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

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