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博碩士論文 etd-0910112-165126 詳細資訊
Title page for etd-0910112-165126
論文名稱
Title
利用核磁共振鬆弛和交換研究質子交換膜Nafion 117內水之狀態
Investigation of the States of Water in Proton Exchange Membrane Nafion 117 with Nuclear Magnetic Resonance Relaxation and Exchange
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
216
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2012-07-03
繳交日期
Date of Submission
2012-09-10
關鍵字
Keywords
核磁共振、質子交換膜、交換、鬆弛
Exchange, Relaxation, Nafion, NMR
統計
Statistics
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中文摘要
我們使用氘及氫自旋核磁共振技術研究Nafion 117質子交換膜內,位於磺酸根團簇裡的水分子及位於界面區域的水分子。在氘自旋的CPMG實驗裡,其長延遲時間的訊號強度變化會呈現振盪的行為,這是因為團簇裡之水分子的殘餘之四極偶合作用所導致的結果。而在短延遲時間的強度變化則呈現指數衰退的行為,這個現像是由於不同區域之水分子會因作用力的不同,而在CPMG實驗裡,訊號會產生相異的行為並相互交疊。不同區域之水分子和其相對應之作用如下: 位在團簇裡之水分子會有殘餘之四極偶合作用力,而在界面區域之水分子則會有磁化率不均勻的影響產生。
在完全水合的質子交換膜內,不同區域之水分子組成百分比可以利用四極回波序列 (quadrupolar echo)來研究。位於磺酸根團簇裡的水分子之比例為70%,而位於界面區域的水分子為30%。在升高溫度的條件下,水分子會從團簇區擴散至界面區域,進而導致質子核磁共振光譜的強度產生變化。因為水分子和磺酸根的結合能較大,在團簇裡之水分子相較於位在界面區域的水分子,會有較高的移動擴散活化能。
磺酸根團簇裡之水分子的射頻加熱效應同時也使用氫自旋CPMG及Rotating-Frame-Relaxation-Dispersion實驗來進行研究。介電響應會產生一個熱源,此熱源會導致水分子化學位移的飄移及橫向鬆弛時間的變化。
Abstract
The clustered water and interfacial water in Nafion 117 membrane have been quantified by NMR deuterium and proton experiments. The oscillation of intensity profile in 2H CPMG sequence with large duration time is induced by the residual quadrupolar interaction in clustered water. While the intensity profile of 2H CPMG sequence at short duration time followed the rule of exponential decay which is the consequence of the profile-overlapping between clustered water with residual quadrupolar interaction and interfacial water with susceptibility effect.
The populations of clustered water and interfacial water in fully hydrated membrane are estimated by quadrupolar echo sequence. The population of former and latter is 70% and 30%,respectively. At an elevated temperature, water in cluster region can transport to the interfacial region and result in change of intensity for proton spectrum. The activation energy of translational diffusion of interfacial water is lower than that of clustered water due to the strong binding energy between sulfonate group and water molecule.
The rf-heating effect on the proton spectrum of clustered water also has been explored by 1H CPMG and rotating-frame-relaxation-dispersion experiments. The dielectric response to a time-dependent external electric field provides a source of heat which causes a drift in chemical shift and interfere with transverse relaxation .
目次 Table of Contents
Chapter 1 Introduction 1
Chapter 2 Basics of NMR Spectroscopy 10
2.1 Representation of Spin Operators in Hilbert Space .10
2.1.1 Hilbert State Vectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 Operator Representation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2.1 Two-Level System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
2.1.2.2 Three-Level System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
2.1.2.3 Tensor Operator Representation. . . . . . . . . . . . . . . . . . . . . . . . . . . .13
2.1.2.3.1 Two-Level System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
2.1.2.3.2 Three-Level System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14
2.1.2.3.3 General Tensor Operator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14
2.1.2.3.4 Higher-Rank Tensor Operators. . . . . . . . . . . . . . .. . . . . . . . . . .15
2.1.2.3.5 Wigner Rotation Operator. . . . . . . . . . .. . . . . . . .. . . . . . . . . . .15
2.1.3 Density Operator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.4 Equation of Time Evolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.4.1 Time-Independent Hamiltonian m . . . . . . . . . . . . . . . . . . . . . . . . . .18
2.1.4.2 Time-Dependent Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
2.1.4.3 Averaged Hamiltonian Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
2.1.5 Spin Interactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.5.1 Chemical Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
2.1.5.2 Dipole-Dipole Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
2.1.5.3 Quadrupolar Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.1.5.4 Magic Angle Spinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
2.2 Spin System in Liouville Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28
2.2.1 Operator in Liouville Space. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 29
2.2.2 Calculation of Matrix Elements for the Liouvillian ( ). . . .. . . . . . . . . . . 30
2.2.2.1 Zeeman Interaction . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
2.2.2.2 rf Interaction . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .33
2.2.3 Exchange and Relaxation in Liouville Space. . . . . . . . . . . . . . . . . . . . . . . 34
2.3 Relaxation Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.3.1 Redfield Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.3.2 Master Equation in Operator Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.4 References……………………………………………………………………..49
Chapter 3 Review on NMR Studies of Nafion . . . . . . . . . . . . . . . . . . . .50
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50
3.2 Morphological Models based on SAXS/SANS Studies . . . . . . .. . . . . . . . . . . .57
3.2.1 Spherical Cluster Model…………………………………………………..57
3.2.1.1 Interparticle Two-Phase Cluster Model……………………………57
3.2.1.2 Intraparticle Core-Shell Model…………………………………….59
3.2.2 Elongated Polymer Particle Model………………………………………..61
3.2.3 Parallel Water-Channel Model…………………………………………….66
3.3 NMR Studies…………………………………………………………………..68
3.3.1 Characterization of Polymer Matrix……………………………………....68
3.3.1.1 Chemical Shift Assignment……………………………………….68
3.3.1.2 Structural Features and Dynamics…………………………………72
3.3.2 Characterization of Solvent Molecule……………………………………79
3.3.2.1 Relaxation Studies…………………………………………………79
3.3.2.2 Diffusion Studies……………………………………………..……91
3.3.2.3 Imaging Studies…………………………………………………..102
3.4 References………………………………………………………………........107
Chapter 4 Experimental Methods. . . . . . . . . . . . . . . . . . . . . . . ………..…111
4.1 Chemical Exchange in Bloch-McConnell equation . . . . . . . . . . . .. . . . . . . . .111
4.2 Chemical Exchange in Carr-Purcell-Meiboom-Gill (CPMG) Experiment . . .115
4.2.1 Chemical Exchange in CPMG for two I=1 spin system without consideration of quadrupolar interaction. . . . . . .. . . . . . . . . . . . . . . . . 118
4.2.2 Chemical Exchange in CPMG for two I=1 spin system with consideration of quadrupolar interaction. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . 123
4.2.2.1 Simulations of two-sites system without chemical exchange. . . . 127
4.2.2.2 Simulations of two-sites system with chemical exchange . . . . . . 129
4.2.3 Chemical Exchange in Quadrupolar-Echo for two I=1 Spin System with Consideration of Quadrupolar Interaction. . . . . . . . . .. . . . . . . . . . . . . 133
4.3 Double Quantum Filter (DQF) Experiments with Considerations of Chemical Exchange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134
4.4 Rotating Frame Relaxation Dispersion (RFRD) Experiments . . . . . . . . . . . . 139
4.5 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.5.1 Spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.5.2 Sample Treatment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

4.6 References………………………………………………………………………144
Chapter 5 NMR Studies of The Water States in Nafion117 . . . . . …. 146
5.1 CPMG Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .146
5.1.1 Results……………………………………………………………………..146
5.1.2 Discussions……………………………………………………………...…180
5.2 DQF Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .. 189
5.2.1 Results…………………………………………………………………..…189
5.2.2 Discussions………………………………………………………………..192
5.3 RFRD Experiments ………………………………………………………….194
5.3.1 Results……………………………………………………………………..194
5.3.2 Discussions………………………………………………………………..195
5.4 Conclusions………………………………………………………………….196
5.5 References…………………………………………………………………...197
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