Combinatorial Search for Optimal Hydrogen-Storage Nanomaterials Based on

Polymers

Hoonkyung Lee,1 Woon Ih Choi,1 and Jisoon Ihm1, ∗

1
Department of Physics and Astronomy, FPRD, and Center for Theoretical Physics,
Seoul National University, Seoul 151-747, Korea
arXiv:cond-mat/0608184v1 [cond-mat.mtrl-sci] 8 Aug 2006

(Dated: April 7, 2018)

We perform an extensive combinatorial search for optimal nanostructured hydrogen storage mate-
rials among various metal-decorated polymers using first-principles density-functional calculations.
We take into account the zero-point vibration as well as the pressure- and temperature-dependent
adsorption-desorption probability of hydrogen molecules. An optimal material we identify is Ti-
decorated cis-polyacetylene with reversibly usable gravimetric and volumetric density of 7.6 weight
percent and 63 kg/m3 respectively near ambient conditions. We also propose “thermodynamically
usable hydrogen capacity” as a criterion for comparing different storage materials.

PACS numbers: 68.43.Bc, 71.15.Nc

Hydrogen storage is a crucial technology to the devel- T, and k is the Boltzmann constant. Here, f per site is
opment of the hydrogen fuel-cell powered vehicles [1, 2]. reduced to
Recently, nanostructured materials receive special at- P
lgl el(µ−εl )/kT
tention because of potentially large storage capacity f = Pl=0 l(µ−εl )/kT
, (1)
(high gravimetric and volumetric density), safety (solid- l=0 gl e
state storage), and fast filling and delivering from the where εl is the adsorption energy per H2 molecule when
fuel tank (short molecular adsorption and desorption the number of adsorbed molecules is l and gl is the multi-
time) [3, 4, 5]. However, when the thermodynamic be- plicity (degeneracy) of the configuration for given l. The
havior of the gas under realistic environments is taken summation is over all different configurations up to the
into account, the usable amount of hydrogen with these maximum number (Nmax ) of adsorbed molecules.
nanomaterials falls far short of the desired capacity for Another important thermodynamic feature in the H2
practical applications and search for novel storage ma- adsorption energetics is the zero-point vibrations of the
terials continues worldwide [6, 7, 8, 9]. It is to be em- H2 molecules with respect to the host metal atom (e.g.
phasized that hydrogen storage in nanostructured mate- Ti) on which H2 ’s sit. (The zero-point vibration within
rials utilizes the adsorption of hydrogen molecules on the the H2 molecule, on the other hand, exists in both gas
host materials and its thermodynamic analysis is distinct and adsorbed states and cancels out in the calculation
from that of metal or chemical hydrides. Each adsorption of f.) The actual energy εl to be used in Eq. (1) is the
site on the nanomaterial behaves more or less indepen- static adsorption energy (usually calculated and reported
dently and the probability of the hydrogen adsorption in the literature) minus the zero-point vibration energy
follows the equilibrium statistics which is a smooth func- which sums up to as large as 25 % of the static adsorption
tion of the pressure and temperature. There is no sharp energy according to our calculation, a value not to be
thermodynamic phase transition between the gas and the neglected at all.
adsorbed state of H2 , in contrast to the case of metal or Considering these thermodynamic aspects, we paid at-
chemical hydrides where an abrupt phase transition oc- tention to the fact that simple polymers decorated with
curs at well-defined pressure at a given temperature [10]. light transition metal atoms may be superior to other re-
With this caveat, a general formalism applicable to the cently reported nanomaterials such as Ti-decorated nan-
hydrogen adsorption on nanomaterials was derived in the otubes [11] or Sc-decorated fullerenes [12] in terms of
present study from the grand partition function with the usable gravimetric and volumetric density. The basi-
chemical potential determined by that of the surround- cally one-dimensional nature of polymers is advantageous
ing H2 gas acting as a thermal reservoir. As each site for compact storage, with a very small number of car-
can adsorb more than one H2 molecule, information on bon atoms needed to accommodate a decorating metal
the multiple adsorption energy is necessary. (The situ- atom which attracts hydrogen molecules. Furthermore,
ation is analogous to the O2 adsorption and desorption entangled chains of long polymers form a solid struc-
on hemoglobin which can bind up to 4 O2 molecules.) ture ideal for safe handling of the hydrogen. A sys-
In equilibrium of the H2 molecules between the adsorbed tematic approach was employed to search for optimized
and desorbed (gas) states, the occupation (adsorption) high-capacity hydrogen storage nanostructures based on
number f is obtained from f=kT ∂lnZ/∂µ, where Z is the polymers. For the supporting backbone materials, we
grand partition function, µ is the chemical potential of first considered trans- and cis-polyacetylene (among lin-
H2 in the gas phase at given pressure p and temperature ear carbon chains), polyaniline, polyphenol, poly para
 2

phenylene, and poly ether ether ketone (chains of hexag-

onal rings), and polypyrrole and polythiophene (chains of
pentagonal rings). For decorating transition metals, we
initially chose all light transition metal elements starting
from Sc in the periodic table. Various possible adsorption
sites of the transition metal atoms were tested for each
case. The maximum number of adsorbed H2 molecules
also varied (up to six) at different sites. In short, the
total combinatorial number in our study exceeded one
thousand. In practice, we were able to reduce the number
considerably by eliminating obviously unfavorable cases
using a few test calculations of the adsorption energy
and structural stability. Many kinds of pentagonal and
hexagonal ring chains were ruled out. For decorating
atoms, only Sc, Ti, and V atoms passed the first-round
candidate screening test. Such a combinatorial search
for the optimized material and geometry yielded a few
promising nanostructures for hydrogen storage.
We employed spin-polarized first-principles electronic
structure calculations based on the density-functional
theory [13]. The plane-wave based total energy mini- FIG. 1: (color online) Atomic structures of the Ti-decorated
mization [14] with the Vanderbilt ultrasoft pseudopoten- polymers with the maximum number of H2 molecules at-
tial [15] was performed. The generalized gradient ap- tached to Ti atoms. Green, blue, purple, yellow, and red
dots indicate the carbon atom, titanium atom, nitrogen atom,
proximation (GGA) [16] of Perdew, Burke, and Ernzer- hydrogen atom composing the polymer, and the molecular
hof (PBE) [17] was used in the calculations. The kinetic hydrogen, respectively. (a) cis-polyacetylene with five H2
energy and the relaxation force cutoff were 35 Ry and molecules attached per Ti atom. H2 ’s are shown on both
0.001 Ry/a.u., respectively. For periodic supercell calcu- sides of the (somewhat distorted) polyacetylene plane. In the
lations, the distance between polymers was maintained rest (b)-(f), H2 ’s are shown only on one side of the polymer for
over 10 Å in all cases. visual clarity. (b) trans-polyacetylene with Ti atoms located
out of the plane of the polymer chain. (c) trans-polyacetylene
The best candidate material we found in our search
with Ti atoms in the plane of the chain. (d) polypyrrole with
using the total energy calculations was cis-polyacetylene Ti atoms out of the pentagonal plane. (e) polyaniline with Ti
decorated with Ti atoms whose structure after the H2 atoms in the hexagonal plane. (f) polyaniline with Ti atoms
molecule adsorption is presented in Fig. 1(a). The out of the hexagonal plane.
binding energy of a Ti atom on this polymer is 2.4 eV.
The structure has about 2 wt% higher storage capac-
ity than Ti-decorated trans-polyacetylene. (Since as- Dewar-Chatt-Duncanson coordination or Kubas interac-
synthesized polyacetylene is of cis-type, it is in princi- tion [18, 19, 20]. We found the elongation of H2 molecules
ple possible to attach Ti atoms to cis-polyacetylene al- by ∼10 % through electron back donation from metal d
though trans-polyacetylene is a more stable structure.) orbitals to the antibonding hydrogen s orbitals, which
Nmax for this structure is five and the H2 molecules supports these theories.
are compactly adsorbed on both sides of the polyacety- We chose to present in Fig. 2 the static adsorption en-
lene plane. The molecular formula corresponding to this ergy following the usual practice in the literature [11, 12].
structure is (C4 H4 ·2Ti·10H2 )n . The maximum gravi- After subtracting zero-point vibration energies (25 % of
metric density (Gmax ) is defined by the weight ratio of the static adsorption energy) for all structures, we ob-
10H2 to C4 H4 ·2Ti·10H2 , which is 12 wt% as shown in tained the true dynamic adsorption energy (εl ) to be
Table I. Gmax for other materials is calculated in the used in Eq. (1). For instance, the zero-point vibration
same way. We also present other important polymer ge- energy per H2 molecule for cis-polyacetylene was 0.09
ometries in Fig. 1 with the maximum number of H2 eV for H2 on top of the Ti atom and 0.12 eV for H2 at-
molecules attached to the decorating Ti atoms. The cal- tached to the side [21]. We employed the experimental
culated (static) adsorption energies per H2 as a func- chemical potential in the literature [22] in the calcula-
tion of the adsorption number are presented in Fig. 2 tion of f. The degeneracy factor was approximated by
for easy comparison among different materials. In cis- the number of calculated local energy minima for given
polyacetylene, for example, they are 0.55, 0.58, 0.48, 0.42, l. The largest gl we found was 3 and, since the expo-
and 0.46 eV/H2 for l =1, 2, 3, 4, and 5, respectively. As nential factor el(µ−εl )/kT dominated, gl ’s turned out to
pointed out in previous works, the adsorption of a large give a minor correction to the result. The occupation
number of H2 molecules presumably occurs through the number f as a function of p and T for representative
 3

TABLE I: Hydrogen storage capacity of representative nano-

materials from GGA calculations. PA, polyacetylene; PPY,
polypyrrole; PANI, polyaniline; CNT, carbon nanotube. All
are decorated with Ti except for Sc-decorated C48 B12 . -out
means an out-of-plane configuration described in Fig. 1. Nads
and Ndes are the numbers of attached H2 ’s per site at the con-
dition of adsorption (30 atm-25 ◦ C) and desorption (2 atm-
100 ◦ C), respectively. Nuse is the practically usable number
(Nads −Ndes ) and Nmax is the maximum number of adsorbed
H2 ’s. G and V are gravimetric and volumetric density, re-
spectively.

Materials Nads -Ndes Nuse /Nmax Guse /Gmax Vuse /Vmax

(wt%) (kg/m3 )
cis-PA 5.00-1.84 3.16/5 7.6/12 63/100
PPY 3.00-0.05 2.95/3 4.9/5 33/34
FIG. 2: (color online) Calculated static adsorption (bind- PANI-out 3.00-0.96 2.04/3 4.1/6 31/46
ing) energy per H2 molecule for polymers decorated with Sc,
C48 B12 Sc12 2.68-0.02 2.66/5 4.7/8.8 23/43
Ti, or V atoms. The average binding energy per H2 is plot-
ted up to the maximum number of adsorbed H2 ’s allowed for CNT 1.95-0.35 1.60/3 4.1/7.7 not available
each species. PA, PPY, and PANI stand for polyacetylene,
polypyrrole, and polyaniline, respectively. -out and -in mean
out-of-plane and in-plane configurations as previously shown
in Fig. 1, respectively. storage in the list, better than that of Ti-decorated car-
bon nanotubes [11] or Sc-decorated fullerenes [12]. Note
that 60 % desorption of H2 is achieved here at a tem-
nanomaterials is presented in Fig. 3. The occupation- perature as low as 100 ◦ C, which is considerably lower
pressure-temperature (f-p-T) diagram of the nanomate- than the dissociation temperature of usual metal hy-
rial storage in Fig. 3 is the counterpart of the widely-used
pressure-composition isotherms (PCI) in metal hydride
storage [10]. To obtain the usable amount of hydrogen,
it is necessary to specify p and T at the time of adsorp-
tion (filling) and desorption (delivering from the storage
tank). Since an internationally agreed-upon standard has
not been set up, we propose to use the adsorption con-
dition of 30 atm and 25 ◦ C and the desorption condition
of 2 atm and 100 ◦ C, abbreviated to 30-25/2-100. These
numbers, which may be revised in the future by consen-
sus, are based on information in the literature [23, 24]
and reflect practical situations in gas filling and vehi-
cles operations. 30 atm for adsorption and 1.5 atm for
desorption were used in Ref. 24, but they did not take
advantage of the temperature variation.
We adopted an easily achievable temperature range of
25-100 ◦ C here. Then, f at the condition of 30-25 minus
f at 2-100 is the available number of H2 molecules per
site. These numbers are listed in Table 1. For compar-
ison, the same numbers for the Sc-decorated fullerene
(C48 B12 Sc12 ) [12] and the Ti-decorated carbon nan-
otube [11] are presented as well. We confirm that our
results for the static adsorption energy of these materials
agree with reported values [11, 12]. When converted to
FIG. 3: Occupation number-pressure-temperature (f-p-T ) di-
the gravimetric density, Ti-decorated cis-polyacetylene
agram of the hydrogen storage in representative nanomate-
stores usable H2 molecules of 7.6 wt% out of the maxi- rials. The ranges of the pressure and the temperature cover
mum density of 12 wt%, which is much greater than, say, typical conditions of filling and delivering from the storage
the goal of 6 wt% by the year of 2010 set by the Depart- tank. (a) Ti-decorated cis-polyacetylene. (b) Ti-decorated
ment of Energy (DOE) of US [23]. The Ti-decorated cis- polypyrrole. (c) Sc-decorated C48 B12 . (d) Ti-decorated car-
polyacetylene is the best candidate material for hydrogen bon nanotube.
 4

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gravimetric and volumetric density among nanostruc- http://cnmp.snu.ac.kr:8080/b/Members/hkiee/supporting hydrogen/
tures reported so far. We also propose the f-p-T diagram Requests for further information should be directed to
as a criterion for evaluating usable capacity at ambient the corresponding author (J.I.).
[22] Handbook of Chemistry and Physics, edited by D. R.
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We acknowledge the support of the SRC program Chem. Soc. 127, 14582 (2005).
(Center for Nanotubes and Nanostructured Composites) [26] W. R. Schmidt, Proceedings of the 2001 DOE Hydrogen
Storage Program Review NREL/CP-570-30535.
of MOST/KOSEF and the Korea Research Foundation
Grant No. KRF-2005-070-C00041. Computations are
performed through the support of KISTI.

∗
corresponding author. Email: jihm@snu.ac.kr