State of Hydrogen in Idealized Carbon Slitlike Nanopores at 77 K
Piotr Kowalczyk,*
,²
Robert Holyst,
²
Artur P. Terzyk,*
,‡
and Piotr A. Gauden
‡
Department III, Institute of Physical Chemistry, Polish Academy of Science, Kasprzaka Str. 44/52,
01-224 Warsaw, Poland, and Physicochemistry of Carbon Materials Research Group,
Faculty of Chemistry, Nicolaus Copernicus UniVersity, 7 Gagarina Str., 87-100 Torun ˜ , Poland
ReceiVed NoVember 11, 2005. In Final Form: December 24, 2005
The purpose of this letter is to clarify recent findings and answer to the question: “What is the state of hydrogen
in carbon slitlike pores at 77 K?” For this purpose, we determined the volumetric density of hydrogen in idealized
carbon pores of molecular dimension at 77 K and pressure up to 1 MPa. We used quantum corrected grand canonical
Monte Carlo simulation. We recognized the highest volumetric density of confined hydrogen (around 71% of hydrogen
liquid at boiling point) for effective pore width 5.6 Å (H* ) 3.04) in the considered pressure range. Our computational
results are in agreement with the calculations performed by Wang and Johnson and Rzepka et al. In contrast, we did
not observe the high volumetric density of hydrogen in slitlike carbon pores exceeding the density of hydrogen liquid
at the boiling point as was reported by Jagiello and Thommes. Moreover, we obtained qualitative agreement between
the simulation results and some experimental findings reported by Nijkamp.
In light of the recent growing interest in hydrogen storage and
fuel cell applications, it is necessary to develop deep understanding
of the mechanism of hydrogen adsorption on carbonaceous
materials treated as an effective and potential storage medium.
The purpose of this letter is to determine the volumetric density
of hydrogen in idealized carbon slitlike pores of molecular
dimensions at 77 K and pressure up to 1 MPa. This property of
confined hydrogen is critical for adoption of carbonaceous
materials composed of slitlike nanopores (i.e., activated carbons,
activated carbon fibers, and others) as an efficient adsorbent for
hydrogen storage. The high volumetric density of hydrogen in
porous material reduces the size of thank and favorable physical
adsorption overcompression method. The recent experimental
and computational results show a scatter. This scatter brings us
to the current study. Since the volumetric density of hydrogen
fluid in nanopores is not directly measured by experiment, we
concentrate on the theoretical reports. Rzepka et al.
1
reported
volumetric density of hydrogen in idealized carbon slitlike
nanopores at 77 K and pressures up to 30 MPa. The authors used
standard grand canonical Monte Carlo simulation (GCMC)
neglecting the quantum effects for fluid-fluid and solid-fluid
interactions. For idealized carbon slitlike pores of width 10 and
7 Å and at 1 MPa, the values of the volumetric density of hydrogen
fluid were around 52 and 45 g L
-1
, respectively (see Figure 7
in ref 1). Wang and Johnson
2
performed the path integral grand
canonical Monte Carlo simulations (PIGCMC) of hydrogen in
idealized carbon slitlike pores at 77 K up to 10 MPa. The authors
reported the volumetric density of hydrogen fluid 41, 62, 59, and
50 g L
-1
at 10 MPa for pore widths 6.2, 9.2, 12.3, and 20.5 Å,
respectively (see Figure 2 in ref 2). In another study, Jagiello and
Thommes
3
reported the density of hydrogen at 77 K up to 0.1
MPa in carbon micropores of different sizes. The authors adopted
nonlocal density functional theory (NDFT) for classical fluids
neglecting quantum effects for fluid-fluid and solid-fluid
interactions. Moreover, the authors used nonoptimized Lennard-
Jones parameters without their numerical values.
3
According to
this work, the highest volumetric density of hydrogen at 77 K
and 0.1 MPa equal to 40 mmol cm
-3
(i.e., 80.6 g L
-1
) was
observed for the pore having the effective width 3 Å (see Figure
1 in ref 3). This Value exceeds density of hydrogen liquid at the
boiling point (T ) 20.268 K and F) 71 g L
-1
). In other words,
the supercritical hydrogen fluid is in liquid state in the smallest
carbon slitlike nanopores at 77 K.
From this short summary of recent reports we see that the
answer to the question “What is the state of hydrogen in carbon
slitlike pores at 77 K?” is a timely and controversial problem.
In a series of works by Levesque,
4,5
Johnson et al.,
2,6-8
Tanaka
et al.,
9-13
Kowalczyk et al.,
14
and others, the importance of the
quantum effects at 77 K and room temperature were recognized.
Generally, the adsorption of quantum molecules is smaller than
the classical ones due to Heisenberg’s uncertainty principle. The
quantum correction enlarges an effective diameter of a molecule
in comparison to its classical counterpart and therefore reduces
adsorption in nanopores.
For atomic systems, a simple test of the classical hypothesis
is obtained by computing the de Broglie thermal wavelength Λ,
defined as
15
here ) (k
b
T)
-1
, p ) h/2π, m is the mass of an atom, h denotes
the Planck’s constant, k
b
is the Boltzmann’s constant, and T is
* Corresponding author.
²
Polish Academy of Science.
‡
Nicolaus Copernicus University.
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Λ ) (2πp
2
/m)
1/2
(1)
1970 Langmuir 2006, 22, 1970-1972
10.1021/la053041n CCC: $33.50 © 2006 American Chemical Society
Published on Web 01/25/2006