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研究生：	楊鼎盛 Yang, Ding-Sheng
論文名稱：	氫原子於奈米載具內的量子力學計算 Quantum-mechanics calculations of hydrogen atoms in nanoscale carriers
指導教授：	王雲哲 Wang, Yun-Che
學位類別：	碩士 Master
系所名稱：	工學院 - 土木工程學系 Department of Civil Engineering
論文出版年：	2013
畢業學年度：	101
語文別：	英文
論文頁數：	135
中文關鍵詞：	量子分子動力學、氫原子、富勒烯、奈米碳管、石墨層
外文關鍵詞：	Quantum molecular dynamics, hydrogen atom, carbon fullerene, carbon nanotube, graphene
相關次數：	點閱：117 下載：0
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模擬原子及分子系統是為了瞭解物理力學和系統穩定度，以及計算其物理性質
如楊氏模數、黏滯性及擴散係數等。本文利用量子分子動力模擬(Quantum molecular dynamics simulation QMD)相對於一般常用的分子動力學(Molecular dynamics MD)，由於在極封閉構型裡，計算碳氫間的交互作用在MD上難以運用經驗相互作用勢能來準確描述建立。而在QMD內，可以藉由密度泛函理論(Density functional theory DFT)公式解薛丁格方程式而計算原子間的交互作用力。此外，應用Born-Oppenheimer approximation假設，以牛頓第二定律計算原子核的移動。
氫的經濟價值是對於環境提供低量的碳化合物排放，但是在市場和其他替代能源仍非常競爭。為了得到氫體積儲存率高於10 wt%，因此建議使氫吸附於奈米級載具，例如富勒烯、奈米碳管以及石墨層。本文中用於儲存氫的奈米載具為C60富勒烯以及石墨層。藉由壓力跟溫度為變數的長時間MD模擬獲得奈米載具的結構穩定性，模擬的結果發現在300 K(室溫)溫度下，碳球內可以存放12顆氫原子，且都呈現氫分子形態。更進一步的透過控制系統的外在壓力以及提升溫度可能使氫從奈米載具內釋放或擠壓進去，使得氫燃料可以被使用，碳球在高達10 GPa的環境下仍可以維持穩定，在此環境下於外部加入氫原子發現氫會往碳球內部移動，但由於我們是放置氫原子也導致碳球構型遭到破壞。模擬顯示，氫在距離碳原子約大於1.3 Ang的情況下能以氫分子的型態存在奈米載具內，否則碳原子會吸引氫原子以致形成碳氫鍵。碳氫系統的釋放以及填入機制，其長時間穩定度還須更長時間的模擬和進一步的研究，可能有最佳的模擬時間、壓力以及溫度。石墨層在低於500 K的環境下仍可以維持穩定構型，於單層石墨加入氫分子，雖然它不會像氫原子一樣破壞石墨但發現卻不會被石墨層吸附，因此將氫分子分別置於三層石墨的夾層內，發現可藉由碳層的束縛將氫分子穩定於碳夾層內，由此推斷氫分子可能無法藉由物理吸附於石墨層。未來研究有機金屬載具(Metal-organic frameworks MOFs)可以獲得更高含氫量是一個重要課題。

Simulations of atomic and molecular systems are of particle use to understand the physical mechanisms and stability of the systems, as well as estimations of their physical properties, such as elastic constants, viscosity, diffusional coefficients and others. In this work, the quantum molecular dynamics simulation (QMD), as opposed to conventional molecular dynamics (MD), is first reviewed and then preformed to study the hydrogen-carbon systems since the interaction between hydrogen and carbon atoms in the extremely confined geometry through packing cannot be correctly modeled by empirical interatomic potentials in MD. In QMD, the interatomic forces are calculated by solving the Schrödinger’s equation with the density functional theory (DFT) formulation, and the positions of the atomic nucleus are calculated with the Newton’s second law in accordance with the Born-Oppenheimer approximation.
Hydrogen economy provides low carbon dioxide emission to the environment, but must compete with other alternative energy sources in the market. In order to obtain high volume fraction hydrogen storage, more than about 10 wt%, it has been proposed to adopt nano-scale cages, such as carbon fullerenes, carbon nanotubes, graphene layers. The carbon nanocages investigated in this work is the C60 fullerene. The structural stability of the nanocages is tested by long-time MD simulations under various pressures and temperatures. At 300 K our result is that 10 hydrogen atoms can be stored in C60 as molecule form. Furthermore, by controlling the external pressure and elevated temperature of the simulation box, the hydrogen may be released from or squeezed into the nanocages, C60 can be stable under 10 GPa environment. Under high pressure environment, two hydrogen atoms which are on the outside of C60, are moving forward into C60, but we use hydrogen atoms that case the C60 broken. Simulation results show hydrogen can exist as H2 molecules in the nanocages, if hydrogen atoms are not placed too near carbon atoms about smaller than 1.3 Ang. Otherwise, C-H bonds form first due to the size of carbon atom is larger than that of hydrogen. Long-term stability of the hydrogen-carbon systems under the refilling/release environments requires further investigation. There may be an optimal time, pressure and temperature for refilling and release of hydrogen from the nanocages. Graphene can be stable at lower than 500 K, placed hydrogen molecule on the surface although it does not like hydrogen atom destroy the structure of C60 but it does not adsorb to graphene, thus we placed two hydrogen molecules between graphene layers, we observe that hydrogen can be stable in it by the bound of graphene layers, and thus we surmise that hydrogen can't adsorb to graphene by physical adsorption. In the future work, study of metal-organic frameworks (MOFs) is necessary to obtain higher hydrogen content.

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
CHINESE ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 Goals and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1 Formulation of govering equations . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1 The Schr¨odinger equation . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 Hamiltonian in the Hartree atomic units . . . . . . . . . . . . . . . . . 10
1.3 Hamiltonian in the Rydberg atomic units . . . . . . . . . . . . . . . . 11
1.4 Decomposition of the Hamiltonian . . . . . . . . . . . . . . . . . . . . 11
1.5 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 The Wave function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1 Variational principle of quantum mechanics . . . . . . . . . . . . . . . 12
3 The quantum-mechanics problem . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.1 One-electron atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 N-electron atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Born-Oppenheimer approximation . . . . . . . . . . . . . . . . . . . . 17
3.4 Hartree-Fock approximation . . . . . . . . . . . . . . . . . . . . . . . 18
4 Classical solution of the hydrogen-like problem . . . . . . . . . . . . . . . . . 19
5 The helium-like atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6 The Ab-initio method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
7 Density Functional Theory (DFT) . . . . . . . . . . . . . . . . . . . . . . . . 28
8 The Kohn-Sham ansatz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
9 Functionals for exchange and correlation . . . . . . . . . . . . . . . . . . . . . 34
9.1 Local Density Approximation (LDA) . . . . . . . . . . . . . . . . . . 34
9.2 Generalized Gradient Approximation (GGA) . . . . . . . . . . . . . . 35
10 The self-consistent coupled Kohn-Sham equations . . . . . . . . . . . . . . . 36
11 Conjugate Gradient (CG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
12 Remarks on the DFT methodology . . . . . . . . . . . . . . . . . . . . . . . . 42
13 DFT for effective one-electron Schr¨odinger’s equation . . . . . . . . . . . . . 43
14 Particle in a Three-Dimensional Box . . . . . . . . . . . . . . . . . . . . . . . 44
Computational quantum mechanics . . . . . . . . . . . . . . . . . . . . . . . . . 47
1 Overview of atomic-orbital basis implemented in SIESTA . . . . . . . . . . . . 48
2 Basis set and KB projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.1 Size: number of orbitals per atom . . . . . . . . . . . . . . . . . . . . 50
2.2 Range: cutoff radii of orbitals . . . . . . . . . . . . . . . . . . . . . . 52
2.3 Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3 SIESTA Input File Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.1 FDF file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
1 Model preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2 Verification of SIESTA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3 Carriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.1 H2O in C60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2 Hydrogen atom and hydrogen molecule in C60 . . . . . . . . . . . . . 62
3.3 Graphene for hydrogen atom and hydrogen molecule . . . . . . . . . . 76
4 Microfluid diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.1 NAMD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.2 SIESTA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.1 CNT as a mass sensor . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
APPENDICES
Appendix A: The SIESTA input files . . . . . . . . . . . . . . . . . . . . . . . . 107
Appendix B: The input file for H4C60 . . . . . . . . . . . . . . . . . . . . . . . . 111
Appendix C: The input file for H8C60-nose-300k . . . . . . . . . . . . . . . . . . 115
Appendix D: The input file for Grephene72-cg . . . . . . . . . . . . . . . . . . . 119
Appendix E: The input file for Grephene72-Nose-300k . . . . . . . . . . . . . . . 123
Appendix F: The input file for 55tube200-cg . . . . . . . . . . . . . . . . . . . . 127
VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
                                    

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校內：2018-02-07公開
校外：不公開電子論文尚未授權公開，紙本請查館藏目錄

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