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 |  موضوع: رسالة دكتوراة بعنوان Adsorption of Gases in Carbon Nanotubes الخميس 01 يوليو 2021, 8:30 pm | |
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رسالة دكتوراة بعنوان
Adsorption of Gases in Carbon Nanotubes
A Thesis in Physics
by
Milen K. Rostov
Submitted in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy
The Pennsylvania State University
The Graduate School
Department of Physics
و المحتوى كما يلي :
IV
Table of Contents
List of Tables vm
List of Figures x
Acknowledgments xv
Chapter 1. Introduction 1
1.1 Distinguishing Properties of Nanotubes 5
1.1.1 Structure 5
1.1.2 Electronic Properties 7
1.1.3 Mechanical Properties 12
1.2 Nanofuture with Carbon Nanotubes 13
1.3 Physical Adsorption of Gases in Nanotubes 15
1.4 Outline of this Work 16
Chapter 2. Overview: Phases of Gases Adsorbed in Nanotube Bundles 19
2.1 Introduction 19
2.2 Adsorption Potential 21
2.3 Gases Within ICs 22
2.4 Adsorbed Phases Within the Tubes 26
2.4.1 Single-particle problem 26
2.4.2 Collective properties 27V
2.5 Gases on the External Surface 29
Chapter 3. Many-Body Interactions Among Adsorbed Molecules Within SWNTs 30
3.1 Many-body interactions among adsorbed atoms and molecules within
SWNTs 31
3.1.1 Introduction 31
3.1.2 Adsorbates in IC and Groove Phases 33
3.2 Gas condensation within a bundle of SWNTs: effects of screening . . 43
3.3 Summary 51
Chapter 4. Model adsorption potential. Hindered rotation of interstitial H2 in nanotube bundles 53
4.1 Introduction 54
4.2 Rotation of Interstitial H2 in SWNTs 56
4.2.1 The potential function 56
4.2.2 Rotational levels 59
4.3 Results 63
4.4 Determination of Rotational Barrier by Molecular Simulations . . . . 64
4.5 Summary 66
Chapter 5. MD Simulations of Hydrogen Storage in Carbon Nanotube Arrays . 68
5.1 Influence of Carbon Curvature on Molecular Adsorptions in CarbonBased Materials: A Force Field Approach 69
5.1.1 Introduction 69VI
5.1.2 Force field methodology 71
5.2 MD simulations of H2 in carbon nanotubes 75
5.3 Summary 79
Chapter 6. Isotopic and Spin Selectivity of H2 Adsorbed in Bundles of Carbon
Nanotubes 81
6.1 Introduction 81
6.2 Ortho-Para Selectivity 86
6.3 Rotational Specific Heat 90
6.4 Isotope Selectivity 95
6.5 Isosteric Heat 100
6.6 Conclusions 104
Chapter 7. Phonons and Specific Heat of Quasi-ID Phases of Atoms Adsorbed on
the External Surface of a Nanotube Bundle 106
7.1 Introduction 106
7.2 Phonons of Quasi-ID Groove phases of Ne and CH4 108
7.3 Phonons of CH4 in the Three-Stripe Phase 118
7.4 Specific Heat of Ne and CH4 Phases 127
Chapter 8. Matter on a cylindrical surface 138
8.1 Introduction 138
8.2 Variational Approach to the Coulomb Problem on a Cylinder . . . . 139
8.2.1 Introduction 139Vll
8.2.2 Analysis 140
8.2.3 Donors on SWNTs 148
8.3 Enhanced Cohesion of LJ Systems on a Cylindrical Surface 150
8.3.1 Two-body ground-state problems 150
8.3.2 Many-body problems 157
8.4 Summary 161
Chapter 9. Summary 164
References 169Vlll
List of Tables
3.1 DDD effect for H2, He and Ne adsorbates confined within IC’s of a nanotube bundle. All lengths are in A units; e and CQ are in meV 40
3.2 DDD effect for H2, He, Ne, Ar, Kr and Xe adsorbates confined into the
groove of a nanotube bundle. All lengths are in A units; e and CQ are in
meV. The free space potential parameters for Ar, Kr and Xe were taken
from Ref. [85] 43
4.1 Transition energies (meV) predicted and measured (DINS data) for indicated transitions[47]. Free space transition energies are given in parentheses 64
2 3 * 2
5.1 The values of the main forcefield parameters for sp , sp , and quasi-sp
(q-sp2) carbon and hydrogen 76
6.1 The zero point energies ( hoj ), rotational energy references (C) and shifts
(CQQ) and binding energies ( E (expressed in Kelvin). D2 — i72 means
the difference between the corresponding values 98
6.2 The isotope isosteric heats (Q) in the IC, groove and experimental results
(expressed in Kelvin) 102
7.1 Lennard-Jones parameters of gas-gas (gg) and gas-carbon (gc) interaction
for Ne and CHq 111
7.2 Adsorbate-adsorbate force constants a and /3 for the equilibrium and
compressed groove phases of Ne and CHq 114IX
7.3 Zero-point energy E% p and its ratio to the total potential energy of the
different phases considered in this work 137X
List of Figures
1.1 Schematic of a closed carbon nanotube 4
1.2 Symmetry properties of SWNT 6
1.3 Examples of ”armchair”, ’’zigzag” , and ’’chiral’ nanotubes 7
1.4 Real space unit cell and Brillouin zone for (a) armchair and (b) zigzag
nanotubes 9
1.5 ID energy dispersion relations for (10,10) armchair tube; a 2.46 A is
the graphite lattice constant, 7Q ~ 3 eV is the nearest-neighbor carboncarbon overlap integral [3] 11
2.1 Schematic depiction of adsorption sites within and outside a nanotube
bundle 20
2.2 Angular average of the potential energy (lower panel) and probability
density (upper panel) as a function of radial coordinate for H2 molecules
in an IC corresponding to nanotubes of radius 6.9 A 24
9 (3)
3.1 Free-space potential (circle/full curve), the DDD potential
(2)
(triangle/full curve) and the effective pair potential (solid curve) for
H2 molecules adsorbed within the IC’s of nanotube bundles are shown.
(2)
The inset shows the behavior of TQj close to the sign-reversal point. . . 37
3.2 Same as Fig.3.1 for He 39XI
3.3 Same as Fig.3.1 for Ne. The inset shows that there is no reversal in sign
(2)
for in this case 41
3.4 Energy per molecule of ID H2 within a single channel (dashed curve
from Ref.[90]) compared with the energy per molecule in the case when
interchannel interaction is included (full curve) 45
3.5 Potential energy of interaction between two H2 molecules in free space
(dashed curve) and in adjacent channels (full curve) are shown. The difference arises from the DDD interaction of the two H2 molecules and the
surrounding carbon atoms (dotted curve). The abscissa is the difference
in z coordinates of the two molecules 47
3.6 Same as Fig. 3.5 but for He 49
3.7 Same as Fig. 3.5 but for Ne 50
2
4.1 Surface orientational potential as a function of cos 6 61
5.1 Radial distribution functions for exohedral H2 over the 100 000 steps of
the 100 ps MD simulation 78
6.1 H2 rotational spectrum in free space and in IC. The number of lines in a
level represents the degeneracy of that energy level, o and p mean ortho
and para, respectively. 85
6.2 D2 and H2 spin selectivity in IC and groove channel as a function of T . 91
6.3 Ortho (dashed line), para (dotted line) and non-equilibrium (full line)
specific heat (without spin equilibration) of H2 molecules (a) in IC, (b)
in free space 94Xll
6.4 The equilibrium rotational specific heat of H2 (full line) and of D2
(dashed line) 96
6.5 Isotope selectivity in the IC (full line), groove (dashed line) and on
graphite (dotted line) 99
6.6 The calculated H2 (dotted line), D2 (dashed line) and the difference D2
H2 (full line) isosteric heats (a) in the IC and (b) in the groove. The
experimental values at 85 K are shown in symbols: circle for D2, square
for H2 and triangle for the difference D2-H2 103
7.1 Schematic depiction of three hypothetical phases investigated. Top portion is view looking down on the x-z plane. Bottom view is of the x-y
plane. The region marked by the dashed line represents the unit cell.
(a)Linear phase, (b) Zig-zag phase, (c) 3-stripe phase 109
7.2 Phonon dispersion relations( u vs. q/qmax) between the BZ center(g
0) and the BZ edge ( q 7r/ a ) for (a) equilibrium groove phase of
Ne(a = 3.08 A ); (b) compressed groove phase of Ne (a = 2.92 A ). . . . 116
4.17 A );
max
7.3 Same as Fig. 7.2 for (a) equilibrium groove phase of CH^a
(b) compressed groove phase of CH^ (a = 4.00 A ) 117
7.4 Schematic depiction of the 3D structure of the three-stripe phase of
CH4(lattice constant a 4.08 A ) 119
7.5 Phonon dispersion curves for three-stripe phases of CH4 (a 4.08A ). . 126
7.6 Total specific heat of Ne adsobate chain in an equilibrium groove phase(a
3.08A ) as a function of temperature 129Xlll
7.7 Same as Fig. 7.6 for Ne compressed groove phase(a 2.92A ) 131
7.8 Same as Fig. 7.6 for CH4 equilibrium phase(a = 4.17A ) 132
7.9 Same as Fig. 7.6 for CH4 compressed groove phase(a = 4.00A ) 134
7.10 Total specific heat of CH4 three-stripe phase(”squares” line) as a function
of T 135
7.11 Total specific heat of CH4 as a function of coverage(lD density p ) at T
20K, 40K, and 60K 136
7.12 Specific heat of Xe, Kr, Ne, Ar, and CH4 adsorbate chains (at their
equilibrium separation) in a groove as a function of T 136
8.1 Comparison of variational theory calculations with two different trial
wave functions 143
8.2 a variational parameter as a function of QQ/ R 144
8.3 Threshold value of the de Boer quantum parameter for existence of a
dimer 151
4 o
8.4 Ground state energy of He (circles), °He (stars) and H2 (up-triangles)
dimers on a cylinder 152
8.5 Probability density ( | TQ |2) for (a) 3He, (b) ^He, and (c) H2 dimers on
surfaces of optimal radius cylinders are shown
Ground state cohesive energy (per atom) of a ^He fluid on a cylinder as
155
8.6
a function of radius 158
8.7 Reduced Boyle temperature T* = kgT/e for classical gases on a cylinder
of radius R 160XIV
8.8 Energy per particle (in units of the pair potential’s well depth) as a
function of reduced radius, for various assumed ring numbers, v=1, 2, 3
4, 5, 6, and 8, from left to right 162
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