Article
pubs.acs.org/JPCC
MgH2 in Carbon Scaffolds: A Combined Experimental and Theoretical
Investigation
P. Vajeeston,*,†,‡ S. Sartori,§ P. Ravindran,†,∥ K. D. Knudsen,§ B. Hauback,§ and H. Fjellvåg†
†
Center for Materials Sciences and Nanotechnology and ‡Center of Theoretical and Computational Chemistry, Department of
Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
§
Department of Physics, Institute for Energy Technology, P.O. Box 40, Kjeller NO-2027, Norway
∥
Department of Physics, Central University of Tamil Nadu, Thiruvarur 610 004, Tamil Nadu, India
ABSTRACT: Understanding the thermodynamics of metal
hydrides is crucial in order to employ them for reversible
hydrogen storage. The use of a supporting nanoporous matrix
for embedding the hydride can improve the kinetics of metal
hydride reactions and even change the overall reaction path. In
this study, density functional theory calculations were
performed to understand the size effect of MgH2 particles
and changes in the physical and chemical properties of these
nano-objects embedded in an amorphous carbon matrix. A
stable amorphous carbon structure was successfully generated
with two different approaches and further used as a template to construct the scaffold for nanophases of MgH2. Using five
different structure models, we have studied the physical and chemical changes of the nano-MgH2 in this carbon scaffold. In
addition, from small-angle neutron scattering studies, we could demonstrate experimentally that it is possible to incorporate such
ultrasmall objects into the carbon scaffolds.
■
INTRODUCTION
Magnesium is an attractive element for hydrogen-storage
applications because of its aboundace, lightweight, low
manufacture cost, and high hydrogen-storage capacity (7.66
wt %). Unfortunately, the use of magnesium hydride is
hampered by relatively slow kinetics for hydrogen release and
uptake. Moreover the thermodynamics is rather unfavorable,
with the formation enthalpy of ΔHf = −75 kJ/mol H2 (i.e.,
MgH2 must be heated to ca. 300 °C in order to release
hydrogen at p(H2) = 1 bar). Several factors hinder the rate of
hydrogenation and dehydrogenation of the Mg/MgH2 system.
In order to use MgH2 as an energy carrier in mobile
applications, one has to find the possible ways to decrease
the hydrogen desorption temperature. Numerous studies have
been focused on improving the problematic sorption kinetics,
including mechanical ball milling and chemical alloying.
However, it is found that these methods can only improve
the absorption and not the desorption kinetics, possibly
because even the smallest particle sizes (20 nm) obtainable
by these methods still primarily display bulk desorption
characteristics. The hydrogenation/dehydrogenation kinetics
can be effectively improved either by accreting Mg particles
with transition metals such as Ti, V, and Nb (or their
corresponding oxides) or by nanostructuring. Indeed, application of severe plastic deformation treatments (ball milling,1
equal channel angular pressing,2 and cold rolling3) have not
changed noticeably the thermodynamics of the Mg−H system.
However, recently, the McPhy energy system4 has demonstrated that nanophases of Mg hydride with proper additives
© 2012 American Chemical Society
can store large quantities of hydrogen at low pressure within
tens of minutes (for more details see ref 4).
From our theoretical simulations, we have found that most of
the nanoparticles of complex hydrides have a critical particle
size of the order ∼2 nm (for more details see refs 5−7). It is
difficult to prepare such nanoparticles from the available
experimental techniques (such as ball milling, etc.). Alternatively, one can prepare/isolate such types of particles in
porous scaffold structures. For example, recently Nielsen et al.8
synthesized nanoparticles of magnesium hydride through
embedding them in nanoporous carbon aerogel scaffold
materials in order to explore their kinetic properties of
hydrogen uptake and release. The hydrogen-storage properties
of nanoconfined MgH2 were studied by Sievert’s measurements
and thermal desorption spectroscopy, which clearly demonstrated that the dehydrogenation kinetics of the confined
hydride depends on the pore size distribution of the scaffold
material; that is, smaller pores mediated faster desorption rates,
most likely due to the size reduction of the confined
magnesium hydride.
An improvement in kinetics attributed to the nanoconfinement has also been demonstrated for NaAlH4 infiltrated in
mesoporous carbon9 or dispersed on carbon nanofibers.10,11 A
similar kinetic effect was found for LiBH4 infiltrated in
mesoporous scaffolds.12−14 The reduced diffusion distances
Received: January 25, 2012
Revised: September 19, 2012
Published: September 20, 2012
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For the nanowhisker construction, the vacuum is included only
in the x and y directions. The vacuum thickness was considered
wide enough to prevent whisker-to-whisker/cluster-to-cluster
interactions, and we found that a width of 14 Å is sufficient to
ensure that the energy converged to less than 1 meV/atom.
To gauge the bond strength, we have used the bond overlap
population (BOP) values calculated on the basis of the
Mulliken population analysis implemented in the CASTEP27
code. The Born effective charges in all the structure models of
amorphous carbon (AC)−MgH2 were calculated using density
functional perturbation theory with an external electric field.
For the CASTEP computation, we have used the optimized
structures obtained from VASP as input, and the structure is
again optimized with Norm-conserving pseudopotentials and
the GGA exchange correlation functional proposed by PBE.22
Small-Angle Neutron Scattering (SANS) Investigations. To verify the possibility of effectively confine particles
of MgH2 with sizes on the order of the calculated ones, we
prepared a sample of MgD2 nanoparticles and investigated their
infiltration in activated carbon fiber (ACF25) by using SANS. A
procedure of impregnation/drying of a Bu2Mg solution on
pretreated ACF25 was performed under protective atmosphere
following a method described previously in ref 28. After the
infiltration, the composite was converted into MgD2 by
deuteration of the Bu2Mg inside the voids of the carbon
scaffold. It should be noted that the observed X-ray diffraction
(XRD) reflections of MgD2 in the MgD2/ACF25 nanocomposite indicated that a small fraction of hydride was not
incorporated into the voids but left on the surface of the carbon
scaffold. These fractions of the hydrides should be responsible
for shifting the ΔH value to some extent.28 The deuterated
variant of MgH2, that is, MgD2, was employed in order to
reduce the incoherent scattering background in the SANS
experiments. A sample of bulk MgD2 was also measured for
comparison.
The SANS experiments were carried out at the JEEP II
reactor at IFE, Kjeller, Norway. The q range employed in the
experiments was 0.008−0.25 Å−1. Samples of bulk MgD2,
MgD2/ACF25 composite, and the scaffold alone were filled in 1
mm Hellma quartz cuvettes. For all samples, it was ensured that
the transmission was sufficiently high (>90%), to disregard
multiple scattering. Standard reductions of the scattering data
including transmission corrections were conducted by incorporating data collected from empty cell, beam without cell, and
blocked-beam background. The data were transformed to an
absolute scale (coherent differential cross section (dΣ/dΩ)) by
calculating the normalized scattered intensity from direct beam
measurements.29
and increased surface areas for LiBH4 were proposed to be
responsible for the decrease as large as 75 °C in dehydrogenation temperature when the complex hydride was incorporated
into aerogels and activated carbon.15,16 Furthermore, an
indication of the effect of nanoconfinement on the thermodynamic properties was proposed for NaAlH4 infiltrated in
activated carbon.17 In the bulk phases, during the dehydrogenation of a complex hydride, such as NaAlH4, the solid end
products, NaH and Al, can separate and thereby reduce the
complete rehydrogenation back to NaAlH4. In contrast, the
physical description of the nanoconfined system is complicated
and not yet complete. However, it was suggested that the use of
a nanoscale matrix embedded with the complex hydride could
force the products to stay in close vicinity, thus enhancing the
reversibility.15,16,18 At the same time, the higher degree of
disorder due to a larger contribution of phase boundaries to the
overall volume is supposed to increase the entropy of the
system, leading to a destabilization of the hydride.18 The
limited particle sizes also likely increase the contact area
between the product decomposition phases, which can further
improve the kinetics of the rehydrogenation reaction.15,16,19 In
the present study, we have investigated the changes in nanoobjects of MgH2 when they are embedded into the carbon
scaffold. Nanoconfinement of the Mg/MgH2 within carbon
nanotubes was also investigated quantum mechanically by
Liang and Kung.20 They found that the loading level increases
on increasing the confinement and the net energy change in the
hydrogen sorption/desorption process decreases significantly,
when the loading approaches the maximum. The confinement
was found to be independent of length of the confining
nanotubes.20 To our knowledge, this is the first theoretical
work where MgH2 nanoparticles were confined into different
types of carbon media/scaffold to study their changes in the
physical and chemical properties. To the best of our knowledge,
this is also the first theoretical report on a scaffold material with
experimental confirmation on the nanosize of the confined
particles.
■
MATERIALS AND METHODS
Computational Details. The quantum-mechanical calculations have been performed in the framework of density
functional theory (DFT) using the generalized gradient
approximation (GGA)21,22 as implemented in the VASP
code.23,24 The interaction between the ion and the electron is
described by the projector augmented wave method.25,26 For
the present calculations, we have used a plane-wave cutoff
energy of 500 eV that gives well converged results with respect
to the basis set. The k points were generated using the
Monkhorst−-Pack method with a grid size of 8 × 8 × 12, and 8
× 8 × 1, for the bulk and surfaces (structure models M1, M2,
M3, M4, and M5; for more details about the structure models
see the MgH2 with Amorphous Carbon section), respectively.
Iterative relaxation of atomic positions was stopped when the
change in total energy between successive steps was less than 1
meV/cell. With this criterion, the maximum forces generally
acting on the atoms were found to be less than 10 meV/Å.
Different sizes of the nanoclusters and nanowhiskers have been
constructed from optimized bulk phases through different
supercell sizes. The k points were generated using the
Monkhorst−Pack method with a grid size of 1 × 1 × 1 and
2 × 2 × 1, for structural optimization for nanoclusters and
nanowhiskers, respectively. During the nanoclusters/whisker
construction, the MgH2 stoichiometry was always maintained.
■
RESULTS AND DISCUSSION
Amorphous Structure Construction. Carbon is an
impressively versatile chemical element. As it is found in
three distinct hybridizations, sp3, sp2, and sp, each with a welldefined local topology, this element can form a variety of
different allotropes. For instance, the bulk hardness of diamond
and the laminar softness of graphite can be tracked down to
carbon sp3 tetrahedron-like bonding and sp2 planar configuration, respectively. Although these two materials exhibit quite
distinctive physical and chemical properties, they represent only
a small fraction of possible carbon solids. Noncrystalline carbon
materials have a mixture of sp3 and sp2 hybridized C−C
bonding and have lately received much attention due to their
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Figure 1. Optimised amorphous carbon structure obtained from method I (a) and II (b; see text for more details). The pair distribution functions
are shown as a function of distance in Å for the amorphous carbon obtained from the two methods (see text).
rotational states combined with the stepwise nature of the chain
construction process implemented in the Materials studio 5.0
package,34 in which at each step, we have selected a
continuation of the chain from a series of candidates according
to a set of probabilities. During this process, we have used the
following three steps: (1) rotational states are chosen according
to a pair wise interdependent RIS model; (2) a single-chain
backbone bond and its pendant atoms are added to the system;
and (3) the set of probabilities comprises the modified
conditional probabilities for the allowed states of the added
bond. In this approach, the number and location of minima in
the bond’s torsional potential are first noted. Next, the height of
the barrier between states is examined to decide whether
adjacent states are mutually accessible. If the factor exp(−barrier height/RT) (where R is the gas constant and T is the
temperature] exceeds 0.00005, the states are considered to
communicate, and the full set of torsional potential minima is
used to define allowed states.
Such constructed amorphous carbon structures were further
used as a starting point for the vicarious DFT calculations. The
unit-cell volume and shape as well as atomic positions were
relaxed simultaneously in a series of calculations made with
progressively increasing precision. A final high accuracy
calculation of the total energy was performed after completion
of the relaxations with respect to k-point convergence and
plane-wave cutoff. The optimized final structures of AC1
(density 2.85 cm−3) and AC2 (density 2.78 cm−3) are shown in
Figure 1a and b, respectively. In these two optimized
amorphous structure models from the above-mentioned
methods, the majority of the C atoms are tetrahedrally
coordinated with the neighboring C atom in the matrix. The
calculated C−C distances versus the number of bonds (pair
distribution function, PDF; see Figure 1) for the AC1 and AC2
models indicate that the PDF values were scattered between
1.35 and 1.65 Å in AC1 while the corresponding values in AC2
vary from 1.34 to 1.72 Å. This type of structural arrangement is
expected in nano and amorphous phases with no threedimensional crystallinity owing to reduction in coordination
number of the atoms. It may be noted that the C−C distance in
graphite is 1.42 Å and that for diamond is 1.54 Å. The presently
constructed models cover these values indicating they have
both sp3 and sp2 hybridized C−C bonds in their structures. In
order to understand the electronic structure and structural
many industrial applications. This class of material can be
produced by chemical vapor deposition at a low cost.
In experimental studies, the complex hydrides are typically
incorporated/dispersed into either mesoporous carbon, carbon
nanofibers, aerogels, or activated carbon matrices that may or
may not have any three-dimensional periodic structural
arrangements. Activated carbon fibers are carbon sorbents
with a narrow and uniform pore size distribution. They are
utilized as supports for catalysts and electrical materials due to
their microporosity with high specific surface cyclic effects.
Simulations on such carbon forms are very challenging, because
of the large number of atoms as well as lack of information on
the starting structures for the simulations. In the present study,
we have assumed that all these media (either mesoporous
carbon, carbon nanofibers, aerogels, or activated carbon) are
amorphous structures and that the pore sizes are directly
related to the density of the amorphous structures. Hence, we
have constructed several amorphous carbon structures with
varying densities using two different amorphous construction
methods (see the following section for more details). These
starting structures are optimized with the VASP code, and the
resultant structure models are further used to construct the
nano-MgH2 embedded structures.
In our first approach, the amorphous carbon structures
(hereafter referred to as AC1) were obtained by a liquid quench
within a Metropolis Monte Carlo scheme (MC scheme). At
each MC step, each atom is given a random displacement, and
the resulting change in total energy (ΔE) of the system is
calculated. This new position is accepted with a probability
minimum (1, exp(−ΔE/kBT)), where kB is the Boltzmann
constant and T is the temperature in kelvin. We have melted a
128 atoms cubic cell at a density of 3 g cm−3 and at a
temperature of 5000 °C (method I) using the Monte Carlo
technique by exploiting the Tersoff potential30,31 with the cutoff
distance set at 2.45 Å to correctly locate the second-neighbor
coordination shell of the tetrahedral amorphous carbon
structure.32,33 The amorphous carbon structures were obtained
by cooling (exponentially along the MC steps) the hot carbon
from 5000 °C down to a temperature of 1040 °C. In our
second approach (method II), for the amorphous structure
construction (hereafter referred as AC2; the number of atoms
and density are the same as for AC1; i.e., 128 atoms cubic cell
at a density of 3 g cm−3), we have used the familiar concept of
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stability of the considered models,we have calculated the
electronic structure of AC1 and AC2 (see Figure 2). Because of
Figure 3. Calculated total energy as a function of particle size for the
MgH2 nanoclusters (open squares; the corresponding chemical
composition of the MgH2 units are presented in the upper horizontal
scale), nanoparticles of Mg together with H2 molecules (i.e.,
EMg(nano) + EH2(mol)) (open circles), and formation energy as a
function of particle size (filled circles) are displayed. The involved
energy difference between two first curves at the particle size of 2.25
nm is −0.76 eV/f.u. (−73.4 kJ/mol).
Figure 2. Calculated total density of states for amorphous carbon
structures I and II obtained from the two methods (see text). The
Fermi level is set at zero energy and marked by the vertical dotted line.
the well scattered C−C bond-length values, the calculated
density of states for both phases is well dispersed. From Figure
2, it is evident that both structure models have finite electrons
at the Fermi level (EF) having metallic character. Further, the
EF is exactly at the pseudogap (a deep valley at/near to the EF).
A strong correlation has often been emphasized between the
position of the pseudogap and structural stability.35−38 It has
been demonstrated in intermetallics both experimentally and
theoretically that the material is found to be more stable in a
particular structure if the filling of the bonding states is
maximum. For the most stable structures, there is enough room
to accommodate all the valence electrons into the bonding
states so as to bring the EF to the pseudogap thus making the
antibonding states fully empty. In other words, the stable
structure is often characterized by a low N(EF ).37,39−42 From
this point of view, the considered two models are stable, both
methods give a similar result, and AC2 is lower in energy.
However, the calculated total energy difference between these
two models is 0.00013 eV/atom. Hence, we have used the AC2
structure as the scaffold matrix in our present study.
Nanoclusters of MgH2. α-MgH2 crystallizes in a TiO2
rutile-type structure at ambient pressure and low temperatures.43,44 At higher temperatures and pressures, it transforms
into several other polymorphs.45−50 In this study, we have
concentrated mainly on the ambient condition α-MgH2 phase.
As the interatomic distances in the nanophases are different
than those in the corresponding bulk materials, different
physical and chemical properties could be expected compared
to the bulk materials. Upon decreasing the particle size below a
certain range (critical particle size), a large fraction of the atoms
become exposed to the surface, and the total energy starts to
deviate from its constant value. In order to identify the critical
particle size, we have calculated the total energy as a function of
the cluster size for MgH2 as shown in Figure 3. From this
figure, it is evident that, if the cluster size decreases, the total
energy becomes more positive. In particular, there is a steep
increase in the total energy when the size of the MgH2 cluster is
below ∼1 nm. Furthermore, the positive change in the total
energy for the nanoparticles suggest that there will be
modifications in the thermodynamical properties and in
particular the hydrogen sorption temperature is expected to
be reduced in the nanophases compared to the bulk materials.
The reason is that the surface-to-volume ratio increases upon
decreasing the cluster size. Since the surface atoms have lower
coordination (generally found to occupy the less stable top and
bridge sites) than that in bulk materials, the average number of
bonds between constituents is lower for smaller clusters. This
could explain why the decomposition temperature for nanoparticles is usually lower than that in bulk materials. If one
compares the variation in total energy with particle size for
MgH2 and that with the combination of nanoparticles of Mg
with H2 molecules (see Figure 3), the nanoparticles of MgH2
are energetically unstable below 1 nm compared to the
corresponding decomposed phases (i.e., nanoparticles of Mg
with remaining H2 gas). This is opposite to the conclusion we
reached on nanoparticles of AlH3 and borohydrides, where
below the critical particle size, these nanoparticles will be more
stable than the corresponding decomposed phases.51 Therefore,
the present result suggests that one can destabilize nanoparticles of MgH2 below 1 nm size. In order to substantiate this
observation, we have calculated the formation energy (ΔH) as a
function of particle size using the following equation:
ΔH = EMgH2(nano) − [EMg (nano) + E H2(mol)]
(1)
where, EMgH2(nano) and EMg(nano) are the total energy of the
MgH2 and Mg nanoclusters, respectively. EH2(mol) refers to the
total energy of the hydrogen molecule. The calculated ΔH
value for the bulk α-MgH2 phase is −73.5 kJ/mol. This result is
in good agreement with the experimental value for the bulk
phase (varies from −74.4 ± 0.4 to −76.2 ± 9.2 kJ/mol).52,53
The calculated ΔH as a function of the particle size (see Table
1) is also displayed in Figure 3 where the critical particle size is
found to be 2.2 nm and the corresponding ΔH value is −73.4
kJ/mol, which is closer to that of the bulk phase. A recent
study54 by Liang found that, as thickness of the film decreases,
the enthalpy also decreases, to a value of 5 kJ/mol for a two
unit-cell depth compared to that of the bulk phase. The present
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Table 1. Calculated Formation Energy (ΔH)a as a Function
of Particle Size for the Nanoparticles of MgH2
a
particle size (nm)
ΔH (kJ/mol)
0.5
0.6
0.83
1.1
1.3
1.6
2.2
2.8
49.46
31.39
−4.938
−53.04
−67.01
−71.82
−73.43
−73.46
of qr ≫ 1, where r is the particle size, the scattered intensity
I(q) can be well approximated as proportional to q−α. The
power-law scattering exponent α can thus be evaluated from a
plot of log(I) versus log |q|. The composite material, MgD2/
ACF25, and the scaffold alone follow the same behavior at lowmedium q (see Figure 4), whereas a clear difference in slope
For calculation method, see eq 1.
results for MgH2 nanoclusters provide a useful way to compare
our methods to other approaches and to consider the strengths
and limitations of our calculations. Possibly, the most direct
comparison we can make with experimental data is via the
experiments of Li et al., who examined hydrogen evolution
from MgH2 nanowires of radii 20, 45, and 80 nm.55 In these
experiments, no noticeable difference in the temperatures
associated with H2 evolution was observed between the
nanowires of different radii, although the thinner nanowires
had better reaction kinetics. From Figure 3, it is evident that,
when the particle size is sufficiently small (below ca. 1.6 nm),
the formation energy of the system becomes much more
positive and the system can be highly unstable compared to the
decomposed phases (i.e., nano Mg + H2). This clearly indicates
that, when the particle size becomes continuously smaller, the
system becomes highly unstable. For practical applications, it is
anticipated that the ΔH value should be around −40 kJ/mol,
and from this point of view, the nanoparticles of MgH2 with
size below 1.6 nm get special attention. However, it is a
challenging task to make bare nanoparticles of MgH2 by
existing experimental techniques. Even if this could be achieved,
the particles may agglomerate and form larger entities that will
not exhibit the expected size effect anymore. This can be
overcome if one encapsulates such nanoparticles in nanoporous
scaffold materials, because the physical and chemical properties
of such nanoparticles may change due to the interface effect. It
is also important to note that the experimental characterization
of such scaffold materials is a very challenging task. From the
stability of the nanoparticles of MgH2, one can anticipate that
the scaffolded nano-objects may have a fundamental structural
framework that is different from that of bulk material. It should
be noted that the recent work by Zhao-Karger et al.28
demonstrated that one can alter the thermodynamic and
kinetic properties of MgH2 by infiltrating them into a
microporous scaffold. In this study, MgH2 nanoparticles were
formed by direct hydrogenation of Bu2Mg inside the pores of a
carbon scaffold, and the authors found that the activation
energy for the dehydrogenation was lowered by 52 kJ/mol
compared with that of the bulk material. Similarly, a
significantly reduced reaction enthalpy of 63.8 ± 0.5 kJ/mol
and entropy of 117.2 ± 0.8 J/mol were found for the
nanoconfined system.
Evaluation of Particle Size in the Scaffold Material. In
order to identify the particle size and the effective infiltration of
the prepared MgD2/ACF25 composite, we performed SANS
on bulk MgD2, the composite MgD2/ACF25, and the scaffold
ACF25 alone. As any particles of bigger size would affect the
low-q range, not visible in our SANS data, they are not
considered here. When the scattering data satisfy the condition
Figure 4. SANS measurements performed at room temperature on
ACF25, MgD2/ACF25, and bulk MgD2.
behavior becomes evident at q values higher than approximately
0.18 Å−1. These values correspond with material deposited in
very small pores (<a few nm).
The slope parameter α has a value well below 3.0 (ca. 1.3) in
the high-q range. This shows that the particle sizes are so small
that the material has a mass fractal behavior even at the shortest
length scale accessible in our experiments, that is, around 1 nm.
Figure 5 shows the size distribution obtained by means of an
indirect Fourier transform of the excess scattering, that is, of the
Figure 5. Volume distribution of sizes obtained via indirect Fourier
transform of the difference between the composite (MgD2/ACF25)
and scaffold scattering (ACF25). The upper size limit for the
transform was 120 Å (12 nm).
data obtained by subtracting the scaffold scattering from the
composite scattering. As commented in our recent paper,56 one
should show some caution here, since there are crosscorrelation terms that may not be nulled out upon subtraction.
However, this curve, with its main peak around 10 Å (1 nm),
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confirms the small sizes of the MgD2 particles when they are
integrated into the scaffold.
As an independent check of the average particle size, we also
performed a Guinier regression in the high-q region (above q ≈
0.1 Å−1), where the “knee” in the composite data is a clear
indication of a characteristic size in this size range. This resulted
in a radius of gyration for the MgD2 particles just below 1 nm
(9.7 Å), see Figure 6. The SANS data therefore seem to
Figure 7. Considered structure models (after the relaxation) in this
study. M1: overlayers of MgH2 in amorphous carbon (AC) substrate
(239 (128 C, 35 Mg, 70 H, and 6 unsaturated broken bonds are
saturated by H atoms; UBBH) atoms involved in this model); M2:
AC−MgH2−AC (sandwich/multilayer; 373 (256 C, 35 Mg, 70 H, and
12 UBBH) atoms involved in this model); M3: MgH2 in the carbon
scaffold (386 (280 C, 32 Mg, H 64, 10 UBBH) atoms involved in this
model); M4: MgH2 nanoparticle (embedded nanoparticle size is 1.5
nm) is placed in the closed scaffolds (424 (304 C, 32 Mg, 64 H, and
14 UBBH) atoms involved in this model); and M5: MgH2 nanowire
(diameter is 1.5 nm, and length of the wire is infinite length) in the
carbon scaffold (386 (294 C, 27 Mg, 54 H, and 11 UBBH) atoms
involved in this model). Vacuum around the structures is removed in
the illustration for better visibility.
Figure 6. Guinier plot in the high-q region (q = 0.12−0.25) of the
difference between the composite and scaffold scattering.
confirm that the nanoinfiltration of MgD2 was successful. The
very small size measured for the confined MgD2 is likely to be
the reason for the observed destabilization effect.45
MgH2 with Amorphous Carbon. As mentioned previously, there is no unique way to describe the starting structure
models for amorphous carbon. Therefore, in the present
theoretical study, we constructed different types of amorphous
carbon models with altered density (corresponding to different
pore size), see Figure 7. From the optimized AC2, we have
constructed various types of models named M1 (overlayers of
MgH2 on AC substrate layers where the nanoparticles stand on
the surface of the carbon media), M2 (MgH2 layers arranged
between two AC layers, also called sandwich/multilayer model,
which corresponds to nano-MgH2 trapped between the carbon
sheets), M3 (MgH2 nanoparticles inserted into a carbon
scaffold; this situation corresponds to nanoparticles of MgH2
trapped inside a carbon cave), M4 (similar to the M3 model,
but the cave is also closed by AC layers), and M5 (where a
MgH2 nanowire is placed into the carbon scaffold matrix; this
situation corresponds to needle shape of MgH2 trapped in a
carbon cave). It may be noted that, as we have used a periodic
boundary condition and no vacuum was introduced in the M5
model along z direction, the length of the nanowire is infinite.
All the above-mentioned models are constructed from the
optimized α-MgH2 structures (i.e., M1 and M2, nanoclusters
and nanowire configurations) and the relaxed carbon scaffolds
with specific density as described in the Amorphous Structure
Construction section. For more details about the nanophase
construction see ref 5.
Layers of AC have been constructed by cleaving the bulk
phase that was earlier fully relaxed with respect to stress and
strain. We have earlier shown that the (101) slab of α-MgH2
has the lowest surface energy5, and therefore, the layer is
constructed from this surface. All atoms in such created slabs
have been allowed to relax by minimization of the forces acting
on them. In the structure models M1 (a = 12.18, b = 8.33, c =
18.49 Å (28.496 Å with vacuum)) and M2 (a = 12.18, b = 8.33,
c = 26.35 (36.35 Å with vacuum)), each slab is separated from
its neighbors by a vacuum of 10 Å thickness. The thickness of a
slab is usually expressed in terms of number of atomic layers,
where a layer is defined as an integer number of MgH2 formula
units and is thus stoichiometric. For the structure models M3
and M4, the optimized 1.5 nm nanocluster was inserted into
the carbon scaffold, and the calculations were done with the
periodic model (i.e., no vacuum space was introduced in the
model). Similarly, for the M5 structure model, we have used
our previously reported 1.4 nm nanowire.5 In order to prevent
possible direct reaction/interaction (because of the unsaturated
broken C bonds) between the AC and MgH2, we have
saturated all open bonds in the cleaved layers and scaffolds of
AC by H atoms. The passivation of carbon surface dangling
bonds with hydrogen does not correspond to a real situation.
However, it is worth noting that MgH2 nanoparticles are
formed by direct hydrogenation of Bu2Mg inside the pores of a
carbon scaffold. Such a procedure could result in a saturation of
carbon dangling bonds by hydrogen simultaneously with MgH2
synthesis. The numbers of broken bonds in M1, M2, M3, M4,
and M5 models are 6, 12, 10, 16, and 11, respectively, and
corresponding supplementary H atoms are added. Hence, the
total number of atoms involved in the M1, M2, M3, M4, and
M5 models are 239 (128 C, 35 Mg, 76 H), 373 (256 C, 35 Mg,
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⎛
⎞
1
ΔE = ⎜E Hvac + E Hmol ⎟ − (Enano)
⎝
⎠
2
82 H), 386 (32 Mg, 74 H, 280 C), 424 (32 Mg, 88 H, 304 C),
and 386 (27 Mg, 65 H, 294 C), respectively.
In all these structure models, the calculated Mg−H distances
versus number of bonds (see Figure 8) for the optimized
(2)
where EHvac and Enano refer to the energy of the nano-object/
models with and without a H vacancy and EHmol is the total
energy of a free H2 molecule. In all these studied models, H is
situated in four different chemical environments: the center of
the model (H1), adjacent to the center (H2), near the interface
(H3), and at the interface (H4), see Figure 9. The calculated
Figure 8. Calculated interatomic distances between Mg−H (pair
distribution function, PDF) in the optimized M1, M2, M3, M4, and
M5 models. The corresponding Mg−H distance in the bulk phase
(1.95 Å) is marked as a dotted vertical line.
Figure 9. Hydrogen sites used to calculate the hydrogen site energies
are marked as H1 (center of the sandwich; 20 kJ/mol), H2 (adjacent
to the center; 43.10 kJ/mol), H3 (near to the interface; 80.43 kJ/mol),
and H4 (at the interface; 108.4 kJ/mol). The corresponding value for
the bulk MgH2 phase is 83 kJ/mol. Total number of atoms involved in
this model is 373 (256 C, 35 Mg, 70 H, and 12 UBBH). The structure
is magnified two times along the x axis for better view.
models indicate that the values were scattered compared to
those in the corresponding bulk phase (Mg−H distance in the
bulk phase is 1.95 Å). In particular, a number of Mg−H bonds
have longer bond distances than that in the corresponding bulk
material. This type of structural arrangement is expected in
nano and amorphous phases without three-dimensional
crystallinity, owing to reduction in coordination number of
atoms. It should be noted that, in all these structure models, the
initial MgH2 structure is completely rearranged even in the
central region. In general, we found that the inner part of the
nanowhisker/nanoclusters has almost the same H−Mg−H
atomic arrangement as that in the bulk α-MgH2 phase.57 This
finding clearly indicates that the scaffold materials are having
different atomic arrangement than that of the free nanophase
materials and hence one can expect the thermodynamic
behavior of scaffolds to be different from that in the bulk and
nanophases. The atomic arrangement of these nano-objects in
the scaffold materials is close to that of an amorphous structure.
A similar situation is also present in scaffolded NaAlH4.17 It is
important to recall that recent work by Lohstroh et al.17 found
that cycled material consisting of NaAlH4 nanoconfined in
activated carbon showed equilibrium sorption properties
considerably different from those of Ti-doped and ball-milled
material. The solubility of hydrogen was greatly enhanced, and
the two-step behavior vanished.17 This is the first experimental
evidence that thermodynamic effects may also be observed in
such systems. It is a challenging task for experimentalists to
identify any rearrangement in the structure when particles are
incorporated into scaffold materials. In these situations,
simulations can be helpful in order to understand and explain
such unusual behaviors, and our pair distribution analysis shows
that the atomic distribution in the scaffolded MgH2 is similar to
that of the amorphous state.
In order to substantiate this observation, we have calculated
the H site energy (HSE; ΔE) in these nanophases. The H site
energy is calculated in the following manner:
Table 2. Calculated Bond Overlap Population (BOP) and
Hydrogen-Site Energy (in kJ/mol) for the Bulk and M1−
M5a
model
BOP
bulk α-MgH2
M1
M2
M3
M4
M5
0.64
0.40−0.78
0.45−0.87
0.36−0.82
0.38−0.75
0.33−0.78
HSE (in kJ/mol)
83
H1:
H1:
H1:
H1:
H1:
25;
22;
24;
26;
23;
H2:
H2:
H2:
H2:
H2:
43;
43;
48;
45;
48;
H3:
H3:
H3:
H3:
H3:
83;
80;
88;
83;
88;
H4:
H4:
H4:
H4:
H4:
102
108
102
105
101
a
M1: overlayers of MgH2 in amorphous carbon (AC) substrate; M2:
AC−MgH2−AC (sandwich/multilayer) model; M3: MgH2 in the
carbon scaffold; M4: MgH2 nanoparticle placed in closed scaffolds;
and M5: MgH2 nanowire wrapped by carbon scaffolds. H position in
the center of the model (H1), adjacent to the center (H2), near the
interface (H3), and at the interface (H4).
HSE for the bulk phase is 83 kJ/mol (see Table 2). The
calculated HSE for models M1−M5 are scattered in a wide
energy range (see Table 2), which is highly dependent upon
the environment of the H sites. In general, the calculated HSE
for the H1 site for different structure models are almost similar,
being several orders of magnitude smaller than the HSE of the
bulk phase. This finding clearly indicates that the energy
required to remove H from the center of the scaffolded material
is much smaller than that from the bulk phase. It should be
noted that, in free nanophase materials (either cluster or
whiskers), it is easier to remove H from the surface than from
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the inner part of the nano-object.57 In contrast, in the
scaffolded materials, removal of H from the center of the
material is much easier than from other lattice sites. This clearly
indicates that the scaffolded materials behave differently from
the free nanophases as well as from bulk materials. In all these
studied systems, the HSE value of H1 is always lower than that
in H2, H3, and H4, and the magnitude of the HSE values vary
in the following sequence H1 < H2 < H3 < H4. The calculated
higher HSE value for the H4 site indicates that the C/MgH2
interface plays a significant role on the decomposition process.
In order to obtain a better understanding of the bonding
interaction between the constituents, the bond overlap
population (BOP) values were calculated on the basis of
Mulliken population analysis. The BOP values can provide
useful information about the character of the bonding
interaction between atoms. A high BOP value indicates a
strong covalent bond, while a low BOP value indicates an ionic
interaction. For the practical use of MgH2 as hydrogen-storage
materials, the Mg−H bonds should be weakened. The
calculated BOP values for the studied structure models are
listed in Table 2. Similar to the HSE values, the calculated BOP
values are also scattered in a wide range (see Table 2 and
Figure 10). Due to the ionic interaction, the calculated BOP
desorption process in the carbon scaffolds are under
investigation. The results will be published in a forthcoming
article.
■
CONCLUSIONS
In summary, we have systematically studied changes in
formation energy with respect to the size of a MgH2 particle.
We have predicted that the critical particle size for the MgH2
nanocluster is less than 2.2 nm. The calculated formation
energy as a function of particle size revealed that the
nanoparticles of MgH2 are more unstable than the corresponding decomposed phases. From experimental SANS studies, we
have demonstrated that it is possible to incorporate nanoobjects into the carbon scaffolds. Stable amorphous carbon
structures have been successfully generated with two different
approaches and have been used as a template to construct the
scaffold MgH2 material. Using five different structure models,
we studied the physical and chemical changes in the scaffold
MgH2 materials. The calculated hydrogen-site energy as well as
bond overlap analysis revealed that the bonding interactions in
the inner part of the scaffold materials are considerably weaker
than those at the AC/MgH2 interface. As a result, one can
expect that the removal of hydrogen from the center of the
scaffold is easier than that from the bulk or from the interface of
the scaffold.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail: Ponniah.Vajeeston@kjemi.uio.no.
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
This work was funded by European Union seventh framework
program under the ”NanoHy” (grant agreement no. 210092)
project. P.V. gratefully acknowledges the Research Council of
Norway for providing the computer time at the Norwegian
supercomputer facilities and Fichtner for useful discussions.
■
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