臺灣博碩士論文加值系統

碎形理論是一種有系統的空間切割方法，在工程應用上有許多實例，如熱傳、冷卻、散熱器鰭片設計、以及自動加工路徑等。本文採用碎形幾何圖形，應用於直接甲醇燃料電池之集電板幾何設計，探討集電板其開口方式、開口面積、以及開口周長，對電池性能的影響與電化學交流阻抗分析。
本文提出三種集電板幾何設計，第一種集電板設計使用Sierpinski Carpets碎形幾何生成，其幾何形狀設計可以對集電板作有系統的切割，其開口率最大為30%。隨著碎形階數越大，可以具有較大的開口率與開口周長，使電池性能較佳，電化學阻抗較低。
第二種集電板設計使用Hilbert Curve碎形幾何生成，其幾何形狀是對集電板做有系統的連續性切割，開口型態可以在平面區域中進行有效的伸展與平均分佈，開口率最大可達50%。隨著碎形階數越大，可以提供更大的開口率與開口周長，使電池性能提升，電化學阻抗較低。
第三種集電板設計使用對稱排列矩形開口幾何設計，開口率分別為30%、40%、50%與60%，開口分佈型態設計為對稱式排列，排列方式為，5×5之開口排列，7×7之開口排列與10×10之開口排列。選用適當的開口設計，可以使甲醇與空氣能均勻的分佈於膜電極組中進行電化學反應，並且在陽極端所產生的二氧化碳與陰極端所產生的水得以順利排出，進而提高電池性能。

The fractal theory is a methodology to systematically segment the space. There are many real examples in the engineering applications, such as heat transfer, cooling, fin design of heatsink, and automatic polishing path. This dissertation adopts fractal geometries to apply on the design of the current collectors of the direct methanol fuel cell and discuss the effect on the cell performance as well as the electrochemical spectroscopy impedance by the free open style, the total free open ratio, and total perimeter length of openings on the current collectors.
This dissertation presents three geometric designs on the current collectors. The first design is to adopt the Sierpinski carpet fractal geometry to systematically make separate segments on the current collectors. The maximum total free open ratio is 30% by this design. The higher fractal order could provide the current collectors larger total free open ratio as well as longer total perimeter length of openings, such leads the cell have better performance and lower electrochemical impedance.
The second design is to adopt the Hilbert curve fractal geometry to systematically make continuous segments on the current collectors. Such open style could give effective line extension and average openings spread in the planar area. The maximum free open ratio could reach 50% by this design. The higher fractal order could further provide larger total free open ratio as well as longer total perimeter length of openings, such leads the cell have better performance and lower electrochemical impedance.
The third design is to adopt the regular rectangle free openings design on the current collectors. The free open ratio is 30%, 40%, 50%, and 60%, respectively. The arrangement of the free openings distribution is 5x5, 7x7, and 10x10, respectively. The proper free openings design could allow the methanol and air uniformly distribute to the membrane electrolyte assembly, such that the electrochemical reactions are able to proceed and the carbon dioxide produced at the anode side could drain successfully, and the cell performance would be further enhanced.

目錄
中文摘要 I
英文摘要 III
目錄 V
圖目錄 VIII
表目錄 XIII
符號索引 XIV
第一章 緒論 1
1.1 研究背景 1
1.2 研究動機 3
1.3 文獻回顧 6
1.3.1 可攜式直接甲醇燃料電池 6
1.3.2 直接甲醇燃料電池雙極板研究 9
1.3.3 直接甲醇燃料電池之電化學交流阻抗分析 11
1.4 論文架構 13
第二章 基礎理論 16
2.1 直接甲醇燃料電池簡介 16
2.1.1 直接甲醇燃料電池構造 16
2.1.2 直接甲醇燃料電池運作原理 18
2.1.3 直接甲醇燃料電池之過電位與極化現象 19
2.2 燃料電池之雙極板介紹 21
2.3 燃料電池之電化學交流阻抗分析 24
第三章 Sierpinski Carpets碎形集電板設計分析 28
3.1 碎形理論介紹 28
3.2 Sierpinski Carpets碎形幾何設計 30
3.3 Sierpinski Carpets碎形集電板 31
3.4 實驗架設與實驗規劃 36
3.4.1 測試單電池模組 36
3.4.2 電池性能分析實驗 38
3.4.3 電化學交流阻抗分析實驗 39
3.4.4 實驗規劃 40
3.5 結果討論 42
第四章 Hilbert Curve碎形集電板設計分析 50
4.1 Hilbert Curve碎形幾何設計 50
4.2 Hilbert Curve碎形集電板 54
4.3 實驗架設與實驗規劃 57
4.4 結果與討論 59
第五章 不同開口面積之集電板設計分析 66
5.1 不同開口面積之集電板設計 66
5.2 不同開口面積之集電板 67
5.3 實驗架設與實驗規劃 74
5.3.1 主動式直接甲醇燃料電池 74
5.3.2 被動式直接甲醇燃料電池 75
5.3.3 實驗架設與實驗規劃 76
5.4 結果與討論 79
第六章 結論 87
6.1 結論 87
6.2 建議與未來展望 89
參考文獻 91
論文著述目錄 100

圖目錄
圖1.1 推疊式直接甲醇燃料電池堆雙極板 5
圖1.2 平板式直接甲醇燃料電池堆 5
圖1.3 研究架構圖 15
圖2.1 直接甲醇燃料電池構造圖 17
圖2.2 直接甲醇燃料電池組合圖 17
圖2.3 直接甲醇燃料電池之反應機制[4, 46] 19
圖2.4 燃料電池性能曲線圖[3] 21
圖2.5 常用流道的基本設計[2, 3] 22
圖2.6 平板式直接甲醇燃料電池[19] 23
圖2.7 Nyquist圖及相對應等效電路[46, 47] 25
圖3.1 Koch Curve Construction[54] 29
圖3.2 Random Koch Curve[54] 30
圖3.3 Sierpinski Carpets碎形圖形[54] 31
圖3.4 標準圓形集電板 33
圖3.5 圓形碎形1階集電板 33
圖3.6 圓形碎形2階集電板 34
圖3.7 標準矩形集電板 34
圖3.8 矩形碎形1階集電板 35
圖3.9 矩形碎形2階集電板 35
圖3.10 測試單電池模組 37
圖3.11 燃料電池組件分解示意圖 37
圖3.12 電池性能分析實驗架構圖 38
圖3.13 電化學交流阻抗分析實驗架構圖 39
圖3.14 實驗規劃架構圖 41
圖3.15 圓形碎形集電板電池性能圖 43
圖3.16 矩形碎形集電板電池性能圖 43
圖3.17 矩形碎形集電板Nyquist圖 44
圖3.18 圓形碎形集電板電池性能圖 45
圖3.19 矩形碎形集電板電池性能圖 46
圖3.20 矩形碎形集電板Nyquist圖 46
圖3.21 圓形碎形集電板電池性能圖 48
圖3.22 矩形碎形集電板電池性能圖 48
圖3.23 矩形碎形集電板Nyquist圖 49
圖4.1 Hilbert Curve用於L-Systems介紹圖[54] 52
圖4.2 Hilbert Curve用於L-Systems說明圖[54] 53
圖4.3 標準極電板(SRCC) 55
圖4.4 Hilbert Curve碎形1階集電板(HFCC1) 56
圖4.5 Hilbert Curve碎形2階集電板(HFCC2) 56
圖4.6 Hilbert Curve碎形3階集電板(HFCC3) 57
圖4.7 實驗架構圖 59
圖4.8 標準集電板電池性能圖 60
圖4.9 碎形1階集電板電池性能圖 60
圖4.10 碎形2階集電板電池性能圖 60
圖4.11 碎形3階集電板電池性能圖 61
圖4.12 甲醇流量5cc min-1集電板電池性能圖 62
圖4.13 甲醇流量10cc min-1集電板電池性能圖 63
圖4.14 甲醇流量15cc min-1集電板電池性能圖 63
圖4.15 直流負載0.5V之Nyquist圖 65
圖4.16 直流負載0.4V之Nyquist圖 65
圖5.1 開口率30%開口排列5×5之集電板 68
圖5.2 開口率30%開口排列7×7之集電板 68
圖5.3 開口率30%開口排列10×10之集電板 69
圖5.4 開口率40%開口排列5×5之集電板 69
圖5.5 開口率40%開口排列7×7之集電板 70
圖5.6 開口率40%開口排列10×10之集電板 70
圖5.7 開口率50%開口排列5×5之集電板 71
圖5.8 開口率50%開口排列7×7之集電板 71
圖5.9 開口率50%開口排列10×10之集電板 72
圖5.10 開口率60%開口排列5×5之集電板 72
圖5.11 開口率60%開口排列7×7之集電板 73
圖5.12 開口率60%開口排列10×10之集電板 73
圖5.13 主動式燃料電池測試治具 75
圖5.14 被動式燃料電池測試治具 76
圖5.15 主動式燃料電池實驗架設圖 77
圖5.16 被動式燃料電池實驗架設圖 78
圖5.17 主動式燃料電池實驗規劃圖 78
圖5.18 被動式燃料電池實驗規劃圖 79
圖5.19 主動式燃料電池不同開口率比較 80
圖5.20 主動式燃料電池不同開口率比較 81
圖5.21 主動式燃料電池不同開口率比較 81
圖5.22 被動式燃料電池不同開口率比較 81
圖5.23 被動式燃料電池不同開口率比較 82
圖5.24 被動式燃料電池不同開口率比較 82
圖5.25 主動式燃料電池不同開口排列比較 84
圖5.26 主動式燃料電池不同開口排列比較 84
圖5.27 主動式燃料電池不同開口排列比較 84
圖5.28 主動式燃料電池不同開口排列比較 85
圖5.29 被動式燃料電池不同開口排列比較 85
圖5.30 被動式燃料電池不同開口排列比較 85
圖5.31 被動式燃料電池不同開口排列比較 86
圖5.32 被動式燃料電池不同開口排列比較 86

表目錄
表3.1 圓形圖形定義參數表 36
表3.2 矩形圖形定義參數表 36
表3.3 實驗設計組合 41
表4.1 Hilbert Curve尺寸參數表 57
表5.1 集電板幾何參數定義表 74

[1]G. Weaver, World Fuel Cells - An Industry Profile with Market Prospects to 2010, Elsevier Science, December 2002.
[2]Fuel Cell Handbook, EG & G Services, Parsons, Inc. and Science Applications International Corporation, 5th ed., October 2000.
[3]F. Barbir, PEM Fuel Cells. Elsevier Inc., 2005.
[4]J. Larminie and A. Dicks, Fuel cell systems explained, 2nd ed. John Wiley and Sons Ltd., 2003.
[5]H. Tsuchiya and O. Kobayashi, “Mass production cost of PEM fuel cell by learning curve,” International Journal of Hydrogen Energy, Vol. 29, pp. 985– 990, 2004.
[6]G. Apanel and E. Johnson, “Direct Methanol Fuel Cells-Ready to Go Commercial?,” Fuel Cells Bulletin, Vol. 2004, pp. 12–17, November 2004.
[7]K. Scott, W. M. Taama, P. Argyropoulos, “Engineering aspects of the direct methanol full cell system, ”Journal of Power Sources, Vol. 79, pp. 43–59, May 1999.
[8]J. Ge and H. Liu, “Experimental studies of a direct methanol fuel cell,” Journal of Power Sources, Vol. 142, pp. 56–69, March 2005.
[9]C. Xie, J. Bostaph, and J. Pavio, “Development of a 2W direct methanol fuel cell power source,” Journal of Power Sources, Vol. 136, pp. 55–65, September 2004.
[10]A. Oedegaard, S. Hufschmidt, R. Wilmshoefer, and C. Hebling, “Portable size DMFC-stack,” Fuel Cells, Vol. 4, pp. 219–224, July 2004.
[11]C. Y. Chen, J. Y. Shiu, and Y. S. Lee, “Development of a small DMFC bipolar plate stack for portable applications,” Journal of Power Sources, Vol. 159, pp. 1042–1047, September 2006.
[12]A. Blum, T. Duvdevani, M. Philosoph, N. Rudoy, and E. Peled, “Water-neutral micro direct-methanol fuel cell (DMFC) for portable applications,” Journal of Power Sources, Vol. 117, pp. 22–25, May 2003.
[13]C. Y. Chen, D. H. Liu, C. L. Huang, and C. L. Chang, “Portable DMFC system with methanol sensor-less control,” Journal of Power Sources, Vol. 167, pp. 442, 2007.
[14]Y. H. Pan, “Advanced air-breathing direct methanol fuel cells for portable applications,” Journal of Power Sources, Vol. 161, p. 282, 2006.
[15]R. O’Hayre, D. Braithwaite, W. Hermann, S.-J. Lee, T. Fabian, S.-W. Cha, Y. Saito, and F. B. Prinz, “Development of portable fuel cell arrays with printed-circuit technology,” Journal of Power Sources, Vol. 124, pp. 459–472, November 2003.
[16]A. Schmitz, M. Tranitz, S. Wagner, R. Hahn, and C. Hebling, “Planar self-breathing fuel cells,” Journal of Power Sources, Vol. 118, pp. 162–171, May 2003.
[17]A. Schmitz, S. Wagner, R. Hahn, H. Uzun, and C.Hebling, “Stability of planar PEMFC in printed circuit board technology,” Journal of Power Sources, Vol. 127, pp. 197–205, March 2004.
[18]S. W. Lim, S. W. Kim, H. J. Kim, J. E. Ahn, H. S. Han, and Y. G. Shul, “Effect of operation parameters on performance of micro direct methanol fuel cell fabricated on printed circuit board,” Journal of Power Sources, Vol. 161, pp. 27–33, October 2006.
[19]Y.-D. Kuan and C.-H. Chang, “Experimental investigation on the process-induced damage of a direct methanol fuel cell assembled by the printed circuit board technique,” Journal of fuel cell Science and Technology, Vol. 6, 011016-1-011016-9, February 2009.
[20]Y.-D. Kuan, S.-M. Lee, J.-Y. Chang, and M.-F. Sung, “A novel flow design on the planar printed-circuit-board DMFC modules,” Proceedings of FuelCell2008 Sixth International Fuel Cell Science, Engineering, and Technology Conference, Denver, Colorado, USA, June 16-18 2008.
[21]Y.-D. Kuan, S.-M. Lee, and M.-F. Sung, “Experimental study on the characterization of airflow effect on the direct methanol fuel cell,” Renewable Energy, Vol. 34, pp. 1962–1968, August 2009.
[22]Y.-D. Kuan, S.-M. Lee, and M.-F. Sung, “The cathode airflow effect on the direct methanol fuel cell from single cell to a planar module,” Journal of fuel cell Science and technology, Vol. 6, 011004-1-011004-9, February 2009.
[23]A. Hermann, T. Chaudhuri, and P. Spagnol, “Bipolar plates for PEM fuel cells: a review,” International Journal of Hydrogen Energy, Vol. 30, pp. 1297– 1302, September 2005.
[24]P. L. Hentall, J. B. Lakeman, G. O. Mepsteda, P. L. Adcock, and J. M. Moore, “New materials for polymer electrolyte membrane fuel cell current collectors,” Journal of Power Sources, Vol. 80, pp. 235–241, July 1999.
[25]R. C. Makkus, A. H. H. Janssen, F. A. de Bruijn, and R. K. A. M. Mallant, “Use of stainless steel for cost competitive bipolar plates in the SPFC,” Journal of Power Sources, Vol. 86, pp. 274–282, 2000.
[26]R. C. Makkus, A. H. H. Janssen, F. A. de Bruijn, and R. K. A. M. Mallant, “Stainless steel for cost-competitive bipolar plates in PEMFCs,” Fuel Cell Bulletin, Vol. 3, pp. 5–9, February 2000.
[27]J. Wind, R. Spah, W. Kaiser, and G. Bohm, “Metallic bipolar plates for PEM fuel cells,” Journal of Power Sources, Vol. 105, pp. 256–260, March 2002.
[28]H. Wang, M. A. Sweikart, and J. A. Turner, “Stainless steel as bipolar plate material for polymer electrolyte membrane fuel cells,” Journal of Power Sources, Vol. 115, pp. 243–251, April 2003.
[29]B. R. Padhy and R. G. Reddy, “Performance of DMFC with SS 316 bipolar/end plates,” Journal of Power Sources, Vol. 153, pp. 125–129, January 2006.
[30]H. Guo, C. F. Ma, M. H. Wang, F. Ye, J. Yu, Y. Wang, and C. Y. Wang, “Experimental investigation of effect of flow bed design on performance of liquid feed direct methanol fuel cells,” Fuel Cells, Vol. 4, pp. 86–89, April 2004.
[31]K. Tüber, A. Oedegaard, M. Hermann, and C. Hebling, ”Investigation of fractal flow-fields in portable proton exchange membrane and direct methanol fuel cells,” Journal of Power Sources, Vol. 131, pp. 175–181, May 2004
[32]H. Yang and T. S. Zhao, “Effect of anode flow field design on the performance of liquid feed direct methanol fuel cells,” Electrochimica Acta, Vol. 50, pp. 3243–3252, May 2005.
[33]C. W. Wong, T. S. Zhao, Q. Ye, and J. G. Liu, “Experimental investigations of the anode flow field of a micro direct methanol fuel cell,” Journal of Power Sources, Vol. 155, pp. 291–296, April 2006.
[34]J. J. Hwang, S. D. Wu, L. K. Lai, C. K. Chen and D. Y. Lai, “Effect of breathing-hole size on the electrochemical species in a free-breathing cathode of a DMFC,” Journal of Power Sources, Vol. 161, pp. 240–249, October 2006.
[35]J.-Y. Chang, Y.-D. Kuan, S.-M. Lee, and S.-R. Lee, “Characterization of a liquid feed direct methanol fuel cell with Sierpinski carpets fractal current collectors,” Journal of Power Sources, Vol. 184, pp. 180–190, September 2008.
[36]Y.-D. Kuan, J.-Y. Chang, S.-M. Lee, and S.-R. Lee, “Characterization of a direct methanol fuel cell using hilbert curve fractal current collectors,” Journal of Power Sources, Vol. 187, pp. 112–122, February 2009.
[37]J. T. Muller, P. M. Urban, and W. F. Holderich, “Impedance studies on direct methanol fuel cell anodes,” Journal of Power Sources, Vol. 84, pp. 157–160, December 1999.
[38]J. C. Amphlett, B. A. Peppley, E. Halliop, and A. Sadiq, “The effect of anode flow characteristics and temperature on the performance of a direct methanol fuel cell,” Journal of Power Sources, Vol. 96, pp. 204–213, June 2001.
[39]K. Furukawa, K. Makino, K. Okajima, H. Minakuchi, Y. Okano, and M. Sudoh, “Intelligent structure design of membrane cathode assembly for direct methanol fuel cell,” International Journal of Energy Research, Vol. 29, no. 12, pp. 1073–1082, 2005.
[40]T. V. Reshetenko, H.-T. Kim, H. Lee. and M. Jang, and H.-J. Kweon, “Performance of a direct methanol fuel cell (DMFC) at low temperature: Cathode optimization,” Journal of Power Sources, Vol. 160, pp. 925–932, October 2006.
[41]A. Oedegaard, “Characterisation of direct methanol fuel cells under near-ambient conditions,” Journal of Power Sources, Vol. 157, pp. 244–252, June 2006.
[42]P. Piela, R. Fields, and P. Zelenay, “Electrochemical impedance spectroscopy for direct methanol fuel cell diagnostics,” Journal of The Electrochemical Society, Vol. 153, pp. A1902–A1913, August 2006.
[43]M. K. Jeon, J. Y. Won, K. S. Oh, K. R. Lee, and S. I. Woo, “Performance degradation study of a direct methanol fuel cell by electrochemical impedance spectroscopy,” Electrochimica Acta, Vol. 53, pp. 447–452, December 2007.
[44]C.-M. Lai, J.-C. Lin, K.-L. Hsueh, C.-P. Hwang, K.-C. Tsay, L.-D. Tsai, and Y.-M. Peng, “On the electrochemical impedance spectroscopy of direct methanol fuel cell,” International Journal of Hydrogen Energy, Vol. 32, pp. 4381–4388, December 2007.
[45]Y.-D. Kuan, S.-M. Lee, J.-Y. Chang, and M.-F. Sung, “The experimental investigation of a direct methanol fuel cell using hilbert fractal current collectors,” The First International Conference on Applied Energy (ICAE’09), Hong Kong, January 5-7 2009.
[46]R. O’Hayre, S.-W. Cha, W. Colella, F. B. Prinz, Fuel cell fundamentals. John Wiley and Sons Ltd., 2006.
[47]C. M. A. Brett and A. M. O. Brett, Electrochemistry: Principles, Methods, and Applications, Oxford University Press, USA, 1993.
[48]B. B. Mandelbrot, The Fractal Geometry of Nature. W. F. Freeman, 1983.
[49]D. J. Lee and W. W. Lin, “Second law analysis on fractal-like fin under crossflow,” Journal of AIChE, Vol. 41, pp. 2314–2317, October 1995.
[50]G. A. Ledezma, A. Bejan, and M. R. Errera, “Constructal tree networks for heat transfer,” Journal of Applied Physics, Vol. 82, pp. 89–100, July 1997.
[51]C. C. A. Chen,Y.-S. Juang, and W. Z. Lin, “Generation of fractal tool-paths for irregular shapes of surface finishing areas,” Journal of Materials Processing Technology, Vol. 127, pp. 146–150, September 2002.
[52]S. R. Lee, Y. C. Wang, and C. C. A. Chen, “Thermal performance of novel fractal heat sink fins,” Journal of The Chinese Society of Mechanical Engineers, Vol. 25, no. 6, pp. 547–556, 2004.
[53]R. M. Crownover, Introduction to Fractals and Chaos. Jones and Bartlett Publishers, January 1995.
[54]H. O. Peitgen, H. Jurgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science, Springer-Verlag, 1992.
[55]D. Hilbert., “Ueber die stetige abbildung einer line auf ein flachenstuck,” Mathematische Annalen, Vol. 38, No. 3, pp. 459–460, September 1891.
[56]H. V. Jagadish, “Analysis of the hilbert curve for representing two-dimensional space,” Information Processing Letters, Vol. 62, pp. 17–22, April 1997.
[57]N. Max, “Visualizing hilbert curves,” IEEE Visualization 1998 (VIS’98), pp. 447–450, 1998.
[58]J. Romeu and S. Blanch, “A three dimensional hilbert antenna,” Proc. IEEE Antennas and Propagation Society International Symposium, Vol. 4, pp. 550– 553, 2002.