Super-dense Hydrogen Adsorption
below Critical Temperature(ྡֆԻౕҐԾͶ͕͜Ζ௔߶ືౕਭો‫ٷ‬஥)ָҒखಚ೧݆ 2023 ೧ 3 ݆Ᲊ ߄೯Abstract
In this work, the cryogenic H2 adsorption properties were systematically investigatedbelow the critical temperature of H2 (33 K). Especially, we focused on the studies for the “superdense H2 adsorption” which had much higher density than liquid H2 density. This is of great interest
because the properties of super-dense H2 are contrary to the general understanding that the upper
limit of adsorbed H2 density is equivalent to the density of liquid H2. However, the reports about
super-dense H2 adsorption are still few, and the factors and conditions leading to the super-dense H2state is not understood well. This work is the first report as systematic research of the cryogenic H2
adsorption to understand the super-dense H2 adsorption by investigating the material dependence,
temperature dependence, adsorbed layer dependence and gas dependence.
The densities of adsorbed H2 were measured by the volumetric method using PCI(Pressure-Composition-Isotherm) apparatus equipped with a cryostat system. The 9 kinds ofmaterials with different elements and textural properties (specific surface area, pore size, porevolume), such as carbon materials, MOFs, and silica gels, were used as absorbents. The temperaturechange of adsorbed H2 densities were evaluated below the critical temperature of H2. In order toinvestigate the adsorbed layer dependence of the super-dense H2 adsorption, BET theory was used
and the monolayer and multilayer H2 were evaluated separately. These results for H2 were comparedwith that for deuterium (D2), neon (Ne), and nitrogen (N2) at each liquefied temperature.
As a result, it is revealed that the density of monolayer H2, which is adsorbed just on thesurface of adsorbents, is evaluated to be 50 mmol/cm3 regardless of temperature changes below 33 K
and the differences of elements and textural properties of adsorbents. In other words, the monolayer
adsorption is the factor leading to the super-dense H2 adsorption without the material andtemperature dependence. It is noteworthy that the monolayer H2 as the super-dense state has higher
density than not only the liquid H2 density (35 mmol/cm3) but also the solid H2 density (43,mmol/cm3). From the practical point of view, the volumetric H2 uptake including the volume ofadsorbents themselves is the important value for the H2 storage. it is found that the volumetricsurface area of adsorbents is a unique factor to increase the volumetric H2 uptake.
In contrast to the results of super-dense H2 adsorption as described above, the density ofadsorbed Ne and N2 are almost equivalent to that of liquid phase at each liquified temperature,indicating that Ne and N2 do not form the super-dense state. On the other hand, the density ofadsorbed D2 shows higher density than that of liquid D2, and the temperature independence similar
to the super-dense H2 is also revealed. Furthermore, the monolayer D2 and H2 have equivalentdensity of 50 mmol/cm3, even though the density of liquid D2 is 1.15 times higher than that of H2 ateach boiling point. It is known that the lower density of liquid H2 is caused by the higher zero-point
energy compared with that of D2. Therefore, it can be expected that the quantum effect caused by thedifferent zero-point energy is cancelled out by interactions between adsorbates and adsorbents at
cryogenic conditions, and the super-dense H2 is formed.

,,Contents
1. Introduction ...................................................................................................................................1
1.1

Carbon neutral society

1.2

Properties of Hydrogen

1.3

Hydrogen storage

1.4

Previous work on hydrogen physical adsorption

2. Purpose........................................................................................................................................20
3. Theory and Experiments .............................................................................................................22
3.1

Theory of gas adsorption on solid surface

3.1.1.

Van der Waals Forces

3.1.2.

Langmuir and BET theory

3.1.3.

Adsorption isotherms

3.1.4.

Isosteric heat of adsorption

3.2

Materials

3.3

Experiment and analysis of gas adsorption

3.3.1

Principle of volumetric method by Sievert’s apparatus

3.3.2

N2 adsorption isotherms for investigation of textural properties

3.3.3

Measurement of skeletal density

3.3.4

Cryogenic adsorption measurement

3.3.5

Evaluation of density of adsorbate

4. Results and discussion ................................................................................................................62
4.1

Textural properties of adsorbent

4.2

Material dependence of the super-dense hydrogen adsorption

,,,

4.2.1

Hydrogen adsorption isotherms at 20.4 K

4.2.2

Density of adsorbed hydrogen at the boiling point

4.3

Temperature dependence of the super-dense hydrogen adsorption

4.3.1

Hydrogen adsorption isotherms

4.3.2

Density of adsorbed hydrogen

4.3.3

Isobars of volumetric hydrogen capacity

4.4

Adsorbed layer dependence of the super-dense hydrogen adsorption

4.5

Gas dependence of the super-dense hydrogen adsorption

4.5.1

Density of adsorbate for deuterium, neon and nitrogen

4.5.2

Two-dimensional density

5. Conclusion ................................................................................................................................ 107,9

1. Introduction
1.1 Carbon neutral society
Energy is the most fundamental ingredient for human society. But we mostly obtain energy
from fossil fuels, which is a major cause of global warming and climate change due to the carbon
dioxide (CO2) emission. The Intergovernmental Panel on Climate Change (IPCC) reported that
“Human influence on the climate system is clear” in the fifth assessment report in 2013,1
furthermore, the sixth assessment report emphasizes human influence as “It is unequivocal thathuman influence has warmed the atmosphere, ocean and land” published in 2022.2 The 21st sessionof the Conference of the Parties (COP21), which is the international climate summit, was held, and
the Paris Agreement was adopted by 194 parties. Its goal is to keep the increase in global
temperature increase below 2 ºC, preferably to 1.5 ºC compared to pre-industrial levels. The aim ofJapan in the Paris Agreement is 26% of reduction in greenhouse gas emissions by 2030 and 80% of
reduction by 2050 compared to that in 2013. In this recent year, the Japanese government declared
the aim of carbon neutrality by 2050. To achieve these goals, renewable energy such as wind, solar,
and hydropower should be mainstream power sources. However, renewable energy supply is not agood match to energy demand because of the lack of adjustment ability of renewable energy. Somesuitable energy storage devices, such as rechargeable batteries, pumped hydropower, heat storage,
compressed air, and flywheel, are necessary. Hydrogen (H2) is the most important candidate torealize not only energy storage but also energy transportation. Therefore, it has been widely
recognized that a hydrogen-based energy system is necessary to realize a carbon-free society becauseof the H2 ability of regenerative properties with zero emissions of pollute gases such as CO2 andhigh gravimetric energy density. However, the technological development of H2 storage andtransportation still needs challenges for the realization of a hydrogen-based society.



1.2 Properties of Hydrogen
The hydrogen atom (Protium) is the simplest element in the universe. Protium is composedof one proton and one electron. There are two isotopes of hydrogen, which are deuterium and tritiumwith one and two neutrons, respectively. The elemental hydrogen usually exists as a hydrogenmolecule (H2) with a covalent bond. Table 1.2.1 shows the physical properties of H2 and deuterium
molecules (D2). Fig. 1.2.1 shows the binding energy of hydrogen molecule, and the energy levels of
the stretching vibration as a function of internuclear distance3,4 . The vibration frequency ( ) of H-Hbinding as the harmonic oscillator at the ground state of the binding energy is given by

=

where

is the reduced mass given by

∙

;

1
2

(1.2.1),is the mass of atomic hydrogen;is the curvature of

the potential of the harmonic oscillation. According to the quantum theory, the vibration energy() is given by=

where ℎ is the Planck constant. The

+

1
ℎ ,
2

= 0,

= 0,1,2 ∙∙∙,

(1.2.2)(= ℎ ) is called zero-point vibration energy,

which depends on the mass of the atom. The lighter mass of hydrogen gives a higher zero-point
vibration energy compared with that of deuterium, resulting in different physical properties as shownin Table 1.2.1.
Since the excitation energy of the stretching vibration is quite large, most of the H2
molecules exist on the ground state below 2000 K, and the partition function is given by
=

exp −

≈ exp −The partition function for the rotational motion ( ) is given

(1.2.3)

=

1
2

ℎ

=

8

where is the rotational quantum number;(2 + 1)exp −(1.2.4)( + 1),(1.2.5)= 0, 1, 2 ∙∙∙,) is the moment of inertia. The important thing(=that rotational motion provides is that there are two distinct states of ortho-H2 and para-H2. Protium
is a fermion with a nuclear spin of 1/2, so the H2 molecule has total nuclear spins ( ) of = 1 or =0, which are categorized as ortho-H2 and para-H2, respectively. In the case of = 1, the ortho-H2 is
3-fold degenerate and it takes = odd. In the case of = 0, the para-H2 is 1-fold degenerate and it
takes =even. These distinctions are due to the requirement of fermions that the wave function must
be antisymmetric under particle exchange. The ratio of ortho-H2 and para-H2 in thermal equilibrium
is given by() ∑(2 + 1)exp −

=

where

( ) iseach degeneracy (

,
(

) ∑

(

) = 3 and(1.2.6)(2 + 1)exp −() =1).

Fig. 1.2.2 shows the ratio of ortho-

H2/para-H2 as a function of temperature, obtained from equation 1.2.6. At room temperature, theortho-para ratio is approximately 3:1 (75%:25%), since the statistical multiplicities for eachrotational state are equivalent. On the other hand, almost all of H2 exists as para-H2 at the boilingpoint (20.4 K), because the distribution of the rotational state at the ground state ( = 0) increases ata lower temperature.

Table. 1.2.1 Some properties of H2 and D2.3,5,6

unit

H2

D2

Molecular mass

g/mol

2.016

4.282

Natural abandance%

99.9850.015

Binding energy

eV

4.748

4.748

Dissociation energy

eV

4.478

4.556

Zero point vibration energy

eV

0.270

0.192

Triplet point (temperature)

K

13.96

18.73

Triplet point (pressure)

kPa

7.2

17.15

Critical point (temperature)

K

32.98

38.34

Critical point (pressure)

kPa

1.298

1.649

Boiling point at 0.1 MPa

K

20.41

23.67

Latent heat

J/mol

913

1235

Fig. 1.2.1 Adiabatic potential and energy levels of the stretching vibration of H2 molecule. 3,4



Fig. 1.2.2 Equilibrium ortho-para ratio of hydrogen as a function of temperatures.



1.3 Hydrogen storage
Table 1.3.1 shows the gravimetric and volumetric energy density (Higher Heating Value;
HHV) of H2 and common fuels.7 H2 has a very high gravimetric energy density compared with otherfuels such as gasoline, diesel, and natural gas. On the other hand, the volumetric energy density of
H2 under ambient conditions is extremely low compared with other fuels. In order to increase thevolumetric and gravimetric energy density of H2, the following techniques have been considered:Compressed H2, Liquid H2, and H2 ab/adsorption on materials, which are described below.

Table 1.3.1 Gravimetric and volumetric energy density (HHV) of fuels.7

Fuel

Hydrogen
Gasoline
Desel
Natural gas

Gravimetric dnergy density Volumetric energy density
MJ/kg
MJ/L
ambient condition
0.012
compressed (70 MPa) 142
5.6
liquid (20 K)
10.1
ambient condition
46.4
34.2
ambient condition
45.4
34.6
compressed 25 MPa
953.6
liquid22.2
ConditionCompressed hydrogen
Compressed H2 is the most common method of H2 storage and transportation. A typicalsteel cylinder stores the compressed H2 at 15 MPa. A new type of high-pressure H2 tank, which
consists of three layers made from the plastic liner, carbon fiber reinforced plastic (CFRP), and grassfiber reinforced plastic layer (GFRP), is used for the fuel cell vehicle (FCV). The high-pressure tankdeveloped by TOYOTA stores compressed H2 at 70 MPa and the gravimetric H2 density is 6.0 wt.%
including the weight of the H2 tank.8 Even for H2 highly compressed at 70 MPa, volumetric energy
density is not high compared with other fuels as shown in Table 1.3.1.

Liquid hydrogen
Fig. 1.3.1 shows the phase diagram of H2, which is referred from the National Institute ofStandards and Technology (NIST) chemistry Web Book.9 The boiling point of H2 is 20.4 K under 0.1
MPa of pressure, and the triplet point of H2 is at 14.0 K and 0.007 MPa. Since the critical point of H2
is 33.0 K at 1.3 MPa, thus H2 can’t be liquified at room temperature even under high the pressure.
The volumetric density of liquid H2 is 35.2 mmol/cm3 at the boiling point, which is about 800 times
higher than the density of gaseous H2 at the standard ambient temperature and pressure (0.040
mmol/cm3 at 298.15 K and 0.1 MPa) and much higher than the density of compressed H2 at 70 MPa(19.5 mmol/cm3).
Liquid H2 is considered as a practicable method for large-scale H2 transport due to the highvolumetric H2 density. In this recent years, Kawasaki Heavy Industries, Ltd. has built a large-scaleliquid H2 carrier.10 The technique of liquid H2 storage is being developed, but there are stillchallenges, which are the development of a high energy-efficient liquefaction technique, and the
suppression of H2 losses by evaporation of liquid H2 (boil-off). The boil-off is caused by heat input
from an outer wall of the storage tank, and internal heat generation by the ortho-para conversion.
The ortho-para ratio is approximately 3:1 at room temperature, while almost all of H2
exists as para-H2 at the boiling point (20.4 K). This ortho-para conversion is the exothermic reaction
with 1.406 kJ/mol of heat generation ( = 1 ˢ 0 ), which is higher than the heat of vaporization of
H2 (913 J/mol).4 Since interconversion between these isomers is a forbidden process in an isolated
molecule, it takes a long time more than 100 h to complete the ortho-para conversion reaction. In
long-term storage of liquid H2, the ortho-para conversion gradually proceeds and it leads to the boiloff due to the internal heat generation. To avoid this problem, it is necessary to complete the orthopara conversion at the moment of liquefying H2 by using ortho-para conversion catalysts improving
the sluggish kinetics.

H2 ab/adsorption on materials
In order to achieve higher gravimetric and volumetric H2 density compared with thecompressed H2 and liquid H2, various kinds of material-based H2 storage methods have been
investigated. There are two types of sorption to store H2 in solid-state materials, which are “chemical
absorption” and “physical adsorption”.
In the case of chemical absorption, the atomic hydrogen is bonded to materials, andhydrides are formed with metallic, ionic, or covalent bonds, which lead to relatively high volumetricH2 density. However, they generally require thermal management to control the reaction of H2
absorption and desorption due to the enthalpy change for the formation of hydrides. For example,
magnesium hydride (MgH2) with the enthalpy of formation of 74 kJ/mol requires 300 °C to desorb
H2 at 0.1 MPa.3,11 Furthermore, the slow kinetics of reactions are often problematic to control of theH2 absorption and desorption. In the case of MgH2, it requires a higher temperature than 300 °C for
H2 absorption reaction as a thermal activation even though it proceeds in an exothermic reaction.12 In
order to improve the kinetic issues, the use of catalysts and several activation processes are generallyrequired.11–15 Thus, the H2 storage by chemical absorption using materials realize the highvolumetric H2 density, while there are thermodynamic and kinetic issues for the practical H2absorption and desorption process.
On the other hand, molecular H2 can be stored on the surface of materials by physicaladsorption (hereinafter, this is just called “adsorption”). The H2 adsorption is mainly due to the weakvan der Waals interaction between the H2 molecule and material surface, and this phenomenon issimilar to the condensation from a gas to a liquid phase. The enthalpy of the physical adsorption isless than 10 kJ/mol,16 which is slightly higher than the enthalpy of liquefaction. In consequence, lowtemperature and high pressure are required to obtain high H2 capacity for the H2 adsorption. The
processes of H2 adsorption and desorption show good reversibility with fast kinetics.



Fig. 1.3.1 Phase diagram of H2. The boiling point is at 20.4 K and 0.1 MPa, the critical point of H2 is
at 33.0 K and 1.3 MPa, the triplet point of H2 is at 14.0 K and 0.007 MPa.

1.4 Previous work on hydrogen physical adsorption
The H2 adsorption storage on the surface of materials has long been studied to improve thegravimetric and volumetric H2 density. In 1997, Dillon et al.17 published the quite high gravimetricstorage density (5~10 wt.%) on single-walled nanotubes (SWNTs) under ambient conditions.
However, the inadequacy of this report has been proved by Hirscher et al.18 who clarified that thetitanium alloy contained in the synthesis process of SWNTs stored H2, and the true capacity of only
SWNTs was just around 1 wt.%. In 1998, Chambers et al.19 also published the extremely highgravimetric H2 density (~67 wt.%) on graphite nanofibers (GNF), but the result has not been
reproduced even though many validation experiments have been performed.20–22 The above huge H2capacity of carbon materials has not been confirmed unfortunately. However, these high-impact
reports stimulated this research field and accelerated the research and development more actively.
The porous carbon materials with a high specific surface area have been developed,23–37
because it has been revealed that the gravimetric H2 uptake approximately corresponds to 1 wt.% H2
per 500 m2/g of specific surface area at 77 K, which is the so-called Chahine’s rule.38,39 Fig. 1.4.1
shows the linear relationship between H2 uptake and specific surface area for carbon materials,24
indicating that the specific surface area is the critical factor to increase the H2 adsorption capacity.
The super-activated carbon of “MAXSORB”,40–42 which is manufactured by an alkali activation
process, has the highest specific surface area (more than 3000 m2/g) in the carbon materials, and it
shows the gravimetric H2 uptake of 5 wt.% at 77 K above 2 MPa of pressure.23 However, theresearch field of carbon materials for H2 storage tends to stagnate due to the limit of material
development to obtain higher surface area.
In late 1990, a new type of high surface area material of Metal-Organic Framework (MOF)
was developed.43 MOFs are crystalline porous materials composed of metal ions and organic ligands,
which act as the joints and linkers in the network structure, respectively. By changing the metal ionsand organic ligands, it is possible to design the desired pore structure. The first paper for H 2 storage
using MOFs was reported in 2003 using MOF-5 with a surface area of 2500 m2/g,44 which shows 4.5
wt.% of the gravimetric H2 uptake at 77 K below 0.1 MPa, but this result was corrected to 1.3 wt.%
at 77 K and 0.1 MPa.45 After that, a lot of MOFs were developed and H2 adsorption uptakes were
investigated.24,46–63 Fig. 1.4.2 shows the gravimetric H2 uptake for each MOFs material obtained at
77 K as a function of the specific surface area.24 The linear relationship between the gravimetric H2
uptake and the specific surface area is also observed on MOF materials, and it was clarified that
Chahine’s rule is adequate for MOF materials as well.64 Therefore, it can be concluded that thegravimetric H2 uptake on solid materials is proportional to the specific surface area, namely, thespecific surface area is the critical factor to increase the gravimetric H2 storage uptake.
The volumetric H2 density is also an important value as the practical performance for H2
storage. However, there is a trade-off relationship between volumetric and gravimetric surface area,i.e., volumetric and gravimetric H2 uptake, for porous materials.65,66 For example, although ultraporous MOF materials, e.g., MOF-210,61 NU110,62 and DUT6063 have a relatively high gravimetricsurface area in the range of 6000-8000 m2/g, they have a relatively low volumetric surface area andH2 uptake due to the high pore volume and large pore size. Some papers have focused on thedevelopment of MOFs to optimize the gravimetric and volumetric H2 capacity.65,66 As describedabove, the history of H2 adsorption storage using porous materials can be said to be the history of thedevelopment of materials with a high specific surface area.
In order to improve the H2 adsorption capacity, it is important not only to develop porous
materials but also to understand the properties of adsorbate (adsorbed H2) on the material surface. In
general understanding, adsorbates are regarded as a liquid phase at the boiling point of theadsorbates. The cross-sectional area of N2, which is a two-dimensional area per molecule widelyused for the evaluation of the surface area, at the boiling point of N2 (77 K) is determined based onthe three-dimensional (3D) density of liquid N2.67 For the adsorbate of H2, the density of adsorbed
H2 is also regarded as that of liquid H2 in a lot of papers,23,24,68 in other words, the upper limit ofadsorbed H2 density is regarded as the density of liquid H2. This indicates that the volumetric H2
capacity using porous materials would never be superior to that of liquid H2, no matter how high a
specific surface area of the material is developed. However, the conventional experiments carried out
at 77 K are inadequate to understand the essential properties of adsorbed H2 because the boilingpoint of H2 is 20.4 K.
In 1949, Livingston67 reported the anomalously low cross-sectional areas of H2 (8.3
Å/molecule) adsorbed on the surface of Ni foil at 20 K compared with the value estimated fromliquid H2 density (14.2 Å/molecule), indicating the anomalously high two-dimensional (2D) densityof monolayer H2 on the material surface. In the quite recent year 2022, Xicohténcatl et al.69 reported
the anomalously high 2D density of monolayer H2 on mesoporous silica at 20.4 K, which shows 7.1
Å/molecule of H2 cross-sectional area with the density larger than bulk-liquid and solid H2. These
results are contrary to the general understanding that the upper limit of adsorbed H2 density isequivalent to the density of liquid H2. They called the highly condensed H2 “super-dense H2”. In thisstudy, we also found the super-dense H2 on a super-activated carbon at 20.4 K, which showed thethree-dimensional (3D) density of 43.1 mmol/cm3 with the density higher than bulk-liquid and bulksolid H2. This result is described later in the section 4.2.1. This is expected to further enhancement of
H2 adsorption capacity from the practical point of view and further understanding of the physicalproperties of adsorbed H2 from the academic point of view.



Fig. 1.4.1 The liner relationship between H2 uptake and the surface area at 77 K and 0.1 MPa forcarbon materials: (˛) Nijkamp et al.,36 (˖) Pang et al.,34 (˙) Parra et al.,35 (˔) Takagi et al.,33 (˝)
Zhao et al.,32,37 (˟) Texier-Mandoki et al.,29 ( ) Gadiou et al.,31 and (⾥) Gogotsi et al.30

Fig. 1.4.2 The liner relationship between H2 uptake and the surface area at 77 K with Langmuir
surface area for metal-organic frameworks (MOFs). 24

ReferencesPahchauri, R. K., Allen, M. R., R., V., Barros, J. B. & Wolfgang Cramer. Climate Change 2014:
Fifth Assessment Report. Journal of Crystal Growth vol. 218 (2000).

2.

Valerie, M.-D. et al. Climate Change 2021: Sixth Assessment Report. Climate Change 2021: The
Physical Science Basis. 1–16 (2021) doi:10.1017/9781009157896.

3.

Fukai, Y. The Metal-Hydrogen System. (Springer, 2004).

4.

Van Kranendonk, J. SOLID HYDROGEN. (Plenum, 1983).

5.

Haissinsky, M. Nuclear Chemistry and Its Appplications. (Addison-Wesley, 1964).

6.

Vargaftik, N. B. Tables on the thermophysical properties of liquids and gases. (Hemisphere Pub.
Corp., 1975).

7.

Mazloomi, K. & Gomes, C. Hydrogen as an energy carrier: Prospects and challenges. Renewable
and Sustainable Energy Reviews 16, 3024–3033 (2012).

8.

https://www.toyota.co.jp/fuelcells/en/technology.html.

9.

Eric W. Lemmon, Ian H. Bell, Marcia L. Huber, and Mark O. McLinden, "Thermophysical
Properties of Fluid Systems" in NIST Chemistry WebBook, NIST Standard Reference Database
Number 69, Eds. P.J. Linstrom and W.G. Mallard, National Institute of Standards and Technology,
Gaithersburg MD, 20899, https://webbook.nist.gov/chemistry/, (retrieved September 19, 2022).

10.

https://global.kawasaki.com/en/corp/newsroom/news/detail/?f=20220422_3378.

11.

Kimura, T., Miyaoka, H., Ichikawa, T. & Kojima, Y. Hydrogen absorption of catalyzed magnesium
below room temperature. Int J Hydrogen Energy 38, 13728–13733 (2013).

12.

Gi, H. et al. Effective Factor on Catalysis of Niobium Oxide for Magnesium. ACS Omega 5, 21906–
21912 (2020).

13.

Barkhordarian, G., Klassen, T. & Bormann, R. U. Effect of Nb2O5 content on hydrogen reaction
kinetics of Mg. J Alloys Compd 364, 242–246 (2004).

14.

Barkhordarian, G., Klassen, T. & Bormann, R. Catalytic mechanism of transition-metal compounds
on Mg hydrogen sorption reaction. Journal of Physical Chemistry B 110, 11020–11024 (2006).

15.

Hanada, N., Ichikawa, T. & Fujii, H. Catalytic effect of Ni nano-particle and Nb oxide on Hdesorption properties in MgH2 prepared by ball milling. J Alloys Compd 404–406, 716–719 (2005).

16.

Boateng, E. & Chen, A. Recent advances in nanomaterial-based solid-state hydrogen storage. Mater
Today Adv 6, 100022 (2020).

17.

Dillon, A. C. et al. Storage of hydrogen in single-walled carbon nanotubes. Nature 386, 377–379


(1997).
18.

Hirscher, M. et al. Hydrogen storage in sonicated carbon materials. Appl Phys A Mater Sci Process
72, 129–132 (2001).

19.

Chambers, A., Park, C., R., B. T. K. & M., R. N. Hydrogen storage in platelet graphite nanofibers.
Sep Purif Technol 58, 219–223 (2007).

20.

Ahn, C. C. et al. Hydrogen desorption and adsorption measurements on graphite nanofibers. Appl
Phys Lett 73, 3378–3380 (1998).

21.

Ströbel, R. et al. Hydrogen adsorption on carbon materials. J Power Sources 84, 221–224 (1999).

22.

Ye, Y. et al. Hydrogen adsorption and cohesive energy of single-walled carbon nanotubes. Appl Phys
Lett 74, 2307–2309 (1999).

23.

Kojima, Y. et al. Hydrogen adsorption and desorption by carbon materials. J Alloys Compd 421,
204–208 (2006).

24.

Thomas, K. M. Hydrogen adsorption and storage on porous materials. Catal Today 120, 389–398(2007).

25.

Man Mohan, Vinod Kumar Sharma, Gayathri, E. Anil Kumar, V. G. Hydrogen storage in carbon
materials. Energy Storage 1, 1–26 (2019).

26.

Ströbel, R., Garche, J., Moseley, P. T., Jörissen, L. & Wolf, G. Hydrogen storage by carbon materials.
J Power Sources 159, 781–801 (2006).

27.

Sevilla, M. & Mokaya, R. Energy storage applications of activated carbons: Supercapacitors andhydrogen storage. Energy Environ Sci 7, 1250–1280 (2014).

28.

Xia, Y., Yang, Z. & Zhu, Y. Porous carbon-based materials for hydrogen storage: Advancement andchallenges. J Mater Chem A Mater 1, 9365–9381 (2013).

29.

Texier-Mandoki, N. et al. Hydrogen storage in activated carbon materials: Role of the nanoporous
texture. Carbon N Y 42, 2744–2747 (2004).

30.

Gogotsi, Y. et al. Tailoring of nanoscale porosity in carbide-derived carbons for hydrogen storage. J
Am Chem Soc 127, 16006–16007 (2005).

31.

Gadiou, R. et al. The influence of textural properties on the adsorption of hydrogen on ordered
nanostructured carbons. Microporous and Mesoporous Materials 79, 121–128 (2005).

32.

Zhao, X. B., Xiao, B., Fletcher, A. J. & Thomas, K. M. Hydrogen adsorption on functionalized
nanoporous activated carbons. Journal of Physical Chemistry B 109, 8880–8888 (2005).

33.

Takagi, H., Hatori, H., Yamada, Y., Matsuo, S. & Shiraishi, M. Hydrogen adsorption properties ofactivated carbons with modified surfaces. J Alloys Compd 385, 257–263 (2004).
34.

Pang, J., Hampsey, J. E., Wu, Z., Hu, Q. & Lu, Y. Hydrogen adsorption in mesoporous carbons. Appl
Phys Lett 85, 4887–4889 (2004).

35.

Parra, J. B. et al. Textural development and hydrogen adsorption of carbon materials from PET
waste. J Alloys Compd 379, 280–289 (2004).

36.

Nijkamp, M. G., Raaymakers, J. E. M. J., van Dillen, A. J. & de Jong, K. P. Hydrogen storage using
physisorption-materials demands. Appl Phys A Mater Sci Process 72, 619–623 (2001).

37.

Zhao, X., Villar-Rodil, S., Fletcher, A. J. & Thomas, K. M. Kinetic Isotope Effect for H 2 and D 2
Quantum Molecular Sieving in Adsorption/Desorption on Porous Carbon Materials. (2006)
doi:10.1021/jp060748p.

38.

Poirier, E., Chahine, R. & Bose, T. K. Hydrogen adsorption in carbon nanostructures. Int J Non
Linear Mech 26, 831–835 (2001).

39.

Bénard, P. & Chahine, R. Storage of hydrogen by physisorption on carbon and nanostructured
materials. Scr Mater 56, 803–808 (2007).

40.

Zhao, W., Fierro, V., Fernández-Huerta, N., Izquierdo, M. T. & Celzard, A. Impact of synthesis
conditions of KOH activated carbons on their hydrogen storage capacities. Int J Hydrogen Energy 37,
14278–14284 (2012).

41.

Zhao, W. et al. Activated carbons with appropriate micropore size distribution for hydrogen
adsorption. Int J Hydrogen Energy 36, 5431–5434 (2011).

42.

Otowa, T., Tanibata, R. & Itoh, M. Production and adsorption characteristics of MAXSORB: Highsurface-area active carbon. Gas Separation and Purification 7, 241–245 (1993).

43.

Li, H., Eddaoudi, M., O’Keeffe, M. & Yaghi, O. M. Design and synthesis of an exceptionally stable
and highly. Nature 402, 276–279 (1999).

44.

Rosi, N. L. et al. Hydrogen storage in microporous metal-organic frameworks. Science (1979) 300,
1127–1129 (2003).

45.

Rowsell, J. L. C., Millward, A. R., Park, K. S. & Yaghi, O. M. Hydrogen Sorption in Functionalized
Metal-Organic Frameworks. J Am Chem Soc 126, 5666–5667 (2004).

46.

Shet, S. P., Shanmuga Priya, S., Sudhakar, K. & Tahir, M. A review on current trends in potential useof metal-organic framework for hydrogen storage. Int J Hydrogen Energy 46, 11782–11803 (2021).

47.

Grünker, R. et al. A new metal-organic framework with ultra-high surface area. Chemical
Communications 50, 3450–3452 (2014).



48.

Lim, D. W., Yoon, J. W., Ryu, K. Y. & Suh, M. P. Magnesium nanocrystals embedded in a metalorganic framework: Hybrid hydrogen storage with synergistic effect on physi- and chemisorption.
Angewandte Chemie - International Edition 51, 9814–9817 (2012).

49.

Gómez-Gualdrón, D. A. et al. Evaluating topologically diverse metal-organic frameworks for cryoadsorbed hydrogen storage. Energy Environ Sci 9, 3279–3289 (2016).

50.

Bambalaza, S. E., Langmi, H. W., Mokaya, R., Musyoka, N. M. & Khotseng, L. E. Experimental
Demonstration of Dynamic Temperature-Dependent Behavior of UiO-66 Metal-Organic Framework:
Compaction of Hydroxylated and Dehydroxylated Forms of UiO-66 for High-Pressure Hydrogen
Storage. ACS Appl Mater Interfaces 12, 24883–24894 (2020).

51.

Sumida, K. et al. Hydrogen storage and carbon dioxide capture in an iron-based sodalite-type metalorganic framework (Fe-BTT) discovered via high-throughput methods. Chem Sci 1, 184–191 (2010).

52.

Xia, L. & Liu, Q. Adsorption of H2 on aluminum-based metal-organic frameworks: A computational
study. Comput Mater Sci 126, 176–181 (2017).

53.

Orcajo, G. et al. Li-Crown ether complex inclusion in MOF materials for enhanced H2 volumetricstorage capacity at room temperature. Int J Hydrogen Energy 4, 19285–19293 (2019).

54.

Furukawa, H., Miller, M. A. & Yaghi, O. M. Independent verification of the saturation hydrogen
uptake in MOF-177 and establishment of a benchmark for hydrogen adsorption in metal-organic
frameworks. J Mater Chem 17, 3197–3204 (2007).

55.

Panella, B., Hirscher, M., Pütter, H. & Müller, U. Hydrogen adsorption in metal-organic frameworks:
Cu-MOFs and Zn-MOFs compared. Adv Funct Mater 16, 520–524 (2006).

56.

Bordiga, S. et al. Adsorption properties of HKUST-1 toward hydrogen and other small molecules
monitored by IR. Physical Chemistry Chemical Physics 9, 2676–2685 (2007).

57.

Lin, K. S., Adhikari, A. K., Ku, C. N., Chiang, C. L. & Kuo, H. Synthesis and characterization of
porous HKUST-1 metal organic frameworks for hydrogen storage. Int J Hydrogen Energy 37,
13865–13871 (2012).

58.

Murray, L. J., Dinca, M. & Long, J. R. Hydrogen storage in metal-organic frameworks. Chem Soc
Rev 38, 1294–1314 (2009).

59.

Hirscher, M. & Panella, B. Hydrogen storage in metal-organic frameworks. Scr Mater 56, 809–812(2007).

60.

Saha, D., Wei, Z. & Deng, S. Equilibrium, kinetics and enthalpy of hydrogen adsorption in MOF177. Int J Hydrogen Energy 33, 7479–7488 (2008).



61.

Furukawa, H. et al. Ultrahigh porosity in metal-organic frameworks. Science (1979) 329, 424–428(2010).

62.

Farha, O. K. et al. Metal-organic framework materials with ultrahigh surface areas: Is the sky thelimit J Am Chem Soc 134, 15016–15021 (2012).

63.

Hönicke, I. M. et al. Balancing Mechanical Stability and Ultrahigh Porosity in Crystalline
Framework Materials. Angewandte Chemie - International Edition 57, 13780–13783 (2018).

64.

Wong-Foy, A. G., Matzger, A. J. & Yaghi, O. M. Exceptional H2 saturation uptake in microporous
metal-organic frameworks. J Am Chem Soc 128, 3494–3495 (2006).

65.

Chen, Z. et al. Balancing volumetric and gravimetric uptake in highly porous materials for clean
energy. Science (1979) 368, 297–303 (2020).

66.

Ahmed, A. et al. Balancing gravimetric and volumetric hydrogen density in MOFs. Energy Environ
Sci 10, 2459–2471 (2017).

67.

Livingston, H. K. The cross-sectional areas of molecules adsorbed on solid surfaces. J Colloid Sci 4,
447–458 (1949).

68.

Hirscher, M. et al. Materials for hydrogen-based energy storage – past, recent progress and future
outlook. J Alloys Compd 827, (2020).

69.

Balderas-Xicohténcatl, R. et al. Formation of a super-dense hydrogen monolayer on mesoporous
silica. Nat Chem (2022) doi:10.1038/s41557-022-01019-7.





2. Purpose
The H2 adsorption storage using porous materials have long been studied. It is well known
that the H2 capacity strongly depends on the specific surface area of porous materials. Therefore, themain efforts of this research field have been the development of porous materials to increase thespecific surface area, such as porous carbon materials and MOFs. However, in recent years, theimprovement of H2 adsorption capacity seems to be stagnating due to the limit of the material
development to obtain a higher specific surface area. Most of previous researches have been focusedon H2 adsorption capacity at the boiling point of N2 (77 K), which is higher than the boiling point ofH2 (20.4 K). Meanwhile, in this study carried out at 20.4 K, the “super-dense H2 adsorption” with ahigher density of adsorbed H2 compared with that of bulk-liquid and solid H2 was reported. This
result is contrary to the general understanding that the upper limit of adsorbed H2 density isequivalent to the density of liquid H2. The super-dense H2 adsorption is expected to lead to further
enhancement of H2 adsorption capacity from the practical point view and further understanding ofphysical properties of the adsorbed H2 from the academic point of view. However, the reports about
super-dense H2 adsorption are still few, and the details of the super-dense H2 have not been
understood well.
In this thesis, the factors leading to the super-dense H2 adsorption under the cryogenic
condition were discussed from the following point of view. In addition, for the H2 storage as liquid
phase, the feasibility about suppression of boil-off by using the H2 adsorption phenomena on porous
materials was discussed.

1)

Material dependence
In the previous studies, the super-dense H2 adsorption was reported on only a few

materials, and the material dependences were not understood well. In this work, various kind ofmaterials, such as the carbon materials, MOFs, and other porous materials, were used for theadsorption tests at the boiling point of H2 (20.4 K). The influence of different material species,
specific surface area, and pore structure, for the density of super-dense H2 were investigated.

2)

Temperature dependence
The super-dense H2 adsorption has been observed only at the boiling point of H2 (20.4 K)in previous studies. In this work, the temperature dependence of the super-dense H2 density wasinvestigated below the critical point of H2 (33 K). In addition, the feasibility of suppression for liquid
H2 boil-off was discussed by using the effect of super-dense H2 on porous materials.

3)

Adsorbed layer dependence
Molecules of adsorbates can be divided into the two types; molecules adsorbed just on thematerial surface (monolayer) and molecules adsorbed on adsorbates (multilayer). Analysis methods
to distinguish between the monolayer and multilayer adsorption have been established based on the
BET theory, which is explained next section in detail, and the densities of monolayer and multilayer
H2 were independently evaluated in order to discuss the adsorption state in furhter detail.

4)

Gas dependence
The phenomenon of the super-dense adsorption has been investigated only for H2 undercryogenic condition so far. In order to understand the gas dependence of the super-dense adsorption
state, the densities of deuterium (D2), neon (Ne), and nitrogen (N2) on the carbon materials were
investigated at the boiling points 23.6, 27.1, and 77.1 K, respectively.








3. Theory and Experiments
3.1 Theory of gas adsorption on solid surface
3.1.1.

Van der Waals Forces
Van der Waals force is a weak intermolecular force existing between molecules andsurfaces due to dipolar interactions. The van der Waals force is usually categorized three different
types of interactions; Keesom interaction, Debye interaction, and London dispersion interaction as
summarized in Fig. 3.1.1. The Keesom interaction and Debye interaction are based on electrostaticmechanisms. The Keesom interaction arises from the interaction between two permanent dipoles,
which is a so-called orientation force. The Debye interaction arises from a molecule with apermanent dipole, inducing charge redistribution to neighboring molecules with no dipole moments,
which is a so-called induction force. The London dispersion interaction is most widely known as thevan der Waals interaction based on two molecules without permanent dipole. The electron cloud inthe atom can yield an instantaneous dipole, and it can induce a dipole to neighboring molecules. The
induced dipoles are weakly attracted to another molecule by the dispersion force. The strength of the
London dispersion force increases with the number of electrons in the molecules. The potential) is given byenergy of the van der Waals force (

where

,

,

where

=

+

+

(3.1.1)

=−

,

, and

are constants for each interaction, and is the distance between

two molecules. The potential energy decreases with 1/ . The interaction between H2 molecules anda solid surface is basically dominated by this London dispersion interactions.



Lennard-Jones potential
Lennard-Jones potential is described as the total potential of repulsion and attraction on thevan der Waals force as a function of the distance between molecules. This is a typical model toexplain the interactions between molecules. The potential of=4
where corresponds to minimum potential, and
When

=2 /

,

is given by(3.1.2)−is the value of the distance ( ) whenshows a minimum value of . Table 3.1.1 shows the parameters of /each species of molecule, whereforis Boltzmann constant, and the Lennard-Jones potential between

H2-H2 molecule is calculated and shown in Fig. 3.1.2. The attraction term of 1/
by the London dispersion force. The repulsive term of 1/

is basically given

is the Pauli repulsion due to theoverlapping electron orbitals.

Table. 3.1.1 Parameters of Lennard-Jones potential ( /is zero.

and).1

Fig. 3.1.1 Types of van der Waals forces (Keesom interaction, Debye interaction, London
distribution interaction).2

Fig. 3.1.2 Lennard-Jones potential (−4) for H2-H2 molecules. Blue curve is the attraction term of, Orange curve is the repulsive term of 4




.

3.1.2.

Langmuir and BET theory

Langmuir theory
The Langmuir adsorption model is the simplest model representing the monolayer
adsorption between adsorbates and adsorbents. This adsorption model was proposed by Irving
Langmuir in 1918.3 The Langmuir adsorption model is based on the assumptions as shown below.

Assumptions of Langmuir theory
1. Gas molecules behave ideally
2. Only monolayer forms
3. All adsorption sites on the surface are equivalent
4. There are no interactions between adsorbate - adsorbate
5. Adsorbed molecules are immobile

The Langmuir equation is given based on the above assumptions, and it is derived below.
The rate of adsorption ( ) and desorption ( ) are described as(3.1.3)

=
=
where

and

adsorbate,(3.1.4),are constants of adsorption and desorption reaction,is the number of free sites on the surface, andadsorbate on the surface. Both rate ofandis the partial pressure of theis the number of sites occupied byshould be equal in the equilibrium state and theequation 3.1.3 and 3.1.4 give
=
where

= ,

is the equilibrium constant. The total number of sites ( ) is given by

(3.1.5)

=

+

=

+

=

1+

(3.1.6)Since the fraction of the occupied sites, i.e., the fractional coverage, on the surface ( ) can be givenas=,(3.1.7)the Langmuir equation is given by=

1+

Fig. 3.1.4 shows the Langmuir isotherm for different values of . The different values of(3.1.8)give thedifferent isotherms. The fractional coverage increases and approaches 1 with increasing pressure.

BET theory
The BET theory is widely used to determine the specific surface area dealing withmultilayer adsorption, which is developed by Stephen Brunauer, Paul Emmett, and Edward Teller in
1938.4 The BET model is an extension of Langmuir model based on the following assumptions.

Assumptions of BET theory
1.

The surface is homogeneous (All sites are equivalent)2.

Gas molecules behave ideally3.

Multilayers can be formed on each site infinitely

4.

After first layer, each molecule provides adsorption site for next layer

5.

The Langmuir theory can be applied to each layer

6.

Adsorbed molecules are immobile

7.

Gas molecules only interact with adjacent layers

8.

There are no lateral interaction between molecules




9.

The enthalpy of adsorption for the first layer is constant for all sites

10. Adsorbate molecules in the second and higher layers are assumed as liquid and they havethe same enthalpy of liquefaction

The image of BET adsorption model is illustrated in Fig. 3.1.5. The BET equation isderived based on the assumption in the following paragraph.
In the multilayer adsorption with 0, 1, 2 … … layers, the number of adsorption site isrepresented

,

,

…

, … for each layer. At equilibrium state of the adsorption, the rate ofadsorption on ( − 1) layer is equal to the evaporation from layer. Since the rate of adsorption ( )on the layer is proportional to the pressure ( ) of adsorbate and the number of sites on the layer( − 1), therefore

is given by
=

where

is a rate constant. Since the rate of evaporation from layer (), sonumber of sites on layer and exp (− /=where

(3.1.9),is a rate constant,) is proportional to theis given by
exp −

,

(3.1.10)is the heat of adsorption on layer , R is the gas constant, and T is atemperature. Thus, both rate ofandshould be equal, and the equation 3.1.9 and 3.1.10 give
=

exp −

Here, the total number of adsorbed molecules ( ) and the number of monolayer sites ((3.1.11)) on anadsorbent are given by=(3.1.12)=(3.1.13)

Considering the assumption (10) of “Adsorbate molecules in the second and higher layers areassumed as liquid and they have the same enthalpy of liquefaction”, it gives( ≥ 2)=( ≥ 2),(3.1.15)is the heat of liquefaction. Now, the number of site ( ,… ) can be expressed by only

=
where
using

(3.1.14)= constant.
=, where=, where= ( / )exp (

=
=

=

=

=

(3.1.16)= ( / ) ∙ exp ( /R )(3.1.17)/R )(3.1.18)=, where =

=

exp((

−

)/R )

(3.1.19)

Inserting equation (3.1.19) into equation (3.1.12), it is given by==(1 − ),(3.1.20)

Inserting equation (3.1.19) into equation (3.1.13), it is given by
=

1+

=

1+

1−

(3.1.21)

In equation 3.1.20 and 3.1.21, the sum of an infinite geometric progression is expressed by==(3.1.22)

1−

d
dx

=

(1 − )(3.1.23)

Therefore, equations 3.1.20 and 3.1.21 are changed to=(1 − )(1 − +)(3.1.24)In this adsorption model, it is assumed that the number of layers can accumulate to infinity at thesaturation pressure ( ). When= ˁ at=,expressed bymust be equal to 1, and equation 3.1.17 can be

exp

R

= 1, and(3.1.25)=

Inserting equation (3.1.25) into equation (3.1.24), the BET equation is given by⁄( − 1)1=+∙ ⁄(1 − ⁄ )(3.1.26)

Fig. 3.1.6 shows the BET isotherms for different values of , which is large when the enthalpy ofdesorption from a monolayer is large compared with the enthalpy of vaporization of the liquid phase.
The value ofincreases infinitely with increasing pressure because there is no limit of the/multiple adsorbed layers.

BET surface area
The BET surface area is evaluated by the amount of monolayer molecules on the BET
adsorption model. An experimentally measured adsorption isotherm can be fitted by the BET) and an intercept (1⁄equation 3.1.26, and the value of a slope ( ( − 1)⁄) can be obtainedin the BET plot. Usually, the fitting of BET plot is applied in the relative pressure range of 0.03-0.35.
The BET plot gives the amount of monolayer molecule ((: mol/g), and the BET surface area

) of adsorbents can be evaluated by
=

where

×

×

(3.1.27)is the cross-sectional area (Å /molecule). Usually, N2 is used for the BET method and thecross-sectional area of N2 is 16.2 Å /molecule. Typically, the cross-sectional area can be evaluatedby equation 3.1.26 based on two assumptions, which are (1) the density of adsorbate is regarded asbulk-liquid density; (2) adsorbates form a hexagonal- close-packed layer.5
⁄

=
where

(g/mol) is the molar mass of molecule,

packing factor.

is the density of bulk-liquid phase,= 1.091 is well used as the hexagonal close-packed factor. 5

(3.1.28)∙is theFig. 3.1.3 Image of Langmuir adsorption model.

1
K=100

Fractional coverage, θA

0.8
K=10
0.6

0.4
K=1
0.2

0
0

0.2

0.4

0.6

0.8

1

Pressure (atm)Fig. 3.1.4 Langmuir isotherms for different values of K.

Fig. 3.1.5 Image of BET adsorption model.

5

N/Nmono4

3

2

c=1000
c=100
c=10

1

c=1

0
0

0.2

0.4

0.6

0.8

Pressure, p/p0

Fig. 3.1.6 BET isotherms for different values of c.

3.1.3.

Adsorption isotherms

Type of adsorption isotherms
Adsorption properties are usually investigated by adsorption isotherms which is the plot of adsorbed
amounts as a function of the pressure. It is well known that the shape of adsorption isotherms isrelated to a pore structure of adsorbents. In 1985, an International Union of Pure and Applied
Chemistry (IUPAC) technical report6 was published, and typical adsorption isotherms wereclassified to six types as shown in Fig. 3.1.7. According to the report, the pore structures are definedasi)Pores with widths exceeding about 50 nm; macropores

ii)

Pores of widths between 2 nm and 50 nm; mesopores

iii)

Pores with widths not exceeding about 2 nm; micropores

Type I shows a steep uptake at very low pressure, and the uptake approaches to a saturated
value with increasing pressure. This is due to a microporous material, where micropores enhance theinteraction between adsorbates and adsorbents. The saturated uptake is governed by the micropore
volume rather than the external surface area. Especially, Type I(a) isotherm represents the typicalmicroporous materials with mainly narrow micropores less than 1 nm. Type I(b) isotherms are given
by materials with pore size distributions including wider micropores and narrow mesopores (<2.5nm).
Type II isotherms are given by microporous or nonporous materials. The end point of steep
uptake at low pressure, which is called “B-point”, corresponds to the completion of monolayer
coverage, and after that, the uptake gradually increases by multilayer adsorption.
Type III isotherms doesn’t show the B-point, i.e., the monolayer adsorption is notobservable. The interactions between adsorbent and adsorbate are relatively weak, and then the heatsof adsorption are less than the heat of liquefaction of the adsorbate. The additional adsorption on anadsorbed layer proceeds because the heat of additional adsorption is greater than the adsorption on
the material surface.
Type IV isotherms are shown by mesoporous adsorbents. The initial adsorption stepcorresponds to the path of Type II isotherm on mesopore wall, and the final saturation plateau
correspond the complete filling of the pore. The typical feature of Type IV(a) is the hysteresis loop
in the final step, which is associated with capillary condensation in the mesopores. This phenomenon
occurs when the pore size exceeds a certain size, which depends on the adsorption system andtemperature. When the pore size is smaller than the certain size, Type IV(b) isotherms are obtainedwith completely reversible loop.
Type V isotherm in the low-pressure range is similar to that of Type III without the B-point,
because of the relatively weak adsorbent–adsorbate interactions. In the high pressure, the shape issimilar to that of Type IV.
Type VI isotherm is representative of layer-by-layer adsorption on a highly uniform
nonporous surface, such as a graphitized carbon

Quantitative definitions of adsorption
The adsorption isotherm represents the amount of adsorbate on the adsorbent surface as afunction of the pressure of the gas, and it is usually measured by volumetric method described laterin the section 3.3.1 “Principle of volumetric apparatus”. The experimental method doesn’t directly
measure the real amount of adsorbate because it is difficult to define the boundaries between theadsorbate and free gas. In general, there are four concepts to express the amount of adsorbed gas(uptake) on adsorbents, which are “Net”, “Excess”, “Absolute”, and “Total” uptake as illustrated inFig. 3.1.8.
), the amount of molecules with higher density thanIn the concept of “Net” uptake (free-gas in the cell is counted, i.e., the amount of free-gas in the cell volume (), corresponding to “A − D” in Fig. 3.1.8.

from the total introduced amount into the cell (Therefore,is given by
=

where

) is subtracted(3.1.29)−is the density of gaseous adsorbate. In the concept of “Excess” uptake (of molecules with higher density than that of free-gas in the free volume (), the amount) is counted, i.e., theamount of free-gas in the free volume is subtracted from the total introduced amount, corresponding
to “A” in Fig. 3.1.8. Therefore,=is given by−,

In the concept of “Absolute” uptake (

where

−

−

), the adsorbed amounts in the volume(3.1.30)
is counted,

is given bycorresponding to “A + B” in Fig. 3.1.8, and
=

=

−

,

where

=

(3.1.31)

In the concept of “Total” uptake, the amount of molecules in the free volume is counted,
corresponding to “A + B + C” in Fig. 3.1.8, and=is given by
(

+




−

)

(3.1.32)

In this study, the adsorbed uptake was evaluated as “Absolute” uptake. To discuss the gravimetriccapacity for each adsorbent,

was represented as the gravimetric units of “wt.%” and “mmol/g”.% [wt. %] =

/

where

is the mass of materials, and+[mmol/g] =1000 ,

is the molar mass of gases.




× 100

(3.1.33)(3.1.34)

Fig. 3.1.7 IUPAC classification of adsorption isotherms.6



Fig. 3.1.8 Concept of “Net”, “Excess”, “Absolute” and “Total” adsorption capacities,7 where Openand solid dots of “a” are “Excess adsorbed molecule” and “Adsorbed molecule normally present ingas phase”, respectively; solid dots of “g” is “Bulk gas molecule”; Vsk is the skeletal volume ofmaterial; Vad is the volume of adsorbate; Vp is the pore volume; Vgas is the volume of bulk-gas; ρgasis the density of bulk-gas; region of “A” corresponds to “Excess adsorbent”; region of “B”
corresponds to “Adsorbed molecule normally present in the gas phase”; region of “C” is “Bulkgaseous molecule”; region of “D” is “Free gas that would occupy Vsk.



3.1.4.

Isosteric heat of adsorption

Clausius-Clapeyron equation
Clausius-Clapeyron equation describes a characteristic of phase boundaries, i.e., the solidliquid boundary and the vapor-liquid boundary. In this study, the Clausius-Clapeyron equation wasapplied into the adsorption isotherms representing the properties of the adsorbed-vapor phaseboundary, and the heat of adsorption was evaluated on adsorbents.
In order to derive the Clausius-Clapeyron equation, two phases α and β are considered inan equilibrium condition at temperature ( ) and pressure ( ). Since the free energies ( ) of bothphases are equal, it is expressed as( , )=( , )(3.1.35)

Based on the principles of thermodynamics, the variations of free energy with temperature andpressure are given as=−(3.1.36)=−(3.1.37)

When the equilibrium pressure and temperature change fromto+ ∆ and from

to

+∆ ,

respectively, equation 3.1.35 can be given by( +∆ ,(+∆ )=( +∆ ,

+

+

)=(

+∆ )

)

(3.1.38)(3.1.39)

Inserting equation 3.1.35 into equation 3.1.39, the equation 3.1.39 is transformed into
(3.1.40)=
According to equation 3.1.36 and equation 3.1.37, equation 3.1.40 is transformed into
−

=
=

−
−
−

When ∆ is the heat of phase transformation at a temperature, the entropy change (

(3.1.41)(3.1.42)) can bedescribed as
−

=

=

∆

(3.1.43)

Finally, the Clausius-Clapeyron equation is given by inserting equation (3.1.43) into (3.1.42)∆=(3.1.44)−

Considering the gas adsorption on solid surface, the α and β phases are defined as the adsorbed
phase and the gaseous phase, respectively. In this case, the volume of gaseous phase is much larger
than that of adsorbed phase (), so equation 3.1.44 is transformed into

≫
=

∆

=

∆

,

R

where

=

R

(3.1.45)

and,
=

∆

(3.1.46)

R

When the equilibrium pressure and the temperature change fromtoand fromto,respectively, equation 3.1.46 is expressed as
=
ln

=

∆

(3.1.47)

R

∆

1
R

−

1

(3.1.48)

Finally, the Clausius-Clapeyron equation for evaluating the heat of adsorption is derived in equation
3.1.48.

Procedure of evaluation of heat adsorption
The adsorption isotherms measured at different temperatures were used to evaluate theheat of adsorption. Fig. 3.1.9 shows the typical isotherms measured at different temperature ofand. The equilibrium pressures ofamount (( ) and( ) and( ) , corresponding to a certain adsorbed), were defined as shown in Fig. 3.1.9. By substituting these values (,,( ),) into equation 3.1.48, the heat of adsorption at a certain adsorbed amount wasevaluated. The heat of adsorption for different adsorbed amount was evaluated, and the relationshipbetween the adsorbed amount and the heat of adsorption for each adsorbent was shown in the result
section of Fig. 4.3.2.

Fig. 3.1.9 Schematic drawing the equilibrium pressures (P) at two temperatures (T1>T2) with acertain adsorbed amount () on an adsorbent.



3.2 Materials
Various materials were used as the adsorbents in this study, and the information ofmaterials were listed in Table. 3.2.1. Prior to the measurement, all adsorbents were degassed at 200ºC for 12 h under dynamic vacuum condition in a stainless tube.

Table 3.2.1 Information of adsorbent materials

Adsorbent
MSC-30
GNPs
MOF-177
HKUST-1
MOFs Fe-Mil-100
MIL-53
ZIF-8
Wakogel C-300
Silica gel
Aerogel
Crbon

Suplyer

Information for MOFs

Kansai Coke and Chemicals Co., Ltd
STREM chemicals (item number: 06-0235)
Sigma-Aldrich (Basolite Z377)
Air Liquide Laboratories
Air Liquide Laboratories
Sigma-Aldrich (Basolite A100)
Sigma-Aldrich (Basolite Z1200)
FuJIFILM Wako
Air Liquide Laboratories




Metal

Ligand

Zn
Cu
Fe
Al
Zn

Benzenetribenzoate
1,3,5-Benzenetricarboxylate
Trimesic acid
Terephthalate
2-Methylimidazolate

Definitions of material’s volume and density
In order to perform the volumetric measurement and discuss the volumetric capacity ofadsorbates, it is important to understand the definitions of volume and density of materials. There areseveral concepts to define the volume and density for the material level and the system level asshown in Fig. 3.2.1.7
Fig. 3.2.1 (a) shows the materials level definitions, and there are some concepts of densityand volume for the porous materials. The pores can be classified as “open” and “closed” pores,
which are defined as whether a gas can freely access in the pores. In the actual materials forexperiments, there are intermediate pores between open and closed pores because the size of theaccessible pores is dependent on the species of gas probe, i.e., the size of the molecule. The absoluteor true volume (density () is defined as the volume of materials themselves without any pores, and the true

) is described as
=

where

(3.2.1),is the mass of the material. The skeletal volume () can be defined as the volume

occupied by the materials themselves plus the volume of the closed pores, and the skeletal density() can be described as(3.2.2)=

Fig. 3.2.1 (b) shows the systems level definitions of the density and volume. The
aggregations of powder materials are packed in a cell, and there is a space between grains due to theimperfect packing. The apparent volume including the space between grains is called a bulk volume(), and then the bulk density can be described as=/. The bulk density is easilychanged by the packing methods, e.g., tapping, shaking, compression, and making pellets. The cellvolume () is the volume of the inside empty cell without materials. The free volume (




) is

the cell volume excluding the skeletal volume of materials, described aswhich is also called “Dead volume”.




=

−

/

,

Fig. 3.2.1 Definitions of volume and density for (a) material level and (b) system level

3.3 Experiment and analysis of gas adsorption
3.3.1

Principle of volumetric method by Sievert’s apparatus
The volumetric method (known as Sievert’s type apparatus) is widely used for the gas

sorption measurement to obtain the isothermal curves. In this chapter, the principle of volumetricapparatus is described. Fig. 3.3.1 shows a schematic diagram of a typical Sievert’s apparatus
composed of a reservoir with a specific volume, gas cylinder, line part, sample cell, and vacuum
pump system. The initial gas amount ( ) in the system (in the reservoir, line part and sample cell)
can be given by
=
where
,

,

, and

, and

∙ ( ,

)+

∙ ( ,

)+

∙ ( ,

−

)

(3.3.1)is the volume of the reservoir, line part, and sample cell, respectively,

is the temperature of the reservoir, line part and sample cell, respectively, ρ(P,T) is thedensity of real gas at a certain pressure and temperature,is the skeletal of density of a material. Thus, (−is the mass of a material in the cell, and) represents the free volume of the/sample cell.
At the first step, the gas is introduced into the reservoir at pressure of
G and closing valve S, and then the gas amount ( ) in the
=

∙ ( ,

∙ ( ,

)+

,

)+

and
−

by opening valve

is given by∙ ( ,After opening the valve S (valve G is closed), the pressure changes from)

(3.3.2)

toin a certain time,

due to the gas introduction from the reservoir into the line part and sample cell. The gas amount in
the system ( ) at

can be given by
=

∙ ( ,

)+

Therefore, the sorbed gas amount (

∙ ( ,

−

∙ ( ,

)

(3.3.3)) can be evaluated by.
_

=(

−




)+

)=∆

(3.3.4)_ ) is given by

At the second step, the sorbed gas amount (_=_(3.3.5)+∆

Repeating the above process by times, the sorbed gas at the steps is expressed as
_

=

_(

The typical isotherms can be obtained by plotting the relationship between(3.3.6)

)+∆

_

and

.

Fig. 3.3.1 Schematic diagram of a typical volumetric apparatus (Sievert’s apparatus)

3.3.2N2 adsorption isotherms for investigation of textural properties
N2 adsorption isotherms for all adsorbents were measured by a Sievert’s apparatus(Belsorp-max 12N-VP-LTC, Microtrac BEL) at the liquid N2 temperature (77 K). Fig. 3.3.2 shows
the schematic diagram and picture of the experimental system. Prior to the measurement, alladsorbents were heated up to 200 ºC for 12 h under dynamic vacuum condition, and water and othergases on adsorbents were degassed. The degassed adsorbent was put into the sample cell in a globe
box filled in high purity Ar gas (>99.9999%), where oxygen level and water level were less than 5
and 2 ppm, respectively. A glass rod was used to reduce the free volume in the sample cell. The twocells with materials and one empty cell (reference cell) were installed as shown in Fig. 3.3.2 because
this apparatus allows the measurement for two sample cells at the same time. The free volume of thesample cells was measured by He gas as a non-adsorbing gas at room temperature. After vacuuming
the sample cells at room temperature, the cells were put in the dewar vessel with liquid N2, and themeasurement of N2 adsorption isotherm was carried out in the automatic operation system. An
equilibrium pressure was determined when the pressure variation was within 0.1 % in each 5 min
period. As the adsorption measurement proceeds, the level of liquid N2 in the dewar vessel decrease
due to the evaporation of liquid N2. This leads to a change of the cooling volume in the sample cell.
The change of cooling volume in the reference cell was measured at each measurement point, it
allows a correction of the volume change of the sample cells due to the decrease of the liquid N2
level in the dewar vessel.The measured N2 adsorption isotherms give the information about the
textural properties of adsorbents, such as the specific surface area, total pore volume, and average ofpore diameter, as described below.

Specific surface area
The specific surface area (m2/g) of each adsorbent was evaluated by applying BETequation (equation 3.1.26) into the measured N2 adsorption isotherms. Usually, the results in therelative pressure ( ⁄ ) range of 0.03-0.35 is used for the BET analysis, however it is not suitablefor Type I adsorption attributed to micropores because the monolayer adsorption is completed atlower pressure than ⁄= 0.35. The appropriate range of ⁄for microporous materials were

determined by a method proposed by Rouquerol et al,8 i.e. the ⁄range with increasing the valueof (1 − ⁄ ) was applied. In this study, the volumetric surface area was defined as the surface
area per the skeletal volume of the material, and it was evaluated to multiply the gravimetric surface
area by the skeletal density.

Total pore volume
The specific total volume was evaluated by(3.2.7)=
whereis the amount of adsorbate at ⁄is the density of liquid for the adsorbate.

= 0.99,Average pore diameter
The average of pore diameter was evaluated by considering the total pore volume as thecylindrical shape of pore. The total volume

and the surface area (), i.e. the lateral area ofthe cylindrical pore were given by=(3.2.8)4(3.2.9)=whereis the height of cylindrical pore andis the diameter of cylindrical pore, i.e. the averagepore diameter. Therefore, the average pore diameter of
=

4




was given by(3.2.10)

Fig. 3.3.2 Schematic diagram of Sievert’s apparatus (Belsorp-max 12N-VP-LTC, Microtrac BEL) forN2 adsorption measurement

Fig. 3.3.3 Picture of Sievert’s apparatus (Belsorp-max 12N-VP-LTC, Microtrac BEL) and sample
and sample cell

3.3.3

Measurement of skeletal density
The skeletal densities of all materials were measured by volumetric method using Sievert’s

apparatus (Belsorp-max 12N-VP-LTC, Microtrac BEL). He gas was used as a non-sorbing gas, and atemperature of the sample cell was maintained at 40 ºC by water bath. At the first step, the volume ofthe empty cell () with a glass rod was measured. After that,(g) of degassed material was put

into the sample cell in the grove box, and the free volume of the sample cell () was measured.

Finally, the skeletal density of a material was evaluated by=−(3.3.11)

It was carried out 6 times, and the average values were shown in the result section for each adsorbent.



3.3.4

Cryogenic adsorption measurement
The cryogenic adsorption measurement was carried out by using the Sievert’s typeapparatus, which is called Pressure-Composition isothermal (PCI) system, provided by Suzuki
Shokan Co., Ltd., and then the sample cell (12.3 cm3) was cooled by the cryostat system with He
cryocooler (C200G) provided by Suzuki Shokan Co., Ltd.. Fig. 3.3.4 and Fig. 3.3.5 show theschematic diagram and pictures of the PCI and the cryostat system. By using this system, theintroduced gas amount into the sample cell can be accurately evaluated as following steps: (1). a gas
was introduced at desired pressure ( ) into the reservoir with a specific volume (at room temperature () which was kept); (2). The valve connected to the sample cell (valve S) was opened, and thegas was introduced into line part and the sample cell from the reservoir. The equilibrium pressure( ) was determined when the pressure variation is within 0.01 MPa in each 5-10 min period. (3).
The introduced gas amount ( ) into the line part and the sample cell was evaluated by comparing
in the step (1) with that at the pressure

the gas amount in the reservoir at the pressure ofstep (2), therefore

in thewas given by
∙ ( ,

=

∙ ( ,

)−

)

(3.3.12)

where the gas density of ( , ) was obtained from the NIST chemistry Web Book;9 (4). Steps 1-3
were repeated. At the second cycle, the total introduced gas amount was given by
=

+

∙ ( ,

)−

∙ ( ,

)

(3.3.13)Subsequently, the total introduced gas amount at the -th cycle was given by
=

+

∙ ( ,

)−

∙ ( ,

)

(3.3.14)

These cycles were repeated until the pressure in the sample cell was reached up to 1.5 MPa; (5). In
order to obtain the introduced gas amount into the sample cell, the introduced gas amount into theline part was evaluated by the measurement of step 1-4 with blind gasket between the line part andthe sample cell, and then the result was subtracted from the introduced gas amount into the line partand the sample cell.
Prior to the measurement, all materials were degassed at 200 ºC for 12 h under dynamic
vacuum condition in a stainless tube, and the materials were put into the sample cell in a glove box
filled by highly purified Ar gas (>99.9999%). When the sample cell was connected to the cold head,
Apiezon N high vacuum grease (Apiezon products M&L Materials LTD) was used to make close
contact between the sample cell and the cold head to obtain good thermal conductivity and lesstemperature gradient. Ar gas in the sample cell was evacuated to 1×10-4 MPa by rotary pump at room
temperature, and the air in the vacuum insulation container (cryostat) was evacuated to 1×10-2 Pa byturbo molecular pump with diaphragm pump. Then, the sample cell was cooled by the He cryocooler
and the temperature was adjusted to desired temperature by heater block with a temperature
controller surrounding the sample cell.
The measurements of isotherms for H2 were carried out by using the cell with and without
adsorbents listed in Table. 3.2.1 at the boiling point of H2 (20.4 K). The temperature dependence ofH2 adsorption using MSC-30, GNPs, and MOF-177 was investigated below the critical temperatureof H2 at 20.4 K (0.10 MPa), 23.3 K (0.22 MPa), 26.5 K (0.44 MPa), and 30.6 K (0.88 MPa), where
inside of brackets showed the phase transition pressure at each temperature. In order to investigate
the gas dependence of adsorption properties, the measurements using MSC-30 were carried out for
H2, D2, Ne, and N2 at each boiling point of 20.4, 23.6, 27.1, and 77.2 K, respectively. The
temperature dependence on each gas was investigated at 23.6 K (0.10 MPa), 26.6 K (0.22 MPa),29.9 K (0.44 MPa), and 33.9 K (0.88 MPa) for D2, and at 27.1 K (0.10 MPa), 29.4 K, 32.5 K for Ne,
and at 77.2 (0.10 MPa), 85.1 K (0.22 MPa) and 92.9 K (0.44 MPa) for N2. These temperatures were
determined by referencing the liquefaction pressure obtained from the results of isotherms and the
database in NIST chemistry Web Book.9

Fig. 3.3.4 Schematic diagram PCI and the cryostat systems.

Fig. 3.3.5 Picture of the PCI system and the cryostat and inside of cryostat

3.3.5

Evaluation of density of adsorbate
The densities of adsorbed H2 (; mol/cm ) for all the adsorbents were evaluated.

based on the results obtained from the experiment in the section 3.3.4. Figs. 3.3.6 show a typicalresult of the isotherms for an empty cell (Blank) and a cell with adsorbents, representing the i-H2
amount into both cells as a function of H2 pressure. In Fig. 3.3.6, the points of “α” and “β” were
defined, corresponding to the “beginning” and “end” point of liquefaction, respectively. The densityof adsorbed H2 (; mol/cm ) was evaluated by following identities related to the points α and.

β. Initially, the read value of i-H2 amount at the point α (
=
where

.

+

.

; mol) is given by.

(3.3.15),.

is the amount of adsorbed H2 as unknown value, and.

(mol) is the amount of.

gaseous H2 as unknown value. At the point β, the read value of i-H2 amount (
=
where

.

.

+

+

.

is assumed to be equal to that of point Ѝ,

unknown value, and.

.

; mol) is given by(3.3.16)

,

.

.

.

(mol) is the amount of liquid H2 as(mol) is the amount of gaseous H2 as unknown value.

The identity equations about the volume in the cell occupied with adsorbents at the point Ѝ and Ў
are shown below. At the point of Ѝ, the total volume of the cell (V
=

V
where

.

and

.

.

+

.

.

+

.

=

+

= 12.3 cm ) is represented as.

.

+(3.3.17),.

(cm3) are the volume of adsorbed H2 and gaseous H2, respectively,.

(cm3) is the skeletal volume of an adsorbent,.

(mol/cm3) is the density of gaseous H2 obtained

from NIST chemistry Web Book9 at each phase transition point,and.

(g/cm3) is the skeletal density,(g) is the mass of an adsorbent put in the cell. By the same procedure, V

at the point Ў isgiven by
V

=

.

+

.

+

.

.

+

=




.
.

+

.
.

+

.

.
.

+

,

(3.3.18)

where.

is the density of liquid H2 obtained from NIST chemistry Web Book9 at each phasetransition point. Here, the volume of the homogeneous temperature region was defined as thevolume occupied by liquid H2 in Blank ((a)), where

=

/ρ

.

) at the point Ў (see image in Fig. 3.3.6.

is the amount of liquid H2 in Blank. Assuming that.

of Blank is equivalent towith adsorbents at the point Ў can be given bythat with adsorbents,

=V

−

.

=V

.

.

−

.

(3.3.19).

Accordingly, the equation 3.3.18 can be changed to equation 3.3.20
=
(=

.

/ρ

3.3.16 (without

.

+

.

+

.

=

.

) can be determined by evaluating

.

.

.

+

) and 3.3.18 (without,.

Fig. 3.3.6 (a). Finally, five of unknown values, ((3.3.20)+.

to solve the two identity equations.

) based on the result of Blank as shown in
.

,

.

,

.

.

,

.

.

.

), can beevaluated by five identities of equation 3.3.15, 3.3.16, 3.3.17, 3.3.19, 3.3.20. By using the above
processes, the value of.

was evaluated for each adsorbent. For other gas such as D2, Ne, andN2, this method is available to evaluate the density of adsorbates. In this evaluation, the errors were
evaluated to consider that the read value of,

have errors of 0.001 and 0.003 mol, anderror of 0.5 g/cm3.




has

Fig. 3.3.6 Typical result of isothermal properties of H2 introduction (left side) and image of inside of
the cell at the bigging and end point of liquefaction for (a) an empty cell and (b) a cell withadsorbentsReferences
1.

Mamedov, B. A. & Somuncu, E. Analytical treatment of second virial coefficient overLennard-Jones potential and its application to molecular systems. J Mol Struct 1068, 164–
169 (2014).

2.

Butt, H.-J. & Kappl, M. Surface and Interfacial Forces. (WILET-VCH, 2010).

3.

Langmuir, I. The Adsorption of Gases on Plane Surfaces of Glass, Mica and Platinum. J Am
Chem Soc 40, 1361–1403 (1918).

4.

Brunauer, S., Emmett, P. H. & Teller, E. Adsorption of Gases in Multimolecular Layers. J.
Am.Chem.Soc. 60, 309–319 (1938).

5.

Livingston, H. K. The cross-sectional areas of molecules adsorbed on solid surfaces. J
Colloid Sci 4, 447–458 (1949).

6.

Thommes, M. et al. Physisorption of gases, with special reference to the evaluation of
surface area and pore size distribution (IUPAC Technical Report). Pure and Applied
Chemistry 87, 1051–1069 (2015).

7.

Parilla, P. A., Gross, K., Hurst, K. & Gennett, T. Recommended volumetric capacity
definitions and protocols for accurate, standardized and unambiguous metrics for hydrogenstorage materials. Appl Phys A Mater Sci Process 122, 1–18 (2016).

8.

Rouquerol, J., Llewellyn, P. & Rouquerol, F. Is the BET equation applicable to microporous
adsorbents. Stud Surf Sci Catal 160, 49–56 (2007).

9.

Eric W. Lemmon, Ian H. Bell, Marcia L. Huber, and Mark O. McLinden, "Thermophysical
Properties of Fluid Systems" in NIST Chemistry WebBook, NIST Standard Reference
Database Number 69, Eds. P.J. Linstrom and W.G. Mallard, National Institute of Standards
and Technology, Gaithersburg MD, 20899, https://webbook.nist.gov/chemistry/, (retrieved
September 19, 2022).



4. Results and discussion
4.1 Textural properties of adsorbent
Textural properties of materials are investigated by the N2 adsorption/desorption isotherms
at 77 K as shown Figs. 4.1.1 (a) for carbon materials, (b) for MOFs, (c) for silica gel. The types of
N2 isotherms are classified by International Union of Pure and Applied Chemistry (IUPAC)
categorization (see the Fig. 3.1.7), and summarized in Table. 4.1.1. The N2 adsorption isotherms of
MOF-177, HKUST-1, ZIF-8 are classified as Type I(a) given by the typical microporous adsorbents.
Type I(b) isotherms are observed on MSC-30 and Fi-Mil-100, given by the microporous adsorbents
with wider micropores or narrow mesopores. The isotherms of GNPs and Aerogel can be classified
as Type II given by the typical nonporous or microporous adsorbents. The isotherm of MIL-53
includes Type I and II isotherm. The isotherms of Wakogel can be classified as Type IV, illustrating
hierarchical structure including mesopore and micropore in the adsorbent, and the hysteresis loop isdue to the effect of the capillary condensation as explained the experimental section. The gravimetricsurface area is evaluated by BET method, and all results are in good agreement with the reported
values.1–10 MOF-177 shows the highest surface area of 3950 m2/g. The volumetric surface area isevaluated to multiply the gravimetric surface area by the skeletal density, and then MSC-30 shows
the highest value of 7975 m2/cm3. The total pore volume and the average of pore size are also
evaluated and summarized in Table. 4.1.1. In addition, the referred pore size analyzed by thenonlocalized density functional theory (NLDFT) method, which provides more detailed pore size,
are added in Table. 4.1.1 for microporous materials.

a 1200

b 1200N2 (77 K)

1000

Adsorbed N2 amoutnt (cm3/g-STP)

Adsorbed N2 amoutnt (cm3/g-STP)

N2 (77 K)

800

600

400

200

0

MSC-30 ads/des
GNPs ads/des
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1000

600

400

200

0

1

Relative pressure (P/P0)

MOF-177 ads/des
Fe-Mil-100 ads/des
HKUST-1 ads/des
ZIF-8 ads/des
MIL-53 ads

800

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Relative pressure (P/P0)

c 3000Adsorbed N2 amoutnt (cm3/g-STP)

N2 (77 K)
2500

2000
Aerogel ads/desWakogel ads/des
1500

1000

500

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Relative pressure (P/P0)

Figs. 4.1.1 N2 isotherms at 77 K (a) carbon materials of MSC-30 and GNPs, (b) MOFs of MOF-177,
Fe-Mil-100, HKUST-1, MIL-53 and ZIF-8 (c) silica gel of Aerogel and Wakogel.

Table. 4.1.1 Summary of textural properties of the materials.
Adsorption Gravimetric Volumetric Total poretype
surface area surface area volume
m2/g
m2/cm3
cm3/g
MSC-30 Type I
3190
7975
1.6
Crbon
GNPs
Type II
810
1782
1.3
MOF-177 Type I
3950
6320
1.6
HKUST-1 Type I
1812
3443
0.8
MOF
Fe-Mil-100 Type I
1867
3734
0.9
MIL-53
Type I, II 967
1837
0.5
ZIF-8
Type I
2061
3298
0.7
Wakogel Type IV
388
815
0.6
Silica gel
AerogelType II
1279
1919
5.6
Adsorbent

Average of Pore size*
pore size [ref]
nm
nm
2.2
6.3
1.7
1.7
1.9
2.3
1.3
3.6
26.0

Skeletaldensityg/cm3
1.1~3.0[11, 12] 2.5
2.2
[13]
1.6
1.7~2.0
1.9
1.0~1.2[13][14]2.0
1.2~2.1[13, 15]
1.9
6~1.0
[13]
1.6
1.2~1.7
2.1
1.5*The pore size is based on the nonlocalized density functional theory (NLDFT)11–15



4.2 Material dependence of the super-dense hydrogen adsorption
4.2.1

Hydrogen adsorption isotherms at 20.4 K
Figs. 4.2.1 show the H2 adsorption isotherms at the boiling pint of H2 (20.4 K), which

represents the gravimetric H2 uptake (wt.%) as a function of the relative pressure p/p0, where p0 is
the liquefied pressure (0.1 MPa) at the boiling point. The shapes of all H2 isotherms are similar to theN2 adsorption isotherms of Figs. 4.1.1, and can be classified as the same type of N2 isotherms
according to the IUPAC classification. This indicates that there are no significant differences in thephysical adsorption phenomena between N2 and H2. The gravimetric H2 uptakes at 0.1MPa for allmaterials are summarized in Table. 4.2.1. For all adsorbents, the H2 uptakes at 20.4 K are higher thanthat at 77 K even under the condition of high pressure above 1 MPa. MOF-177 shows the highest
gravimetric H2 uptake of 13.0 wt.%, which is much higher than 1.36 wt.% obtained at 0.1 MPa, and7.5 wt.% obtained at 7 MPa examined at 77 K by Dipendu et al..3 Fig. 4.2.2 shows the liner
relationship between the H2 uptake and the specific surface area of adsorbents, indicating that
adsorbents with higher surface area give the higher H2 uptake, which is in good agreement with thetrend in the previous research.16–18 According to the Chahine’s rule,19,20 the gravimetric H2 uptakes
approximately correspond to 1 wt.% per 500 m2/g of the specific surface area under the condition at
77 K. In the result of Fig. 4.2.2 under the condition at 20.4 K, the H2 uptakes approximately
correspond to 1wt.% per 300 m2/g and 100 m2/g on Type I and Type II-IV materials, respectively.
The relatively high H2 uptake per specific surface on Type II-IV adsorbents is due to the multilayer
H2 adsorption.




a

b 14

14

H2 (20.4 K)

H2 (20.4 K)
12Adsorbed H2 amoutnt (wt.%)

Adsorbed H2 amoutnt (wt.%)

12
10
8
6
4

MSC-30
GNPs

2
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

MOF-177
Fe-Mil-100
HKUST-1
MIL-53
ZIF-8

10
8
6
4
2

0.9

0

1

Relative pressure (P/P0)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Relative pressure (P/P0)c
14

H2 (20.4 K)

Adsorbed H2 amoutnt (wt.%)

12
10

AerogelWakogel

8
6
4
2
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Relative pressure (P/P0)

Figs. 4.2.1 H2 adsorption isotherms on (a) carbon materials of MSC-30 and GNPs, (b) MOFs of
MOF-177, Fe-Mil-100, HKUST-1, MIL-53 and ZIF-8 (c) silica gel of Aerogel, Wakogel at 20.4 K.

Table. 4.2.1 Gravimetric H2 uptake and density of adsorbed H2 on all adsorbents.21,22

Gravimetric H2 uptake
Adsorbent

Adsorption
type

MSC-30 Type I
GNPs
Type IIMOF-177 Type I
HKUST-1 Type I
MOF
Fe-Mil-100 Type I
MIL-53
Type I, II
ZIF-8
Type I
Wakogel Type IV
Silica gel
AerogelType II
CarbonGravimetricsurface area
m2/g
3190
810
3950
1812
1867
967
2061
388
1279




@ 20.4 K@ 77 K[ref]wt.% (0.1 MPa)

wt.% (Pressure)

12.2
6.6
12.9
7.1
5.3
3.5
4.4
5.5
10.0

5.0 (30 bar)[21]
7.5 (70 bar)[22]
3.6 (50 bar)[22]
3.3 (25 bar)[22]
3.8 (16 bar)[22]
1.5 (40 bar)[22]-Adsorbed H2 amoutnt @ 20.4 K, 0.1 MPa (wt.%)18

H2 (20.4 K, @0.1 MPa)

16

Type II, IV

14

Type I

1210
MOF-177
MSC-30HKUST-1
Fe-Mil-100
MIL-53
ZIF-8

8
6
4

GNPs
WakogelAerogel200500 1000 1500 2000 2500 3000 3500 4000

SSA (m2/g)

Fig. 4.2.2 The liner relationship between the adsorbed H2 uptake (wt.%) and the surface area (m2/g)
at 20.4 K and 0.1 MPa for all materials. The solid symbols and open symbols correspond to theresults on Type I and Type II, IV, respectively.



4.2.2

Density of adsorbed hydrogen at the boiling point
Figs. 4.2.3 show the isothermal curves, representing the introduced H2 (i-H2) amount into

the empty sample cell for blank measurements and the cell with each adsorbent of (a) carbon
materials, (b) MOFs, and (c) other materials. The densities of adsorbed H2 for all adsorbents areinvestigated by the method described in the experimental section 3.3.5. In Figs, 4.2.3, the blank
result shows the characteristics of the pure H2, which shows subtle increase in i-H2 amount as thegaseous H2 below 0.1 MPa, and then i-H2 amount simply increases at 0.1 MPa as the phasetransformation from gas to liquid. At the end point of liquefaction, which is defined as the point in
Fig. 3.3.6, the volume occupied by liquid H2 in the blank measurement is evaluated to be 9.3 cm3(see also experimental section 3.3.5), where the volume of liquid H2 illustrated in blue color isdefined as homogeneous temperature region as shown in Fig. 4.2.3 (d). Above 0.1 MPa, i-H2 amountgradually increase with increasing the pressure because the region of the gaseous H2 illustrated inorange color in Fig. 4.2.3 (d) has slight temperature gradient. This phenomenon can be understoodby the expansion of liquefied H2 region, which is caused by satisfying the liquefaction conditions
above H2 boiling point (at 20.4 K and 0.1 MPa).
In the case of the isotherms with adsorbents, i-H2 amount clearly increase by H2 adsorption
on adsorbents below 0.1 MPa as a main contribution. At 0.1 MPa, liquefaction of H2 starts, then thefree volume, which is the cell volume excluding the volume of adsorbents and adsorbed H2, is filledwith liquefied H2. Fig. 4.2.3 (d) illustrates the image of occupation in the cell filled with liquid H2,
gaseous H2, adsorbents and adsorbed H2 at 0.1 MPa. Here, I’d like to focus on the result of MSC-30.
Comparing the i-H2 amount at the end point of liquefaction (inset of Fig. 4.2.3), the value of MSC30 is almost equivalent to that of the blank result even though the H2 molecules cannot occupy thevolume with carbon atoms of MSC-30. In other words, the free volume (defined in Fig. 3.2.1) in theempty cell, in which the H2 molecule can exist, should be larger than that with MSC-30 (see also Fig.


4.2.3 (d)). According to this result, it can be expected that the density of adsorbed H2 on MSC-30 ismuch higher than that of liquid H2. In this case, this anomalously high density of adsorbed H2 at 20.4
K is suggested as the “super-dense H2 adsorption”.
In order to quantitatively discuss the superdense state of H2, the densities of adsorbed H2(.

) on each adsorbent at 20.4 K and 0.1 MPa, and the results are summarized in Table 4.2.2.

Interestingly,.

on almost all of the adsorbents (excluding MIL-53) show higher density thanthe density of liquid H2 (particular,.

.

:35.2 mmol/cm3) at 20.4 K as the super-dense adsorption. In

on adsorbents with Type I adsorption isotherms (MSC-30, MOF-177, HKUST-1,

Fe-Mil-100 and ZIF-8) shows relatively high value in the range of 43.0~47.4 mmol/cm3, comparedwith that on adsorbents with Type II or IV adsorption isotherms (GNPs, Wakogel, Aerogel) whichshow.

around 40 mmol/cm3. Especially, the values ofhigher density than the solid H2 density (.

.

for Type I adsorbents show

: 43 mmol/cm3), which is known as a hexagonalclose-packed (hcp) structures below 14 K.23–25 These results suggest that the influence of superdense effect depends on the adsorption type of adsorbents rather than the surface element ofadsorbents. The adsorption types are determined by the pore structure (micropore, mesopore andmacropore), and the significant difference between Type I and Type II-IV adsorption is the amountof the monolayer and multilayer adsorption, where Type I adsorption is mostly occupied by themonolayer adsorption. Therefore, it can be expected that the monolayer H2 forms the super-dense H2state due to a direct interaction between H2 molecules and the surface of adsorbents. This monolayer
H2 properties are discussed later in the section 4.4.
Next, it is discussed the reason why only MIL-53 shows the much lower
mmol/cm3 compared with.

(35.2 mmol/cm3) and.

.

of 27.3

on all adsorbents. MIL-53 has thesmallest micropore size (6~10 Å) analyzed by nonlocalized density functional theory (NLDFT)
method as shown in Table 4.2.1, which is relatively close to the intermolecular distance of H2-H2 inbulk-solid (3.76 ̅).26 The values of.

were evaluated by using the skeletal densities ofadsorbents, which were experimentally measured by He gas. Since the size of He atom is smaller
than that of H2 molecule, He can fill the smaller pores compared with that of H2. In other words,
pores, that H2 molecule cannot fill, are regarded as closed pores, and the skeletal density for H2 mustbe smaller than that for He. Therefore, it is possible that.

on MIL-53 is evaluated to be lower

than actual value. If the pore size, that is bigger than He molecule and smaller than H2 molecule,exists, the skeletal density measured by He and H2 must be different.




b

a
0.35 H2 (20.4 K)

0.35 H2 (20.4 K)
0.3

Blank
MSC-30GNPs

0.25

Introduced H2 amount (mol)Introduced H2 amount (mol)

0.3

0.36

0.2
0.34

0.15

0.32

0.1

0.3

0.28

0.05

0

0.1

0.2

0.2

Blank
HKUST-1
Fe-Mil-100
MIL-53
ZIF-8
MOF-177

0.15
0.1
0.05

0.1

0

0.25

0.15

0.3

0.2

0.4

0

0.5

Pressure (MPa)

0

0.1

0.2

0.3

0.4

0.5

Pressure (MPa)c0.35 H2 (20.4 K)

Introduced H2 amount (mol)

0.3
0.25
0.2

Blank
AerogelWakogel

0.15
0.1
0.05
0

0

0.1

0.2

0.3

0.4

0.5

Pressure (MPa)Figs. 4.2.3 Isothermal properties of H2 introduction into the cell (12.3 cm3) with and without
adsorbents for (a) carbon materials of MSC-30 and GNPs, (b) MOFs of MOF-177, Fe-Mil-100,
HKUST-1, MIL-53 and ZIF-8 (c) silica gel of Aerogel, Wakogel and at 20.4 K. (d) Image of insideof cryogenic cell with and without adsorbent at 0.1 MPa.

Table. 4.2.2 Density of adsorbed H2 together with textural properties of adsorption type, gravimetricsurface area, pore size.

Adsorbent

MSC-30
GNPs
MOF-177
HKUST-1
MOF
Fe-Mil-100
MIL-53
ZIF-8
WakogelSilica gel
AerogelCrbon

Adsorption Gravimetrictypesurface area
Type I
Type II
Type I
Type I
Type I
Type I, II
Type I
Type IV
Type II

m2/g
3190
810
3950
1812
1867
967
2061
388
1279

Å
11~30[11, 12]
17~20[13]10~12[13]12~21[14]6~10[13, 15]
12~17[13]-Pore size[ref]Density ofadsorbed H2
mmol/cm3
43.6
40.0
47.3
44.8
47.4
27.4
43.0
39.0
38.4

4.3 Temperature dependence of the super-dense hydrogen adsorption
4.3.1

Hydrogen adsorption isotherms
Figs. 4.3.1 show the H2 adsorption isotherms which represent the gravimetric H2 uptake asa function of H2 pressure at 20.4. 23.3, 26.5, 30.6 K on MSC-30, GNPs and MOF-177. The
maximum H2 uptakes on all adsorbents decreases with increasing pressure. This is a general trend of
the typical physical adsorption. The heat of adsorption on MSC-30, GNPs and MOF-177 isestimated by applying the Clausius-Clapeyron equation to the H2 adsorption isotherms in Figs. 4.3.1
at different temperature, and the results are shown in Fig. 4.3.2. The three adsorbents show the heatof adsorption between 1-3 kJ/mol in descending order of MOF-177, MSC-30 and GNPs. The heat ofadsorption in the region of low H2 uptake cannot be estimated because of the low pressure below thelimit of pressure gauge. This low pressure region represents the monolayer adsorption, so it isinadequate for discussing the superdense H2 adsorption.




a 14

b 7
MSC-30

13

GNPs
6

11

Gravimetric H2 uptake (wt.%)

Gravimetric H2 uptake (wt.%)

12
10
9
8
7
6

MSC-30 (20.4 K)
MSC-30 (23.3 K)
MSC-30 (26.5 K)
MSC-30 (30.6 K)

5
4
3
2

5
4
3
2

GNPs (20.4 K)
GNPs (23.3 K)
GNPs (26.5 K)
GNPs (30.6 K)

1

1
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

1

Pressure (MPa)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pressure (MPa)c 14
MOF-177
Gravimetric H2 uptake (wt.%)

12
10
8

MOF-177 (20.4 K)
MOF-177 (23.3 K)
MOF-177 (26.5 K)
MOF-177 (30.6 K)

6
4
2
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pressure (MPa)Fig. 4.3.1 Temperature change of H2 adsorption isotherms at 20.4, 23.3, 26.5 and 30.6 K on (a)MSC-30, (b) GNPs, (c) MOF-177, respectively.




3

Heat of adsorption (kJ/mol)

2.5

2

1.5

1
MOF-177
MSC-30
GNPs

0.5

0

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15

Amont of adsorbed H2 (wt.%)

Fig. 4.3.2 Heat of adsorption on MSC-30, MOF-177 and GNPs.



4.3.2

Density of adsorbed hydrogenFigs. 4.3.3 show the isothermal properties of the H2 introduction into the cell with MSC-30,

GNPs, and MOF-177 at 20.4, 23.3, 26.5 and 30.6 K in the same way as the experimentcorresponding to Figs. 4.2.3. The isotherms of the blank cell show each liquefaction step, where H2liquefy at 0.10 MPa (20.4 K), 0.22 MPa (23.3 K), 0.43 MPa (26.5 K), and 0.88 MPa (30.6 K). The iH2 amount in the blank cell above each phase transition pressure tends to decrease with increasing
temperature due to the physical properties of liquid H2 density, which are 35.2 mmol/cm3 (20.4 K,
0.10 MPa), 33.3 mmol/cm3 (23.3 K, 0.22 MPa), 30.9 mmol/cm3 (26.5 K, 0.42 MPa), and 26.2
mmol/cm3 (30.6 K, 0.87 MPa). All isotherms for the cell with adsorbents show similar adsorption
and liquefaction steps at each temperature. Comparing the i-H2 amount of blank results with i-H2 ofadsorbents above each phase transition pressure, it is noteworthy that the i-H2 amount with MOF177 and MSC-30 gradually exceeds the value of blank with increasing temperature. Thesephenomena suggest that the temperature dependence of.

is different from. In other.

words, the density of superdense H2 is less affected by temperature than the density of liquid H2.
The values ofat each temperature and on each adsorbent are evaluated in the same.

way as discussed in the section 4.2.2. The evaluatedFig. 4.3.4 together with.

.

is plotted as a function of temperature inat each phase transition point. It can be seen that

adsorbents shows the higher density thanhighest.

.

.

on anyat any temperatures, and MOF-177 shows the, followed in the order MSC-30 and GNPs. Temperature change ofadsorbents doesn’t significantly decrease with increasing temperature compared withparticular, the values of

.

.

.

on
. In

on MOF-177 and MSC-30 with the large amount of monolayer H2 as

the Type I adsorption show the temperature independent properties. According to these results, it canbe seen that the monolayer H2 strongly interacted with material surface leads to the temperature
independence of super-dense H2 state.



a

0.4

b 0.4

MSC-30

0.3
0.25
0.2
Blank (20.4 K)
Blank (23.3 K)
Blank (26.5 K)
Blank (30.6 K)

0.15
0.1

MSC-30 (20.4 K)
MSC-30 (23.3 K)
MSC-30 (26.5 K)
MSC-30 (30.6 K)

0.05
0

GNPs

0.35

Introduced H2 amount (mol)Introduced H2 amount (mol)

0.35

0

0.2

0.4

0.6

0.8

1

1.2

0.25
0.2
Blank (20.4 K)
Blank (23.3 K)
Blank (26.5 K)
Blank (30.6 K)

0.15
0.1

GNPs (20.4 K)
GNPs (23.3 K)
GNPs (26.5 K)
GNPs (30.6 K)

0.05
0

1.4

Pressure (MPa)

c 0.4

0.3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Pressure (MPa)

MOF-177

Introduced H2 amount (mol)

0.35
0.3
0.25
0.2
Blank (20.4 K)
Blank (23.3 K)
Blank (26.5 K)
Blank (30.6 K)

0.15
0.1

MOF177 (20.4 K)
MOF177 (23.3 K)
MOF177 (26.5 K)
MOF177 (30.6 K)

0.05
0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Pressure (MPa)Figs. 4.3.3 Temperature dependence of isothermal properties for H2 introduction into the empty cell(blank) and into the cell with (a) MSC-30, (b) GNPs and (c) MOF-177 at 20.4, 23.3, 26.5, 30.6 K,
respectively.

Density of adsorbed H2 (mmol/cm3)

50

45

40

35

30
Liquid H2
MOF-177
MSC-30
GNPs

25

20

20

22

24

26

28

30

32

Temperature (K)Fig. 4.3.4 Temperature dependence of the density of adsorbed H2 compared to that of liquid H2. The
density of adsorbed H2;.

at 20.4, 23.3, 26.5, 30.6 K on MOF-177. MSC-30 and GNPs.



4.3.3Isobars of volumetric hydrogen capacity
Fig. 4.3.5 shows the isobaric curve at 0.9 MPa as a function of temperature in the range of

10-80 K, which represents the i-H2 amount (left Y axis) corresponding to the volumetric H2 capacity
in the cell (right Y axis). The volumetric H2 capacity of the cell (=wherecomparing,) can be evaluated by(4.3.1)[mmol] is the i-H2 amount;[cm ] is the volume of cryogenic cell (12.3 cm3). By

in the blank cell andin the cell with MSC-30 and MOF-177, the isobaric

properties of the volumetric H2 capacity in the liquid H2 tank with and without adsorbents are
discussed. The sample cells are filled with 2.30 g of MSC-30 and 2.27 g of MOF-177, whichcorrespond to 9.0 cm3 of bulk-volume for both materials. The isobaric curve of blank shows thecharacteristics of the pure H2. In the temperature range of 30-80 K with the gaseous phase of H2, theresults of MSC-30 and MOF-177 show much higher volumetric H2 capacity compared with that ofblank, which is naturally due to the contribution of H2 adsorption on adsorbents. At 30 K and 0.9
MPa, H2 starts to liquefy and the i-H2 amount (volumetric H2 capacity) increase up to 23.1, 22.3,
20.5 mmol/cm3 for the cell of MSC-30, MOF-177 and blank, respectively. It is notable that the cellswith both adsorbents have higher volumetric H2 capacity than that of blank even in the liquid phaseof H2, especially, the capacity of MSC-30 is 13% higher than that of blank at 30 K and 0.9 MPa.
With decreasing temperature from 30 K, the volumetric H2 capacity increase due to the increase in
the density of liquid H2. The capacity of MSC-30 and MOF-177 gradually increase with decreasing
temperature compared with that of blank. This is because of the temperature independence ofadsorbed H2 density as the super-dense state, which is in good agreement with the temperaturechange of the isotherms and.

in Figs. 4.3.3 and Fig. 4.3.4, respectively. The volumetric H2

capacity in the blank cell is equivalent to that of MOF-177 at 27.5 K and MSC-30 at 23.0 K. Here,behaviors of these isobar are considered in the viewpoint of H2 losses by temperature increase (Boiloff). Fig. 4.3.6 shows the H2 losses with increasing temperature from 23 K to 30 K for the results ofblank and MSC-30 based on the values in Fig. 4.3.5. It is clearly found that the amount of H2 losses
in the blank cell is larger than that of MSC-30 at higher temperature, which is due to the contributionof the temperature independent properties of super-dense H2. At 30 K, the H2 losses in the blank celland with MSC-30 are 6.3 and 4.3 mmol/cm3, respectively, which correspond to 32% of the
suppression of H2 losses by temperature increase from 23 to 30 K at 0.9 MPa by using MSC-30
adsorbent. Thus, this result suggests that H2 storage of cryo-adsorption using porous materials
provides not only the volumetric H2 capacity equivalent to that of liquid H2 but also the availabilityof the suppression of H2 boil-off in the liquid H2 storage tanks.




0.5

H2 @ 0.9MPa

40

0.4

0.3

0.2

35
30

25

25

Blank
MSC-30
MOF-177

20

20

15
20

25

30

35

15
10

0.1

5
0

Volumetric H2 capacity (mmol/cm3)

Volumetric H2 density (mmol/cm3)

Amount of introduced H2 (mol)

30

0
10

20

30

40

50

60

Temperature (K)7080Fig. 4.3.5 Isobar of the introduced H2 amount (left axis) corresponding to the volumetric H2 density(right axis) in the blank cell and the cell with MSC-30 and MOF-177 at 0.9 MPa as a function oftemperature in the range of 10-80 K.



H2 loss basis at 23 K (mmol/cm3)

7
6

Blank
MSC-30

5
4
3
2
1
0
23

25

27

29

31

Temperature (K)Fig. 4.3.6 H2 losses with increasing temperature from 23 K at 0.9 MPa in the cell with and without
MSC-30.

4.4 Adsorbed layer dependence
adsorption

of

the

super-densehydrogen

Here, microscopic structures of adsorbed H2 molecules are pictured by taking account ofadsorption Types I and II to discuss the superdense H2 state and the temperature dependence. Type I
adsorption isotherms for MSC-30 and MOF-177 are given by micropores filling of H2 at low
pressure due to the strong interaction with the material surface in narrow micropores. It can beconsidered that the adsorption with strong interaction makes the adsorption state to be thesuperdense H2 state. In the case of Type II adsorption isotherms for GNPs, it is understood that theend point of steep H2 uptake at low pressure corresponds to the completion of monolayer coverage
and after that, H2 uptake gradually increases by multilayer adsorption. In the BET theory, it isassumed that the multilayer adsorption region is equivalent to liquid phase and the monolayer
adsorption region just on the surface is more stable than the liquid phase.27 H.K. Livingston28 and
Xicohténcatl et al.26 reported the anomalously low cross-sectional areas of H2 at 20 K on the Ni foil
and a mesoporous silica compared with bulk-liquid and bulk-solid H2 density, indicating the superdense H2 state just on the material surface similar to our result.
In this work, the region of monolayer adsorption was focused on and the density ofmonolayer H2 (.

) just on the material surface was evaluated based on the BET theory. It is

possible to determine the monolayer H2 uptake (.% ) by applying BET equation to the adsorption

isotherms in Figs. 4.3.1, and the ratio of monolayer H2 uptake to the total uptake (
=
where

.% is

) is given by.%(4.4.1).%the maximum H2 uptake obtained from Figs. 4.3.1. The values ofareevaluated to be 74%, 42% and 90% for MSC-30, GNPs and MOF-177, respectively, at 20.4 K.
at other temperature on each adsorbent show similar values and they are summarized in Table.
4.4.1. Thus, the density of monolayer H2 (.

) is given bywhere

.

=

.

.

=

.

.

.

.

=

−

.

.

−

.

(mol) is the amount of monolayer H2,(4.4.2),.
.

(cm3) is the volume of monolayer H2.

.

(cm3) is the volume of total adsorbed H2,.

(cm3) is the volume of multilayer H2,.

(mol) is the total amount of adsorbed H2;is the ratio of multilayer H2 given by(4.4.3)=1−
Here, the density of multilayer H2 () can be considered as liquid phase (.

) at each phase.

transition point, which is following the assumption of the BET theory. Finally,.

can beevaluated by
.

=

.
.

−

.

The evaluated.

(4.4.4).
.

on MSC-30, GNPs and MOF-177 are plotted in Fig. 4.4.1 as a function oftemperature below critical point of H2. As a result,on all adsorbents show the constant value.

of 50 mmol/cm3 without temperature dependence below the critical point of H2. Therefore, it can beconcluded that the super-dense H2 state is strongly related to the monolayer adsorption with directinteraction from material surface, irrespective of the adsorption types and temperature below criticalpoint.
Focusing on the introduced H2 (i-H2) amount into the sample cell at 20.4 K above 0.1 MPashown in Fig. 4.2.3, MSC-30 shows the highest i-H2 amount, even though MOF-177 has the higher
gravimetric H2 uptake and larger amount of adsorbed H2. In order to clarify this mystery, weevaluated the volumetric H2 uptake (as discussed above,

/

/

.

=
.

is regarded as+.

at each condition(4.4.5),(cm3) is the skeletal volume of adsorbents given by




.

is defined by
/

where

). Since⁄,(g) is the weight of(g/cm3) is the skeletal density of materials. According to the above discussion,materials;/

can be evaluated by

/

.

=

(4.4.6).

+.

Accordingly,/

for each adsorbent and temperature are evaluated and plotted in Fig. 4.4.2 asa function of temperature below the critical point of H2.

/

shows constant values of 34

mmol/cm3, 17 mmol/cm3, and 33 mmol/cm3 for MSC-30, GNPs, and MOF-177, respectively,
without temperature dependence (see also the Table 4.4.1). MSC-30 shows the highest value of/, and it is comparable toat 22 K and 30% higher than.

.

at 30.6 K, that areconsistent with the result of isobar of Fig. 4.3.5 representing the volumetric H2 capacity in the cell
discussed in section of 4.3.3.
When the density of monolayer H2 shows the constant without temperature and material
dependences, the cross-sectional area ( ; m ⁄molecule), which is a value of occupied area by one
molecule of adsorbate, of H2 must be a constant. By using the parameters of the cross-sectional area
; m ⁄g), and mass of adsorbate (m; g), equations 4.4.5 and 4.4.6( ), gravimetric surface area (are changed as

.

∙
N

=

(4.4.7)∙

where N

N

=

.

ρ

is the Avogadro number (6.022 × 10

introduced into equation 4.4.5,

∙

mol

=

1

ρ

.

+

1
N σ

,

(4.4.9)∙) corresponds to the volumetric surface area (m2/cm3) of adsorbents.
). When equations 4.4.7 and 4.4.8 are

is given by/Here, the value of ((4.4.8),.

Since the values of ρ.

and σ are constant regardless of temperature and adsorbents based on theabove discussion, equation 4.4.9 suggests that the volumetric surface area (factor to determine the volumetric H2 uptake ofresult, the highest value of//) is a uniqueunder the super-dense H2 phenomena. As acorresponding to the i-H2 amount in Fig. 4.2.3 are shown on

MSC-30 with the highest volumetric surface area (




∙

∙

= 7975 m /cm ).

Density of monolayer H2 (mmol/cm3)50

Liquid H2
MOF-177
MSC-30
GNPs

40

30

20

22

24

26

28

30

32

Temperature (K)Fig. 4.4.1 Temperature dependence of the density monolayer H2 (.

)c on MSC-30, GNPs andMOF-177 at 20.4, 23.3, 26.5, 30.6 K, compared to the density of liquid H2.

Volumetric H2 uptake (mmol/cm3)40

nmmol/cm3

3530
Liquid H2
MSC-30
GNPs
MOF-177

25

20

15

10

20

22

24

26

28

30

32

Temperature (K)Fig. 4.4.2 The temperature dependence of the volumetric H2 uptake (range of 20.4-30.6 K on MOF-177. MSC-30 and GNPs, respectively




/

in the temperatureTable. 4.4.1 Summary of the gravimetric H2 uptake (wt.%), density of adsorbed H2 (mmol/cm3), density of adsorbed H2 in monolayer ((/.

, mmol/cm3), and volumetric H2 uptake.

, mmol/cm3) for MOF-177, MSC-30, and GNPs at each temperature and pressure.

Condition
T [K] P (MPa)Liquid H2

Adsorbent
MSC-30

MOF-177

Gravimetric H2 uptake[wt.%]

0.10
0.22
0.43
0.88

-

12.9 (90%)
12.6 (87%)1
12.4 (88%)1
11.9 (86%)1

12.2 (74%)
11.9 (60%)1
11.5 (71%)1
10.8 (76%)1

6.6 (42%)1
6.1 (42%)1
5.9 (41%)1
5.3 (41%)1

Density of adsorbed H2

20.4
23.3
[mmol/cm3]
26.5
30.6

0.10
0.22
0.43
0.88

35.2
33.3
30.9
26.2

47.3 (134%)2
47.1 (141%)2
45.8 (148%)2
45.1 (172%)2

43.6 (124%)2
42.4 (127%)2
42.2 (137%)2
41.5 (159%)2

40.0 (114%)2
38.0 (114%)2
36.4 (118%)2
32.9 (125%)2

Density of monolayer H2

20.4
23.3
[mmol/cm3]
26.5
30.6

-

35.2
33.3
30.9
26.2

49.3 (140%)2
50.0 (150%)2
49.0 (159%)2
50.6 (193%)2

46.7 (133%)2
52.1 (156%)2
49.8 (161%)2
51.2 (195%)2

49.3 (140%)2
47.3 (142%)2
48.8 (158%)2
51.8 (198%)2

Volumetric H2 uptake

20.4
23.3
[mmol/cm3]
26.5
30.6

-

35.2
33.3
30.9
26.2

33.5 (95%)2
33.4 (100%)2
32.7 (106%)2
32.6 (124%)2

34.1 (97%)2
34.1 (102%)2
34.5 (112%)2
34.2 (130%)2

18.5 (52%)2
17.7 (53%)2
17.1 (56%)2
16.3 (62%)2

.

.

/

1

1

GNPs

20.4
23.3
26.5
30.6

.%

1 Ratio (%) of monolayer adsorption in the H uptake
22

Ratio (%) compared to density of liquid H2 (3. 2 ) at each phase transition point, 35.2 mmol/cm

3

3(20.4 K, 0.10MPa), which are 33.3 mmol/cm (23.3 K, 0.22 MPa), 30.9 mmol/cm (26.5 K, 0.43 MPa), 26.2 mmol/cm3 (30.6 K,
0.88 MPa)




,

4.5  Gas dependence of the super-dense hydrogen adsorption
4.5.1

Density of adsorbate for deuterium, neon and nitrogen
In order to compare the superdense H2 for different gases, the adsorption properties for

deuterium (D2), neon (Ne) and nitrogen (N2) were investigated at each boiling point (23.6 K for D2,
27.1 K for Ne and 77.2 K for N2) in the same way as section 4.2.2. Fig. 4.5.1 shows the isothermal
properties of the gas introduction into the cell with and without 1.5 g of MSC-30, where theintroduced gas (i-gas) amount is plotted as a function of the pressure. For all gases, the isotherms
show the similar adsorption and liquefaction steps to H2 isotherm. When the i-gas amount in blankcell and the cell with MSC-30 are compared at 0.1 MPa for each gas, the i-gas amount for D2, Ne, N2(except for H2) in the blank cell are clearly higher than that of MSC-30. These behaviors for D2, Ne,
N2 consistent to the general understanding of adsorption state of “liquid state ≈ adsorbed state”
because the free volume in cell with adsorbents is smaller than that of blank cell. As discussed in thesection 4.2.2, the comparable i-H2 amount in the blank cell and with MSC-30 is due to the effect of
the super-dense H2 adsorption, therefore this result qualitatively suggests that the super-dense effecton D2, Ne and N2 are not clearly shown, in other words, the super-dense adsorption is a unique
phenomenon for H2 or strongly enhanced in H2.
Figs. 4.5.2 show the temperature change of the gas introduction isotherms for D2, Ne andN2. The measurements were carried out at 23.6 K (0.10 MPa), 26.4 K (0.22 MPa), 29.8 K (0.44MPa) and 33.9 (0.88 MPa) for D2, at 27.1 K (0.10 MPa), 29.4 K (0.22 MPa) and 32.5 K (0.44 MPa)
for Ne, at 77.2 K (0.10 MPa), 85.1 K (0.22 MPa) and 92.9 K (0.44 MPa) for N2, where the pressurein brackets is the liquefaction pressure at each temperature. It is observed that the i-D2 amount with
MSC-30 gradually exceeds the amount in the blank cell with increasing temperature, which is thesimilar trend to that of H2 as shown in Fig. 4.2.3 (a). This trend suggests that the density of adsorbed
D2 is also less affected by increasing temperature compared with that of liquid D2. On the other hand,the i-Ne and N2 amount with MSC-30 are always lower than that of blank cell even at higher
temperature, suggesting the densities of adsorbed Ne and N2 are relatively affected by temperature
increase unlike the trend of H2 and D2.
In the same way as section 4.2.2, the densities of adsorbates for D2, Ne, and N2 arequantitively evaluated and the results are summarized in Figs. 4.5.3 and Table. 4.5.1. The density ofadsorbed D2 shows the value in the range of 40.4~31.4 mmol/cm3 in the temperature range from
23.6 to 33.9 K, which is slightly higher than that of H2. At any temperature, the densities of adsorbed
D2 show higher density than that of liquid D2, and they are less affected by temperature increasesimilar to the temperature independent properties of the super-sense H2. The density ratios ofadsorbed phase to liquid phase (seen that././. ) for each gas are summarized in Table. 4.3.1. It can be. ratios for H2 and D2 increase with temperature in the range of 1.24~1.61 and1.19~1.35, respectively. Comparing the ratio of H2 (.

/.

ratio is always higher than

.

/

.

.

/

.

) with that of D2 (

.

/

.

),

ratio at any temperature. It suggests thatthe adsorbed H2 is more strongly affected by the effect of super-dense adsorption compared with D2
adsorption. On the other hand, the temperature changes of the adsorbed Ne and N2 density are totallycomparable to that of liquid Ne and N2, and both./.

ratios are around 1.0 at any temperature,

which are in the good agreement with the general understanding of adsorption state of “liquid state ≈adsorbed state”. In addition, the experimentally observed super-dense adsorption of H2 and D2 areconfirmed as the special adsorption compared with the adsorption of Ne and N2.
The monolayer densities of H2 and D2 are evaluated in the same way as section 4.4.
Fig.4.5.4 shows the densities of monolayer D2 in the temperature range of 23.6-33.9 K. The densityof monolayer D2 also shows a constant value of around 50 mmol/cm3 without temperaturedependence below the critical temperature of D2. It is remarkable that the densities of adsorbed D2
and H2 are comparable in the super-dense state of monolayer, even though the density of liquid D2 is1.15 times higher than that of H2 at each boiling point. The H2 molecule with light mass is strongly
affected by quantum effects at low temperature, yielding the lower density of bulk-liquid H2 due tothe high zero-point energy compared with that of D2 (see the introduction section 1.2). However, thedifference of adsorbed density between the monolayer H2 and D2 is not observed below each criticalpoint. The quantum effects in bulk-liquid H2 and D2 seem to be cancelled by interactions ofadsorption with the material surface.




0.65

Amount of introduced gases (mol)

0.6
0.55
0.5
0.45
0.4
0.35
0.3

Ne_Blank_27.1K
Ne_MSC-30_27.1 K
D2_Blank_23.6 K
D2_MSC-30_23.6 K
H2_Blank_20.4 K
H2_MSC-30_20.4 K
N2_Blank_77.2 K
N2_MSC-30_77.2 K

0.25
0.2
0.15
0.1
0.05
0

0

0.1

0.2

0.3

0.4

0.5

0.6

Pressure (MPa)Fig. 4.5.1 Isothermal properties of gas introduction into the empty cell (Blank) and the cell with 1.5
g of MSC-30 for H2, D2, Ne and N2 at each boiling point of 20.4 K, 23.6 K, 27.1 K and 77.2 K,
respectively.




b

0.45

D2

Amount of introduced D2 (mol)

0.4
0.35
0.3
0.25

Blank_23.6 K
Blank_26.4 K
Blank_29.8 K
Blank_33.9 K
MSC-30_23.6 K
MSC-30_26.4 K
MSC-30_29.8 K
MSC-30_33.9 K

0.2
0.15
0.1
0.05
0

Ne

0.6

Amount of introduced Ne (mol)

a

0.5
0.4
0.3

0.1
0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Blank_27.4 K
Blank_29.6 K
Blank_32.8 K
MSC30_27.4 K
MSC30_29.6 K
MSC30_32.8 K

0.2

0

0.1

Pressure (MPa)

0.2

0.3

0.4

0.5

0.6

0.7

Pressure (MPa)c
N2Amount of introduced N2 (mol)

0.3

0.2
Blank_77.2 K
Blank_85.1 K
Blank_92.9 K
MSC30_77.2 K
MSC30_85.1 K
MSC30_92.9 K

0.1

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Pressure (MPa)Fig. 4.5.2 Temperature dependence of isothermal properties of gases introduction for (a) D2, (b) Ne
and (c) N2 into the empty cell (Blank) and the cell with 1.5 g of MSC-30, at 23.6, 26.4, 29.8 and 33.9
K for D2, at 27.4, 29.6, 32.8 K for Ne, 77.2, 85.1, 92.9 K for N2.




a
55

Density of H2 or D2 (mmol/cm3)

50
45
40
35
30

Ads.D2 on MSC-30
Ads.H2 on MSC-30
Liq.D2
Liq.H2

25
20

20

22

24

26

28

30

32

34

Temperature (K)

b

c 40

64

Density of adsorbed N2 (mmol/cm3)

Density of adsorbed Ne (mmol/cm3)

62
60
58
56
54
52
50
48

Liq. Ne
Ads. Ne on MSC-30

46
44

35

30

25

20

Liq. N2
Ads. N2 on MSC-30

15

42
40

10
26

28

30

32

34

76

Temperature (K)

78

80

82

84

86

88

90

92

94

Temperature (K)Fig. 4.5.3 Temperature dependence of the density of adsorbate for (a) H2 and D2, (b) Ne and (c) N2,
compared with the density of liquid phase.

Density of monolayer H2 or D2 (mmol/cm3)

55
50
45
40
35
30

Ads.H2 on MSC-30
Ads.D2 on MSC-30
Liq.D2
Liq.H2

25
20

20

22

24

26

28

30

32

34

Temperature (K)Fig. 4.5.4 Temperature dependence of the density of monolayer H2 and D2 compared with thedensity of liquid phase.

Table. 4.5.1 Density of adsorbate and liquid phase for H2, D2, Ne and N2 and monolayer, andMonolayer density for H2 and D2 at each temperature below critical point.

Condition
Gas Temp.
K
H2

20.4

D2
Ne
N2
H2
D2
Ne
N2
H2
D2
Ne
N2
H2
D2

23.6
27.1
77.2
23.3
26.4
29.4
85.1
26.5
29.8
32.5
92.9
30.6
33.9

Liquefied Liquidpressure density
MPa

0.10

0.22

0.44

0.88

Density ofadsorbate

mmol/cm3 mmol/cm3%

mmol/cm3

%

35.2

43.6

124

47.6

135

40.4
59.5
28.8
33.3
38.3
57.5
27.5
30.9
35.6
54.3
26.0
26.2
31.4

47.9
59.3
29.1
42.9
46.2
58.2
27.4
42.7
44.9
54.4
26.2
42.1
42.2

119
100
101
129
121
101
100
138
126
100
101
161
135

52.4
48
50.9
50.1
50.8
52
49.7

130
144
133
162
143
204
158




Ads./Liq.㽢 Monolayer Ads./Liq.
100
㽢100
density4.5.2

Two-dimensional density
Figs. 4.5.5 show the adsorption isotherms for H2, D2, Ne and N2 on MSC-30, which

represent the molar basis uptake (mmol/g) as a function of the relative pressure, where eachtemperature was determined so that the liquefaction pressure was at 0.10 MPa for (a), at 0.22 MPafor (b), at 0.44 MPa for (c) and at 0.88 MPa for (d). Fig. 4.5.5 (a) shows the adsorption isotherms for
H2, D2, Ne and N2 at each boiling point of 20.4, 23.6, 27.1, and 77.2 K, respectively. The allisotherms can be classified as Type I. The maximum adsorption uptake is in order of Ne, D2, H2 andN2 corresponding to the trend of liquid density as shown in Table 4.5.2. The monolayer uptakes foreach gas were evaluated by applying the BET equation into the isotherms, and the points ofmonolayer completion, defined as B-point in the experimental section 3.1.3., are marked as open
dots in Figs. 4.5.5 (a), and the results are summarized in Table. 4.5.2. It is observed that B-point of
H2 is equivalent or close to the point of D2 and Ne even though D2 and Ne have much higher total
uptake (at p0/p=1) than that of H2. As a result, the ratio of the monolayer uptake to the total

uptake (⁄) for H2 shows the highest ratio of 79 % compared with the ratios of D2 (69%),

Ne (60%) and N2 (67%) at each boiling point. The monolayer ratio for H2 is clearly higher than theratios for other gases even using the same adsorbent of MSC-30, which is obviously due to thesuper-dense adsorption of monolayer H2 and the region of multilayer adsorption correspond to theproperties of liquid phase. In this way, the anomalously high area density (two-dimensional density)of super-dense H2 is revealed. For other temperatures in Figs. 4.5.5 (b), (c), and (d), the similar
trends to the result of Fig. 4.5.5 (a) are observed. The monolayer H2 capacities (B-point) are
relatively close to that of D2 and Ne, even though the total uptake of D2 and Ne are clearly higher
than H2, especially, the monolayer capacity of H2 is higher than that of Ne in Fig. 4.5.5 (c).
In order to discuss the area densities of adsorbates in more details, the cross-sectional areas( ) for all adsorbates were evaluated by equation 4.5.1.



=
(m2/g) is the gravimetric surface area,

where

defined in equation 3.1.34,(4.5.1),∙/(mmol/g) is the monolayer capacity asis the Avogadro number (6.02×1023 mol-1). The evaluated , which iscalled “experimental ” below, for each adsorbate and temperature is shown in Table 4.5.2. Emmett
et al. propose that the cross-sectional area of adsorbates is related to the volume factor of

⁄

.

is

given by=whereis the molar mass of adsorbates,

sectional area∙

(4.5.2),is the density of liquid or solid phase. Thus, the cross-can be theoretically evaluated by
⁄

=
where
evaluatedis the packing factor.

∙(4.5.3),= 1.091 is well used as the hexagonal close-packed factor 28. The

from equation 4.5.3 is called “theoretical ”. The theoreticalis evaluated based on theliquid density and the hexagonal close-packed factor, and the results are summarized in Table 4.5.2.
The experimentalof Ne and N2 are comparable to the theoreticalat each boiling point,

indicating the properties of Ne and N2 adsorbates are close to the liquid phase. On the other hand, theexperimentalof H2 and D2 are 10.3 and 10.1 Å2/molecule, respectively, which are quite lower than

the theoreticalof 14.2 and 13.0 Å2/molecule, respectively, indicating the anomalously high area

density due to the super-dense H2 and D2. In addition, the packing factors ofexperimentally to introduce the experimental

are evaluatedinto the equation 4.5.3 (called “experimental

below), and the results are summarized in Table 4.5.2. The experimental”of H2 and D2 are 0.79 and

0.85, respectively, at each boiling point, which are also unusually low compared with the typical
packing factor of 1.091. These results indicate the anomalously high two-dimensional density of H2and D2 on the adsorbent, not expected from the liquid phase. For other temperatures, theexperimentalof H2 and D2 shows relatively constant value in the range of 10.3-11.3 and 10.1-11.4,

respectively, even at higher temperature up to each critical point, which are much lower than thetheoreticalin the range of 14.2-17.3. Thus, temperature independence of area density of the super-

dense H2 and D2 are revealed.




a

b

100

90

80

Adsorption uptake (mmol/g)

Adsorption uptake (mmol/g)

90

B

70

BB

60
50
B

40
30

Ne_27.1 K
D2_23.6 K
H2_20.4 K
N2_77.2 K

20
10
0

100

0

0.2

0.4

0.6

0.8

80
70
60
50
40
30

Ne_29.4 K
D2_26.4 K
H2_23.3 K
N2_85.1 K

20
10
0

1

0

0.2

Pressure (MPa)

d

90

80

80

70
60
50
40
Ne_32.5 K
D2_29.8 K
H2_26.5 K
N2_92.9 K

20
10
0

0

0.2

0.4

0.6

0.6

0.8

1

0.8

1

100

90

Adsorption uptake (mmol/g)

Adsorption uptake (mmol/g)

c 100

30

0.4

Pressure (MPa)

0.8

70
60
50
40
30

D2_33.9 K
H2_30.6 K

20
10
0

1

Pressure (MPa)

0

0.2

0.4

0.6

Pressure (MPa)Fig. 4.5.5 Adsorption isotherms of the molar basis uptake for H2, D2, Ne and N2 on MSC-30 as afunction of the relative pressure, and each temperature correspond to the liquefaction pressure at (a)0.10 MPa, (b) 0.22 MPa, (c) 0.44 MPa and (d) 0.88 MPa. The points of monolayer completion (Bpoint) are marked as open dots.

Table. 4.5.2 Adsorption uptakes and cross-sectional area for H2, D2, Ne and N2 at each temperature.
Condition

LiquidTemp.

Liquefied Liquidpressure density

K

MPa

Adsorption uptake
Total
uptakemmol/cm3 mmol/g

Monolayer
uptakeMonolayer Cross-sectional
ratio
area (this study)

mmol/g%Packing factor Cross-sectional area
( )( =1.091)

̅2/molecule̅2/molecule

H2

20.4

35.2

65.2

51.5

79

10.3

0.79

14.2

D2
Ne
N2
H2
D2
Ne
N2
H2
D2
Ne
N2
H2
D2

23.6
27.1
77.2
23.3
26.4
29.4
85.1
26.5
29.8
32.5
92.9
30.6
33.9

40.4
59.5
28.8
33.3
38.3
57.5
27.5
30.9
35.6
54.3
26.0
26.2
31.4

76
96.2
49
63.5
74.3
94.5
48.1
60.9
71.6
90.3
47.2
52.3
66.2

52.4
58.1
32.7
49.8
51.8
55.9
30
46.7
49.5
33.8
27.9
44.4
46.3

69
60
67
78
70
59
62
77
69
37
59
85
70

10.1
9.1
16.2
10.6
10.3
9.5
17.7
11.3
10.7
15.7
19
10.7
11.4

0.85
0.99
1.09
0.79
0.83
1.01
1.15
0.8
0.83
1.6
1.19
0.67
0.81

13.0
10.0
16.3
14.8
13.5
10.3
16.8
15.5
14.1
10.7
17.4
17.3
15.4

0.10

0.22

0.44

0.88




References

Otowa, T., Tanibata, R. & Itoh, M. Production and adsorption characteristics of MAXSORB:
High-surface-area active carbon. Gas Separation and Purification 7, 241–245 (1993).

2.

Zhao, W., Fierro, V., Fernández-Huerta, N., Izquierdo, M. T. & Celzard, A. Impact ofsynthesis conditions of KOH activated carbons on their hydrogen storage capacities. Int J
Hydrogen Energy 37, 14278–14284 (2012).

3.

Saha, D., Wei, Z. & Deng, S. Equilibrium, kinetics and enthalpy of hydrogen adsorption in
MOF-177. Int J Hydrogen Energy 33, 7479–7488 (2008).

4.

Furukawa, H., Miller, M. A. & Yaghi, O. M. Independent verification of the saturationhydrogen uptake in MOF-177 and establishment of a benchmark for hydrogen adsorption inmetal-organic frameworks. J Mater Chem 17, 3197–3204 (2007).

5.

Huo, S. H. & Yan, X. P. Metal-organic framework MIL-100(Fe) for the adsorption ofmalachite green from aqueous solution. J Mater Chem 22, 7449–7455 (2012).

6.

Lin, K. S., Adhikari, A. K., Ku, C. N., Chiang, C. L. & Kuo, H. Synthesis andcharacterization of porous HKUST-1 metal organic frameworks for hydrogen storage. Int J
Hydrogen Energy 37, 13865–13871 (2012).

7.

Soleimani Dorcheh, A. & Abbasi, M. H. Silica aerogel; synthesis, properties andcharacterization. J Mater Process Technol 199, 10–26 (2008).

8.

Do, X. D., Hoang, V. T. & Kaliaguine, S. MIL-53(Al) mesostructured metal-organic
frameworks. Microporous and Mesoporous Materials 141, 135–139 (2011).

9.

Tsai, C. W. & Langner, E. H. G. The effect of synthesis temperature on the particle size ofnano-ZIF-8. Microporous and Mesoporous Materials 221, 8–13 (2016).

10.

Nitta, Y., Yamanishi, O., Sekine, F., Imanaka, T. & Teranishi, S. Effect of supports onenantioselectivity of modified Ni catalyst. J Catal 79, 475–480 (1983).

11.

Murialdo, M., Stadie, N. P., Ahn, C. C. & Fultz, B. Krypton Adsorption on Zeolite-Templated
Carbon and Anomalous Surface Thermodynamics. Langmuir 31, 7991–7998 (2015).

12.

Seo, S., Mikšík, F., Maeshiro, Y., Thu, K. & Miyazaki, T. Performance evaluation of anadsorption heat pump system using msc‐30/r1234yf pair with the impact of thermal masses.
Applied Sciences (Switzerland) 11, 1–25 (2021).

13.

Sosa, J. E. et al. Exploring the Potential of Metal–Organic Frameworks for the Separation of
Blends of Fluorinated Gases with High Global Warming Potential. Global Challenges
2200107, (2022).
14.

Wickenheisser, M., Herbst, A., Tannert, R., Milow, B. & Janiak, C. Hierarchical MOFxerogel monolith composites from embedding MIL-100(Fe,Cr) and MIL-101(Cr) in
resorcinol-formaldehyde xerogels for water adsorption applications. Microporous andMesoporous Materials 215, 143–153 (2015).

15.

Cho, K. H. et al. Pore control of Al-based MIL-53 isomorphs for the preferential capture ofethane in an ethane/ethylene mixture. J Mater Chem A Mater 9, 14593–14600 (2021).

16.

Boateng, E. & Chen, A. Recent advances in nanomaterial-based solid-state hydrogen storage.
Mater Today Adv 6, 100022 (2020).

17.

Wong-Foy, A. G., Matzger, A. J. & Yaghi, O. M. Exceptional H2 saturation uptake inmicroporous metal-organic frameworks. J Am Chem Soc 128, 3494–3495 (2006).

18.

Thomas, K. M. Hydrogen adsorption and storage on porous materials. Catal Today 120, 389–
398 (2007).

19.

Bénard, P. & Chahine, R. Storage of hydrogen by physisorption on carbon andnanostructured materials. Scr Mater 56, 803–808 (2007).

20.

Poirier, E., Chahine, R. & Bose, T. K. Hydrogen adsorption in carbon nanostructures. Int J
Non Linear Mech 26, 831–835 (2001).

21.

Kojima, Y. et al. Hydrogen adsorption and desorption by carbon materials. J Alloys Compd
421, 204–208 (2006).

22.

Latroche, M. et al. Hydrogen Storage in the Giant-Pore Metal–Organic Frameworks MIL100 and MIL-101. Angewandte Chemie 118, 8407–8411 (2006).

23.

van Kranendonk, J. SOLID HYDROGEN. (Plenum, 1983).

24.

Kogan, V S; Lazarev, B G; Bulatova, R. F. The crystalline structure of hydrogen anddeuterium. Soviet Phys. JETP 4, (1957).

25.

WH Keesom, J De Smedt, H. M.-P. R. A. A. On the crystal structure of para-hydrogen atliquid helium temperatures. Proc Royal Acad Amsterdam 33, 814 (1930).

26.

Balderas-Xicohténcatl, R. et al. Formation of a super-dense hydrogen monolayer onmesoporous silica. Nat Chem (2022) doi:10.1038/s41557-022-01019-7.

27.

Thommes, M. et al. Physisorption of gases, with special reference to the evaluation of
surface area and pore size distribution (IUPAC Technical Report). Pure and Applied
Chemistry 87, 1051–1069 (2015).




28.

Livingston, H. K. The cross-sectional areas of molecules adsorbed on solid surfaces. J
Colloid Sci 4, 447–458 (1949).



5. Conclusion
In this thesis, the systematic investigation of the cryogenic H2 adsorption properties was
carried out to understand the super-dense H2 state, which showed higher density than liquid H2density, from the following point of view, 1) Material dependence, 2) Temperature dependence, 3)
Adsorbed layer dependence and 4) Gas dependence.

1) Material dependence
The densities of adsorbed H2 at the boiling point of H2 (20.4 K) for various kind ofadsorbents, such as carbon materials, MOFs, and the silica gels, show the values in the range of38.4~47.3 mmol/cm3, which are higher than that of liquid H2 (35.2 mmol/ cm3). Namely, the supersense H2 state can form on any adsorbents regardless of material species and pore structures. In
particular, the adsorbents with Type I adsorption isotherms given by micropores show relatively highdensities of adsorbed H2 in the range 43.0~47.4 mmol/cm3, which is higher than that of solid H2 (43mmol/cm3).

2) Temperature dependence
The temperature dependence of the super-dense H2 state is investigated below the criticaltemperature of H2 (33 K) for the adsorbents of MSC-30 and MOF-177 with Type I adsorption, and
GNPs with Type II adsorption. For all adsorbents, the phenomenon of super-dense H2 adsorption isobserved at any temperatures. Especially, the densities of adsorbed H2 on MSC-30 and MOF-177
with micropores do not significantly decrease with temperature rise compared with that of liquid H2,suggesting that the temperature dependence of super-dense H2 state is not large. The feasibility ofsuppression for liquid H2 boil-off by using the super-dense H2 with small temperature dependence isdiscussed. In the case of a temperature increase from 23 to 30 K under isobaric condition at 0.9 MPa,the boil-off amount of liquid H2 is reduced by 32% when MSC-30 is filled in the cell.

3) Adsorbed layer dependence
In order to discuss the super-dense H2 state in more details, the behaviors of monolayer
and multilayer H2 are discussed separately. The density of monolayer H2 is evaluated based on the
BET theory, and then the multilayer H2 is assumed to be the liquid phase. It is clarified that thedensity of monolayer H2 has a constant value of 50 mmol/cm3 without temperature and material
dependence. Interestingly, the density of monolayer H2 clearly exceeds the density of solid H2 (43mmol/cm3). In order to increase the volumetric H2 uptake including the volume of adsorbents
themselves, it is found that the volumetric surface area of adsorbents is a unique factor, and it is
proportional to the volumetric H2 uptake. This is important for developing materials to obtain higher
volumetric H2 uptake for the super-dense H2 adsorption. In this work, MSC-30 with the highest
volumetric surface area (7975 m2/cm3) shows the highest volumetric H2 density (33 mmol/cm3),
which is comparable to that of liquid H2 at 23 K.

4) Gas dependence
The density of adsorbed H2 is compared with those of adsorbed D2, Ne, and N2 at eachboiling point, and the temperature dependence of adsorbed density is discussed for each gas. It isfound that the densities of adsorbed Ne and N2 are equivalent to that of each liquid phase, indicatingthat Ne and Ne do not form the superdense state. On the other hand, the density of adsorbed D2 ishigher than that of liquid D2, which is the similar trend to H2. In addition, the density of monolayer
D2 shows a constant value of 50 mmol/ cm3 without temperature dependence below the critical pointof D2 (38.3 K). It is clarified that the densities of monolayer D2 and H2 are comparable, even though
the density of bulk-liquid D2 is 1.15 times higher than that of bulk-liquid H2 at each boiling point. Itis known that the lower density of bulk-liquid H2 is caused by the higher zero-point energy
compared with that of D2. From these results, it can be expected that the difference between bulkliquid H2 and D2 density due to the quantum effect is cancelled out by interactions between
adsorbates and adsorbents at cryogenic conditions, and the super-dense H2 is formed.

Acknowledgements
I would like to express my great appreciation to my supervisor, Professor Takayuki Ichikawa for his
supervision, helpful guidance, discussions. He gave me a lot of opportunity and experience forhelping the progress of this work, my career and my growth as a person. I would like to express my
special thanks to Associate Professor Hiroki Miyaoka for all supports and encouragement. He always
supports my research, presentations, and writing papers. I would like to great appreciate to Professor
Norio Ogita for helping my experiments, and for the valuable comments and discussions. I would
like to offer my special thanks to my co-researcher of Mr. Laurent Prost, Dr. Marolop Simanullang,
Mr. Ogawa Tomofumi in Air Liquide, Research & Development, Innovation Campus Tokyo for allof cooperations and for providing the samples for this work. Finally, I gratefully acknowledge to thepast and present members of my laboratory, Mr. Tomoyuki Ichikawa, Dr. Khushbu Sharma, Mr. Yuki
Kashiwara, Mr. Yuki Itoh, Project Professor Hitoshi Saima, Assistant Professor Fangqin Guo, Project
Assistant Professor Rini Singh, and Dr. Keita Shinzato for their king help in my doctoral course.

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