Hydrogen storage in metal organic framword mil 88s a computational study = nghiên cứu lưu trữ khí hydro sử dụng vật liệu khung hữu cơ kim loại mil 88s bằng phương pháp mô phỏng

VIETNAM NATIONAL UNIVERSITY HO CHI MINH CITY
HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY

Nguyen Thi Xuan Huynh

HYDROGEN STORAGE IN METAL-ORGANIC FRAMEWORK
MIL-88S: A COMPUTATIONAL STUDY

A dissertation submitted for the degree of
Doctor of Philosophy

Ho Chi Minh City – 2019


VIETNAM NATIONAL UNIVERSITY HO CHI MINH CITY
HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY

Nguyen Thi Xuan Huynh

HYDROGEN STORAGE IN METAL-ORGANIC FRAMEWORK
MIL-88S: A COMPUTATIONAL STUDY

Major: ENGINEERING PHYSICS
Major code: 62520401

Independent Reviewer 1: Assoc. Prof. Dr. Pham Tran Nguyen Nguyen
Independent Reviewer 2: Assoc. Prof. Dr. Nguyen Thanh Tien

Reviewer 1: Assoc. Prof. Dr. Phan Bach Thang
Reviewer 2: Assoc. Prof. Dr. Huynh Quang Linh
Reviewer 3: Dr. Phan Hong Khiem

SCIENTIFIC SUPERVISORS:
1. Dr. Do Ngoc Son
2. Dr. Pham Ho My Phuong


DECLARATION
I declare that this doctoral dissertation was written by myself, that the work
contained herein is my own except where explicitly stated otherwise in the text, and
that this work has not been submitted for any other degrees or professional
qualification except as specified.
Parts of this dissertation were published in the following papers:
[1] T. T. T. Huong, P. N. Thanh, N. T. X. Huynh, and D. N. Son, “Metal-Organic
Frameworks: State-of-the-art Material for Gas Capture and Storage,” VNU Journal of
Science: Mathematics – Physics, vol. 32, pp. 67-84, 2016.
[2] N. T. X. Huynh, O M. Na, C. Viorel, and D.N. Son, “A computational approach
towards understanding hydrogen gas adsorption in Co-MIL-88A,” RSC Advances, vol.
17, pp. 39583-39593, 2017.
[3] N. T. X. Huynh, C. Viorel, and D.N. Son, “Hydrogen storage in MIL-88 series,”
Journal of Materials Science, vol. 54, pp. 3994-4010, 2019.

Author of dissertation

Nguyen Thi Xuan Huynh

i


ABSTRACT
Fossil fuel-based energy consumption causes serious environmental impacts such

as air pollution, greenhouse effect, and so on. Therefore, searching clean and
renewable energy sources is urgent to meet the demand for sustainable development of
the global society and economy. Hydrogen gas (H2) is a reproducible, clean, and
pollution-free energy carrier for both transportation and stationary applications.
Hydrogen gas has a much higher energy density than other fuels; and thus, it becomes
one of the most promising candidates to replace petroleum. Therefore, in recent years,
the interest in the research and development of hydrogen energy has grown constantly.
A safe, efficient, and commercial solution for hydrogen storage is based on adsorption
in porous materials, which have the exceptionally large surface area and ultrahigh
porosity such as metal-organic framework (MOF) materials. In order to be selected as
porous materials for gas storage, MOFs must be stable to avoid collapsed under humid
conditions. MIL-88 series (abbreviated as MIL-88s including MIL-88A, MIL-88B,
MIL-88C and MIL-88D) is highly stable and flexible sorbents. For these reasons,
MIL-88s becomes a suitable candidate for the storage of hydrogen gas based on the
physisorption. Moreover, coordinatively unsaturated metal centers in MIL-88s are able
to enhance gas uptakes significantly at ambient temperatures and low pressures. These
materials have been investigated and highly evaluated for various applications such as
gas storage/capture and separation of binary gas mixtures in recent years; however,
they have not yet been evaluated for hydrogen storage. These outstanding features
have attracted my attention to consider the hydrogen storage capacity in
MIL-88 series.
In this dissertation, the van der Waals dispersion-corrected density functional
theory (vdW-DF) calculations were used to examine the stable adsorption sites of the
hydrogen molecule in MIL-88s and clarify the interaction between H2 and MIL-88s
via electronic structure properties. This observation showed an implicit role of
electronic structures on the H2 adsorption capacity at the considered temperature and
pressure conditions. Besides, it was found that the H2@MIL-88s interaction is
dominated by the bonding state () of the hydrogen molecule and the p orbitals of the

ii

O and C atoms in MIL-88s. For MIL-88A and B, the d orbitals of the metals also play
an important role in the interaction with H2.
Moreover, grand canonical Monte Carlo (GCMC) simulations were used to
compute hydrogen uptakes in MIL-88s at the temperatures of 77 K and 298 K and the
pressures up to 100 bar. For Fe based-MIL-88 series, we found that MIL-88D is very
promising

for

the

gravimetric

hydrogen

storage

(absolute/excess

uptakes

= 5.15/4.03 wt% at 77 K and 0.69/0.23 wt% at 298 K), but MIL-88A is the best
alternative for the absolute/excess volumetric hydrogen storage with 50.69/44.32 g/L
at 77 K and 6.97/2.49 g/L at 298 K. Via this research, scandium (Sc) was also found as
the best transition metal element for the replacement of Fe in MIL-88A for the
hydrogen storage, in which absolute/excess uptakes are 5.30/4.63 wt% at 77 K and
0.72/0.29 wt% at 298 K for gravimetric uptakes; 51.99/45.51 g/L at 77 K and
7.08/2.83 g/L at 298 K for volumetric uptakes. The hydrogen storage capacity is the

decrease in the order: Sc-, Ti-, V-, Cr-, Mn-, Fe-, and Co-MIL-88A. The calculations
showed that the results are comparable to the best MOFs for the hydrogen storage up
to date. The results also elucidated that the gravimetric hydrogen uptakes depend on
the specific surface area and pore volume of the MIL-88s. These important structural
features, if properly improved, lead to an increase in the capability of hydrogen storage
in MIL-88s.

iii


TÓM TẮT LUẬN ÁN
Tiêu thụ năng lượng dựa trên nguồn nhiên liệu hóa thạch ngày càng ảnh hưởng
nghiêm trọng đến mơi trường như gây ơ nhiễm khơng khí, hiệu ứng nhà kính. Do đó,
để đáp ứng nhu cầu phát triển bền vững cho đời sống xã hội và nền kinh tế tồn cầu,
việc tìm kiếm các nguồn năng lượng sạch và có thể tái tạo là vấn đề hết sức cấp thiết.
Như đã biết, hydro là nguồn khí rất phong phú đáp ứng cho nhu cầu năng lượng sạch,
có thể tái tạo và không gây ô nhiễm môi trường cho cả các ứng dụng di chuyển và tại
chỗ. Hydro lại có mật độ năng lượng cao hơn nhiều so với các nhiên liệu khác nên nó
được chọn như là ứng viên sáng giá cho việc thay thế xăng dầu. Với những đặc tính
như vậy nên sự quan tâm đến nghiên cứu và phát triển năng lượng hydro đã tăng lên
không ngừng trong những năm gần đây. Một giải pháp đảm bảo tính an tồn, hiệu quả
và kinh tế cho lưu trữ hydro đó là hấp phụ khí vào trong vật liệu xốp. Những vật liệu
xốp được đánh giá cao cho khả năng lưu trữ khí hydro hiện nay đó là các vật liệu xốp
có diện tích bề mặt rất lớn và tính xốp cực cao như họ vật liệu khung hữu cơ kim loại
(MOF). Để được chọn làm vật liệu lưu trữ khí, các vật liệu MOF phải có tính ổn định
và bền để tránh hiện tượng phá vỡ cấu trúc trong môi trường ẩm. Chuỗi MIL-88A,
MIL-88B, MIL-88C và MIL-88D (viết tắt là MIL-88s) có thể đáp ứng được yêu cầu
trên vì chuỗi vật liệu này có cấu trúc rất linh hoạt và rất bền trong mơi trường ẩm. Do
đó, chuỗi MIL-88s này được dự đoán là những ứng viên sáng giá cho lưu trữ hydro
dựa trên tính chất hấp phụ. Hơn nữa, MIL-88s còn chứa các tâm kim loại chưa bão hịa

mà đặc tính này được cho là một trong những giải pháp chiến lược có thể tăng cường
đáng kể lượng khí hấp phụ vào trong MOF ở điều kiện nhiệt độ phòng và áp suất thấp.
Trong thời gian gần đây, chuỗi MIL-88s đã từng được nghiên cứu và được đánh giá
cao cho nhiều ứng dụng như lưu trữ, bắt giữ và tách khí; tuy nhiên, chúng chưa được
đánh giá cho khả năng lưu trữ hydro bằng cả phương pháp thực nghiệm và tính tốn.
Với những tính năng nổi bật như trên, các phương pháp tính tốn được sử dụng để
xem xét khả năng lưu trữ hydro của MIL-88s và giải thích chi tiết tương tác giữa các
trạng thái điện tử của phân tử H2 với các nguyên tử của MIL-88s.
Trong luận án này, phương pháp lý thuyết phiếm hàm mật độ (DFT) có hiệu
chỉnh van der Waals (vdW-DF) được sử dụng để tính năng lượng liên kết hay năng

iv


lượng hấp phụ và từ đó tìm các vị trí hấp phụ bền cho H2 trong chuỗi MIL-88s. Cụ thể
hơn, dựa trên tính chất cấu trúc điện tử, tương tác giữa H2 và MIL-88s được làm sáng
tỏ. Kết quả tính tốn chỉ ra được các vị trí hấp phụ bền nhất của H 2 trong các cấu trúc
MIL-88s. Kết quả cũng chỉ ra rằng tương tác giữa H2 và MIL-88s được đóng góp
chính bởi trạng thái liên kết ( - trạng thái bonding) của phân tử H2 tương tác với các
quỹ đạo p của các nguyên tử O và C trong MIL-88s. Đối với MIL-88A và B, tính tốn
vdW-DF cũng chỉ ra các quỹ đạo d của kim loại cũng đóng vai trị quan trọng trong
tương tác với H2.
Bên cạnh đó, để đánh giá định lượng khả năng lưu trữ hydro trong MIL-88s ở
nhiệt độ 77 K và 298 K với áp suất lên đến 100 bar, phương pháp mô phỏng Monte
Carlo chính tắc lớn (GCMC) được sử dụng. Phương pháp này cũng được dùng để đánh
giá độ mạnh tương tác giữa H2 và MIL-88s qua nhiệt hấp phụ Qst.
Đánh giá khả năng lưu trữ hydro của chuỗi MIL-88s (với thành phần kim loại là
Fe), kết quả chỉ ra rằng MIL-88D có tiềm năng nhất cho khả năng lưu trữ hydro tính
theo phần trăm trọng lượng (dung khối) với dung lượng hấp phụ toàn phần/bề mặt
tương ứng là 5,15/4,03 wt% ở 77 K và 0,69/0,23 wt% ở 298 K, nhưng nếu đánh giá

theo dung tích thì MIL-88A lại tốt hơn cho lưu trữ hydro (dung tích tồn phần/bề mặt
tương ứng là 50,69/44,32 g/L ở 77 K, và 6,97/2,49 g/L ở 298 K). Kết quả của luận án
cũng chỉ ra rằng với việc thay thế Fe trong MIL-88A lần lượt bởi một số kim loại
chuyển tiếp có thể nâng cao khả năng lưu trữ H2 và kim loại tốt nhất trong chuỗi kim
loại được khảo sát đó là scandium (Sc). Cụ thể, kết quả lưu trữ toàn phần/bề mặt đạt
5,30/4,63 wt% ở 77 K và 0,72/0,29 wt% ở 298 K tính theo dung khối; 51,99/45,51 g/L
ở 77 K và 7,08/2,83 g/L ở 298 K tính theo dung tích. Khả năng lưu trữ hydro trong
M-MIL-88A theo thứ tự giảm dần là Sc-, Ti-, V-, Cr-, Mn-, Fe- và Co-MIL-88A.
Kết quả nghiên cứu bước đầu cho thấy tiềm năng của chuỗi MIL-88s cho lưu trữ
hydro và kết quả này có thể so sánh được với nhóm vật liệu MOF đã từng được đánh
giá cao cho lưu trữ H2 đến nay. Các kết quả cũng giải thích được khả năng hấp phụ
hydro phụ thuộc mạnh vào các đặc tính cấu trúc như diện tích bề mặt riêng, thể tích lỗ
rỗng của MIL-88s. Những đặc tính quan trọng này nếu được cải thiện phù hợp sẽ tăng
được khả năng hấp phụ hydro trong MIL-88s.

v


ACKNOWLEDGEMENTS
This work couldn’t be completed without the help and support of many people to
whom I would like to express my gratitude.
First of all, I would like to thank my supervisors, Dr. Do Ngoc Son and Dr. Pham
Ho My Phuong at Ho Chi Minh City University of Technology in VNU-HCM
(HCMUT), for their guidance and helpful comments throughout my doctorate course. I
am grateful to express my deepest appreciation to Dr. Do Ngoc Son when I perform
my research at HCMUT. His enthusiasm, valuable suggestions and comments were
very helpful during this research.
I would like to thank Prof. Viorel Chihaia (Institute of Physical Chemistry “Ilie
Murgulescu” of the Romanian Academy, Splaiul Independentei 202, Sector 6, 060021
Bucharest, Romania) for helpful comments to my research papers. I acknowledge the

usage of the computer time and software granted by the Institute of Physical
Chemistry of Romanian Academy, Bucharest (HPC infrastructure developed under the
projects Capacities 84 Cp/I of 15.09.2007 and INFRANANOCHEM 19/01.03.2009).
I am very thankful to Prof. Vo Van Hoang for helping me more advantageous in
this work at the Computational Physics Laboratory. I will also remember nice and
fruitful conversations with other members of this Lab. Additionally, I also would like
to thank all lecturers and secretaries of Faculty of Applied Science, HCMUT giving
me useful knowledge and helping during my research herein.
I am very thankful to the lecturers and co-workers at Department of Physics, Quy
Nhon University (QNU) who helped me to have a chance to participate in PhD project
at HCMUT and do well my work at QNU. I would like to acknowledge the financial
support from Quy Nhon University and the Vallet scholarship foundation.
Last but not least, I would like to thank my beloved husband for taking care,
understanding and sympathy. He is the one who strongly believed in me, encouraged
me to start the PhD project and was always with me in good and bad times I had
during that four years. I am grateful to my sons for understanding, sympathy and they
are always lovely babies giving me a great motivation to complete this study. I am also
vi


big thanks to other members in my family for understanding and helping me during the
time for my PhD course.
This research was funded by the Vietnam National Foundation for Science and
Technology Development (NAFOSTED) under grant number 103.01-2017.04; the
research project T2015.460.05 of Quy Nhon University; and the research project
TNCS-2015-KHUD-33 of Ho Chi Minh City University of Technology.

vii

TABLE OF CONTENTS
DECLARATION ..............................................................................................................i
ABSTRACT ................................................................................................................ ii
TÓM TẮT LUẬN ÁN ....................................................................................................iv
ACKNOWLEDGEMENTS ...........................................................................................vi
TABLE OF CONTENTS ............................................................................................ viii
LIST OF FIGURES ........................................................................................................xi
LIST OF TABLES ..................................................................................................... xvii
LIST OF ABBREVIATIONS ......................................................................................xix
INTRODUCTION ........................................................................................................... 1
1. Motivation for study .............................................................................................. 1
2. Structure of PhD dissertation ................................................................................ 3
CHAPTER 1: LITERATURE REVIEW OF METAL-ORGANIC FRAMEWORKS .. 5
1.1. General overview of metal-organic frameworks ............................................... 5
1.1.1. Definition of metal-organic frameworks ..................................................... 5
1.1.2. Structural aspects of MOFs ......................................................................... 6
1.1.3. History of MOFs ......................................................................................... 8
1.1.4. Nomenclature of MOFs............................................................................. 11
1.1.5. Current research of MOFs in Vietnam ...................................................... 12
1.2. Major applications of MOFs ............................................................................ 13
1.2.1. Gas storage, capture, and separation ......................................................... 13
1.2.2. Biomedical applications ............................................................................ 20
1.3. Overview of synthesis and research methods for MOFs ................................. 21
1.3.1. Synthesis methods for MOFs .................................................................... 21
1.3.2. Theoretical studies .................................................................................... 23
1.4. MIL-88s for hydrogen storage ......................................................................... 24
CHAPTER 2: COMPUTATIONAL METHODS ........................................................ 26
2.1. Density functional theory calculations ............................................................ 26

viii

2.1.1. The Schrödinger equation ......................................................................... 26
2.1.2. Born-Oppenheimer and adiabatic approximations ................................... 28
2.1.3. Thomas-Fermi theory ................................................................................ 29
2.1.4. Hohenberg- Kohn theorems ...................................................................... 29
2.1.5. Variational condition and Levy constrained search formulation .............. 30
2.1.6. The Kohn-Sham equations ........................................................................ 31
2.1.7. Exchange-correlation functional ............................................................... 34
2.1.8. The basis sets ............................................................................................. 37
2.1.9. Pseudopotentials ........................................................................................ 38
2.1.10.

Self-consistent field methods ................................................................. 39

2.1.11.

Van der Waals density functional (vdW-DF) calculations .................... 40

2.1.12.

Computational details ............................................................................ 41

2.2. Grand canonical Monte Carlo simulations ...................................................... 42
2.2.1. Introduction ............................................................................................... 42
2.2.2. Computational details................................................................................ 47
CHAPTER 3: HYDROGEN ADSORPTION IN Co-MIL-88A .................................. 49
3.1. Optimization of Co-MIL-88A unit cell ........................................................... 49
3.2. Searching stable adsorption sites of hydrogen ................................................. 50
3.3. Adsorption isotherms of hydrogen in Co-MIL-88A ........................................ 56

3.4. Short summary ................................................................................................. 59
CHAPTER 4: HYDROGEN STORAGE IN MIL-88 SERIES .................................... 60
4.1. Geometry optimization of MIL-88 series ........................................................ 60
4.2. Isotherms and isosteric heats of hydrogen adsorption ..................................... 61
4.3. The most favourable H2 adsorption configurations ......................................... 67
4.4. Electronic structure properties of H2 – MIL-88s interaction ........................... 69
4.5. Short summary ................................................................................................. 72
CHAPTER 5: EFFECTS OF TRANSITION METAL SUBSTITUTION IN MIL-88A
ON HYDROGEN ADSORPTION................................................................................ 74
5.1. Optimization of M-MIL-88A unit cell ............................................................. 74

ix


5.2. Stable hydrogen adsorption sites ..................................................................... 75
5.3. Isotherms and isosteric heats of hydrogen adsorption ..................................... 79
5.4. Short summary ................................................................................................. 82
CHAPTER 6: CONCLUSIONS ................................................................................... 83
6.1. The main findings ............................................................................................ 83
6.2. Scientific contributions .................................................................................... 84
6.3. Outlook............................................................................................................. 84
LIST OF PUBLICATIONS ........................................................................................... 85
REFERENCES .............................................................................................................. 88
APPENDIX

.............................................................................................................107

x

LIST OF FIGURES
Figure 1.1. Simple topology of MOFs. ........................................................................... 5
Figure 1.2. Structure of MOF-5 [26]. ............................................................................. 6
Figure 1.3. Several common coordination geometries of metal ions used for MOF
construction. The numbers indicate the numbers of functional sites [30]. ..................... 7
Figure 1.4. Several common organic ligands used for MOF construction [28]. ............ 7
Figure 1.5. Several common SBUs of MOFs [31, 32]. .................................................. 8
Figure 1.6. 1D, 2D, and 3D MOF structures from 1970 to 2015 [35]. .......................... 9
Figure 1.7. NU-110 structure with the highest BET surface area of MOFs reported
until now [23] with CCDC data taken from [38]. ......................................................... 10
Figure 1.8. BET surface areas (m2/g) and pore volumes (cm3/g) of representative
MOFs, compared to conventional porous materials (zeolites, silicas, and activated
carbons). From Ref. [29]. Reprinted with permission from AAAS. ............................. 11
Figure 1.9. Application areas of porous reticular materials (MOFs, ZIFs and COFs)
[35]................................................................................................................................. 13
Figure 1.10. H2 storage in MOFs relatively compared to zeolite and empty tank.
Reproduced with permission of Royal Society of Chemistry from Ref. [74]. ............. 15
Figure 1.11. CH4 storage in MOFs relatively compared to active carbon and empty
tank. Reproduced with permission of Royal Society of Chemistry from Ref. [74]. ..... 18
Figure 1.12. Volumetric CO2 capacity of MOF- 177 relatively compared to zeolite
13X pellets, MAXSORB carbon powder, and pressurized CO2. Reproduced with
permission from Ref. [37]. Copyright © 2005, American Chemical Society. .............. 19
Figure 1.13. CO2 uptakes of MOFs at 298 K. Reprinted from Ref. [36] Reprinted with
permission from AAAS. ................................................................................................ 19
Figure 1.14. Schematic diagram of the drug and biomedical gas delivery by MOFs
[23]................................................................................................................................. 20
Figure 1.15. (a) Synthesis conditions commonly used for MOF preparation; (b)
indicative summary of the percentage of MOFs synthesized using the various
preparation routes [75]. ................................................................................................. 22
Figure 1.16. Schematic representation of PMS [110]. ................................................. 22

Figure 1.17. Multiscale methodology scheme, showing the different levels of theory
and the corresponding size of systems under study. Reproduced with permission of
Royal Society of Chemistry from Ref. [109]. ............................................................... 24
Figure 2.1. Schematic illustration for all-electron (solid lines) and pseudo wave
potentials (dashed lines) and their corresponding wave functions [117]. ..................... 39
xi


Figure 2.2. Flow chart of a self-consistent loop of the Kohn Sham equation. ............. 40
Figure 2.3. The IUPAC classification for adsorption isotherms [143]. ....................... 45
Figure 2.4. The scheme for the multi-scale simulation method [151]. ........................ 46
Figure 3.1. The unit cell of Co-MIL-88A: (a) side view, (b) top view of the unit cell,
(c) the μ3-O-centered trimer of Co metals, and (d) the fumarate ligand of MIL-88A.
The blue, red, brown, and white coloured balls represent Co, O, C, and H atoms,
respectively. ................................................................................................................... 50
Figure 3.2. Volume optimization for Co-MIL-88A structure by Murnaghan fitting
method: (a) Relative energy as a function of the lattice constant a for each c/a ratio,
where the solid lines are the fitting curves, while the points are the calculated values
by vdW-DF; The minimum relative energy points (fitted from (a)) are plotted versus
(b) the lattice constant a and (c) the c/a ratio. ............................................................... 50
Figure 3.3. The favourable adsorption configurations of H2 in Co-MIL-88A. The bond
distance to the reference atoms is correspondingly shown for each configuration. H1
and H2 are hydrogen atoms of hydrogen gas. ............................................................... 51
Figure 3.4. CDD for the favourable adsorption configurations of H2 in Co-MIL-88A.
The orbitals are drawn at an isosurface value of 0.0002 e/Bohr3. Yellow (positive) and
cyan (negative) clouds indicate charge gain and loss. The blue, red, brown, white balls
denote Co, O, C, and H atoms of MIL-88A, respectively. ............................................ 53
Figure 3.5. The electronic density of state of the hydrogen molecule and the s and d
orbitals of the Co atoms of the Co-MIL-88A at the sites: (a) hollow, (b) ligand, (c)
metal (side-on), and (d) metal (end-on). ....................................................................... 54

Figure 3.6. The real part of the wave functions of the H atom of the H 2 molecule and
the Co atom of the MIL-88A along the x-direction. The dots indicate for the position
of the atoms. .................................................................................................................. 54
Figure 3.7. (a) A demonstration of the overlapping of DOS, the filled area (turquoise
area); (b) the overlapping area of the H2 DOS with the total DOS (blue line), and the
DOS area of the adsorbed H2 molecule (magenta line) versus the binding energy. ..... 55
Figure 3.8. Excess H2 uptake for Co-MOF-74 at 77 K: (a) GCMC simulation with the
generic force field for MOFs and the DDEC charge assignment, compared to the
experimental data extracted with permission from Ref. [159]. (b) GCMC simulation
with the DDEC charges of this work and the charges from the library of RASPA. ..... 57
Figure 3.9. Absolute (red solid line) and excess (green dash line) adsorption isotherms
for the Co-MIL-88A at (a) 77 K and (b) 298 K. ........................................................... 58
Figure 3.10. The density of the adsorbed hydrogen molecules in the Co-MIL-88A.
The blue, red, brown, white balls represent the cobalt, oxygen, carbon, and hydrogen

xii


atoms of MOF, respectively. Each pair of green balls represents an adsorbed hydrogen
molecule. The cyan, red and blue bands refer to the hollow, ligand and metal sites,
respectively. ................................................................................................................... 58
Figure 4.1. The unit cell of MIL-88s with the different ligands: (a) FMA, (b) BDC, (c)
NDC, and (d) BPDC. The copper, red, brown, and white colours represent the iron,
oxygen, carbon, and hydrogen atoms, respectively....................................................... 60
Figure 4.2. Absolute (abs.) and excess (ex.) gravimetric hydrogen adsorption
isotherms of MIL-88s (s = A, B, C, and D) at (a) 77 K and (b) 298 K. Solid and dash
lines imply the absolute and excess adsorption isotherms. ........................................... 62
Figure 4.3. Absolute (abs.) and excess (ex.) volumetric H2 adsorption isotherms of
MIL-88s at (a) 77 K and (b) 298 K. Solid and dash lines imply the absolute and excess
adsorption isotherms. ..................................................................................................... 64

Figure 4.4. Size view of the density of H2 adsorbed in MIL-88s at 77 K and 1 bar. The
copper, red, brown, white small balls represent the Fe, O, C, and H atoms of MIL-88s,
respectively. Each pair of the green balls represents a hydrogen molecule. ................. 65
Figure 4.5. Correlation between the maximum absolute and excess uptakes and the
specific surface area (SSA) of MIL-88s at (a) 77 K and (b) 298 K. ............................. 66
Figure 4.6. Correlation between the maximum absolute and excess uptakes and the
pore volume (Vp) of MIL-88s at (a) 77 K and (b) 298 K. ............................................. 66
Figure 4.7. The isosteric heats of adsorption versus the number of the H2 molecules
adsorbed per the unit cell of MIL-88s. .......................................................................... 67
Figure 4.8. The average adsorption energy and the isosteric heat of the H2 adsorption
in MIL-88s. .................................................................................................................... 69
Figure 4.9. DOS of the adsorbed H2 and the C, O, Fe atoms of MIL-88s in the most
stable adsorption configurations. ................................................................................... 70
Figure 4.10. The p orbitals of the C and O atoms of MIL-88s for the most favourable
adsorption configurations: (a) MIL-88A, (b) MIL-88B, (c) MIL-88C and (d) MIL88D. ............................................................................................................................... 71
Figure 4.11. The d orbitals of the Fe atoms for the most favourable adsorption
configurations: (a) MIL-88A, (b) MIL-88B, (c) MIL-88C, and (d) MIL-88D. ............ 71
Figure 4.12. The CDD of the most favourable adsorption site of each MOF: (a) MIL88A, (b) MIL-88B, (c) MIL-88C, and (d) MIL-88D. Yellow and cyan clouds represent
charge gain and loss, respectively. ................................................................................ 72
Figure 5.1. Relationship between the volume of the unit cell and the ionic radius of
metal of the M-MIL-88A structures. Data of Fe-MIL-88A and Co-MIL-88A were
taken from Refs. [162] and [18], respectively. .............................................................. 75

xiii


Figure 5.2. CDD of H2 and atoms of V-MIL-88A: (a) side-on (isosurface is 410-4
e/Bohr3); (b) end-on (isosurface = 310-5 e/Bohr3). Cyan/yellow clouds indicate charge
loss/gain. The slate-gray, red, brown, white balls denote V, O, C, and H atoms of MIL88A, respectively. .......................................................................................................... 77
Figure 5.3. DOS of the adsorbed H2 and the orbitals of C, O and M atoms of M-MIL88A configurations at side-on site: (a) Sc-MIL-88A, (b) Ti-MIL-88A, (c) V-MIL-88A,

(d) Cr-MIL-88A, (e) Mn-MIL-88A and (f) Fe-MIL-88A. ............................................ 78
Figure 5.4. Absolute (solid) and excess (dashed) gravimetric adsorption isotherms of
hydrogen in M-MIL-88A series at: (a) 77 K and (b) 298 K. Data of Fe-MIL-88A and
Co-MIL-88A were taken in Ref. [162] and Ref. [18], respectively. ............................. 80
Figure 5.5. Absolute (solid) and excess (dashed) volumetric adsorption isotherms of
H2 in M-MIL-88A series at: (a) 77 K and (b) 298 K. Data of Fe-MIL-88A was taken in
Ref. [162]. ...................................................................................................................... 80
Figure 5.6. Isosteric heats of H2 adsorption in M-MIL-88A series. Data of Fe-MIL88A was taken in Ref. [162]. ......................................................................................... 81
Figure A1. Electrostatic charges and LJ parameters for the H2 molecule according to
the TraPPE force field. Hydrogen molecule is modeled as a three-site rigid model at
the center of mass (dH-H = 0.74 Å). ..............................................................................111
Figure A2. DOS of the isolated hydrogen molecule. Fermi level is set to zero. ........111
Figure A3. Volume optimization for Fe-MIL-88A structure by Murnaghan fitting
method: (a) Relative energy as a function of the lattice constant a for each c/a ratio,
where the solid lines are the fitting curves, while the points are the calculated values
by vdW-DF; The minimum relative energy points (fitted from (a)) are plotted versus
(b) the lattice constant a and (c) the c/a ratio. .............................................................111
Figure A4. Volume optimization for MIL-88B structure by Murnaghan fitting
method: (a) Relative energy as a function of the lattice constant a for each c/a ratio,
where the solid lines are the fitting curves, while the points are the calculated values
by vdW-DF; The minimum relative energy points (fitted from (a)) are plotted versus
(b) the lattice constant a and (c) the c/a ratio. .............................................................112
Figure A5. Volume optimization for MIL-88C structure by Murnaghan fitting
method: (a) Relative energy as a function of the lattice constant a for each c/a ratio,
where the solid lines are the fitting curves, while the points are the calculated values
by vdW-DF; The minimum relative energy points (fitted from (a)) are plotted versus
(b) the lattice constant a and (c) the c/a ratio. .............................................................112
Figure A6. Volume optimization for MIL-88D structure by Murnaghan fitting
method: (a) Relative energy as a function of the lattice constant a for each c/a ratio,

xiv


where the solid lines are the fitting curves, while the points are the calculated values
by vdW-DF; The minimum relative energy points (fitted from (a)) are plotted versus
(b) the lattice constant a and (c) the c/a ratio. .............................................................112
Figure A7. Most favourable adsorption sites of the H2 molecule in Fe-MIL-88A. ...113
Figure A8. Most favourable adsorption sites of the H2 molecule in MIL-88B. .........114
Figure A9. Most favourable adsorption sites of the H2 molecule in MIL-88C. .........115
Figure A10. Most favourable adsorption sites of the H2 molecule in MIL-88D........116
Figure A11. Volume optimization for Sc-MIL-88A structure by Murnaghan fitting
method: (a) Relative energy as a function of the lattice constant a for each c/a ratio,
where the solid lines are the fitting curves, while the points are the calculated values
by vdW-DF; The minimum energy points (fitted from (a)) are plotted versus (b) the
lattice constant a and (c) the c/a ratio. .........................................................................117
Figure A12. Volume optimization for Ti-MIL-88A structure by Murnaghan fitting
method: (a) Relative energy as a function of the lattice constant a for each c/a ratio,
where the solid lines are the fitting curves, while the points are the calculated values
by vdW-DF; The minimum energy points (fitted from (a)) are plotted versus (b) the
lattice constant a and (c) the c/a ratio. .........................................................................117
Figure A13. Volume optimization for V-MIL-88A structure by Murnaghan fitting
method: (a) Relative energy as a function of the lattice constant a for each c/a ratio,
where the solid lines are the fitting curves, while the points are the calculated values
by vdW-DF; The minimum energy points (fitted from (a)) are plotted versus (b) the
lattice constant a and (c) the c/a ratio. .........................................................................117
Figure A14. Volume optimization for Cr-MIL-88A structure by Murnaghan fitting
method: (a) Relative energy as a function of the lattice constant a for each c/a ratio,
where the solid lines are the fitting curves, while the points are the calculated values
by vdW-DF; The minimum energy points (fitted from (a)) are plotted versus (b) the
lattice constant a and (c) the c/a ratio. .........................................................................118

Figure A15. Volume optimization for Mn-MIL-88A structure by Murnaghan fitting
method: (a) Relative energy as a function of the lattice constant a for each c/a ratio,
where the solid lines are the fitting curves, while the points are the calculated values
by vdW-DF; The minimum energy points (fitted from (a)) are plotted versus (b) the
lattice constant a and (c) the c/a ratio. .........................................................................118
Figure A16. Adsorption configurations of the hydrogen molecule in the M-MIL-88A
structure: (a) side-on configuration and (b) end-on configuration ..............................118
Figure A17. PDOS of the adsorbed H2 and the orbitals of metals of M-MIL-88A
configurations at side-on site: (a) Sc, (b) Ti, (c) V, (d) Cr, (e) Mn, and (f) Fe. ..........119

xv


Figure A18. PDOS of the adsorbed H2 and the orbitals of carbon atoms of M-MIL88A configuration at side-on site with the M is: (a) Sc, (b) Ti, (c) V, (d) Cr, (e) Mn,
and (f) Fe. ....................................................................................................................120
Figure A19. PDOS of the adsorbed H2 and the orbitals of oxygen atoms of M-MIL88A configuration at side-on site with the M is: (a) Sc, (b) Ti, (c) V, (d) Cr, (e) Mn,
and (f) Fe. ....................................................................................................................121

xvi


LIST OF TABLES
Table 1.1. High hydrogen uptakes in MOFs at 298 K and pressures below 100 bar. .. 16
Table 2.1. The GCMC simulation box of MIL-88s. ..................................................... 47
Table 2.2. The LJ parameters for atom types and atomic partial charges used in
GCMC simulation. ........................................................................................................ 48
Table 2.3. The atomic partial charges of MIL-88s (s = A, B, C and D) used in GCMC
simulation. ..................................................................................................................... 48
Table 3.1. The adsorption energy (Eads in kJ/mol) between H2 and Co-MIL-88A for
the favourable adsorption sites. The average distance between the H2 molecule and the

reference atoms of the MOF is denoted by d H 2  A and the Bader point charge of H2 is
denoted by qH 2 ............................................................................................................... 51
Table 3.2. Overlapping between the DOS of the adsorbed H2 molecule with the DOS
of different components of Co-MIL-88A. ..................................................................... 55
Table 4.1. Cell parameters of the hexagonal MIL-88s compared to the data in Ref.
[115]............................................................................................................................... 61
Table 4.2. The maximum absolute and excess gravimetric hydrogen uptakes in MIL88s at 77 K and 298 K, the pressures below 100 bar. The specific surface area (SSA)
and the pore volume (Vp) are also listed. ....................................................................... 63
Table 4.3. Maximum absolute and excess volumetric H2 uptakes of MIL-88s at 77 K
and 298 K, the pressures under 100 bar. ....................................................................... 64
Table 4.4. Adsorption energy of H2 in MIL-88s (Eads in kJ/mol), the average H2 –
MOF distance ( d H2 -MOF in Å), and the Bader charge of the adsorbed H2 ( qH2 in e-). ..... 68
Table 5.1. Optimal parameters of the M-MIL-88A unit cell and the parameters
correlating to the investigated metals. ........................................................................... 75
Table 5.2. Adsorption energies, H2 – metal distance (in Å) and Bader charges of the
adsorbed H2 in M-MIL88A compared to that of isolated H2 with (-) for the charge loss
and (+) for the charge gain and other relative parameters. ............................................ 76
Table 5.3. Maximum absolute and excess and gravimetric volumetric uptakes of
hydrogen in M-MIL-88A at 77 K and 298 K and the pressures under 100 bar. ........... 81
Table A1. The organic ligand/linker of MOFs ...........................................................107
Table A2. Chemical formula of MOFs .......................................................................108
Table A3. The name of metal-organic frameworks ....................................................109

xvii


Table A4. The maximum absolute and excess gravimetric H2 uptakes in MIL-88s at
77 K and 298 K and the pressures below 100 bar, shown in many other units (mmol/g
and cm3/g). ...................................................................................................................110
Table A5. The maximum absolute and excess gravimetric H2 uptakes in M-MIL-88A

at 77 K and 298 K and the pressures below 100 bar, shown in many other units
(mmol/g and cm3/g). ....................................................................................................110

xviii


LIST OF ABBREVIATIONS

Abbreviation

Definition

AC

Activated Carbon

BDC
BET

1,4-benzendicacboxylate
Brunauer-Emmett-Teller

BTC

1,3,5-benzentricacboxylate

CDD
COF

Charge Density Difference

Covalent Organic Framework

DFT
DOE

Density Functional Theory
United States Department of Energy

DOS
GCMC
IRMOF
IUPAC
MC
MCP
MD

Density of States
Grand canonical Monte Carlo
Isoreticular Metal-Organic Framework
International Union of Pure and Applied Chemistry
Monte Carlo
Microporous coordination polymer
Molecular Dynamics

MIL-88s
MOF
MP2

MIL-88 series
Metal-Organic Framework

Second-order Møller Plesset

OMS
PBU
PCN
PCP
PSM
SBU

Open Metal Site
Primary Building Unit
Porous coordination network
Porous coordination polymer
Post-synthetic Modification
Secondary Building Unit

Ref.
UFF
wt%
ZIF

Reference
Universal Force Field
Weight percent
Zeolitic Imidazolate Framework

xix


INTRODUCTION

1. Motivation for study
Hydrogen gas (H2) is an attractive source for potential clean energy because it is
most abundant in the universe as part of water, hydrocarbons, and biomass, etc.
Moreover, using energy from the H2 gas does not emit the CO2 gas and not pollute the
environment like the burning of fossil fuels. In recent years, the material-based
hydrogen storage is expected to provide the safe, efficient and commercial solution for
hydrogen storage in both transportation and stationary applications. However, in order
to use the hydrogen energy source, most commonly used in the fuel cell technology, it
is necessary to develop a comprehensive system of generating production, storage,
delivery, and fuel cell technologies for hydrogen. In which, the H2 gas storage has
been challenging because of its low density. Therefore, seeking advanced storage
materials plays a vital role in the success of hydrogen energy technology [1–4]. The
2025 targets for the H2 storage set by the U.S. Department of Energy (DOE) are 1.8
kWh/kg (55 mg H2 per gram of the (MOF+H2) system, i.e. 5.5 wt% H2) for
gravimetric storage capacity and 1.3 kWh/L (40 g H2/L) for volumetric storage
capacity under moderate temperatures and pressures [5]. Various materials have been
studied for hydrogen storage such as metal hydrides, carbon-based materials, zeolites,
zeolitic imidazolate frameworks (ZIFs), covalent organic frameworks (COFs), and
MOFs [4–7]. Among them, MOFs having the ultrahigh surface area, high porosity and
controllable structural characteristics are the most promising candidates for the
commercial hydrogen storage [8–11]. Although thousands of MOFs have been
successfully synthesized, only a few of them have been tested for hydrogen storage.
MIL-88 series (hereafter denoted as MIL-88s, where s = A, B, C and D; MIL =
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