臺灣博碩士論文加值系統

鋰離子電池相較於其他二次電池有著較高的能量密度與較佳之重量比功率，已經被廣泛應用於各種儲能元件。本研究針對鋰離子電池當中電解液的鋰離子擴散行為，從其結構與能量和分子動力學模擬進行分析及討論。
在本研究中首先考慮沒有溫度及時間的效應之下，鋰離子與EC分子與DEC分子互相吸引時可能會出現的幾何結構，並且計算此結構其能量之大小，發現EC分子以及DEC分子皆容易以羰基上的氧原子與鋰離子結合，形成放射狀或對稱狀的結構，隨後在第一原理的分子動力學中，加入了時間的效應，可以在模型中發現到鋰離子與EC分子或是DEC分子形成溶劑化時所產生的配位數約為四左右，這與結構與能量的計算中相同，並且發現周圍已經形成溶劑化的EC分子或DEC分子仍有機會與其他未產生溶劑化的分子進行交換。
為了仔細地觀察鋰離子的擴散行為，本研究使用更大的模型，並使用了經驗式參數去模擬電解液中鋰離子的運動。此部分先以較巨觀的方式比較鋰離子在不同的環境底下擴散係數的差異，因此將EC分子與DEC分子以不同比例混合，並且考慮溫度以及電場的效應，可以發現在低溫時，由於EC溶液的流動性差，鋰離子的擴散與EC成分的比例大小有著絕對的關係。不同比例的溶液在未加入電場前，擴散係數的大小最主要由溶液本身的特性所決定，溶液本身流動性越好者，其擴散係數越高，而加入電場後可以發現電場對於溶液中的EC分子與DEC分子影響並不大，解離的鋰離子雖受到電場的作用，但其作用力仍小於溶劑分子對鋰離子的吸引，因此擴散係數並沒有明顯的加大。利用擴散係數推導得到導電度，說明影響溶液的導電性質同時受到擴散係數以及解離度的影響。

Lithium-ion batteries compared to other secondary batteries have a higher energy density and better Power-to-weight ratio, has been widely applied to various energy storage product. In our research, the diffusion of lithium ions in electrolyte of lithium-lon battery was studied by geometry optimization and molecular dynamics simulations.In the geometry optimization analysis, lithium ions prefer attracting the dielectric molecule like EC than the DEC.Our research shows that the max solvation number of lithium ion in the electrolyte is about four to five.In the molecular dynamics simulations, we found that the exchange between the solvated molecules and unsolvated molecules.After the solvation behavior, we studied the diffusion of lithium ions in the elecrtrolyte. We checked the temperature effect and the electric field effect. We found that the diffusion coefficient is controlled by the viscosity of the solution and the dissociation of the LiPF6 in the solution.Our research explains mechanism of the movement of lithium ions in the electrolyte.

摘要 I
DIFFUSION BEHAVIOR OF LI IONS IN THE ELECTROLYTE OF LI-ION BATTERY : FIRST-PRINCIPLE CALCULATION AND MOLECULAR DYNAMICS SIMULATIONS III
誌謝 VII
目錄 VIII
表目錄 XI
圖目錄 XII
第一章 前言 1
第二章 文獻回顧 4
2.1 電解液發展現況 4
2.2 分子動力模擬電解液的相關文獻 6
第三章 原子級模擬基礎理論 8
3.1 密度泛函(DFT)方法 8
3.2 自然鍵軌道理論 9
3.3 分子動力學之基本假設與流程圖 9
3.4 勢能函數 11
3.4.1 Lennard-Jones勢能 11
3.4.2 Coulomb Interaction 12
3.5 週期性邊界(Periodic Boundary Condition) 12
3.6 初始條件設定 14
3.7 系綜 15
3.8 運動方程式 16
3.8.1 Verlet algorithms 16
3.8.2 Leap Frog algorithms 17
3.8.3 Velocity Verlet algorithms 18
3.9 Nosé–Hoover thermostat 20
3.10 截斷勢能 20
3.10.1 Verlet表列法 21
3.10.2 Cell Link表列法 21
3.10.3 Verlet表列法結合Cell Link表列法 22
第四章 物理模型與模擬設計 24
4.1 電解液有機分子與鋰鹽的介紹 24
4.1.1 EC 24
4.1.2 DEC 24
4.1.3 LiPF6 25
4.2 模擬方法 26
4.2.1結構優化與能量變化 26
4.2.2第一原理分子動力學模擬 27
4.2.3經驗式分子動力學模擬 30
4.3 分析方法 32
4.3.1 Solvation Energy 32
4.3.2 MSD與擴散係數 32
4.3.3 Radial Distribution Function(RDF) 32
4.3.4 解離度(Degree of dissociation) 33
第五章 結果與討論 35
5.1 結構優化與能量變化 35
5.1.1 EC分子與DEC分子結構優化之結果 36
5.1.2 溶劑化的傾向位置 38
5.1.3 鍵結前後鍵長與電荷的改變 40
5.1.4 不同溶劑化數的結構和能量 43
5.1.5 不同溶劑化數的鍵長與電荷 46
5.1.6 混合成分的溶劑化能量 48
5.2 第一原理分子動力學模擬 49
5.2.1 DEC分子完整溶劑化的鋰離子在EC溶劑中 49
5.2.2 EC分子完整溶劑化的鋰離子在DEC溶劑中 53
5.2.3 DMC分子完整溶劑化的鋰離子在EC溶劑中 56
5.2.4 EC分子完整溶劑化的鋰離子在DMC溶劑中 59
5.3 經驗式分子動力學模擬 62
5.3.1 純溶劑的EC分子與DEC分子特性比較 62
5.3.2 鋰離子在不同比例的電解液溶液中 63
5.3.3 鋰鹽在不同比例的電解液溶液中 65
5.3.4 考慮溫度對於擴散係數的影響 70
5.3.5 考慮電場對於擴散係數的影響 72
第六章 結論 77
參考文獻 78

1.Xu, K., Nonaqueous liquid electrolytes for lithium-based rechargeable batteries. Chemical Reviews, 2004. 104(10): p. 4303-4417.
2.Aurbach, D., et al., Design of electrolyte solutions for Li and Li-ion batteries: a review. Electrochimica Acta, 2004. 50(2-3): p. 247-254.
3.Desjardins, C.D., et al., LITHIUM CYCLING PERFORMANCE IN IMPROVED LITHIUM HEXAFLUOROARSENATE 2-METHYL TETRAHYDROFURAN ELECTROLYTES. Journal of the Electrochemical Society, 1985. 132(3): p. 529-533.
4.Campbell, S.A., C. Bowes, and R.S. McMillan, THE ELECTROCHEMICAL-BEHAVIOR OF TETRAHYDROFURAN AND PROPYLENE CARBONATE WITHOUT ADDED ELECTROLYTE. Journal of Electroanalytical Chemistry, 1990. 284(1): p. 195-204.
5.Xu, K. and C.A. Angell, High anodic stability of a new electrolyte solvent: Unsymmetric noncyclic aliphatic sulfone. Journal of the Electrochemical Society, 1998. 145(4): p. L70-L72.
6.Leung, K., et al., Using Atomic Layer Deposition to Hinder Solvent Decomposition in Lithium Ion Batteries: First-Principles Modeling and Experimental Studies. Journal of the American Chemical Society, 2011. 133(37): p. 14741-14754.
7.Leung, K. and J.L. Budzien, Ab initio molecular dynamics simulations of the initial stages of solid-electrolyte interphase formation on lithium ion battery graphitic anodes. Physical Chemistry Chemical Physics, 2010. 12(25): p. 6583-6586.
8.Vatamanu, J., O. Borodin, and G.D. Smith, Molecular Dynamics Simulation Studies of the Structure of a Mixed Carbonate/LiPF6 Electrolyte near Graphite Surface as a Function of Electrode Potential. Journal of Physical Chemistry C, 2012. 116(1): p. 1114-1121.
9.Xing, L., et al., Electrode/Electrolyte Interface in Sulfolane-Based Electrolytes for Li Ion Batteries: A Molecular Dynamics Simulation Study. Journal of Physical Chemistry C, 2012. 116(45): p. 23871-23881.
10.Ushirogata, K., et al., Additive Effect on Reductive Decomposition and Binding of Carbonate-Based Solvent toward Solid Electrolyte Interphase Formation in Lithium-Ion Battery. Journal of the American Chemical Society, 2013. 135(32): p. 11967-11974.
11.Leung, K., Two-electron reduction of ethylene carbonate: A quantum chemistry re-examination of mechanisms. Chemical Physics Letters, 2013. 568: p. 1-8.
12.Wang, Y.X., et al., Theoretical studies to understand surface chemistry on carbon anodes for lithium-ion batteries: Reduction mechanisms of ethylene carbonate. Journal of the American Chemical Society, 2001. 123(47): p. 11708-11718.
13.Sanghun, L. and P. Sung Soo, Thermodynamic and dynamic properties in binary mixtures of propylene carbonate with dimethyl carbonate and ethylene carbonate. Journal of Molecular Liquids, 2012. 175: p. 97-102.
14.Bhatt, M.D., M. Cho, and K. Cho, Density functional theory calculations and ab initio molecular dynamics simulations for diffusion of Li+ within liquid ethylene carbonate. Modelling and Simulation in Materials Science and Engineering, 2012. 20(6).
15.Bhatt, M.D., M. Cho, and K. Cho, Interaction of Li+ ions with ethylene carbonate (EC): Density functional theory calculations. Applied Surface Science, 2010. 257(5): p. 1463-1468.
16.Liu, H. and E. Maginn, Effect of ion structure on conductivity in lithium-doped ionic liquid electrolytes: A molecular dynamics study. Journal of Chemical Physics, 2013. 139(11).
17.Capelle, K., A bird's-eye view of density-functional theory. Brazilian Journal of Physics, 2006. 36(4A): p. 1318-1343.
18.Kohn, W. and L.J. Sham, SELF-CONSISTENT EQUATIONS INCLUDING EXCHANGE AND CORRELATION EFFECTS. Physical Review, 1965. 140(4A): p. 1133-＆.
19.Hohenberg, P. and W. Kohn, INHOMOGENEOUS ELECTRON GAS. Physical Review B, 1964. 136(3B): p. B864-+.
20.Salahub, D.R. and M.C. Zerner, QUANTUM-CHEMISTRY THROUGHOUT THE PERIODIC TABLE. Acs Symposium Series, 1989. 394: p. 1-16.
21.Becke, A.D., DENSITY-FUNCTIONAL THERMOCHEMISTRY .3. THE ROLE OF EXACT EXCHANGE. Journal of Chemical Physics, 1993. 98(7): p. 5648-5652.
22.Lee, C.T., W.T. Yang, and R.G. Parr, DEVELOPMENT OF THE COLLE-SALVETTI CORRELATION-ENERGY FORMULA INTO A FUNCTIONAL OF THE ELECTRON-DENSITY. Physical Review B, 1988. 37(2): p. 785-789.
23.Miehlich, B., et al., RESULTS OBTAINED WITH THE CORRELATION-ENERGY DENSITY FUNCTIONALS OF BECKE AND LEE, YANG AND PARR. Chemical Physics Letters, 1989. 157(3): p. 200-206.
24.Vosko, S.H., L. Wilk, and M. Nusair, ACCURATE SPIN-DEPENDENT ELECTRON LIQUID CORRELATION ENERGIES FOR LOCAL SPIN-DENSITY CALCULATIONS - A CRITICAL ANALYSIS. Canadian Journal of Physics, 1980. 58(8): p. 1200-1211.
25.Jones, J.E., On the determinations of molecular fields - 1 From the variation of the viscosity of a gas with temperature. Proceedings of the Royal Society of London Series a-Containing Papers of a Mathematical and Physical Character, 1924. 106(738): p. 441-462.
26.Verlet, L., Computer Experiments on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules. Physical Review, 1967. 159(1): p. 98.
27.Verlet, L., Computer Experiments on Classical Fluids. II. Equilibrium Correlation Functions. Physical Review, 1968. 165(1): p. 201.
28.Feynman, R.P., R.B. Leighton, and M.L. Sands, The Feynman lectures on physics. 1963, Reading, Mass.,: Addison-Wesley Pub. Co.
29.Swope, W.C., et al., A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters. The Journal of Chemical Physics, 1982. 76(1): p. 637-649.
30.Nose, S., A UNIFIED FORMULATION OF THE CONSTANT TEMPERATURE MOLECULAR-DYNAMICS METHODS. Journal of Chemical Physics, 1984. 81(1): p. 511-519.
31.Hoover, W.G., CANONICAL DYNAMICS - EQUILIBRIUM PHASE-SPACE DISTRIBUTIONS. Physical Review A, 1985. 31(3): p. 1695-1697.
32.Seward, R.P. and E.C. Vieira, THE DIELECTRIC CONSTANTS OF ETHYLENE CARBONATE AND OF SOLUTIONS OF ETHYLENE CARBONATE IN WATER, METHANOL, BENZENE AND PROPYLENE CARBONATE. Journal of Physical Chemistry, 1958. 62(1): p. 127-128.
33.Payne, R. and Theodoro.Ie, DIELECTRIC PROPERTIES AND RELAXATION IN ETHYLENE CARBONATE AND PROPYLENE CARBONATE. Journal of Physical Chemistry, 1972. 76(20): p. 2892-＆.
34.Soetens, J.C., et al., Molecular Dynamics simulation and X-ray diffraction studies of ethylene carbonate, propylene carbonate and dimethyl carbonate in liquid phase. Journal of Molecular Liquids, 2001. 92(3): p. 201-216.
35.Perelygin, I.S., N.N. Beloborodova, and G.R. Mustafina, ION ION AND ION MOLECULE INTERACTIONS IN SOLUTIONS OF LITHIUM PERCHLORATE, LITHIUM-NITRATE, AND LITHIUM THIOCYANATE IN BINARY DIMETHYL-SULFOXIDE ACETONE SOLVENTS. Journal of Structural Chemistry, 1989. 30(1): p. 84-91.
36.Caleman, C., et al., Force Field Benchmark of Organic Liquids: Density, Enthalpy of Vaporization, Heat Capacities, Surface Tension, Isothermal Compressibility, Volumetric Expansion Coefficient, and Dielectric Constant. Journal of Chemical Theory and Computation, 2012. 8(1): p. 61-74.
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