraction of small and medium particles. These results will help to design the well-packed particle compacts having improved diffusion properties for various applications including porous electrodes.

Fibers have been used to improve the mechanical properties of the asphalt paving mixture. It is known that the enhancement of powder compact mechanical properties is related to the compact packing microstructure. This study focuses on the evaluation of the packing microstructure of powder compacts produced from ternary mixtures of spherical particles and fibers. The discrete element method is employed to generate the compacts of particle mixtures of different compositions under gravity. The compact microstructure is quantitatively characterized by utilizing the developed image analysis technique to approximate the size distribution of voids among particles in X, Y and Z directions. As a result, the denser packing was obtained with a greater fraction of small spherical particles. The inclusion of fibers resulted in the high-density compact with uniform distribution of small size voids.

This study reports the synthesis of a few-layered graphene (GF) thin film on Ni foam by chemical vapor deposition (CVD) technique and investigation of its electrochemical performance as a negative electrode for lithium-ion batteries (LIBs). A standard deposition procedure with a methane precursor was employed to prepare the GF films. The SEM studies revealed the formation of a dark uniform film on the surface of Ni foam’s wires upon the CVD deposition. The film consisted of numerous GF sheets replicating the shape of the Ni grain boundaries over the Ni wire surface. The Raman spectroscopy of the prepared films on the Ni foam confirmed that the samples are a few-layered GF with high quality and purity. In order to evaluate the potential of the use of the prepared materials as an anode in LIBs, their electrochemical performance was studied in coin-type lithium half-cells using cyclic voltammetry (CV) and galvanostatic cycling. The results of CV showed that both graphene and native oxide layer (NiO) on nickel foam exhibit electrochemical activity with respect to lithium ions. Galvanostatic cycling revealed that both GF and NiO contribute to the overall capacity, which increases upon cycling with a stable Coulombic efficiency of around 99%. The designed 3D GF coated NiO/Ni anode demonstrated a gradual increase of its areal charge capacity from 65 μAh cm-2 at the initial cycle to 250 μAh cm-2 at the final 250th cycle.

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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. References [1] Kishimto M, Iwai H, Saito M and Yoshida H 2009 ECS Transactions 25 1887 [2] Iwai H, Shikazono N, Matsui T, Teshima H, Kishimoto M, Kishida R, Hayashi D, Matsuzaki K, Kanno D, Saito M, Muroyama H, Eguchi K, Kasagi N and Muroyama H 2010 Journal of Power Sources 195 955 [3] Tjaden B, Lane J, Withers P, Bradley R, Brett D and Shearing P 2016 Solid State Ionics 288 315 [4] Semeykina V, Malkovich E, Bazaikin Y, Lysikov A and Parkhomchuk E 2018 Chemical Engineering Science 188 1-10 [5] CFDEM®WORKBENCH, DCS Computing, Linz, Austria (2019) [6] Akhmetov Z, Boribayeva A, Berkinova Z, Yermukhambetova A and Golman B 2019 Chemical Engineering Transactions 74 385 Figure 1