以離散元素法設計鋰電池正極之最密堆積及其效能評估

Abstract

本研究透過離散元素法DEM分析鋰電池電極顆粒堆積行為，並藉由分析電極堆積以及經過壓延程序的模擬結果探討不同顆粒組成比例、粒徑分布以及顆粒形狀時堆積密度以及導電效能的差異。透過Altair® EDEM™軟體模擬電極正極的壓延程序，透過數值分析探討不同電極條件下的效能。由結果可得，當NMC顆粒為橢球時有較大的堆積密度，最大可達0.57，且不同體積時的橢球可達到最大密度；而改變組成比例當碳黑為2wt%至6wt%時，可以發現當碳黑的比例升高時，會造成堆積密度下降，但電子導電度上升，最高可達4.35×10-2，原因在於碳黑所佔體積比例增加，藉由分析碳黑以及PVDF的組成比例，發現兩者在比值1.5至2.0之間有較佳的堆積密度，最大可達約0.57；改變粒徑分布時，堆積密度受到的影響較小，但在NMC顆粒標準差為0.02時，有較大的導電度，可達約7.78×10-2，此時雖然堆積密度以及碳黑所佔體積比例較接近，但碳黑配位數較大；改變碳黑尺寸，發現碳黑在小尺寸時，堆積密度較小，但導電度較大，最高可達1.21×10-2，由於在固定重量組成比例時，小尺寸碳黑顆粒有較大的體積分率。此外，本研究分析電極壓延後的彈性恢復曲線，分別施以150MPa、300MPa、600MPa以及1200MPa，發現當正向壓延力較大時，電極密度最大可達0.74，但回彈(Spring back)的比例較大。而在壓延過程中，為了確保電極的輾壓無各向異性，透過應力張量以及結構張量的計算來分析對角向XX、YY以及ZZ，由結果可以發現，應力張量計算結果在XX、YY向數值相近，而在ZZ方向較大，顯示電極有達到近完整且平均的輾壓，且透過結構張量的分析確保顆粒在各向所受力皆隨著壓延正向力增加而上升，且XX以及YY向數值接近，表示在平面的受力平均。

This study utilized the discrete element method (DEM) to analyze the particle packing behavior of lithium-ion battery electrodes. By analyzing the electrode packing and simulating the calendaring process, the study explored the differences in packing density and conductivity performance based on various particle composition ratios, particle size distributions, and particle shapes. The Altair® EDEM™ software was used to simulate the rolling process of the positive electrode, and numerical analysis was conducted to investigate the performance under different electrode conditions. The results showed that when the NMC particles were ellipsoidal, a higher packing density was achieved, with a maximum of 0.57. Additionally, ellipsoids with different volumes exhibited larger packing densities. When the composition ratio of carbon black increased from 2wt% to 6wt%, it was observed that the packing density decreased while the electronic conductivity increased, reaching a maximum of 4.35×10-2. This was because the volume fraction of carbon black increased. By analyzing the composition ratio of carbon black and PVDF, it was found that the best packing density was achieved when the ratio was between 1.5 and 2.0, with a maximum of approximately 0.57. Changing the particle size distribution had a relatively small impact on the packing density. However, when the standard deviation of NMC particles was 0.02, a higher conductivity was obtained, reaching approximately 7.78×10-2. At this point, although the packing density and the volume fraction of carbon black were closer, the coordination number of carbon black was larger. When changing the size of carbon black, it was found that smaller carbon black particles resulted in a lower packing density but higher conductivity, with a maximum of 1.21×10-2. This was because smaller carbon black particles had a larger volume fraction under a fixed weight composition ratio. Furthermore, the study analyzed the elastic recovery curve after electrode calendaring with applied pressures of 150MPa, 300MPa, 600MPa, and 1200MPa. It was found that a higher normal compacting force resulted in a maximum electrode density of 0.74 but with a larger spring back proportion. During the calendaring process, in order to ensure isotropy of the electrode calendaring, stress tensor and fabric tensor calculations were used to analyze the diagonal directions XX, YY, and ZZ. The results showed that the stress tensor calculations were similar in the XX and YY directions, while larger in the ZZ direction, indicating that the electrode achieved near-complete and uniform compacting. The analysis of the fabric tensor ensured that the forces acting on the particles in all directions increased with the increasing compacting force, with similar values in the XX and YY directions, indicating an average distribution of forces in the plane.