Analysis of hydrogen and deuterium absorption kinetics in Pd nanofilms

Article abstract of DOI:10.1016/S0925-8388(00)01128-2

An electrochemical quartz crystal microbalance was used to study the kinetics of hydrogen or deuterium absorption in a Pd nanofilm. The Pd film in a thickness of 120 nm was deposited on a quartz crystal. Hydrogen was electrolytically charged into the film and monitored by the frequency shift from the microbalance. The kinetics curves of hydrogen or deuterium absorption in the nano-scaled Pd thin film were obtained at reduction potentials ranging from -1.2 to -1.5 V. Based on the Fick's law, the diffusion rates of hydrogen or deuterium in the film were slower than those in bulk Pd by several orders of magnitude. It is proposed that surface effect was the dominant factor for hydrogen/deuterium absorption in the nano-scaled Pd film. By modifying the Fick's law with a first order reaction equation, the kinetics could be interpreted by a surface-controlled process.

Full text of DOI:10.1016/S0925-8388(00)01128-2

Journal of Alloys and Compounds 311 (2000) 283–287
L
www.elsevier.com/locate/jallcom
Analysis of hydrogen and deuterium absorption kinetics in Pd nanofilms
S.-Y. Liua, Y.-H. Kaob, Y. Oliver Sub, T.-P. Pernga ,
*
aDepartment of Materials Science and Engineering, National Tsing Hua University, Hsinchu, Taiwan
bDepartment of Chemistry, National Taiwan University, Taipei, Taiwan
Received 20 May 2000; accepted 19 June 2000
Abstract
An electrochemical quartz crystal microbalance was used to study the kinetics of hydrogen or deuterium absorption in a Pd nanofilm.
The Pd film in a thickness of 120 nm was deposited on a quartz crystal. Hydrogen was electrolytically charged into the film and
monitored by the frequency shift from the microbalance. The kinetics curves of hydrogen or deuterium absorption in the nano-scaled Pd
thin film were obtained at reduction potentials ranging from 21.2 to 21.5 V. Based on the Fick’s law, the diffusion rates of hydrogen or
deuterium in the film were slower than those in bulk Pd by several orders of magnitude. It is proposed that surface effect was the
dominant factor for hydrogen/deuterium absorption in the nano-scaled Pd film. By modifying the Fick’s law with a first order reaction
equation, the kinetics could be interpreted by a surface-controlled process.
2000 Elsevier Science S.A. All rights reserved.
Keywords: Pd; Nanofilm; EQCM; Hydrogen; Diffusion; Deuterium; Surface effect
1. Introduction
neglected in a bulk diffusion-controlled process [15].
However, when the thickness of membrane or hydrogen
pressure is decreased, the permeation rate becomes slower
than that extrapolated from the bulk permeation process.
The non-linear decay phenomenon of diffusion rate in thin
films is considered as being caused by the surface effect.
For hydrogen absorption in a Pd thin film, the surface
effect and diffusion behavior are similar to those in
hydrogen permeation through a membrane sheet. However,
when the film thickness is reduced to the nano-scale,
surface process becomes more important, and hydrogena-
tion of the thin film may also change the stress state of the
film. Therefore, the surface effect or hydrogen diffusion
needs to be modified to explain the hydrogen absorption
kinetics in Pd nanofilms. In this study, hydrogen or
deuterium absorption kinetics in Pd nanofilms was studied
using an electrochemical quartz crystal microbalance
(EQCM) [16]. By modifying the Fick’s law, a first-order
saturation equation was introduced to describe the hydro-
gen absorption kinetics. The surface effect on hydrogen
absorption in the nanofilm is discussed.
Palladium and Pd alloys have been widely used as
catalyst [1,2], separator [3,4], or sensor [5,6] for hydrogen
since the hydrogenation properties of Pd were disclosed in
1886 by Graham. Among them, many applications are
correlated with basic properties such as solubility and
diffusivity of hydrogen in Pd films. Unfortunately, most of
the database are established for bulk Pd [7–10], not for Pd
films. There have been very few reports on the characteris-
tics of hydrogen in Pd thin films [11,12]. It has been noted
that the diffusivity of H in Pd thin films is smaller than that
in bulk Pd at room temperature. Similar results have also
been found for hydrogen gas permeation through Pd
membranes in different thicknesses [13,14]. In a permea-
tion process, the gas molecules are first physically ad-
sorbed and chemically absorbed on the surface, and then
dissociate into atoms at the high-pressure side. Sub-
sequently, the atoms diffuse through the membrane that
obeys Fick’s law. Finally, the gas atoms recombine and
desorb from the surface at the lower pressure side. The
rate-limiting step could be either the surface reaction or
bulk diffusion. In general, when the membrane thickness is
large enough, the diffusion process would dominate the
permeation rate of hydrogen. Surface effects can always be
2. Experimental
The as-received commercial product, 10 MHz polished
AT-cut quartz crystal in a thickness of 166 mm, was used
as the substrate. Both sides of the quartz crystal came with
*Corresponding author. Fax: 1886-3-572-3857.
E-mail address: tpp@mse.nthu.edu.tw (T.-P. Perng).
0925-8388/00/$ – see front matter
PII: S0925-8388(00)01128-2
2000 Elsevier Science S.A. All rights reserved.

284
S.-Y. Liu et al. / Journal of Alloys and Compounds 311 (2000) 283–287
Fig. 1. Schematic diagram of the EQCM and the quartz crystal electrode.
Fig. 2. Hydrogen absorption kinetics curves in the Pd nanofilm at various
potentials. The data points are also fitted with different surface constants.
a coating of gold at the center in a thickness of 100 nm and
a diameter of 0.5 cm. Each was linked with a 2-mm wide
gold line connected to the oscillation circuits. A Pd layer
was then deposited on one side of the gold by magnetron
sputtering. The thickness of the Pd film identified by a
profilometer was approximately 120 nm.
A schematic diagram for the EQCM set-up is shown in
Fig. 1. The EQCM system consisted of a 5-ml three-
compartment glass cell and resonant oscillation circuits. A
0.1-M KOH solution prepared with light or heavy water
was used as the electrolyte. The counter and reference
electrodes were Pt and Ag/AgCl, respectively, and the Pd
film coated on the quartz crystal was used as the working
electrode. The opposite side of the quartz crystal without
the Pd coating was exposed to air. The electrolyte was
de-aerated by bubbling of nitrogen gas to eliminate oxygen
prior to and during the test.
2423 Hz, was caused by the synergistic effects of mass
change and the stress induced by hydrogen absorption
[16], the frequency shift resulted from the stress effect was
2213 Hz. A compressive stress was then calculated to be
21071 MPa based on EerNisse’s equation [18], close to
the value reported by Cheek and O’Grady [19].
The kinetics curves of frequency shift induced by
hydrogen and deuterium absorption at various potentials
are shown in Figs. 2 and 3, respectively. The potentials
were all located in the hydrogen reduction region to ensure
that hydrogen could be charged into the Pd film. The more
negative was the applied potential, the more rapid was the
absorption rate of hydrogen or deuterium in the Pd thin
film. The equilibrium values for all kinetics curves at
different potentials were about the same.
A typical electrochemical reaction for hydrogen dis-
solved in Pd is described as:
In order to know the reduction potential range for
hydrogen and to estimate the amount of hydrogen or
deuterium absorbed in the Pd film, the cyclic voltammetry
was set to scan from 0 V to 21.5 V, and then back to 0 V
at a rate of 5 mV/s. The signals of frequency and current
from the electrodes were transferred to a personal com-
puter through an A/D–D/A interface card.
xH1 1 xe2 1 Pd → Pd Hx
(1)
3. Results and discussion
The loops of electrochemical current and frequency shift
obtained by cyclic voltammetry and the information that
can be derived from the loops have been presented
previously [16]. Briefly, the occurrence of hydrogen
absorption–desorption in the Pd film could be observed
from these curves. Based on the integrated oxidation
current and charge conservation law, the amount of
hydrogen stored in the film was 181 ng, equivalent to a
concentration of H/Pd50.67. According to Sauerbrey’s
equation [17], the frequency shift resulted from the mass
effect was 2210 Hz. Because the total frequency shift,
Fig. 3. Deuterium absorption kinetics curves in the Pd nanofilm at
various potentials. The data points are also fitted with different surface
constants.

S.-Y. Liu et al. / Journal of Alloys and Compounds 311 (2000) 283–287
285
2DH(2n11)2p2
`
where the saturation value for x is about 0.7 at room
temperature [20]. The evolution reaction for hydrogen gas
molecules on the Pd surface is:
8
p2
1
]
]
t
C(t)5C 12
O
exp
S
D
G
(8)
F
(2n11)2
4l2
0
0
2H1 1 2e2 → H2
(2)
With hydrogen diffusivity in bulk Pd being typically in
the order of |1027 cm2 /s at room temperature [8], the
diffusivities of hydrogen deduced from the curves in Figs.
2 and 3 are all lower by four orders of magnitude. A
diffusion barrier on the surface of the film might be the
cause for the low effective diffusivities.
Before saturation, most hydrogen atoms are absorbed in
the Pd film and few of them are recombined. According to
the Nernst equation, the fugacity fH of hydrogen is an
2
exponential function of overpotential h. Under the equilib-
rium condition,
To study the surface effect, several theories and experi-
ments have been proposed to interpret the interaction of
hydrogen with the surface layer in perfect single crystals
and the reconstruction of free surface owing to hydrogen
adsorption [23,24]. However, variation of other parameters
including the geometric roughness, poisoning by other
gases, dissociation rate of hydrogen gas, formation of an
electrical double layer in the electrolyte, and the charging
pressure or voltage in the gas or electrolyte, respectively,
etc., may increase the difficulty to identify the surface
properties. The surface effect of a Pd film in the electrolyte
involves at least surface reconstruction [23,24] and forma-
tion of an electrical double layer in front of the Pd surface
[25]. Due to the surface reconstruction, hydrogen can be
absorbed into the subsurface. Addition of hydrogen to the
sub-surface will result in further reconstruction of the
surface structure, and the corresponding energy barrier will
be increased as well. The formation of an electrical double
layer, mainly caused by adhesion of solvent molecules,
specifically adsorbed anions, and solvated cations, ob-
structs the hydrogen flowing to the surface.
fH 5 exp(22hF/RT)
(3)
2
where R and T are gas constant and temperature, respec-
tively, and F is the Faraday’s constant.
Bockris and Subramanyan have reported that the fugaci-
ty in internal cavities is dependent on the mechanism of
hydrogen evolution and can be raised by several orders of
magnitude in the high-pressure region [21]. From Figs. 2
and 3, the hydrogen absorption rate in the Pd film is
increased when the potential is increased. Since hydrogen
fugacity is exponentially proportional to the applied nega-
tive potential, hydrogen absorption rate is higher at higher
fugacities. The change of hydrogen absorption rate slowed
down as the potential was high enough.
In general, Fick’s second law is used to describe the
kinetics of hydrogen or deuterium absorption:
≠C
≠t
≠2C
]
5 D
(4)
H ≠x2
The initial and boundary conditions in the Pd film coated
on a substrate are given as:
Figs. 4 and 5 show the schematic illustrations for
different saturation processes of hydrogen occlusion in
thick and nano-scaled Pd films, respectively. For a thick
film, a concentration gradient is built through the thickness
based on Fick’s second law to drive hydrogen diffusion
until saturation is reached. The initial surface concentration
is dependent on the applied voltage. To reach equilibrium,
it takes a much longer time for diffusion in the bulk and to
C(x, t) 5 C0 x 5 l, t $ 0
(5)
(6)
≠C(x, t)
]
5 0 x 5 0, t $ 0
≠x
where C(x, t) is the hydrogen concentration at time t (t$0)
and a distance x (0#x#l) from the interface between the
film and the substrate, l is the film thickness; DH is the
diffusivity of hydrogen in Pd, and C0 is the hydrogen
concentration on the Pd surface. The solution of the
diffusion equation in a plane sheet can be obtained as: [22]
`
4
p
(21)n
2n 1 1
(2n 1 1)p
]
Scos D
x
C(x, t) 5 C 1 2
O
F
0
2l
0
2 DH(2n 1 1)2p2
4l2
3 exp
t
(7)
S
DG
From the EQCM measurement, it is noted that each data
point of the frequency shift can be used to calculate the
average hydrogen concentration in the film. From Eq. (7),
by integration to the whole thickness, the average con-
centration across the thickness is given as:
Fig. 4. Hydrogen concentration profiles during absorption in a Pd thick
film. C0 is the initial surface concentration.

286
S.-Y. Liu et al. / Journal of Alloys and Compounds 311 (2000) 283–287
orientation, film geometry, and grain size, etc., will also
influence the absorption rate. In this study, the surface
reaction constant in light water was similar to that for
heavy water at 21.2 V. At higher applied potentials, the
increase in k in heavy water became faster in light water. It
implies that the absorption rate of deuterium in Pd
nanofilm was faster than that of hydrogen.
In classical theory, the diffusivity ratio of hydrogen to
deuterium in most metals is Œ2] . It has been frequently
observed, however, that reversed isotope dependence is
associated with Pd over a broad temperature range from
260 to 2008C [8,26,27]. This inversion has been attributed
to a larger activation energy for hydrogen diffusion [8,28].
In the present study, the surface reaction for deuterium also
appeared to be faster than for hydrogen. The reason for the
absorption rates or higher surface constants for deuterium
requires further study.
Fig. 5. Hydrogen concentration profiles during absorption in
nanofilm. C0 is the initial surface concentration.
a Pd
finish the occlusion so that the surface effect can be
ignored. For a nanofilm, however, the thickness of the film
is small enough, either the surface barrier or repulsion
from the occluded hydrogen in the sublayer could be the
rate-limiting step of hydrogen absorption into the nanofilm.
Therefore, the diffusion time within the film can be
neglected, thus, the concentration profile is treated as a
constant value, as shown in Fig. 5. The repulsion from the
occluded hydrogen in the sublayer involves the stress
induced by lattice expansion, release of reaction heat, and
repulsive force between hydrogen atoms.
The influence of surface barrier and repulsion from the
occluded hydrogen is not included in Eqs. (7) and (8). If
both of them are considered, the average concentration in
the film can be assumed to increase exponentially until the
saturation is reached, which is described as:
4. Conclusion
The kinetics of hydrogen/deuterium absorption in a
nano-scaled Pd film has been studied by means of EQCM.
The surface effect was considered to be the dominant
factor in delaying the hydrogen/deuterium absorption rate
in the Pd nanofilm. The absorption kinetics models for
thick and nanoscaled Pd films are proposed to interpret the
hydrogen/deuterium absorption behavior without and with
the surface effect, respectively. A first-order reaction is
proposed to interpret the surface-controlled absorption in
the nanoscaled Pd film. The surface reaction constants are
obtained for different applied voltages and electrolytes.
The absorption rates as well as the surface reaction
constants of deuterium were larger than those of hydrogen.
dC(t)
]
5 k(C0 2 C(t))
(9)
dt
or
C(t) 1 C0(1 2 e2kt
Acknowledgements
)
(10)
This work was supported by the National Science
Council of ROC under Contract Nos. NSC 88-2216-E-007-
048 and NSC 87-TPC-M-002-001.
where k (unit: s21) stands for the surface reaction constant
and C0 is the surface concentration (which is also the
saturation concentration in the Pd film).
If the surface reaction is the rate-determining step for
hydrogen absorption, the diffusion term in the nanofilm
can be neglected, the kinetics curves can be fitted with Eq.
(10) by adjusting the values of surface reaction constant.
For example, in Fig. 2, neglecting the stress effect and if
the saturation concentration is substituted with the terminal
frequency shift 2415 Hz for 21.3 V, k is calculated to be
0.16. The fitted curves for hydrogen and deuterium absorp-
tion along with the calculated surface reaction constants
are also shown in Figs. 2 and 3, respectively. It is noted
that k increases with the applied potential. In effect, k is
affected by not only the applied potential but also other
factors such as electrolyte, composition, ambient tempera-
ture, or applied stress. The surface roughness, grain
References
[1] V.M. Gryaznov, Platinum Met. Rev. 36 (1992) 70.
[2] M.J. Cole, Platinum Met. Rev. 12 (1981) 25.
[3] F.A. Lewis, X.Q. Tong, R.V. Bucur, Platinum Met. Rev. 35 (1991)
138.
[4] Y.K. Cho, K. Han, K.H. Lee, J. Membrane Sci. 140 (1995) 219.
[5] V.I. Anisimkin, I.M. Kotelyanskii, P. Verardi, E. Verona, Sensors and
Actuators B 23 (1995) 203.
[6] R.C. Thomas, R.C. Hughes, J. Electrochem. Soc. 144 (1997) 3245.
[7] F.A. Lewis, The Palladium Hydrogen System, Academic Press, New
York, 1967.
¨
[8] J. Volkl, G. Wollenweber, K.H. Klatt, G. Alefeld, Z. Naturforsch 26
(1971) 922.

S.-Y. Liu et al. / Journal of Alloys and Compounds 311 (2000) 283–287
287
¨
[9] E. Wicke, H. Brodowsky, in: G. Alefeld, J. Volkl (Eds.), Hydrogen
[20] Y. Fukai, The Metal-Hydrogen System, Springer, New York, 1993.
[21] J.O’M. Bockris, P.K. Subramanyan, Electrochim. Acta 16 (1971)
2169.
[22] J. Crank, The Mathematics of Diffusion, Oxford University Press,
London, 1975.
[23] B.-S. Kang, K.-S. Sohn, Phys. B 205 (1995) 163.
[24] B.-S. Kang, K.-S. Sohn, Phys. B 217 (1996) 160.
[25] A.J. Bard, L.R. Faulkner, Electrochemical Methods, John Wiley and
Sons, Singapore, 1980.
in Metals II, Springer-Verlag, Berlin, 1978.
[10] R.V. Bucur, E. Indrea, Acta Metall. 35 (1987) 1325.
[11] Y. Li, Y.-T. Chen, Int. J. Hydrogen Energy 21 (1996) 281.
[12] H. Hagi, Mater. Trans. JIM 31 (1990) 954.
[13] E. Serra, M. Kemali, A. Perujo, D.K. Ross, Metall. Trans. A 29A
(1998) 1203.
[14] A. Khan, K.J. Dietz, F.G. Waelbroeck, P. Wienhold, J. Nucl. Mater.
77 (1978) 337.
[15] C.-L. Yu, T.-P. Perng, Acta Metall. 39 (1991) 1091.
[16] S.-Y. Liu, Y.-H. Kao, Y. Oliver Su, T.-P. Perng, J. Alloy Comp.
293–295 (1999) 468.
[17] G. Sauerbrey, Z. Phys. 155 (1959) 206.
[18] E.P. EerNisse, J. Appl. Phys. 43 (1972) 1330.
[19] G.T. Cheek, W.E. O’Grady, J. Electroanal. Chem. 277 (1990) 341.
[26] C.-T. Lihn, C.-C. Wan, T.-P. Perng, J Appl. Electrochem. 25 (1995)
61.
[27] G. Bohmholdt, E. Wicke, Z. Physik. Chem. N.F. 56 (1967) 133.
[28] S. Majorowski, B. Baranowski, J. Phys. Chem. Solids 43 (1982)
1119.