低溫燃料電池陰極觸媒目前階段以白金（Pt）為最通用的材料，其仍有極多需改善的問題，比如白金的昂貴性使之極難大量普及等，以及如何將其電化學效率進一步提升，一直都是大家在追求的目標。本論文將深入模擬其催化反應過程，探究其特性並作出效率提升的改善，以利未來發展更有效率及實用的低溫燃料電池。
低溫燃料電池的陰極觸媒「氧還原反應」為最關鍵步驟(rate-limited step)，其真實反應程序極為複雜，反應機制也有很多不同的變化。本研究希望藉由量子力學分析質子交換膜燃料電池(proton exchange membrane fuel cell, PEMFC)中陰極觸媒部分，選擇傳統白金及新穎材料元素「氮」作為陰極觸媒材料，並且利用單層及多層奈米碳管(single walled and multi-walled carbon nanotubes)與石墨烯(graphene, GRN)等導電性良好、大表面積的材料作為其陰極支架，探討其氧還原反應的過程變化，包含反應一開始的氧氣吸附、原子解離、電子質子傳遞、產品生成等。觸媒加入支架內的方式則運用吸附和參雜兩種，以模擬添加觸媒於碳材中的真實情況，並比較兩者對催化反應的影響。
在模擬此一氧還原反應中，我們將以第一原理計算模擬過程，建立分子尺度的奈米碳材結構，以密度泛函理論(density functional theory, DFT) 搭配CASTEP(Cambridge Sequential Total Energy Package)計算，而其中採週期邊界條件，以平面波為其基底函數(basis set)，由固態化學基本理論計算來取得氧氣和奈米碳材結構吸附與解離，以及水合離子作用與產物水的脫附等的最佳化型態，接著計算電子傳導的功函數、重組能及由Marcus theory所推導出的反應速率等，並取用單位晶胞重複性的方式來取代單顆原子互相堆疊的情況，可以達到更真實的反應環境與反應機制。

In low temperature fuel cells, the cathodic reaction, oxygen reduction reaction (ORR), is the main rate-limited step. Normally, the kinetics of oxygen reduction reaction is very slow. For the purpose of speeding up the reaction to reach a practical usable level in a low temperature fuel cell, cathode catalysts are needed to be further investigated. Pt-based materials are the most practical catalysts currently. Because these Pt-based catalysts are too expensive for making commercially viable low temperature fuel cells, extensive research over the past several decades has focused on developing alternative catalysts. This thesis focuses on the reaction processes, and points out the key of improving efficiency.
Some steps which influence the efficiency of low temperature fuel cells includes; oxygen adsorption, oxygen dissociation, protonation, charge transfer, and water desorption among others. we use the method of density functional theory (DFT) to build the nano structures including graphene, single walled and multi-walled carbon nanotube. In addition, We apply adsorption and doping methods to add the cathodic catalysts, Platinum and Nitrogen atoms into the nano structures. Then, we try to use the CASTEP platform to optimize the molecular structures during the oxygen reduction reaction process and analyze about the catalytic properties such as adsorption energy, work function, reorganization energy and rate of electron transfer. In conclusion, we obtain the improvement of catalyst in most of the selected nano structures and cathodic catalysts .

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