提升燃料電池的效率，一直都是學術界與工業界研究追求目標，而陰極部分的氧還原反應 (Oxygen Reduction Reaction, ORR) 為速率決定步驟(Rate-Limited Step)，有效地提升其反應速率便能大幅提升燃料電池的效率，而目前提升的方式以添加觸媒為主，常用的觸媒有白金觸媒或是白金合金觸媒，但由於其數量稀少且價格昂貴，一直是使燃料電池無法普及的最大原因。
本研究為了降低白金觸媒的使用量，利用單層奈米碳管與石墨烯等導電性良好，且高比表面積材料作為陰極奈米支架，並將白金參雜於其中，分析其氧還原反應的機制。由於實驗上極難量測其氧還原反應的詳細過程，因此本論文以第一原理計算 (First Principles) 配合密度泛函理論 (Density Functional Theory, DFT) 研究反應機制，同時探討燃料電池陰極觸媒氧還原反應的詳細過程，並計算出吸附能、系統總能、反應能與活化能。
氧還原反應的第一個步驟即為氧分子 (O2) 的吸附，因此藉由分析不同初始氧吸附形式的吸附能與各步驟相對能，可以發現石墨烯參雜白金提供較穩定的反應環境，但穩定的反應環境並不代表有較良好的反應活性，因此在另一方面，本研究也利用反應能與Sabatier Analysis計算反應活性 (activity)，最後調整白金參雜在奈米支架上的的重量百分比，以利得出具有較高反應活性的組合。本研究發現，石墨烯參雜白金的重量百分比為94.2 wt%時，有良好的反應活性，而奈米碳管參雜白金的重量百分比為14.62 wt%時，有最好的反應活性，兩者都可大幅降低白金的使用量，增加反應面積，並維持良好的反應活性。

Enhancing the conversion efficiency from hydrogen to electricity is always the target of fuel cell research. The oxygen reduction reaction (ORR) in the cathode is regarded the rate-limited step. Platinum alloys are common methods to increase the catalyst activity. However, platinum is rare and expansive, therefore it’s the reason that fuel cell can’t be commercialized.
In this research, platinum doped single wall carbon nanotube and graphene that have good electrical conductivity and high specific surface area are used as nano-frames for reducing the usage amount of platinum in cathode. It is difficult to study the whole process of ORR by experiments. Therefore, this thesis studies the mechanisms of the reaction by First Principles calculation using Density Functional Theory (DFT). The adsorption energy, total energy of the system, reaction energy and activation energy of the ORR are all evaluated.
Since oxygen adsorption is the first step of the ORR, the adsorption energy and relative energy are calculated for different initial adsorption forms. It is found that Pt doped graphene can offer a stable reaction environment. However, a stable reaction environment does not promise a good reaction activity. This research uses Sabatier analysis methodology to calculate the reaction activity. In order to find out the highest reaction activity, the weight percentage of Pt doped nano-frames is tuned. It is found that the 94.2 wt% has its best reaction activity for Pt doped graphene and the 14.62 wt% has its best reaction activity for Pt doped single wall carbon nanotubes. Both of these two nano-frames can reduce the usage amount of platinum, increase the reaction area and maintain an excellent reaction activity.

摘要 I
Abstract II
符號表 VIII
第一章 緒論 - 1 -
1.1前言 - 1 -
1.2 燃料電池簡介與工作原理 - 2 -
1.3 燃料電池陰極觸媒材料 - 4 -
1.4 研究動機與目的 - 6 -
1.5 氧還原反應文獻回顧 - 7 -
第二章 計算量子力學理論 - 9 -
2.1 第一原理計算 - 9 -
2.2 密度泛函理論 - 9 -
2.2.1 Kohn-Sham方程式 - 11 -
2.2.2 交換相關泛函 - 14 -
2.2.3 週期性系統 - 15 -
2.2.4 贋勢與超軟贗勢 - 16 -
2.2.5 自洽場計算 - 18 -
2.3 氧還原反應 - 21 -
2.4吸附能 - 21 -
2.5 觸媒活性 - 22 -
2.5.1 The Brønsted–Evans–Polanyi relation - 23 -
2.5.2 Microkinetic modeling - 25 -
2.5.3 Sabatier Analysis - 27 -
第三章 系統模型建構與模擬方法 - 31 -
3.1模擬計算流程 - 31 -
3.2 模型建構與參數設定 - 32 -
第四章 模擬計算結果討論 - 38 -
4.1幾何結構最佳化 - 38 -
4.1.1 SWCNT/Pt 幾何結構最佳化 - 38 -
4.1.2 GRN/Pt 幾何結構最佳化 - 39 -
4.1.3 O2幾何結構最佳化 - 40 -
4.1.4 H3O+ 幾何結構最佳化 - 41 -
4.2 氧分子吸附形式 - 43 -
4.3催化過程模擬 - 45 -
4.4反應路徑相對能量分析 - 51 -
4.5 建立BEP relation並以Sabatier Analysis驗證活性 - 52 -
4.6 Sabatier Analysis of Pt-Doped Graphene and SWNT - 56 -
4.7 調整參雜在石墨烯與奈米碳管的白金重量百分比 - 61 -
第五章 結論與未來工作建議 - 65 -
5.2 結論 - 65 -
5.2 未來工作建議 - 66 -
參考文獻 - 67 -

1. Lindstrom, P., Environment, in Annual Energy Review 2011. 2011, U.S. Energy Information Administration. p. 302.
2. Zhang, L.P. and Xia, Z.H., Mechanisms of Oxygen Reduction Reaction on Nitrogen-Doped Graphene for Fuel Cells. Journal of Physical Chemistry C, 2011. 115(22): p. 11170-11176.
3. Dresselhaus, M.S., Dresselhaus, G., and Saito, R., Physics of Carbon Nanotubes. Carbon, 1995. 33(7): p. 883-891.
4. Zhang, S., Shao, Y.Y., Yin, G.P., and Lin, Y.H., Recent progress in nanostructured electrocatalysts for PEM fuel cells. Journal of Materials Chemistry A, 2013. 1(15): p. 4631-4641.
5. Watanabe, M., Tsurumi, K., Mizukami, T., Nakamura, T., and Stonehart, P., Activity and Stability of Ordered and Disordered Co-Pt Alloys for Phosphoric-Acid Fuel-Cells. Journal of the Electrochemical Society, 1994. 141(10): p. 2659-2668.
6. Watanabe, M., Tryk, D.A., Wakisaka, M., Yano, H., and Uchida, H., Overview of recent developments in oxygen reduction electrocatalysis. Electrochimica Acta, 2012. 84: p. 187-201.
7. Daube, K.A., Paffett, M.T., Gottesfeld, S., and Campbell, C.T., Combined Electrochemical Surface Science Investigations of Pt Cr Alloy Electrodes. Journal of Vacuum Science & Technology a-Vacuum Surfaces and Films, 1986. 4(3): p. 1617-1620.
8. Paffett, M.T., Beery, J.G., and Gottesfeld, S., Oxygen Reduction at Pt0.65cr0.35, Pt0.2cr0.8 and Roughened Platinum. Journal of the Electrochemical Society, 1988. 135(6): p. 1431-1436.
9. Beard, B.C. and Ross, P.N., The Structure and Activity of Pt-Co Alloys as Oxygen Reduction Electrocatalysts. Journal of the Electrochemical Society, 1990. 137(11): p. 3368-3374.
10. Jalan, V. and Taylor, E.J., Importance of Interatomic Spacing in Catalytic Reduction of Oxygen in Phosphoric-Acid. Journal of the Electrochemical Society, 1983. 130(11): p. 2299-2301.
11. Toda, T., Igarashi, H., and Watanabe, M., Role of electronic property of Pt and Pt alloys on electrocatalytic reduction of oxygen. Journal of the Electrochemical Society, 1998. 145(12): p. 4185-4188.
12. Santana, J.A., Mateo, J.J., and Ishikawa, Y., Electrochemical Hydrogen Oxidation on Pt(110): A Combined Direct Molecular Dynamics/Density Functional Theory Study. Journal of Physical Chemistry C, 2010. 114(11): p. 4995-5002.
13. Mateo, J., Tryk, D., Cabrera, C., and Ishikawa, Y., Underpotential deposition of hydrogen on Pt(111): a combined direct molecular dynamics/density functional theory study. Molecular Simulation, 2008. 34(10-15): p. 1065-1072.
14. Ishikawa, Y., Mateo, J.J., Tryk, D.A., and Cabrera, C.R., Direct molecular dynamics and density-functional theoretical study of the electrochemical hydrogen oxidation reaction and underpotential deposition of H on Pt(111). Journal of Electroanalytical Chemistry, 2007. 607(1-2): p. 37-46.
15. Greeley, J., Jaramillo, T.F., Bonde, J., Chorkendorff, I.B., and Norskov, J.K., Computational high-throughput screening of electrocatalytic materials for hydrogen evolution. Nature Materials, 2006. 5(11): p. 909-913.
16. Greeley, J. and Norskov, J.K., Large-scale, density functional theory-based screening of alloys for hydrogen evolution. Surface Science, 2007. 601(6): p. 1590-1598.
17. Greeley, J. and Norskov, J.K., Combinatorial Density Functional Theory-Based Screening of Surface Alloys for the Oxygen Reduction Reaction. Journal of Physical Chemistry C, 2009. 113(12): p. 4932-4939.
18. Girishkumar, G., McCloskey, B., Luntz, A.C., Swanson, S., and Wilcke, W., Lithium - Air Battery: Promise and Challenges. Journal of Physical Chemistry Letters, 2010. 1(14): p. 2193-2203.
19. Lin, Y.H., Cui, X.L., Yen, C., and Wai, C.M., Platinum/carbon nanotube nanocomposite synthesized in supercritical fluid as electrocatalysts for low-temperature fuel cells. Journal of Physical Chemistry B, 2005. 109(30): p. 14410-14415.
20. Hayes, K.E. and Lee, H.S., First principles studies of the electronic properties and catalytic activity of single-walled carbon nanotube doped with Pt clusters and chains. Chemical Physics, 2012. 393(1): p. 96-106.
21. Yoo, E., Okata, T., Akita, T., Kohyama, M., Nakamura, J., and Honma, I., Enhanced Electrocatalytic Activity of Pt Subnanoclusters on Graphene Nanosheet Surface. Nano Letters, 2009. 9(6): p. 2255-2259.
22. Shao, Y.Y., Zhang, S., Wang, C.M., Nie, Z.M., Liu, J., Wang, Y., and Lin, Y.H., Highly durable graphene nanoplatelets supported Pt nanocatalysts for oxygen reduction. Journal of Power Sources, 2010. 195(15): p. 4600-4605.
23. Lim, D.H. and Wilcox, J., Mechanisms of the Oxygen Reduction Reaction on Defective Graphene-Supported Pt Nanoparticles from First-Principles. Journal of Physical Chemistry C, 2012. 116(5): p. 3653-3660.
24. Payne, M.C., Teter, M.P., Allan, D.C., Arias, T.A., and Joannopoulos, J.D., Iterative Minimization Techniques for Abinitio Total-Energy Calculations - Molecular-Dynamics and Conjugate Gradients. Reviews of Modern Physics, 1992. 64(4): p. 1045-1097.
25. Vanderbilt, D., Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism. Physical Review B, 1990. 41(11): p. 7892-7895.
26. Thomas, A.H. and William, N.L., The synchronous-transit method for determining reaction pathways and locating molecular transition states. Chemical Physics Letters, 1977. 49: p. 2.
27. Aravind Asthagiri, M.J.J., Computational Catalysis, ed. P.J.J. Spivey. 2014, Cambridge, UK: The Royal Society of Chemistry.
28. Bligaard, T., Norskov, J.K., Dahl, S., Matthiesen, J., Christensen, C.H., and Sehested, J., The Bronsted-Evans-Polanyi relation and the volcano curve in heterogeneous catalysis. Journal of Catalysis, 2004. 224(1): p. 206-217.
29. Falsig, H., Understanding Catalytic Activity Trends for NO Decomposition and CO Oxidation using Density Functional Theory and Microkinetic modeling, in Chemistry. 2010, Danmarks Tekniske Universitet p. 19.
30. Norskov, J.K., Rossmeisl, J., Logadottir, A., Lindqvist, L., Kitchin, J.R., Bligaard, T., and Jonsson, H., Origin of the overpotential for oxygen reduction at a fuel-cell cathode. Journal of Physical Chemistry B, 2004. 108(46): p. 17886-17892.
31. Sorescu, D.C., Jordan, K.D., and Avouris, P., Theoretical study of oxygen adsorption on graphite and the (8,0) single-walled carbon nanotube. Journal of Physical Chemistry B, 2001. 105(45): p. 11227-11232.
32. Wang, S., Petzold, V., Tripkovic, V., Kleis, J., Howalt, J.G., Skulason, E., Fernandez, E.M., Hvolbaek, B., Jones, G., Toftelund, A., Falsig, H., Bjorketun, M., Studt, F., Abild-Pedersen, F., Rossmeisl, J., Norskov, J.K., and Bligaard, T., Universal transition state scaling relations for (de)hydrogenation over transition metals. Physical Chemistry Chemical Physics, 2011. 13(46): p. 20760-20765.