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研究生： 李紀廣
Lee, Chi-Kuang
論文名稱： 分子動力計算質傳係數與電化學預測鋰離子電池整體性能
Molecular Dynamics Calculation of Mass Transfer Diffusion Coefficient and Electrochemical Performance Prediction of Lithium Ion Batteries
指導教授： 洪哲文
Hong, Che-Wun
口試委員: 董瑞安
Doong, Ruey-An
張博凱
Chang, Bor-Kae
三政鴻
San, Cheng-Hung
林洸銓
Lin, Kuang-Chuan
學位類別： 碩士
Master
系所名稱： 工學院 - 動力機械工程學系
Department of Power Mechanical Engineering
論文出版年： 2019
畢業學年度： 107
語文別： 中文
論文頁數： 71
中文關鍵詞： 分子動力學 、擴散係數 、鋰離子電池
外文關鍵詞： Molecular Dynamics, Diffusion Coefficient, Lithium Ion Batteries
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    • 本論文研究鋰離子電池整體性能表現，針對電池充放電過程，自陽極、電解質至陰極做固態與液態情況下，材料、離子與電流平衡分析，研究可能影響電池充放電過程的各項參數分析，如操作溫度、電解質濃度，放電率大小及薄膜材料、陰極材料等，做詳細分析與研究。
    關於計算電池材料之擴散係數的方法有分子動力學、蒙地卡羅法等。當中分子動力學係是利用牛頓方程式產生隨時間變化的粒子確切位置與當時速度，但計算較為費時，且較多粒子數時的計算量則過於龐大。本論文藉由分子動力學模擬鋰離子在單位晶胞內之擴散係數作為整體材料之擴散係數，再以計算質傳(Fick’s Law)配合電化學Bulter-Volmer Equation預測鋰離子電池整體性能。
    本論文藉分子動力學計算鋰離子在石墨中擴散係數之值為 cm2 s-1，其值介於由實驗所得之結果中間，由實驗可知當鋰離子沿著石墨平面移動時，其擴散係數為 cm2 s-1之間；而沿著晶格結構移動時，其擴散係數為 cm2 s-1。由於在進行分子動力學模擬時不會限制粒子行進方向，因此藉此方法所得之鋰離子在石墨中之擴散係數為一可信數值。
    本研究成果除可提供一更精準的鋰離子電池內部細節傳輸現象模擬，更可由材料參數變化及電池尺寸設計，事先選定材料，減少嘗試錯誤實驗，以便找出更適合做為鋰電池的陰、陽極及電解質材料，並做鋰離子電池整體性能優化。

    This thesis studies the overall performance of lithium-ion batteries, especially the charge and discharge process. Ion diffusion and current balance analysis from the anode to the electrolyte and to the cathode are carried out in solid and liquid states. Operating conditions, such as operating temperature, electrolyte concentration, discharge rate are simulated using various materials for the anode, cathode and the separator.
    Molecular dynamics and Monte Carlo simulations are two methods to claculate the diffusion coefficient inside the porous materials in electrodes and the separator. The former uses Newton's equation to calculate the exact position of the particles and the instantaneous velocity.
    This thesis uses the molecular dynamics to calculate the diffusion coefficient of lithum ion in graphite and get cm2 s-1. This value is between the results of the experiment. In the experiment, the value of diffusion coefficient is betwwen cm2 s-1, when lithum ion moves along the graphite plane. The value of coefficient is cm2 s-1, when lithum ion moves along the structure of lattice. The particle isn’t restricted the marching direction when doing the molecular dynamics simulation. Therefore using this method to calculate the diffusion coeffusion of lithum ion in the graphite is a trustworthy way.
    This research adapts the molecular dynamics simulation methodology to calculate the diffusion coefficients for the Fick’s law and also implement the Bulter-Volmer equation to calculate the electrochemical performance of various lithum ion batteries using different materials.

    摘要 II Abstract Ⅲ 誌謝 Ⅳ 目錄 Ⅴ 圖目錄 Ⅷ 表目錄 XI 符號定義 XII 第一章 緒論 1 1.1 背景介紹 1 1.1.1 鉛酸電池 1 1.1.2 鎳鎘電池 2 1.1.3 鎳氫電池 2 1.1.4 鋰離子電池 2 1.2 研究動機 3 1.3 研究目標 4 第二章 理論基礎 7 2.1 分子動力學 7 2.1.1 分子動力學模擬流程 8 2.1.1.1 模型建構 8 2.1.1.2 選用合適的勢能函數 8 2.1.1.3 進行結構最佳化 9 2.1.1.4 設定系統邊界 9 2.1.1.5 設定系統狀態 9 2.1.1.6 數據分析 10 2.1.2 分子間相互作用力勢能 10 2.1.3 鍵結作用力勢能 11 2.1.3.1 鍵長伸縮勢能 11 2.1.3.2鍵角伸縮勢能 13 2.1.3.3兩面角扭轉勢能 14 2.1.3.4倒轉角扭轉勢能 15 2.1.4 非鍵結作用力勢能 15 2.1.4.1 凡德瓦力勢能 16 2.1.4.2 庫倫作用力勢能 17 2.1.5 溫控器 18 2.1.6 邊界條件 19 2.2 鋰離子電池模擬 21 2.2.1 統御方程式 21 2.2.1.1 電子電荷平衡 22 2.2.1.2 質量平衡 23 2.2.1.3 電化學動力學 24 2.2.1.4 能量平衡 25 2.2.2 求解方法 25 第三章 模擬方法 27 3.1 材料選定 27 3.2 擴散係數之計算流程 29 3.2.1 模型建立 32 3.2.2 進行超晶胞 34 3.2.3 嵌入鋰離子 35 3.2.4 結構最佳化 37 3.2.5 進行鋰離子分子動力學模擬 44 3.2.6 數據後處理 44 3.2.6.1 均方位移(Mean Square Displacement, MSD) 45 3.2.6.2 擴散係數 45 3.3 鋰離子電池模擬 46 3.3.1 模型假設及計算維度 46 3.3.2 模型建構及邊界條件 47 第四章 結果與討論 53 4.1 數據後處理 53 4.1.1 均方位移 53 4.1.2 擴散係數 54 4.2 鋰離子電池性能預測 56 第五章 結論與未來工作 68 5.1結論 68 5.2未來工作建議 68 參考文獻 69

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