Hydrogen storage capacity of Li-decorated borophene

and pristine graphene slit pores: A combined ab initio

and quantum-thermodynamic study
Iván Cabria, Alexandre Lebon, M.B. Torres, L.J. Gallego, Andrés Vega

To cite this version:

Iván Cabria, Alexandre Lebon, M.B. Torres, L.J. Gallego, Andrés Vega. Hydrogen storage capacity
of Li-decorated borophene and pristine graphene slit pores: A combined ab initio and quantum-
thermodynamic study. Applied Surface Science, 2021, 562, pp.150019. �10.1016/j.apsusc.2021.150019�.
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 Applied Surface Science
Hydrogen storage capacity of Li-decorated borophene and pristine graphene slit pores:
A combined ab initio and quantum-thermodynamic study
--Manuscript Draft--

Manuscript Number: APSUSC-D-20-15170

Article Type: Full Length Article

Keywords: Hydrogen storage; 2D materials; boron-based materials; Li-decorated materials;

statistical
physics

Corresponding Author: Iván Cabria

University of Valladolid
Valladolid, SPAIN

First Author: Iván Cabria

Order of Authors: Iván Cabria

Alexandre Lebon

M. Begoña Torres

Luis Javier Gallego

Andrés Vega

Abstract: Among the two-dimensional materials of the post-graphene era, borophene has raised
an enormous interest due to its unprecedented diversity of structures and the wide
variety of potential applications, including its ability for hydrogen storage. In the present
paper we use van der Waals-corrected density functional theory in conjunction with a
quantum-thermodynamic model to investigate the hydrogen storage capacity of
confining Li-decorated borophene sheets in its most stable Pmmn8 configuration. Our
theoretical approach surpasses the standard density functional theory calculations only
valid at zero temperature and no pressure, thus providing the gravimetric and
volumetric capacities as well as the isotherms in real conditions. We show that narrow
Li-decorated slit pores of borophene have a good volumetric hydrogen storage
capacity

particularly at low temperature. Accordingly, nanoporous boron frameworks could be

optimal for hydrogen storage in applications at low temperature. We compare the
results with those corresponding to pristine graphene slit pores.

Suggested Reviewers: Roberto C. Longo

roberto.longo@utdallas.edu

Ignacio L. Garzón
garzon@fisica.unam.mx

Roberto Robles
roberto.robles@ehu.eus

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Manuscript Click here to view linked References

Hydrogen storage capacity of Li-decorated borophene and pristine

graphene slit pores: A combined ab initio and quantum-thermodynamic
study

I. Cabriaa,∗, A. Lebonb , M. B. Torresc , L. J. Gallegod , A. Vegaa

a Departamento de Fı́sica Teórica, Atómica y Óptica, Universidad de Valladolid, ES-47011 Valladolid, Spain
b Laboratoire de Chimie Electrochimie Moléculaire et Chimie Analytique, Université de Brest, UMR CNRS 6521, F-29285 Brest,
France
c Departamento de Matemáticas y Computación, Escuela Politécnica Superior, Universidad de Burgos, ES-09006 Burgos, Spain
d Departamento de Fı́sica de la Materia Condensada, Facultad de Fı́sica, Universidad de Santiago de Compostela, ES-15782

Santiago de Compostela, Spain

Abstract

Among the two-dimensional materials of the post-graphene era, borophene has raised an enormous interest
due to its unprecedented diversity of structures and the wide variety of potential applications, including its
ability for hydrogen storage. In the present paper we use van der Waals-corrected density functional theory in
conjunction with a quantum-thermodynamic model to investigate the hydrogen storage capacity of confining
Li-decorated borophene sheets in its most stable Pmmn8 configuration. Our theoretical approach surpasses
the standard density functional theory calculations only valid at zero temperature and no pressure, thus
providing the gravimetric and volumetric capacities as well as the isotherms in real conditions. We show
that narrow Li-decorated slit pores of borophene have a very large volumetric hydrogen storage capacity
particularly at low temperature. Accordingly, nanoporous boron frameworks could be optimal for hydrogen
storage in applications at low temperature, like in satellites and spatial equipments. We compare the results
with those corresponding to pristine graphene slit pores.
Keywords: Hydrogen storage, 2D materials, boron-based materials, Li-decorated materials, statistical
physics

∗ Correspondingauthor
Email address: ivan.cabria@uva.es (I. Cabria )

Preprint submitted to Journal of Power Sources October 16, 2020

1. Introduction

Although the current fleet of hydrogen-powered vehicles is still very limited, they are considered the
next-generation of electric vehicles and firm candidates to replace the conventional fossil fuel vehicles in
the coming years or, at least, be an efficient alternative within a world of presumable multiple solutions to
meet the energy, the pollution and the climate challenges. So far, only some companies offer models, but
quite expensive, and others are currently working in hydrogen car projects. Hydrogen is abundant and cheap
and its combustion produces three times as much energy as an equivalent quantity of petrol; moreover, the
result of this combustion is clean water (i.e., no CO2 and no other harmful gases are produced), so that it is
environmentally benign. Despite its advantages, the use of hydrogen involves technical challenges and rise
questions about efficiency. Hydrogen extraction in the most efficient way requires a chemical process, such
as water-splitting electrolysis or the reaction of hydrocarbon chains at high temperature. Although there
exist non-chemical ways to produce hydrogen, like by means of algae and solar light [1–3], they are very
slow, compared with the chemical ways. Anyway, the hydrogen storage still remains a most critical problem
[4–11].
Currently, hydrogen is stored in high-pressure tanks or in its liquid state at cryogenic facilities. Both
ways present risks and inconveniences, which has made necessary the search for alternative methods of
storage. Adsorption on light materials with large surface/volume ratio is being considered as the next step
for hydrogen storage. Within this context, carbon-based nanostructures such as graphene or nanotubes have
emerged as the most promising alternative due to their remarkable thermal and mechanical properties (see,
e.g., Refs. [12–14] and those cited therein). To be used in hydrogen-powered vehicles, a material requires
a gravimetric storage capacity of 4.5 wt % and a volumetric storage capacity of 0.030 kg/L of H2 at room
temperature and moderate pressure, as established by the U.S. Department of Energy (DOE) [15, 16].
To achieve reversible storage of H2 at room temperature and moderate pressure, the binding energy needs
to be 0.1-0.3 eV per molecule (i.e., in a range between physisorption and chemisorption), as has been shown
for a number of surfaces [17, 18]. Low-dimensional carbon nanotubes and graphene-based systems do not
meet such H2-binding energy requirement. However, it has been found that doping or decoration (since
these are non bulk-like structures) with carefully selected species can substantially increase their hydrogen
storage ability. A pioneering work in this area was performed by Yildirim and Ciraci [19], who used density
functional theory (DFT) to show that Ti-decorated single-walled carbon nanotubes are promising candidates
for high-capacity hydrogen storage media. A similar conclusion was also obtained by Lebon et al. [20] for
Ti-decorated zigzag graphene nanoribbons.

2
 Cabria et al. [21, 22] applied a quantum-thermodynamic model to calculate the storage capacities of
nanoporous carbons in a range of pressures and temperatures as a function of the size and shape of the
carbon pores. The model, which is an improvement of the model proposed by Patchkovskii et al. [23], takes
into account the quantum effects of the motion of H2 in the confining potential of the pores. The storage
capacities calculated at room temperature are far too short to reach the DOE capacity targets. The reason is
that, in spite of the confinement effect, which can be varied by modification of the pore shape and size, the
interaction between H2 and the carbon surfaces is not attractive enough.
Concurrently with the research on carbon-based nanostructures, there has been a growing interest in re-
cent years in two-dimensional (2D) materials beyond graphene (see, e.g., Refs. [24–28]). Theoretical studies
seem to indicate that hundreds of 2D novel compounds should exist, which have since led to the successful
synthesis and characterization of many of them. As one can easily imagine, 2D materials display a large di-
versity of chemical, mechanical, electronic and optical properties and a wide range of potential applications,
such as nanoelectronics, spintronics, optoelectronics or even in nanomedicine. Furthermore, some of those
novel 2D materials have been proposed as electrodes in novel batteries or as novel hydrogen storage solid
state devices. Among the large family of novel 2D compounds, borophene has attracted a great interest be-
cause of its intriguing and diverse properties, which arise from a large variety of geometrical structures and
bonding patterns. Borophene has also been proposed as a suitable material for a wide range of applications,
including metal-ion batteries, supercapacitors, sensors, catalytic devices, and others in medicine, to say the
least (see a recent review in Ref. [29].
We note that although the existence of the boron counterpart of graphene was theoretically predicted few
years ago, it was not synthesized until recently using Ag(111) as underlying substrate [30]. DFT predic-
tions for the structure of borophene went from initial single-atomic layers made of triangular and hexagonal
arrangements, the so-called α-sheet, [31] to novel nonplanar phases that are thermodynamically more fa-
vorable [32]. One of such phases displays a complex buckled geometry with Pmmn symmetry and eight
atoms in the unit cell. In this work we will refer to it as the Pmmn8 phase or the β-sheet. The boron mono-
layer synthesized on Ag(111) [30] shows the same Pmmn symmetry, but first-principles relaxation of such
a monolayer results in loss of corrugation along one of the in-plane directions, while keeping the buckled
structure along the other [30]. The resulting free standing borophene has only two atoms per unit cell. We
will denote it as Pmmn2 or simply the γ-sheet. Phonon spectra calculations [33, 34], by forcing translational
symmetry and rotational symmetry, reveal that the most stable phase of borophene is the β-sheet.
The three phases of borophene indicated above have been investigated as candidates for hydrogen sto-

3
rage. DFT-GGA calculations show that the Li-decorated α-sheet can contain up to 10.7 wt % of molecular
hydrogen [35], with an average binding energy of 0.15 eV, which exceeds the capacity of the graphene-
based counterpart. Moreover, the Li-decorated γ-sheet can reach a capacity of 13.7 wt % and H2-binding
energies that also satisfy the binding energy requirement, as obtained using GGA-DFT and van der Waals
(vdW)-corrected DFT calculations [36]. Recently, Lebon et al. [37] investigated the Li-decorated β-sheet,
using the non-local optB88-vdW functional proposed by Klimeš et al. [38]. Satisfactory H2-binding ener-
gies were reported, but the obtained gravimetric density was of 3.84 wt %, slightly lower than the 4.5 wt
% DOE threshold. However, all these results must be taken cautiously as they correspond to ground state
calculations at T = 0 K; in other words, finite temperature and pressure are not accounted for.
In order to get a more realistic information on the hydrogen storage capacity of borophene, in the work
described here we use the quantum-thermodynamic model of Cabria et al. [21, 22] to investigate the tempera-
ture and pressure-dependencies of the gravimetric and volumetric hydrogen storage capacities of borophene
nanostructures under doping and extreme conditions of confinement. Specifically, we considered a slit pore
consisting of two parallel Li-decorated Pmmn8 borophene sheets (i.e., in the most stable configuration of
borophene), separated by a certain distance, with hydrogen molecules in between. Hence, our aim goes be-
yond the standard (T = 0 K) DFT calculations in this field. We note that the system considered in this paper
is much more complex than that studied by Cabria et al.[21, 22], not only for the complexity of the Pmmn8
structure of the borophene walls, but also for the fact that it is not in pristine form, but doped with Li atoms.
We also note that nanoporous boron frameworks, containing many regions of borophene slit-shaped pores,
could perhaps be formed by using zeolite as a sacrificial template, just as zeolite-template carbons (ZTC)
are formed [39].
The following sections of this paper are organized as follows. In Section 2 we give the essential technical
details of the computational method used, the geometry of the slit pore of Li-decorated β borophene sheets
and of the general features of the quantum-thermodynamic model employed to obtain the temperature and
pressure dependent figures of merit. In Section 3 we present and discuss our results, with two subsections
devoted to obtain the interaction potential confining the hydrogen molecules in the slit pore, and to inves-
tigate the gravimetric and volumetric hydrogen storage capacities of this nanostructure as functions of the
pore width, the temperature and the pressure. The interaction potential and the storage capacities of Li-
decorated borophene and graphene slit pores are also compared. Finally, in Sec. 4, we summarize our main
conclusions.

4
Fig. 1. Front and side views of the relaxed 2 × 2 supercell of the β (Pmmn8) sheet decorated with 4 Li atoms at furrow sites on each
side of the sheet. Li atoms are shown with purple balls. Also shown is an adsorbed H2 molecule in its most stable configuration (with
H atoms in white).

2. Research methodology

2.1. Computational method

The quantum-thermodynamic model employed in this work (briefly outlined in a subsection below)
accounts for quantum-confinement effects due to the nanometric dimensions of the pores in which the H2
molecules are stored. These effects lead to the quantization of the energy spectrum of the molecule within the
interaction potential of the slit pore. Those energy states are required in the quantum-thermodynamic model
and, therefore, solving the Schrödinger equation for the Hamiltonian of the H2 molecule in the interaction
potential of the slit pore is the first step. Previously, we had to accurately determine the three-dimensional
interaction potential of H2 in the slit pore. This was accomplished by performing calculations within the DFT
as implemented in the VASP package [40, 41]. This package solves the Kohn-Sham equations within the
projector-augmented wave (PAW) approach [42]. For the plane-wave basis, a cut-off energy of 500 eV was
used. In the calculations we employed the non-local optB88-vdW functional of Klimeš et al. [38], which
includes the dispersion interactions. A k-point space of about 0.2 Å−1 was used for integrating Brillouin
zones. The width of the Gaussian smearing used was 0.01 eV. The interactions between periodic images of
the sheet along the normal to the surface are negligible, because they were separated by a distance of 23 Å.
As in Ref. [37], we used a 2 × 2 supercell of the β borophene sheet made of 32 B atoms. The sheet
was decorated with 4 Li atoms on both sides, and the resulting hybrid nanostructure was relaxed using the
conjugated-gradient method until the total force on each atom was smaller than 0.01 eV/Å; the accuracy to
convergence for the total energies was 10−6 eV/unit cell. The relaxed structure of the Li-decorated β sheet

5
is schematically represented in Fig. 1, which shows that the preferential adsorption sites of the Li atoms on
the β sheet are the furrow sites. In the same figure also shown is the location of an H2 molecule adsorbed on
the Li-decorated β sheet in its most stable configuration.
The interaction potential energy, V(x, y, z), of a hydrogen molecule located at point (x, y, z) with the
Li-decorated β borophene sheet is defined as

V(x, y, z) = E(H2 @Li-borophene) − E(H2 ) − E(Li-borophene) , (1)

where E(H2 @Li-borophene), E(H2 ) and E(Li-borophene) are the energy of H2 at (x, y, z) on the Li-decorated
β borophene sheet, the energy of an isolated H2 molecule and the energy of the Li-decorated β borophene
sheet, respectively, and z is the distance between the H2 molecule and the sheet surface.
We calculated the physisorption energies (or V(x, y, z)) of a single H2 molecule (at the most stable orien-
tation) on the surface of the relaxed Li-decorated β borophene sheet using the optB88-vdW functional [38].
Thus we obtained the interaction potential energy between the H2 molecule and the Li-decorated borophene
sheet, V(x, y, z). In our calculations we chose a xy grid with ∆x = ∆y = 0.25 Å. This implies 936 grid points
in the xy-plane. Then, for each one of these xy points or regions, we placed the H2 molecule at different
values of z, ranging from 0.8 to 7.6 Å, near to the surface of the sheet, with a step between points ∆z = 0.125
Å. Then, we made calculations for each one of these (x, y, z) grid points, and consequently we obtained a
numerical three-dimensional V(x, y, z) interaction potential.

0.3
V (eV/molecule)
Interaction potential energy (eV/molecule)

0.02
0.02 0.2 Shallowest region
0
0 Graphene
0.02 −0.02
−0.02 Deepest region
0 −0.04
−0.04 0.1
V (eV/molecule)

−0.02 −0.06
−0.06
−0.08
z (Å)

−0.04 −0.08
−0.1 0.0
−0.06 −0.1
−0.08
6
−0.1 6 5
5 4 -0.1
−0.12 4 1 3
1 3 2 3 4 y (Å)
2 3 4 y (Å) 2
2 5 6 1
5 6 1 x (Å) 7
x (Å) 7 8 9 0 -0.2
8 9 0 1 2 3 4 5 6
Molecule-surface distance (Å)

Fig. 2. Interaction potential energy between a single Li-decorated β borophene sheet and a H2 molecule in the planes z = 2.58 and
3.33 Å plotted in 3D (left panel) and its projections in the xy plane (middle panel). The bottom and upper 3D surfaces (planes) of the
left (middle) panel correspond to the planes z = 2.58 and 3.33 Å, respectively. Right panel: Interaction potential energy between a H2
molecule and a single graphene layer, and a single Li-decorated β borophene sheet at the deepest and shallowest xy points, as a function
of the H2 molecule-surface distance.

A slice of the three-dimensional interaction potential energy V(x, y, z) is plotted in left and middle panels
of Fig. 2. It corresponds to the interaction potential energy in two planes, z = 2.58 and 3.33 Å. It can be

6
noticed that the deepest regions correspond to the neighbourhood of the Li atoms. In right panel of Fig. 2,
the potential is shown for two constant pairs of (x, y) grid points, those where the resulting curves V(z) are
the deepest and the shallowest ones among the 936 V(z) curves obtained in the calculations. The latter figure
also contains the interaction potential V(z) between a H2 molecule and a graphene layer in the isotropic
approximation mentioned later, as obtained using the optB88-vdW functional.

2.2. Geometry of the slit pores formed by two parallel Li-decorated borophene sheets
We have used the geometry of the Li-decorated β borophene sheet to conceptually build slit-shaped pores.
According to experiments [43], nanoporous carbons contain many regions that are flat, graphitic-like parallel
surfaces separated by a distance of some nanometers. Those regions are called slit pores. Graphene slit pores
were studied in Ref. [44] using the optB88-vdW functional, with the aforementioned approximation for the
interaction potential of H2 with graphene. The volumetric capacities, vc , of graphene slit pores published in
Ref. [44] will be plotted in this work, for comparative purposes. Other results presented here for graphene
slit pores (the gravimetric capacities, gc , and the interaction potentials) are entirely new, although related
with the results reported in that reference. The upper panel of Fig. 3 shows the model of the slit borophene
pore used in our investigation of the hydrogen storage capacity of these nanostructures, consisting in two
parallel Li-decorated β borophene sheets separated by a distance d.

2.3. Quantum-thermodynamic model

The quantum-thermodynamic model has been explained in detail in Refs. [21, 22, 44]. The model
is based on considering the thermodynamic equilibrium between the adsorbed and compressed phases of
hydrogen gas inside a slit pore. These phases have been drawn schematically in Fig. 3 (lower panel). The H2
molecules stored by physisorption on the pore surface form the adsorbed phase (the blue and purple regions
in the lower panel of Fig. 3) and the H2 molecules stored only by compression, without interacting with the
pore surface, form the compressed phase (the region with red balls in the lower panel of Fig. 3).
The model uses the interaction potential energy V(x, y, z) of one single layer (Li-decorated borophene,
graphene, etc.), where z is the distance to the layer surface. The interaction potential energy of a slit pore
of width d, or slit pore potential, is the sum of the potentials of the corresponding two parallel layers:
Vslit pore (z; d) = V(x, y, z) + V(x, y, d − z). The slit pore is confined in the z direction. The sheets or layers of
the slit pore are located at z = 0 and z = d.
In the case of a graphene slit pore, the potential energy of one single layer depends very little on the sites
(x, y), and hence the approximations V(x, y, z) = V(z) for a single layer and V(z) + V(d − z) for a slit pore are

7
 Mass compressed gas
Mass adsorbed normally
present in the compressed gas
Excess mass adsorbed
Adsorbent material

Fig. 3. Upper panel: Geometrical structure of a Li-decorated borophene slit pore of width d, made of two parallel Li-decorated β
borophene sheets. Lower panel: Schematic representation of the phases of hydrogen stored inside a slit pore.

sound approximations. As regards to the Li-decorated borophene slit pore, the potential energy of a single
layer has a strong dependence on the sites (x, y). Therefore, we have used 3D potentials for a Li-decorated
borophene single layer, V(x, y, z), and for a Li-decorated borophene slit pore, V(x, y, z) + V(x, y, d − z).
The equation of the equilibrium between the two phases inside a pore is, in the quantum-thermodynamic
model,

1 Pads
Z
ln(Zads /Zcom ) = vmol (P, T )dP , (2)
RT Pcom

where Zads and Zcom are the partition functions of the adsorbed and compressed hydrogen phases, respec-
tively, Pcom and Pads are the pressures of the adsorbed and compressed phases, respectively, and vmol (P, T )
is the molar volume of hydrogen. The partition functions are given by

X
Zads = e−ǫi /kB T , (3)

p
Zcom = (d − 2dexcl ) 2πmkB T/h2 . (4)

In those equations, kB is the Boltzmann constant, ǫi are the eigenenergies of the quantum states of a single H2
molecule in the slit pore potential Vslit pore (z; d), obtained by solving the corresponding Schrödinger equation,
m is the mass of a hydrogen molecule, h is the Planck’s constant, d is the slit pore width and dexcl is an

8
exclusion distance due to the repulsive region of the interaction potential energy of a single layer. The
repulsive region is the region close to the atoms that form the layer.
The exclusion distance is defined as the location where the repulsive region of the interaction potential
energy of a single layer is 1 eV. If the interaction potential energy of a single layer depends on (x, y, z), then
there is an exclusion distance for each site (x, y) and the model uses the average exclusion distance. If the
interaction potential energy of a single layer depends only on z, then the exclusion distance is that of the
V(z) potential energy.
The mass of hydrogen stored in the pore is the sum of the masses of the adsorbed and compressed
hydrogen. In this investigation, we will calculate and compare only the storage capacities due to the adsorbed
phase, because the differences between the hydrogen storage capacities of Li-decorated β borophene and
graphene slit pores come from the different interaction with the pore surfaces, which impacts only on the
adsorbed phase. The gc of Li-decorated β borophene and graphene slit pores are also different because of
the different masses of the adsorbent sheets of the pores.
The quantum-thermodynamic model calculates the molar volume and the mass of the adsorbed phase
and uses them to obtain the storage capacity. The model obtains the pressure of the adsorbed phase, Pads ,
from the equation of the thermodynamic equilibrium between the two phases (Eq. 2). This pressure is used
to calculate the molar volume of the adsorbed hydrogen phase, vmol (Pads , T ), in L/mol. The molar volume
of the adsorbed phase is that given by the Mills-Younglove equation of state of H2 [22] at the pressure of the
adsorbed phase: vmol (Pads , T ) = vmolMills−Younglove (Pads , T ). This molar volume will be used to calculate the
volumetric and gravimetric capacities.
The volumetric capacity, vc , of the adsorbed hydrogen phase is calculated, in kg of hydrogen/L, by means
of the equation

M(H2 ) Vadsorbed
vc = , (5)
vmol (Pads , T ) Vpore
where M(H2 ) is the molar mass of H2 in kg/mol, 0.00201588 kg/mol, and Vpore and Vadsorbed are the volume
of the pore and the volume of the adsorbed hydrogen phase, respectively.
An explanation of the calculation of the volume of the adsorbed phase, Vadsorbed , follows. First, it must
be taken into account that the adsorbed phase inside a slit pore can be composed by one or two layers. In
the lower panel of Fig. 3 the adsorbed hydrogen is the blue and violet regions. In that figure, there are two
layers of adsorbed hydrogen. If the slit pore is narrow, then there is only one layer. If the slit pore is wide,
then there are two layers and each layer is attached to one of the sheets of the slit pore.

9
 The volume of the adsorbed phase is Vadsorbed = S wads . The surface of one sheet is S and wads is the
width of the adsorbed phase. If there is only one layer, then wads is the width of the layer. If there are two
layers, then wads is the sum of the widths of the two layers. The width of the adsorbed phase is given by


 zr − zl

 zr − zl ≤ 2L
(6)

wads =
2L > 2L ,


 zr − zl
where zr and zl are the points at which Vslit pore (z; d) = 0, zr > zl and L is the width of a layer adsorbed on a
single and isolated sheet.
The value of L is 3 Å. This value was selected because is approximately the kinetic diameter of a H2
molecule, 2.89 Å [45], the van der Waals diameter of a H2 molecule, 2.76 Å [46], and also the equilibrium
distance of most of the interaction potentials V(z) of a physisorbed H2 molecule on a single and isolated
graphene and on other adsorbent surfaces.
To calculate gc it is necessary to obtain the mass of the adsorbed phase, massH adsorbed . This mass
is obtained, in kg, as the product of the density in kg/L and the volume in liters of the adsorbed phase:
ρadsorbed Vadsorbed . The density of the adsorbed phase is given by a/vmol (Pads , T ). This amount was already
used to calculate the volumetric capacity.
The gc of the adsorbed hydrogen phase is calculated, in wt %, as

massH adsorbed
gc = 100 , (7)
massH adsorbed + massadsorbent material
where massadsorbent material is the mass of the adsorbent material of the slit-shaped pore.

2.4. Interaction potential energy of the graphene slit pore

Although it is a huge computational task, a good sampling of the interaction potential energy landscape
is crucial to accurately determine the adsorption capacities of the slit pore. We note that in previous works
for graphene slit pores [21–23], only a one-dimensional potential, along the normal direction, V(z), corres-
ponding to the most stable physisorption site of H2 on the surface, was calculated and assumed to be the
same along the whole graphene unit cell, thus neglecting anisotropic effects; the hydrogen storage capacities
were calculated according to that potential. This is a first approximation, but as we will see below, deep
and shallow regions decorate the potential energy landscape, which means that results based on an isotropic
potential in x, y, equal to that corresponding to the most stable configuration, slightly overestimate both the

10
gc and vc . In other words, the confining potential used in previous works for carbon based slit pores is a bit
more confining that the real one.
In our comparison of the capacities of the Li-decorated borophene slit pores with those of graphene
slit-pores we have used a correction factor to account for the overestimation of the storage capacities calcu-
lated in a previous work [22]. We performed additional calculations for graphene slit pores to estimate such
correction factor. On that previous work, the H2 adsorption energy was calculated for the nine main confi-
gurations of H2 on graphene [47]. A configuration is a combination of site and orientation of the molecule.
The three main sites are on top of an hexagon (H), on top of a carbon atom (A) and on top of a C-C bond
(B) (see Fig. 4). The three main orientations are perpendicular to the graphene surface (⊥), parallel to the
graphene surface and parallel to two C-C bonds of a graphene hexagon (kk), and parallel to the graphene
surface and perpendicular to two C-C bonds of a graphene hexagon (k⊥). We obtained that the most stable
configuration is Hkk .

A
AH
AB
H B
BH ABH

Fig. 4. Sites of H2 on graphene.

In the present work, we have calculated the binding energy in more sites of graphene, with the H2
molecule in the orientation kk. Specifically, in the sites A, B, H, AB, BH, AH and ABH indicated in Fig. 4
(site AB is located at the middle of the line joining sites A and B, and so on for the other new sites studied).
The results are gathered in Table 1. The binding energies of H2 on all the studied sites of graphene are very
close, being the largest difference 0.0066 eV. The most stable site is H and the less stable site is A.
We have calculated the interaction potential energy V(z) of H2 on graphene for those two configurations,
Hkk and Akk , and then we have used the potentials V(z) to calculate the corresponding storage capacities. The
results are shown in Figs. 5.
The capacities with the H2 molecule on the hexagon and on the carbon atom site are very similar for large
pore widths. The difference between the Hkk and Akk capacities is larger at narrow pores. The capacities of
the exact three-dimensional potential of a graphene slit-pore should be between the Hkk and Akk capacities.

11
Table 1: Binding energy of H2 in eV, Eb , and equilibrium H2-surface distance in Å, de , on different sites of graphene, as obtained by
optB88-vdW calculations. The H2 molecule is in the orientation kk.

Configuration de Eb Configuration de Eb
Akk 3.2 -0.0686 ABkk 3.2 -0.0692
Bkk 3.2 -0.0696 BHkk 3.1 -0.0723
Hkk 3.1 -0.0752 AHkk 3.1 -0.0713
ABHkk 3.2 -0.0704

Hence, a sound approximation consists on calculating the capacities of the graphene slit pores as the average
of the capacities obtained with the H2 molecule on the configurations Hkk and Akk : c = (cHkk + cAkk )/2. The
storage capacities of graphene slit pores presented and discussed in the next sections are these average
capacities.

3. Results and discussion

Using the quantum-thermodynamic model described above, we have investigated the hydrogen storage
ability of slit pores of Li-decorated β borophene by performing extensive calculations of their gc and vc as
functions of pore width, temperature and pressure. The storage capacities depend on the interaction potential
V(x, y, z) between the hydrogen molecules and the confining Li-decorated borophene sheets. The computed
gc and vc of these slit pores will be compared with those obtained for graphene slit pores using the same
DFT functional (optB88-vdW). The results for the hydrogen storage capacities of Li-decorated borophene
slit pores are plotted in the next figures as red solid lines, and those of graphene slit pores are plotted in black.
Two isotherm curves are shown for each type of capacity, gravimetric and volumetric; they correspond to
room temperature, T = 298.15 K, and to a low temperature of T = 80.15 K (most of the experiments of
hydrogen storage on solid nanoporous materials at low temperatures are performed at 77 K [4, 48–50] and a
few at 80.15 K [51], and can be representative for certain applications like in spacecrafts). The width of the
pores has been changed from 4 to 20 Å and the pressure from 0.1 and 25 MPa.

3.1. Dependence of the hydrogen storage capacities on pore width

Figure 6 shows the calculated hydrogen storage capacities of Li-decorated borophene and graphene slit
pores for the maximum value of the studied pressure, 25 MPa, and at the two considered temperatures, 80.15

12
 5.0

Adsorbed phase gravimetric capacity (wt %)

0.08

Adsorbed phase volumetric capacity (kg/L)

80.15 K and 25 MPa 80.15 K and 25 MPa
4.0
On hexagon On hexagon
0.06
On atom On atom
3.0

0.04
2.0
298.15 K and 25 MPa 298.15 K and 25 MPa

0.02
1.0

0.0 0.00
5 10 15 20 5 10 15 20
Pore width (Å) Pore width (Å)

4.0
Adsorbed phase gravimetric capacity (wt %)

0.08

Adsorbed phase volumetric capacity (kg/L)

80.15 K and w=7 Å
80.15 K and w=7 Å
3.0 0.06
On hexagon
On atom

2.0 On hexagon
0.04 298.15 K and w=7 Å
On atom

1.0 298.15 K w=7 Å 0.02

0.0 0.00
0 5 10 15 20 25 0 5 10 15 20 25
Pressure (MPa) Pressure (MPa)

Fig. 5. Gravimetric and volumetric hydrogen storage capacities of graphene slit pores for 80.15 K and 298.15 K and two configurations,
Hkk and Akk . Upper panel: Capacities as functions of the pore width, for a pressure of 25 MPa. Lower panel: Capacities as functions of
the pressure, for a pore width of 7 Å.

K and 298.15 K. The gc and vc of both kinds of pores exhibit a similar dependence with the pore size: the
curves have a maximum and decrease towards a constant value. The gc of the slit pore tends towards a
constant value that is twice the gc of the corresponding single layer under the same conditions of pressure
and temperature. On the other hand, the vc decays to zero because the volume ratio Vadsorbed /Vpore decreases
as the pore width increases.
Although the variations of the hydrogen storage capacities of the Li-decorated borophene and graphene
slit pores with the pore width have similar general features, important differences arise. Specifically, the
maxima of the gravimetric and volumetric curves of Li-decorated borophene slit pores are located at pore
widths smaller than those of the corresponding maxima of the graphene counterparts (see Table 2). On the
other hand, the highest gc at any temperature corresponds always to the graphene slit pore. However, the
highest vc at 80.15 K corresponds to the Li-decorated borophene slit pore, while at 298.15 K the result is in
favour of the graphene one (although in the latter case the differences are small: 0.0371 and 0.0340 kg/L for
graphene and Li-decorated borophene slit pores, respectively; see Table 2).
An important result that can be noticed in Fig. 6 is that, at a given temperature, the hydrogen storage

13
 5.0

Adsorbed phase gravimetric capacity (wt %)

Adsorbed phase volumetric capacity (kg/L)

80.15 K and 25 MPa 80.15 K and 25 MPa
0.08
4.0
Graphene Graphene
Li-decorated borophene Li-decorated borophene
0.06
3.0

0.04
2.0
298.15 K and 25 MPa

298.15 K and 25 MPa

1.0 0.02

0.0 0.00
5 10 15 20 5 10 15 20
Pore width (Å) Pore width (Å)

Fig. 6. Gravimetric and volumetric hydrogen storage capacities of slit pores of Li-decorated β borophene (red curves), as functions of
the pore width, for 80.15 K and 298.15 K, and a pressure of 25 MPa. Capacities for graphene slit pores are also shown (black curves).

Table 2: Maxima of the hydrogen storage capacities of Li-decorated borophene and graphene slit pores at 25 MPa, as functions of the
pore width.

Slit pore Capacity 80.15 K 298.15 K

Graphene gc 11.1 Å 4.23 wt % 7.9 Å 1.61 wt %
Graphene vc 8.4 Å 0.0700 kg/L 7.0 Å 0.0342 kg/L
Borophene-Li gc 8.8 Å 2.70 wt % 6.8 Å 0.93 wt %
Borophene-Li vc 6.4 Å 0.0835 kg/L 5.6 Å 0.0340 kg/L

capacities of Li-decorated borophene slit pores are larger than those of graphene ones for narrow or very
narrow pores. In fact, there are crossing points in that figure: for a pore width below a crossing point, the
hydrogen storage capacity of the Li-decorated borophene slit pore is larger than the corresponding capacity
of the graphene slit pore, and hence the former is more appropriate for hydrogen storage. The specific value
of the crossing point depends on the temperature and the type of capacity, gravimetric or volumetric, as it is
shown in Table 3. Above the crossing points, the situation is the opposite. It is also worth to point out that,
below 5.4 Å, the volumetric capacity of Li-decorated borophene slit pores at room temperature (298.15 K)
is even larger than that of graphene slit pores at a temperature such small as 80.15 K (this is a relevant result
since the decrease of the temperature is a way to increase the hydrogen storage capacity of porous materials,
in general). Although we are comparing different slit pores, this result reflects the great ability of narrow
Li-decorated borophene slit pores for hydrogen storage. In particular, the high vc of these narrow slit pores at
low temperature could be important for applications in outer space vehicles. We note that nanoporous boron

14
frameworks, containing many regions of borophene slit-shaped pores, could perhaps be formed by using
zeolite as a sacrificial template, just as zeolite-template carbons (ZTC) are formed [39], and these structures
could be subsequently doped with Li atoms to obtain solid porous materials with optimal hydrogen storage
capacities.

Table 3: Crossing points (slit pore widths) in Å of the hydrogen storage capacities of Li-decorated borophene and graphene slit pores
at 25 MPa and for two temperatures, 80.15 and 298.15 K.

Capacity 80.15 K 298.15 K

gc 6.1 5.9
vc 9.0 6.4

The large capacities of Li-decorated borophene slit pores of narrow widths can be explained by analyzing
the potential V(x, y, z) + V(x, y, d − z) confining the H2 molecules for different pore widths d (see upper panel
of Fig. 3). Figure 7 shows this potential, V(z) + V(d − z), at the deepest and shallowest regions in the xy
plane for six pore widths: 5.2, 5.6, 6.4, 7, 12 and 20 Å. Results for graphene slit pores (obtained with the
same optB88-vdW functional) are also shown. The confining potential (in the isotropic approximation) has
a single deep minimum for narrow pores and two separated minima for larger pore widths, that become
two independent potentials when the pore width is large. We note that the confining interaction potential
of a Li-decorated borophene slit pore contains xy points or regions of different depths, and that the real
influence of the whole interaction potential is some average between the two extremes cases considered, the
deepest and the shallowest regions. The exact or real three-dimensional interaction potential of graphene
slit pore also contains regions of different depths. However, we have showed before that the graphene slit
pore potential in the isotropic approximation, Vslit pore (z; d), is a good or reasonable approximation to the real
three-dimensional potential.
The confining interaction potential at the deepest region of the Li-decorated borophene slit pore is much
deeper than that of the graphene slit pore for the narrower pores of widths 5.2 and 5.6 Å (see Fig. 7).
Accordingly, in that region Li-decorated borophene slit pores can store much more hydrogen than graphene
slit pores. At many other regions of the xy plane (between the deepest and the shallowest regions), Li-
decorated borophene slit pores of those widths will store also more hydrogen than graphene slit pores.
Thus, one can understand that this is what will happen on average. This explains the larger hydrogen storage

15
 0.10 0.10

0.05 0.05

Interaction energy (eV/molecule)

Interaction energy (eV/molecule)

w = 5.2 Å w = 5.6 Å
0.00 0.00

-0.05 -0.05

-0.10 -0.10

-0.15 -0.15
Shallowest region Shallowest region
-0.20 Graphene -0.20 Graphene
Deepest region Deepest region
-0.25 -0.25
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0
Position of molecule respect to pore center (Å) Position of molecule respect to pore center (Å)

0.10 0.10

0.05 0.05
Interaction energy (eV/molecule)

Interaction energy (eV/molecule)

w = 6.4 Å w= 7Å
0.00 0.00

-0.05 -0.05

-0.10 -0.10

-0.15 -0.15
Shallowest region Shallowest region
-0.20 Graphene -0.20 Graphene
Deepest region Deepest region
-0.25 -0.25
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0
Position of molecule respect to pore center (Å) Position of molecule respect to pore center (Å)

0.10 0.10

0.05 0.05
Interaction energy (eV/molecule)

Interaction energy (eV/molecule)

w = 12 Å w = 20 Å
0.00 0.00

-0.05 -0.05

-0.10 -0.10

-0.15 -0.15
Shallowest region Shallowest region
-0.20 Graphene -0.20 Graphene
Deepest region Deepest region
-0.25 -0.25
-10.0 -5.0 0.0 5.0 10.0 -10.0 -5.0 0.0 5.0 10.0
Position of molecule respect to pore center (Å) Position of molecule respect to pore center (Å)

Fig. 7. Interaction potential Vslit pore (z; d) = V(z) + V(d − z) confining the H2 molecule in slit pores with six pore widths: 5.2, 5.6, 6.4,
7, 12 and 20 Å.

capacities of Li-decorated borophene slit pores of narrow widths, as obtained in our calculations (see Fig. 6).
For pores of medium widths, 6.4 and 7.0 Å, the interaction potentials at the deepest regions of Li-decorated
borophene slit pores are as deep as the interaction potentials of graphene slit pores (see Fig. 7). So, one can
understand again, at least qualitatively, that for pores of these widths the two types of pores can store similar
amounts of hydrogen. Finally, at larger pore widths, 12 and 20 Å, the interaction potential at the deepest
region of the Li-decorated borophene slit pore is again deeper than the interaction potential of graphene slit
pore. However, on average, the graphene potential attracts more hydrogen than the Li-decorated borophene
potential for those larger pore widths.

16
 We note that for pore widths above 7-8 Å, the volumetric capacities, vc , of Li-decorated borophene and
graphene slit pores are similar for the same P and T , but the gravimetric capacities, gc , of graphene slit pores
are about two times larger than those of Li-decorated borophene slit pores (see Fig. 6). This difference has
its origin in the larger surface mass density of Li-decorated borophene with respect to that of graphene (6.75
u/Å2 against 4.59 u/Å2 ). This larger surface mass density implies that Li-decorated borophene slit pores
have a larger mass of adsorbent material than graphene slit pores for a fixed pore volume. Hence, according
to Eq. 7, if the mass of hydrogen (or equivalently the density of hydrogen and pore volume) is the same,
Li-decorated borophene slit pores will have smaller gc than graphene slit pores.

3.2. Dependence of the hydrogen storage capacities on the pressure

Figure 8 shows the calculated gc and vc of Li-decorated borophene and graphene slit pores as functions of
the pressure at a constant temperature (T = 80.15 or T = 298.15 K) for different pore widths. For a pore width
of 7 Å (the width for which the vc of the graphene slit pore at 298.15 K is maximum; see Table 2), the gc
is bigger for graphene slit pores at the two considered temperatures. Note that when the pressure decreases,
the changes in the gc are more important at room temperature, especially for the graphene slit pore below
10 MPa. The vc of the pores of width 7 Å show similar features to those of the gc at room temperature;
however, at low temperature the behavior is quite different: the vc of the Li-decorated borophene slit pore is
bigger than that of the graphene slit pore for all studied pressures.
For a width of 6.4 Å (the width at which the vc of the Li-decorated borophene slit pore is maximum
at 80.15 K; see Table 2), the gravimetric and volumetric curves are similar to those obtained for the pores
with a width of 7 Å. However, for a pore width of 5.6 Å (the width at which the Li-decorated borophene slit
pore has the maximum vc at room temperature; see Table 2), the behaviour changes drastically: the vc and
gc of Li-decorated borophene slit pores become larger than those of graphene slit pores for any value of the
pressure and temperature. It should be noted that, for this pore width, the vc of Li-decorated borophene pores
at 80.15 K are almost twice those of graphene slit pores. Finally, for pores of width 5.2 Å, the trends observed
at the pore width of 5.6 Å are amplified: the capacities of Li-decorated borophene slit pore are larger and
even much larger than those of the graphene slit pore at any value of the pressure and temperature. Above 4
MPa and for a pore width of 5.2 Å, the vc of the Li-decorated borophene slit pore at 298.15 K is even larger
than that of the graphene slit pore at low temperature, 80.15 K.

17
 3.0 3.0

Adsorbed phase gravimetric capacity (wt %)

Adsorbed phase gravimetric capacity (wt %)

80.15 K and w=7 Å
80.15 K and w=6.4 Å
2.5 2.5

2.0 2.0
Graphene Graphene
1.5 Li-decorated borophene 1.5 Li-decorated borophene

1.0 298.15 K and w=7 Å 1.0 298.15 K and w=6.4 Å

0.5 0.5

0.0 0.0
0 5 10 15 20 25 0 5 10 15 20 25
Pressure (MPa) Pressure (MPa)

3.0 3.0
Adsorbed phase gravimetric capacity (wt %)

Adsorbed phase gravimetric capacity (wt %)

Graphene Graphene
2.5 Li-decorated borophene 2.5 Li-decorated borophene

2.0 2.0 80.15 K and w=5.2 Å

80.15 K and w=5.6 Å
1.5 1.5

1.0 298.15 K and w=5.6 Å 1.0

298.15 K and w=5.2 Å

0.5 0.5
80.15 K and w=5.2 Å

298.15 K and w=5.2 Å

0.0 0.0
0 5 10 15 20 25 0 5 10 15 20 25
Pressure (MPa) Pressure (MPa)
Adsorbed phase volumetric capacity (kg/L)

Adsorbed phase volumetric capacity (kg/L)

0.08 0.08
80.15 K and w=7 Å 80.15 K and w=6.4 Å

0.06 0.06
Graphene Graphene
Li-decorated borophene Li-decorated borophene
0.04 0.04

0.02 0.02 298.15 K and w=6.4 Å

298.15 K and w=7 Å

0.00 0.00
0 5 10 15 20 25 0 5 10 15 20 25
Pressure (MPa) Pressure (MPa)
Adsorbed phase volumetric capacity (kg/L)

Adsorbed phase volumetric capacity (kg/L)

80.15 K and w=5.2 Å

0.08 0.08

80.15 K and w=5.6 Å

Graphene Graphene
0.06 Li-decorated borophene 0.06 Li-decorated borophene

0.04 0.04
298.15 K and w=5.2 Å

0.02 298.15 K and w=5.6 Å 0.02 80.15 K and w=5.2 Å

298.15 K and w=5.2 Å

0.00 0.00
0 5 10 15 20 25 0 5 10 15 20 25
Pressure (MPa) Pressure (MPa)

Fig. 8. Gravimetric (upper panels) and volumetric (lower panels) hydrogen storage capacities of the Li-decorated borophene slit pore
(red curves), as a function of pressure, at 80.15 K and 298.15 K, for pore widths of 7, 6.4, 5.6 and 5.2 Å. Capacities of graphene slit
pores are also shown (black curves).

18
4. Conclusions

In this work, we performed extensive vdW-corrected DFT calculations, in conjunction with a quantum-
thermodynamic model, to investigate the gravimetric and volumetric hydrogen storage capacities of Li-
decorated borophene slit pores as functions of width, temperature and pressure. Our results are compared
with those obtained for graphene slit pores, which were partially investigated previously by some of us to
analyze the effect of confinement on the hydrogen storage capacity of undoped carbon nanostructures. The
main result of our calculations is that narrow slit pores of the strongly anisotropic β (Pmmn8) Li-decorated
borophene sheet have an excellent volumetric hydrogen storage capacity, especially at low temperature. The
volumetric capacity of narrow Li-decorated borophene slit pores at room temperature is even larger than that
of narrow graphene slit pores at low temperature, 80.15 K. Li-decorated borophene slit pores store hydrogen
in very narrow pores, below pore widths of 5 Å, while the graphene slit pores do not store hydrogen in those
very narrow pores.
The volumetric storage capacities at room temperature of Li-decorated borophene slit pores with pore
widths in the range 5-6 Å are similar to the volumetric capacities at room temperature of graphene slit pores
with larger pore widths, in the range 6-7 Å. At low temperature and for pore widths below 9 Å, the volumetric
storage capacities of Li-decorated borophene slit pores are larger than the volumetric storage capacities of
graphene slit pores.
We hope that these findings will stimulate the design of nanoporous boron frameworks, composed by
many regions of borophene-like parallel surfaces, with optimal hydrogen storage capacities.

Acknowledgments
This research was financially supported by the Spanish MICINN (Grant PGC2018-093745-B-I00), the
Junta de Castilla y León (Project No. VA124G18), the University of Valladolid, Spain, and the Xunta
de Galicia (ED431E 2018/08 and GRC ED431C 2016/001). We also acknowledge the use of the high
performance computing equipment of the Pole de Calcul Intensif pour la Mer (DATARMOR, Brest) and the
Centro de Proceso de Datos - Parque Cientı́fico (UVa).

References

[1] A. Kanygin, Y. Milrad, C. Thummala, K. Reifschneider, P. Baker, P. Marco, I. Yacoby, K. E. Re-

dding, Rewiring photosynthesis: a photosystem I-hydrogenase chimera that makes H2 in vivo, Energy
Environ. Sci. 13 (2020) 2903–14.

19
 [2] P. S. Krishna, S. Styring, F. Mamedov, Photosystem ratio imbalance promotes direct sustainable H2
production in Chlamydomonas reinhardtii, Green Chem. 21 (2019) 4683–90.

[3] S. Rumpel, J. F. Siebel, C. Farès, J. Duan, E. Reijerse, T. Happe, W. Lubitz, M. Winkler, Enhancing hy-
drogen production of microalgae by redirecting electrons from photosystem I to hydrogenase, Energy
Environ. Sci. 7 (2014) 3296–301.

[4] D. P. Broom, C. J. Webb, G. S. Fanourgakis, G. E. Froudakis, P. N. Trikalitis, M. Hirscher, Concepts

for improving hydrogen storage in nanoporous materials, Int. J. Hydrogen Energy 44 (2019) 7768–79.

[5] M. D. Allendorf, Z. Hulvey, T. Gennett, A. Ahmed, T. Autrey, J. Camp, E. S. Cho, H. Furukawa,

M. Haranczyk, M. Head-Gordon, S. Jeong, A. Karkamkar, D.-J. Liu, J. R. Long, K. R. Meihaus, I. H.
Nayyar, R. Nazarov, D. J. Siegel, V. Stavila, J. J. Urban, S. P. Veccham, B. C. Wood, An assessment
of strategies for the development of solid-state adsorbents for vehicular hydrogen storage, Energy
Environ. Sci. 11 (2018) 2784–812.

[6] C. Ahn, J. Purewal, Storage materials based on hydrogen physisorption, in: Hydrogen Storage Tech-
nology. Materials and Applications, CRC Press, 2016, pp. 213–38.

[7] D. Pukazhselvan, V. Kumar, S. K. Singh, High capacity hydrogen storage: Basic aspects, new deve-
lopments and milestones, Nano Energy 1 (2012) 566–89.

[8] K. J. Gross, K. R. Carrington, S. Barcelo, A. Karkamkar, J. Purewal, P. Parrilla, Reco-

mmended best practices for the characterization of storage properties of hydrogen storage
materials, Report to the Department of Energy Office of Energy Efficiency and Renewa-
ble Energy Hydrogen Storage Program under National Renewable Energy Laboratory Con-
tract No. 147388, H2 Technology Consulting LLC (2012), Accessed October 10, 2020.
http://energy.gov/eere/fuelcells/downloads/recommended-best-practices-characterization-storage-
properties-hydrogen-0 and http://energy.gov/sites/prod/files/2014/03/f12/best practices hydrogen storage.pdf.

[9] D. P. Broom, Hydrogen sorption properties of materials, in: Hydrogen Storage Materials. The Charac-
terisation of Their Storage Properties, Springer-Verlag, London, 2011, pp. 61–116.

[10] C. Liu, F. Li, L.-P. Ma, H.-M. Cheng, Advanced materials for energy storage, Adv. Mater. 22 (2010)
E28–62.

20
[11] L. Schlapbach, A. Züttel, Hydrogen storage materials for mobile applications, Nature (London) 414
(2001) 353–8.

[12] K. Kaneko, F. Rodrı́guez-Reinoso (Eds.), Nanoporous Materials for Gas Storage, Springer Singapore,
New York, 2019.

[13] M. Hirscher, M. Becher, M. Haluska, F. von Zeppelin, X. Chen, U. Dettlaff-Weglikowska, S. Roth, Are
carbon nanostructures an efficient hydrogen storage medium?, J. Alloys Comp. 356 (2003) 433–7.

[14] J. S. Arellano, L. M. Molina, A. Rubio, J. A. Alonso, Density functional study of adsorption of

molecular hydrogen on graphene layers, J. Chem. Phys. 112 (2000) 8114–9.

[15] Office of Energy Efficiency & Renewable Energy, Fuel Cell Technologies Office, Materials-based hy-
drogen storage, https://www.energy.gov/eere/fuelcells/materials-based-hydrogen-storage, 2018. Acce-
ssed February 26, 2020.

[16] Office of Energy Efficiency & Renewable Energy, Fuel Cell Technologies Office, DOE technical tar-
gets for onboard hydrogen storage for light-duty vehicles, https://www.energy.gov/eere/fuelcells/doe-
technical-targets-onboard-hydrogen-storage-light-duty-vehicles, 2018. Accessed February 26, 2020.

[17] S. K. Bhatia, A. L. Myers, Optimum conditions for adsorptive storage, Langmuir 22 (2006) 1688–700.

[18] J. Li, T. Furuta, H. Goto, T. Ohashi, Y. Fujiwara, S. Yip, Theoretical evaluation of hydrogen storage
capacity in pure carbon nanostructures, J. Chem. Phys. 119 (2003) 2376–85.

[19] T. Yildirim, S. Ciraci, Titanium-decorated carbon nanotubes as a potential high-capacity hydrogen

storage medium, Phys. Rev. Lett. 94 (2005) 175501.

[20] A. Lebon, J. Carrete, L. J. Gallego, A. Vega, Ti-decorated zigzag graphene nanoribbons for hydrogen
storage. A van der Waals-corrected density-functional study, Int. J. Hydrogen Energy 40 (2015) 4960–
8.

[21] I. Cabria, M. J. López, J. A. Alonso, Simulation of the hydrogen storage in nanoporous carbons with
different pore shapes, Int. J. Hydrogen Energy 36 (2011) 10748–59.

[22] I. Cabria, M. J. López, J. A. Alonso, The optimum average nanopore size for hydrogen storage in
carbon nanoporous materials, Carbon 45 (2007) 2649–58.

21
[23] S. Patchkovskii, J. S. Tse, S. N. Yurchenko, L. Zhechkov, T. Heine, G. Seifert, Graphene nanostructures
as tunable storage media for molecular hydrogen, Proc. Natl. Acad. Sci. U.S.A. 102 (2005) 10439–44.

[24] F. Ersan, D. Kecik, V. Özçelik, Y. Kadioglu, O. U. Aktürk, E. Durgun, E. Aktürk, S. Ciraci, Two-
dimensional pnictogens: A review of recent progresses and future research directions, Appl. Phys.
Rev. 6 (2019) 021308.

[25] X. Li, L. Tao, C. Zefeng, H. Fang, X. Li, X. Wang, J.-B. Xu, H. Zhu, Graphene and related two-
dimensional materials: Structure-property relationships for electronics and optoelectronics, Appl.
Phys. Rev. 4 (2017) 021306.

[26] C. Tan, X. Cao, X.-J. Wu, Q. He, J. Yang, X. Zhang, J. Chen, W. Zhao, S. Han, G.-H. Nam, M. Sindoro,
H. Zhang, Recent advances in ultrathin two-dimensional nanomaterials, Chem. Rev. 117 (2017) 6225–
331.

[27] Y. Zhang, A. Rubio, G. L. Lay, Emergent elemental two-dimensional materials beyond graphene, J.
Phys. D: Appl. Phys. 50 (2017) 053004.

[28] A. Gupta, T. Sakthivel, S. Seal, Recent development in 2D materials beyond graphene, Prog. Mater.
Sci. 73 (2015) 44–126.

[29] Z.-Q. Wang, T.-Y. Lü, H.-Q. Wang, Y. P. Feng, J.-C. Zheng, Review of borophene and its potential
applications, Front. Phys. 14 (2019) 33403.

[30] A. J. Mannix, X. F. Zhou, B. Kiraly, J. D. Wood, D. Alducin, B. D. Myers, Synthesis of borophenes:

anisotropic, twodimensional boron polymorphs, Science 350 (2015) 1513–6.

[31] H. Tang, S. Ismail-Beigi, Novel precursors for boronnanotubes: the competition of two-center and
three-center bonding, Phys. Rev. Lett. 99 (2007) 115501–4.

[32] X. F. Zhou, X. Dong, A. R. Oganov, Q. Zhu, Y. Tian, H. T. Wang, Semimetallic two-dimensional boron
allotrope with massless dirac fermions, Phys. Rev. Lett. 112 (2014) 085502–4.

[33] J. Carrete, W. Li, L. Lindsay, D. A. Broido, L. J. Gallego, N. Mingo, Physically founded phonon
dispersions of few-layer materials and the case of borophene, Mater. Res. Lett. 4 (2016) 204–11.

22
[34] A. Garcı́a-Fuente, J. Carrete, A. Vega, L. J. Gallego, What will freestanding borophene nanoribbons
look like? An analysis of their possible structures, magnetism and transport properties, Phys. Chem.
Chem. Phys. 19 (2017) 1054.

[35] S. Er, G. A. de Wijs, G. Brocks, DFT study of planar boron sheets: a new template for hydrogen
storage, J. Phys. Chem. C 113 (2009) 18962.

[36] L. Li, H. Zhang, X. Cheng, The high hydrogen storage capacities of Li-decorated borophene, Comput.
Mater. Sci. 137 (2017) 119124.

[37] A. Lebon, R. H. Aguilera del Toro, L. J. Gallego, A. Vega, Li-decorated Pmmmn8 phase of borophene
for hydrogen storage. A van der Waals corrected density-functional study, Int. J. Hydrogen Energy 44
(2019) 1021.

[38] J. Klimeš, D. R. Bowler, A. Michaelides, Chemical accuracy for the van der Waals density functional,
J. Phys.: Condens. Matter 22 (2010) 022201.

[39] H. Nishihara, T. Kyotani, Zeolite-templated carbons - three-dimensional microporous graphene frame-

works, Chem. Commun. 54 (2018) 5648.

[40] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a
plane-wave basis set, Phys. Rev. B 54 (1996) 11169–86.

[41] G. Kresse, J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47 (1993) 558–61.

[42] P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50 (1994) 17953–79.

[43] M.-S. Park, S.-E. Lee, M. I. Kim, Y.-S. Lee, CO2 adsorption characteristics of slit-pore shaped activated
carbon prepared from cokes with high crystallinity, Carbon Lett. 16 (2015) 45–50.

[44] I. Cabria, Simulations of volumetric hydrogen storage capacities of nanoporous carbons: Effect of
dispersion interactions as a function of pressure, temperature and pore width, Int. J. Hydrogen Energy
45 (2020) 5697–709.

[45] A. F. Ismail, K. C. Khulbe, T. Matsuura, Gas Separation Membranes: Polymeric and Inorganic,
Springer, Switzerland, 2015. doi:10.1007/978-3-319-01095-3.

23
[46] R. C. Weast, Chemical Rubber Company, Handbook of Chemistry and Physics: A Ready-reference
Book of Chemical and Physical Data, CRC handbook series, Chemical Rubber Company, 1972.

[47] I. Cabria, M. J. López, J. A. Alonso, Searching for DFT-based methods that include dispersion in-
teractions to calculate the physisorption of H2 on benzene and graphene, J. Chem. Phys. 146 (2017)
214104.

[48] R. Grünker, V. Bon, P. Müller, U. Stoeck, S. Krause, U. Mueller, I. Senkovska, S. Kaskel, A new
metal-organic framework with ultra-high surface area, Chem. Commun. 50 (2014) 3450–2.

[49] Y. Gogotsi, C. Portet, S. Osswald, J. M. Simmons, T. Yildirim, G. Laudisio, J. E. Fischer, Importance

of pore size in high-pressure hydrogen storage by porous carbons, Int. J. Hydrogen Energy 34 (2009)
6314–19.

[50] B. Schmitz, U. Müller, N. Trukhan, M. Schubert, G. Férey, M. Hirscher, Heat of adsorption for
hydrogen in microporous high-surface-area materials, Comput. Phys. Commun. 9 (2008) 2181–4.

[51] N. Ismail, Y. M. Temerk, A. A. El-Meligi, M. A. Badr, M. Madian, Synthesis and characterization of

MnPS3 for hydrogen sorption, J. Solid State Chem. 183 (2010) 984–7.

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Declaration of Interest Statement

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships
that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered
as potential competing interests:
Cover Letter

To Applied Surface Science Editor

Dear Editor:

We hereby submit our manuscript entitled “Hydrogen storage capacity of Li-decorated

borophene and pristine graphene slit pores: A combined ab initio and quantum-
thermodynamic study”, by I. Cabria et al., as candidate to be published in Applied Surface
Science as a full-length article. In this work, we have theoretically investigated the hydrogen
storage capacity of Li-decorated borophene slit pores and pure graphene slit pores. What
makes our work stand out from most theoretical studies on the hydrogen storage ability of
nanostructures is that our combined quantum-thermodynamical approach allows the
volumetric and gravimetric storage capacities to be determined as functions of temperature
and pressure for different pore sizes. Thus, our results could be directly compared with
experiments on these kinds of systems in realistic conditions.

We must point out that our paper was originally submited for publication in Journal of
Power Sources, but it was rejected on the basis of the report of an experimental referee whose
main objections were: i) that our theoretical predictions for the hydrogen storage capacity of
Li-decorated borophene slit pores do not give excelent storage performance, and ii) that our
paper is more appropriate to a journal dedicated to the theoretical/computational methods.
We must point out that there are other theoretical predictions on the hydrogen storage
capacity of borophene and other nanostructures that give very high gravimetric densities, but,
as indicated in the Introduction of our paper, they are not realistic, because they are based on
standard density functional calculations, only valid at zero temperature and no pressure. On
the other hand, although our main goal in this work concerns Li-decorated borophene slit
pores, the same quantum-thermodynamic methodology that we propose can be useful for
investigating the hydrogen storage capacity of confined nanostructures doped with
appropiated species in general. These theoretical calculations could be a useful guide for the
design of new nanoporous systems, composed by many regions of parallel surfaces, with
optimal hydrogen storage capacities.

The version of the paper that we now submit for publication to Applied Surface
Science is a slightly modified version of the one we submit for publication to Journal of Power
Sources, in which we have introduced some modifications in the light of the comments of the
above-mentioned referee, especially in the Conclusions section. The Editor of Journal of Power
Sources suggested us the possibility to transfer our paper to Applied Surface Science

We are sure that our predicted results shall become a fundamental reference for
future research on borophene (and hydrogen-storage nanostructures in general), a material
synthesized a few years ago by Mannix et al. (Science 350 (2015) 1513).

Your sincerely,

Iván Cabria

Corresponding author
Highlights (for review)

Li-decorated borophene slit pores are promising materials for hydrogen storage

Combined DFT and quantum-thermodynamic study outperforms standard DFT calculations

Nanoporous boron frameworks could be ideal for hydrogen storage in spatial equipment

Volumetric capacity at 298 K larger than that of narrow graphene slit pores at 80 K

Li-decorated borophene slit pores store hydrogen in very narrow pores

Graphical Abstract (for review)