Investigation of hydrogen adsorption-absorption on iron by EIS

Article abstract of DOI:10.1016/j.electacta.2007.07.047

This work concerns the interaction between hydrogen and iron in the cathodic potential region. It was motivated by the need for a better understanding of the hydrogen insertion mechanism in metals. Electrochemical deposits of iron with various thicknesses were carried out on a gold substrate and they were characterized by impedance measurements under hydrogen evolution conditions. The processes occurring at the surface and within the iron films deposited on a gold electrode were studied using various electrochemical techniques. The impedance and voltammetric behaviours were strongly dependent on the film thickness. The main result of this study is that the charge transfer resistance increases with the film thickness. A model of the adsorption-absorption of hydrogen into iron films was proposed. It considered two types of absorbed hydrogen in a sublayer richer in hydrogen than the bulk metal. There, the hydrogen transported in the film coexists with another one coming from a direct absorption mechanism and trapped in some sites. The two absorbed hydrogen are reversibly exchanged. The interaction of hydrogen with palladium and iron was compared. It was concluded that for iron, the insertion of hydrogen results from a competition between a one-step direct hydrogen absorption mechanism and the classical two-step indirect penetration in the metal via the adsorbed hydrogen. At the end, a possible explanation of the deep penetration of the direct hydrogen absorption in the metal, detected by the impedance analysis, is proposed. It is based on the imperfections of numerous first layers of the deposited metals on polycrystalline gold.

Full text of DOI:10.1016/j.electacta.2007.07.047

Electrochimica Acta 53 (2007) 700–709
Investigation of hydrogen adsorption–absorption on iron by EIS
∗
N. Amokrane, C. Gabrielli , E. Ostermann, H. Perrot
UPR15-CNRS, LISE, Universit e´ Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France
Received 18 January 2007; received in revised form 19 July 2007; accepted 21 July 2007
Available online 27 July 2007
Abstract
This work concerns the interaction between hydrogen and iron in the cathodic potential region. It was motivated by the need for a better
understanding of the hydrogen insertion mechanism in metals. Electrochemical deposits of iron with various thicknesses were carried out on a
gold substrate and they were characterized by impedance measurements under hydrogen evolution conditions.
The processes occurring at the surface and within the iron films deposited on a gold electrode were studied using various electrochemical
techniques. The impedance and voltammetric behaviours were strongly dependent on the film thickness. The main result of this study is that the
charge transfer resistance increases with the film thickness. A model of the adsorption–absorption of hydrogen into iron films was proposed. It
considered two types of absorbed hydrogen in a sublayer richer in hydrogen than the bulk metal. There, the hydrogen transported in the film
coexists with another one coming from a direct absorption mechanism and “trapped” in some sites. The two absorbed hydrogen are reversibly
exchanged. The interaction of hydrogen with palladium and iron was compared. It was concluded that for iron, the insertion of hydrogen results
from a competition between a one-step direct hydrogen absorption mechanism and the classical two-step indirect penetration in the metal via the
adsorbed hydrogen. At the end, a possible explanation of the deep penetration of the direct hydrogen absorption in the metal, detected by the
impedance analysis, is proposed. It is based on the imperfections of numerous first layers of the deposited metals on polycrystalline gold.
©
2007 Elsevier Ltd. All rights reserved.
Keywords: Hydrogen; Iron; Adsorption; Absorption; Impedance
1
. Introduction
hydrogen enters and diffuses into steel structure and this inser-
tion creates constraints, which induce defects or cracks in the
material.
Numerous studies about hydrogen interaction with metals
havebeencarriedoutbecauseoftheirpotentialinterestinvarious
industrial domains. Hydrogen absorbing materials are important
in hydrogen storage, metal-hydride batteries, and fuel cells. On
the other hand, problems of degradation of steel may occur when
hydrogen is in contact with some materials. This phenomenon,
called hydrogen embrittlement, is frequently encountered in
industrial environment. Hydrogen can penetrate in a metal by
a physical process under high pressure or more often under
an electrochemical driving force. Corrosion, cathodic protec-
tion of steel in sea water produces hydrogen. This production of
hydrogen is also involved during steel production under hydro-
genated environment, in storage and use of this gas or storage
and transport of products which can, by decomposition, pro-
duce hydrogen (natural gas, oil, corrosive products, etc.). This
The adsorption–desorption coupling has been studied thor-
oughly for the hydrogen/palladium system, which is known to
store hydrogen in two possible phases depending on the cathodic
potential: the ␣-PdH phase (0.02 hydrogen atom per Pd atom)
andthe␤-phase(upto0.6hydrogenatomperPdatom). Pyunand
yang [1], have considered the interstitial sites in the ␤-phase and
phase boundaries between the ␣ and ␤ phases as reversible and
irreversible trap sites, respectively, which follow a McNabb and
Foster model [2]. They have also proposed that a thin ␤-PdH
phase layer, sometimes in patches, between the electrode sur-
face and subsurface give rise to the predominant direct hydrogen
absorption reaction and acts as a barrier for hydrogen diffusion
[3]. On similar basis, Gabrielli et al. have proposed a model, in
terms of impedances measured on thin Pd films deposited on
gold, where, in parallel with the classical Volmer–Heyrovsky
absorption two-step mechanism [4], trapped hydrogen atoms,
located in a thin subsurface layer, may exchange charge directly
with protons of the solution [5,6]. More recently, Lasia et al.
∗
Corresponding author. Tel.: +33 144274136; fax: +33 144274074.
E-mail address: cg@ccr.jussieu.fr (C. Gabrielli).
0
013-4686/$ – see front matter © 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2007.07.047

N. Amokrane et al. / Electrochimica Acta 53 (2007) 700–709
701
Thefirststepoftheindirectabsoprtionishydrogenadsorption
(Volmer reaction), with rate v1
k1
+
−
H + M + e ꢀMH + H2O
(1)
ads
k−1
where M is the adsorption site on the metal surface and MHads
is the hydrogen atom adsorbed on the electrode surface.
Adsorbed hydrogen can form gaseous hydrogen by the two
following processes:
(i) electrochemical desorption (Heyrovsky reaction), with rate
v2:
k2
+
−
MHads + H + e ꢀM + H2
(2)
k−2
Fig. 1. Scheme of the reaction mechanism used for the general interaction of
hydrogen with a metal.
(ii) chemical recombination (Tafel reaction), with rate v3:
k3
2
MHads ꢀ2M + H2
(3)
k−3
have shown, for very thin films (0.8–10 monolayers) of pal-
ladium, that two parallel mechanisms participate to hydrogen
entry in the metal: a fast direct hydrogen absorption and a slower
indirect hydrogen absorption via an adsorption step [7–9].
As a first step, in order to understand hydrogen insertion
mechanism, theinteractionbetweenhydrogenandironwasstud-
ied as this material is easier to manipulate than steel, in particular
to deposit thin layers on a gold substrate, which blocks hydro-
gen penetration. Iron deposits with various thicknesses were
electrochemically deposited and characterized by impedance
measurements. The experimental approach was inspired by the
results of electrochemical measurements recently obtained for
the hydrogen/palladium system [4,5]. They have shown the
importance of surface processes on the insertion kinetics of
hydrogen in palladium. An investigation with respect to the
material thickness has been necessary to separate the surface
processes from the volume processes.
The adsorption reaction is followed by hydrogen absorption
into a subsurface layer, with rate v4:
k4
MHads + Msubsurface ꢀM
+ MHabs(subsurface)
(4)
(5)
surface
k−4
and further diffusion into the bulk of metal:
diffusion
MHabs(subsurface) −→ MHabs(bulk)
as Habs diffuses from one site M1 to another M2.
The model proposed in this paper contains two additional
assumptions are considered:
•
•
A direct absorption mechanism (7)–(9) [15] where the
absorbed hydrogen in a subsurface layer is directly exchanged
with protons in the solution bulk, with rate v5:
In spite of the numerous studies carried out on the
iron/hydrogen system [10–14], many problems remain open.
In addition, few investigations have been carried out by using
impedance measurements, which is a very powerful tool to
separate the various processes involved in complex reaction
mechanisms.
k5
+
∗
H + eꢀH
(6)
abs
k
−
5
A possible exchange between the two types of absorbed
hydrogen coming from the direct and indirect absorption:
In this paper, a model of the mechanism of hydrogen pene-
tration in iron under cathodic polarization was proposed. Then,
results obtained by voltammetry and impedance measurements
concerning the interaction of hydrogen with thin films of iron
deposited on a gold substrate were reported and compared with
the model predictions.
kt
∗
HabsꢀH
(7)
abs
kr
Then, this subsurface layer is richer in hydrogen, Habs and
, than the bulk phase where only Habs is present.
∗
H
abs
2.2. Mathematical description of the model
2
. Theory
The rates (mol cm 2
−
s
−1
) of the above reactions can be writ-
2
.1. Electrochemical mechanism
ten as
ν1 = k1(1 − θ) − k−1θ
where ( is the surface coverage of the electrode surface by Hads
(8)
Usually, hydrogen atoms are considered to enter the metal
either by a two-step (indirect) or a direct absorption mechanism.
Equations below are written assuming that the two processes
occur in parallel, which is schematized in Fig. 1.
:
ν2 = k2θ − k−2(1 − θ) (9)

7
02
N. Amokrane et al. / Electrochimica Acta 53 (2007) 700–709
2
is the exchange rate of the trapped hydrogen with the solution.
ν3 = k3θ − 2k−3(1 − θ)
(10)
(11)
Hence:
ν4 = k4θ[1 − X(0)] − k−4(1 − θ)X(0)
ꢀ
d
ν5 = cmax
{k [N(x) − Xt(x)] − k−5Xt(x)}dx
5
(21)
where X(x) = c(x)/cmax is the dimensionless concentration of free
Habs in the metal with respect to the distance x to the electrode
surface, and cmax is the maximum hydrogen concentration in
the bulk of the metal. The concentrations of hydrogen ions and
molecular hydrogen are included in the rate constants k1 and
k−3, respectively.
0
0
In the previous equations, ki = k exp(biE) are in
i
−
2
−1
s
mol cm
s
, for i = 1, −1, 2, −2, and k , k , kt and kr are in
−5
5
−
1
, bi = ± βiF/RT, βi is the symmetry coefficient of the reaction
i, sign ‘± ’ is opposite sign of i, X(0) is the hydrogen con-
centration just under the surface, 1 − X(0) is the dimensionless
subsurface concentration of the free sites in the subsurface layer
The rate v is obtained from the flux, Jt(x), of the “trapped”
hydrogen atoms, H , which cross the electrode surface:
5
∗
abs
[18,19].
ν5 = −Jt(0)
(12)
The faradaic cathodic current density is then equal to
jF = −F(ν1 + ν2 + ν5)
(22)
Then, if the various quantities are supposed to be only x-
dependent:
In the same way the coverage changes of Hads are described
ꢀ
d
by
∂
Jt(x)
ν5 = −
dx
(13)
(14)
∂
x
dθ
0
Γmax
= ν1 − ν2 − 2ν3 − ν4
(23)
dt
However, as
where Γ max is the density of adsorption sites on the metal surface
∂
Xt(x)
∂Jt(x)
−2
(mol cm ).
cmax
= −
∂
t
∂x
The boundary conditions imposed to the metal film are the
following:
where Xt(x) = ct(x)/cmax is the dimensionless concentration of
∗
H
“trapped” in the volume, V, of the metal film. Xt(x) is
abs
•
•
x = 0, the flux of the entering hydrogen in the film is equal to
(24)
supposed to depend on x only, hence:
ꢀ
J(0) = ν + ν5
d
4
dXt(x)
ν5 = cmax
dx
(15)
x = d, the absorbed hydrogen atoms cannot cross the
metal/gold interface, therefore:
dt
0
The diffusion process in the iron film is supposed to be very
fast compared to the rates of the surface and subsurface pro-
cesses [16]. In the subsurface layer, a trapping/releasing process
is supposed to occur such as
J(d) = 0
(25)
In the following, it is assumed that the sites are localized in
the subsurface layer and have the relative density N(x) which
decreases exponentially with the distance from the electrode
surface
kt
ꢁ
ꢂ
∗
Habs + ꢀ ꢁ ꢀ H
(16)
abs
kr
ꢃ
ꢄ
ꢁ
ꢂ
x
∗
where ꢀ ꢁ represents an empty site and H
an occupied site by
N(x) = N exp −
0
(26)
abs
∗
x
0
H
[17]; therefore, the kinetic equation which gives the change
of the concentration of the H is similar to the McKabb and
abs
∗
where N0 = ct,max/cmax is the dimensionless subsurface concen-
tration of the sites, relative to cmax, ct,max is the concentration of
the occupied sites, and x0 represents a characteristic distance of
the sites, i.e. a distance where N(x ) = N /e. This model is ana-
lyzed below, first in a steady state and later for impedance of an
ion-blocking electrode constituted of an iron film of thickness d
deposited on a gold substrate.
abs
Foster model [2]:
∂
Xt(x)
=
νt(x) + νe(x)
(17)
0
0
∂t
where
νt(x) = ktX(x)[N(x) − Xt(x)] − krXt(x)
(18)
2
.3. Steady state
is the rate of hydrogen trapping and N(x) is the relative density
of sites in the metal (i.e. the number per unit volume divided by
cmax). And
The steady-state values of the surface coverage, θ, by
adsorbed hydrogen, Hads, and the dimensionless concentration
of H species under the electrode surface, X(0), are calculated
following the simplifying assumption, that the Tafel desorption
reaction is negligible (k (E) = k (E) = 0) [2]:
At steady state, d/dt 0, then the hydrogen, Habs, concen-
tration is constant throughout the metal film as diffusion is
supposed to be fast
νe(x) = k [N(x) − Xt(x)] − k Xt(x)
(19)
5
−5
is the rate of exchange with the solution, whereas
3
−3
ꢀ
d
ν5 = cmax
νe(x)dx
(20)
0

N. Amokrane et al. / Electrochimica Acta 53 (2007) 700–709
703
From v1 − v2 = v4:
where from Eqs. (21) and (29):
ν = cmaxd{[b k (1 − n) − b
−5 −5
∗
n]N ꢀE
k1 + k−2 + k−4X(0)
ꢀ
k
5
5 5
θ =
(27)
k1 + k−1 + k2 + k−2 + k4(1 − X(0)) + k−4X(0)
and from v1 − v2 = −v5:
∗
−
(k + k )ꢀX }
(34)
(35)
(36)
5
−5
where
k−4X(0) − ν5
ꢀ
d
θ =
(28)
(29)
(30)
1
∗
k4(1 − X(0)) + k−4X(0)
ꢀX = d
ꢀXt(x)dx
0
where from Eq. (21):
Hence
ν = cmaxd{k (1 − n) − k n}N∗
jF = R−t 1ꢀE + FKIꢀθ + FK ꢀX∗
5
5
−5
ꢀ
5
where
where
ꢀ
ꢅ
ꢃ
ꢄꢆ
d
1
x0
d
−1
∗
R
= −F[b1k1(1 − θ) − b−1k−1θ + b2k2θ − b−2k−2(1 − θ)
N =
N(x)dx = N0
1 − exp −
t
d
d
x0
0
∗
+
cmaxN (b k (1 − n) − k
b
n)]
(37)
5
5
−5 −5
isthedimensionlesstotalnumberoftrapsinthemetalpervolume
−3
and
unit (cm ) and n = Xt(x)/N(x) is the fraction of occupied sites
by hydrogen equal to
KI = k1 + k−1 − k2 − k−2
K = cmaxd(k + k
(38)
(39)
ktX(0) + k
5
)
n =
(31)
5
5
−5
kr + ktX(0) + k + k
5
−5
and a small amplitude perturbation of the quantity X, is such
as ꢀX(t) = X(t) − X(steady state). Therefore, the charge transfer
resistance, Rt depends on the thickness of the metal film through
as from Eq. (17), vt + ve = 0 at steady state.
In the case considered here, where the density of sites
decreases with depth, the “trapped” hydrogen atoms in these
sites are located in a “subsurface layer” whose thickness can
be considered as equal to two or three times x0, and their total
quantity in the electrode per volume unit is equal to
*
N (d) and θ (Eqs. (30) and (37)).
Similarly, from Eq. (23) it is possible to obtain
jωΓmaxꢀθ = KꢀE − K0ꢀθ + K4ꢀX(0)
(40)
∗
X = nN∗
where
(32)
K = b1k1(1 − θ) − b−1k−1θ − b2k2θ + b−2k−2(1 − θ) (41)
By equating Eqs. (27) and (28), X(0) is the solution of a
quadratic equation such as
K0 = k1 + k−1 + k2 + k−2 + k4[1 − X(0)] + k−4X(0)
K4 = k4θ + k−4(1 − θ)
(42)
2
aX(0) + bX(0) + c = 0
(43)
where
therefore
KꢀE + K4ꢀX(0)
a = γk4(k1 + k−2) + γk−4(k−1 + k2) − α(k−4 − k4),
b = δk4(k1 + k−2) + δk−4(k−1 + k2) − β(k−4 − k4)
ꢀ
θ =
(44)
jωΓmax + K0
Finally, from Eq. (24):
J(0) = ꢀν4 + ꢀν5
Hence
−
α(k1 + k−1 + k2 + k−2 + k4) − γk4(k1 + k−2),
ꢀ
(45)
(46)
c = −β(k1 + k−1k2 + k−2 + k4) − δk4(k1 + k−2)
and
ꢀ
J(0) = K1ꢀE + K2ꢀθ + K3ꢀX(0) + K ꢀX∗
αX(0) + β
γX(0) + δ
−ktk X(0) + krk
5
ν5 =
= cmaxN∗
−5
5
ktX(0) + kr + k + k
where
5
−5
therefore
∗
K1 = cmaxdN (b k (1 − n) − b
k
n)
(47)
(48)
(49)
5
5
−5 −5
√
2
b ± b − 4ac
K2 = k4[1 − X(0)] + k−4X(0)
K3 = −K4
X(0) = −
2
a
2
.4. Small signal analysis
From Eq. (18), the response of the dimensionless “trapped”
hydrogen concentration, ꢀXt, at a distance x from the electrode,
is governed by
From Eqs. (22)–(24), the responses ꢀθ, ꢀIF, ꢀJ(0), and
X(0) to a small amplitude sinusoidal potential perturbation
E are equal, in the frequency domain, to
ꢀ
ꢀ
dꢀXt
= −(k + k X + k + k )ꢀXt
r
t
5
−5
dt
ꢀ
jF = −F(ꢀν1 + ꢀν2 + ꢀν5)
(33)
+k [N(x) − X (x)]ꢀX
t
t
(50)

7
04
N. Amokrane et al. / Electrochimica Acta 53 (2007) 700–709
where Xt, ꢀXt, and ꢀX are x-dependant, whereas X = X(0), i.e.
from Eq. (50):
This quantity can be obtained also by considering the value of
the admittance calculated in Ref. [2] where diffusion has been
supposed to be a rate limiting step and by assuming that the
diffusion coefficient of hydrogen tends towards infinity. Then,
in this limiting situation, the quantities 1/Q and W/Q involved in
jωꢀXt = −(kr + ktX(0) + k + k )ꢀXt
5
−5
kr + k
−
5
+
kt
Xt(x)ꢀX
(51)
(52)
the calculated admittance [2], tend towards −(jωdcmax + AK )
ktX(0) + k5
5
and A, respectively, which lead to the same value as Eq. (59).
therefore
kt((kr + k )/(ktX(0) + k ))Xt(x)ꢀX
−
5
5
ꢀXt =
2.5. Predictions of the model
jω + kr + ktX(0) + k + k
5
−5
The impedance, Z(ω), and the change of the charge trans-
fer resistance with respect to the thickness of the iron layer, d,
was calculated from Eqs. (59) and (37), respectively (Fig. 2),
However from Eq. (35) and using Eq. (52):
ꢀ
d
1
kt(kr + k )nN(x)ꢀX(x)
∗
−5
ꢀ
X =
dx
d
(jω + kr + ktX(0) + k + k−5)(ktX(0) + kr)
0
5
(53)
Therefore,
∗
ꢀ
X = AꢀX(0)
(54)
where
A=(
kt(kr + k )N0x0(1 − exp(−d/x0))
−
5
jω + kr + ktX(0) + k + k )(kr + ktX(0) + k + k
)
5
−5
5
−5
(
55)
ꢇ
ꢇ
d
0
d
0
However, as (∂ꢀJ/∂x) dx = −cmax (∂ΔX/∂t) dx, one has
ꢀ
J(0) = −jωdcmaxꢀX(0) and therefore
K1ꢀE + K2ꢀθ
ꢀX(0) = −
(56)
jωdcmax + K3 + AK5
From Eq. (44)
1
/(jωΓmax + K0)(K − K1K4/(jωdcmax + K3 + AK ))
5
ꢀθ =
1
+ K2K4/(jωΓmax + K0)(jωdcmax + K3 + AK ))
5
×
ꢀE
(57)
On the other hand, using Eq. (54), and substitution of ꢀX(0)
by its value (Eq. (56)) into Eq. (36) the final form for ac current
is obtained
ꢃ
ꢄ
FAK K1
−
1
5
ꢀjF =
R
−
ꢀE
t
jωdcmax + K3 + AK5
ꢃ
ꢄ
FAK K2
5
+
F
KI −
ꢀθ
(58)
jωdcmax + K3 + AK5
Then the electrochemical admittance YF = ꢀjF/ꢀE of the
hydrogen/electrode interface can be obtained by means of Eq.
(
57):
FAK K1
YF = R−1
5
−
ꢃ
t
Fig. 2. Calculated (a) impedance (frequencies in Hz) and (b) charge
transfer resistance change with respect to the thickness of the iron layer
jωdcmax + K3 + AK5
ꢄ
−
10
−2 −1
s
KI − FAK K2
with the following parameters: k1(E) = 10 exp(−20E) mol cm
,
,
,
,
5
+
F
−7
−2 −1
−9
−2 −1
k−1(E) = 10 exp(50E) mol cm
s
, k2(E) = 10 exp(−10E) mol cm
s
jωdcmax + K3 + AK5
−9
−2 −1
−3
−2 −1
k−2(E) = 10 exp(10E) mol cm
s
,
k3 = 10 exp(−20E) mol cm
s
−
5
−2 −1
−5
−2 −1
K − (K1K4)/(jωdcmax + K3 + AK )
k−3(E) = 0, k4(E) = 2 × 10 mol cm
s
,
k−4(E) = 10 mol cm
k−5(E) = 2 × 10 exp(10E) mol cm
s
5
×
−3
−2 −1
−8
−2
k5(E) = 10 exp(−25E) mol cm
s
,
jωΓmax + K0 + (K2K4)/(jωdcmax + K3 + AK )
5
−1
3
−3 −1
5
−3
s
, kt(E) = 10 mol cm
s
, kd(E) = 0, N0 = 5 × 10 mol cm , x0 = 0.1 ␮m,
= 7 × 10 mol cm , C = 1 ␮F.
cmax = 0.116 mol cm 3, Γ
−
−9
−2
(59)
max
d

N. Amokrane et al. / Electrochimica Acta 53 (2007) 700–709
705
for the values of the parameters given in the caption, in partic-
0
0
−4
ular the ratio k /k = 5 × 10 was tested. The impedance,
5
−5
Z(ω), has the shape of a semi-circle when a double layer capac-
ity is taken into account in parallel on the faradaic impedance,
ZF(ω) (Fig. 2a). The charge transfer resistance increases when
the thickness of the iron film increases (Fig. 2b). This surprising
behaviour is related to the dependence of Rt on the thickness of
*
the iron film through N and n.
3
. Experimental
In this experiment, the working electrode was made of a thin
iron film, whose thickness changed from a few hundreds of
nanometers to several micrometers, deposited on a gold elec-
trode, 5 mm in diameter.
3
.1. Electrodeposition of iron on a gold substrate
The main difficulty of this part of the work was to make
iron deposits, which did not contain hydrogen and sufficiently
adherent to allow impedance measurements to be performed.
Hence, the gold disc electrode was very slightly rotated during
electrodeposition not to facilitate the insertion of hydrogen in
the deposit, which could be detrimental to the conclusions.
The electrodeposition solution was FeSO4·7H2O
−
1
−1
−1
(
0
240 g L ), FeCl2·4H2O (30 g L ) and NH4Cl (22.5 g L ).
.1 M NaOH was added until the yellow colour turned to
green blue, which corresponds to a solution pH between
◦
Fig. 3. Scanning electron microscopic observations of the surface of the iron
films deposited on the gold electrode for thicknesses (a) 4.4 ␮m and (b) 0.44 ␮m.
4
.5 and 6. The solution was maintained at 38 C during
electrodeposition. The counter electrode was a mild steel foil
and the reference electrode was a mercurous/mercurous sulfate
(
Hg/Hg2SO4/K2SO4 saturated). The applied current density
to peak in a 10 kHz to 100 mHz frequency range using 10 mea-
surement points per decade.
−
2
was between 50 and 100 mA cm
.
Before iron electrodeposition, the gold electrode was
mechanically polished (600 and then 1200 emery paper grade),
and then rinsed in deionized water and cleaned with ultrasounds
in acetone. After electrodeposition, the composite electrode was
rinsed in deionized water.
Gold was chosen as a substrate because it does not absorb
hydrogen, then hydrogen entered and crossed the iron film and
then was stopped by the gold substrate.
Obtaining a steady state was particularly important to reach
relevant quantities for impedance measurements. Then, it was
necessary to wait a sufficient long time to reach a complete
charging of hydrogen of the sample characterized by a steady-
state current. In addition, it was necessary to impose an adequate
hydrodynamic regime to eliminate the hydrogen bubbles gener-
ated at the interface.
Hydrogen bubble evolution perturbs the electrochemical
measurements. When a rotating disc electrode is used, bub-
bles are blocked at the centre of the disc electrode as the active
surface is oriented towards the bottom of the cell, the rotation
axis being vertical. Therefore, the current and impedance mea-
surements are difficult to achieve. To eliminate as quickly as
possible the hydrogen bubbles, an impinging jet cell was used
to decrease their influence on the experimental data. A fixed
disc electrode at the bottom of the cell, vertically set to easily
free the bubbles, was positioned under the electrolyte jet, which
was horizontal. This type of cell ensures an uniform accessibil-
ity of the active species to the electrode surface. The volume
of the electrolyte was about 1500 ml and the temperature of the
Fig. 3a and b shows the surface of the iron deposit observed
by a scanning electron microscope. It demonstrates that gold is
uniformly coated by the iron deposit both for a thin (0.44 ␮m)
or a thicker (4.4 ␮m) film deposited on the gold surface.
3
.2. Electrochemical cell
The experiments of hydrogen insertion on deposited iron
on gold were carried out in 0.1 M H2SO4. A 5 mm diameter
solid iron rotating disc electrode (Goodfellow) was also used to
compare its characteristic to the iron film behaviour.
Electrochemical impedance measurements were carried out
by using a frequency response analyzer (FRA: Solartron 1250)
connected with a potentiostat (Solartron 1286). The amplitude
of the perturbating sinusoidal signal was equal to 15 mV peak
◦
solution was maintained at 25 C. The counter electrode was
a large area platinum grid and the reference electrode was a
mercurous/mercurous sulphate electrode. The potential of the

7
06
N. Amokrane et al. / Electrochimica Acta 53 (2007) 700–709
on the imposed potential and the studied iron thickness. From
the observed current transients, a 20 min delay was necessary
for the solid iron electrode to reach a stable current before to
carry out impedance measurements whereas a 60 min delay was
necessary for iron deposited on gold.
Fig. 5 shows the impedance diagrams, measured at
−
1.1 V/SSE, for various thicknesses of the iron layer after sta-
bilisation in a 0.1 M H2SO4 aqueous solution. Whatever the
thickness of the iron layer deposited on the gold electrode or
for a solid iron electrode the impedance diagrams were formed
by an unique capacitive loop, which should represent the charge
transfer resistance, Rt, in parallel on the double layer capacity,
C . The main conclusion is that the charge transfer resistance
d
changed with the thickness of the electrodeposited film. This
demonstrated a surprising behaviour as, in principle, the charge
transfer resistance characterizes solely surface phenomena and
should not vary with the thickness of the tested sample.
Fig. 6 shows the change of Rt with respect to the thickness of
the deposited iron film on a gold substrate at various potentials in
a0.1 MH2SO4 aqueoussolution. Aftertoberatherconstantupto
Fig. 4. Comparison of current–voltage curves obtained on solid iron electrode
and deposited iron electrodes of various thicknesses in an impinging jet cell in
1
␮m, Rt increased with the thickness of the sample and asymp-
totically tended towards the value found for the charge transfer
resistance of the solid iron electrode. For very thin films (smaller
than 1 ␮m), Rt is constant, in agreement with the model predic-
tion, as the surface charge transfer becomes preponderant and
then independent of the thickness. For larger thicknesses (greater
than 1 ␮m) an important increase of the Rt value was observed
when the charge transfer in volume increases. For thicker iron
films (greater than a few ␮m), Rt increased only a little bit as the
charge transfer in volume is limited to a thin layer and finally
tended towards an asymptotic line whose value was equal to the
value obtained for a solid iron electrode.
0
.1 M H2SO4.
working electrode will be given, in the following, versus this
reference electrode (SSE is +0.650 V with respect to the normal
hydrogen electrode—NHE).
4
. Results
The reactivity of the iron electrode and of the iron deposits
on gold electrodes towards hydrogen was evaluated by using
current–voltage curves in the cathodic domain in a first step and
then their characterization was carried out by impedance mea-
surements. The results were compared with the current–voltage
curves and impedances obtained on a rotating iron disc electrode
at a 2000 rpm rate.
4
.1. Current–voltage curves
Current–voltage curves I(E) were obtained by using a low
potential sweep rate. Fig. 4 shows the comparison of the
current–voltage curve of both the solid iron electrode and the
deposited iron electrodes of various thicknesses in aerated 0.1 M
H2SO4 (Fig. 4) medium. The curves are relatively close but the
current was higher when the thickness of the iron deposit was
lower. Measurements were also carried out in deaerated medium
obtained by nitrogen bubbling but the difference due to oxygen
reduction was small, then in the following the iron electrode-
positions and their characterization were carried out in aerated
media.
4
.2. Electrochemical impedances
Before any impedance measurement, some time was neces-
sary to reach a steady-state regime. This time corresponded to
a complete charging of hydrogen in the iron film and depended
Fig. 5. Impedance diagrams measured on electrodeposited iron electrodes on
a gold substrate in 0.1 M H2SO4 obtained in a impinging jet cell for various
thicknesses in at −1.1 V/SSE (frequencies in Hz).

N. Amokrane et al. / Electrochimica Acta 53 (2007) 700–709
707
Fig. 8. Change of the double layer capacitance with respect to the thickness of
the iron deposited film on the gold electrode.
5
. Discussion
Fig. 6. Change of the charge transfer resistance with respect to the thickness
of the iron deposited films on the gold electrode at −1.1 and −1.2 V/SSE
and the limiting values (—) measured on a solid iron disc electrode of the
electrodeposited iron at various potentials in 0.1 M H2SO4.
The main experimental result of this study is the thickness
dependence of the charge transfer resistance of the impedance
of the iron film electrode. As, usually, this resistance is inde-
pendent of the substrate volume as it is a surface dependent
quantity, it is necessary to check that this surprising increase
of the charge transfer resistance was not due to the decrease
of the roughness of the iron film surface. Fig. 8 shows the
variation of the double layer capacitance with respect to the
thickness of the iron layer and the limiting value obtained for
a solid iron electrode obtained from the impedance measure-
ments. In fact, this capacitance decreases when the thickness of
the film increases showing that the active surface is lower for
thick films probably due to a rougher deposit for the thinner
films. The active surface was about two times smaller for thick
deposits than for thin deposits, which explains why the current
is larger for thin deposits in Fig. 4. However, the increase of
the charge transfer resistance is more than three times from
thin to thick deposits, which demonstrates that the increase
of this resistance is not due only to a change of active sur-
face.
The change of Rt with respect to the potential is given in Fig. 7
for various thicknesses of the electrodeposited iron and for the
solid iron electrode. For the latter, a large increase was observed
for potential values lower than E = −1.1 V/SSE, whereas for the
electrodeposited iron electrodes the charge transfer resistance
increased between E = −1.2 and −1.1 V/SSE and then slightly
decreased probably due to the growing influence of the anodic
process. This increase was as much important as the deposit was
thicker. For more cathodic potentials, the value of the charge
transfer resistance decreases proportionally to the inverse of the
cathodic current.
To interpret the Rt thickness dependence it is necessary to
consider, in addition to a classical charge transfer at the elec-
trode surface an extra charge transfer involving the bulk metal.
Then, it is proposed here to consider the competition of two
insertion processes of hydrogen in the iron film, which occur in
parallel and schematized in Fig. 7. The first one is the classi-
cal two-step indirect absorption process, via the Hads adsorbed
intermediate, first proposed by Bockris et al. [20], whose rate
constants are k1, k−1, k4, k−4. The second one can be seen as
a generalization of the one-step Frumkin direct insertion pro-
∗
cess [21–23], which generates the H in a thin sublayer, which
abs
was already proposed for the Pd/H system, and whose rate con-
stants are k , k . In the sublayer, the absorbed monoatomic
5
−5
∗
hydrogen, Habs, and the “trapped” hydrogen, H , are supposed
abs
to interact through kt, kr. On these basis, the model proposed
in the first part of this paper predicts that the charge transfer
resistance is film thickness-dependent if either k or k is not
Fig. 7. Change of the charge transfer resistance with respect to the potential for
various thicknesses of the electrodeposited iron in 0.1 M H2SO4.
5
−5

7
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N. Amokrane et al. / Electrochimica Acta 53 (2007) 700–709
followed by transfer to an interstice below the second surface
monolayer becoming absorbed H” [28,29]. However, this view
is only valid for monocrystals. In fact, even when the deposit
is made on Au(1 1 1) like in Ref. [9], the first layers are not
perfect, because there is not a layer-by-layer deposit at the begin-
ning due to the misfit between the lattice of gold and palladium
[30]. So, Lasia has noted that more than two monolayers are
necessary to get normal absorption, i.e. Habs. In the present
experiment, where iron (and probably palladium in [31]) was
electrochemically deposited on polycrystalline gold, numerous
layers of the deposited metal were probably perturbed before to
reach a more homogeneous structure. This could explain why
the direct absorption mechanism is not limited to a depth equal
to two monolayers as in perfect crystals, but can go much deeper
in the bulk metal (here a few micrometers). This argument can
be related to an hypothesis made by Bucur [32], on the possibil-
ity of two kinds of adsorption sites of hydrogen on palladium: a
weak adsorption site on the crystallographic planes at the surface
of palladium and strong adsorption sites on the surface imper-
fections, which can be distributed in the whole volume of the
palladium. He has supported this assumption by the findings that
on an ideal surface of a palladium monocrystal only the weak
adsorbed species can be identified [33], while on black palla-
dium a quite wide spectrum of strongly bonded forms can be
found [34].
Fig. 9. Scheme of the reaction mechanism proposed for the interaction of hydro-
gen with iron.
zero. In addition, if k = 0, then kt, k4, and k have not to be
5
5
equal to zero and if k 5 = 0, kr and k have not to be equal to
−
5
zero.
Now, when k 5 = 0 the charge transfer resistance is always
−
increasing with the iron film thickness whatever the values of
the other rate constants. When k = 0, the charge transfer resis-
5
tance decreases when the film thickness increases. This means
that for iron a direct absorption of hydrogen has to be consid-
ered to fit the experimental increase of Rct when d increases (at
least k (E) ꢂ k (E) is needed). As a comparison, for palladium
5
−5
this is k (E) ꢂ k (E) which is necessary, as the charge trans-
As the proposed model is not obviously unique, another pos-
sible model, which would have a similar behaviour, would be
to consider a uniform “trap” density in the bulk metal and rate
−5
5
fer resistance is decreasing when the palladium film thickness
increases.
When k 5
ꢃ
= 0, the sense of variation of the charge transfer
constants k and k which would decrease exponentially with
5
the distance from the surface due to a gradient of physical prop-
−
−5
resistancewithrespecttothefilmthicknessdependsofthevalues
of k1 and k−1 whatever the value of k .
erties of the metal. It would give very close predictions on Rt, as
5
*
Finally, the reaction mechanism proposed in this paper to
describe the interaction of hydrogen with iron is depicted in
Fig. 9.
the mathematics are similar, because k , k and N appear as
5
−5
*
*
products k N and k N in the expression of the charge transfer
5
−5
resistance (Eq. (37)).
Usual kinetic models, where charge transfer is supposed to
occur only on the electrode surface, lead to charge transfer resis-
tances independent of the thickness of the specimen. In this
paper, to account for the thickness dependence of the charge
transfer resistance, it was supposed that charge transfer occurs
in a sublayer inside the sample as well. It was assumed that
hydrogen atoms were bonded on some sites with an exponen-
tial distribution from the electrode surface. These sites can be
generated by the coexistence of hydrogen-rich zones in the sub-
layer and hydrogen-poor zones in the deep bulk of the film. They
can be different from the commonly considered traps, which are
generated by compressive stresses, grain boundaries or disloca-
tions. Notice that the hypothesis of the existence of two types
of hydrogen bonded to the metal lattice have been already con-
sidered in the literature (e.g. H and H* in [24,25]). However, a
model taking into account only an heterogeneity of 2D adsorp-
tion sites will not be able to explain such a thickness-dependence
of the charge transfer resistance.
6. Conclusion
The main result of this study, which characterizes the hydro-
gen interaction with iron, is that the charge transfer resistance
increases with the film thickness on the opposite of the behaviour
of the transfer resistance measured on palladium films [31]. A
model taking into account the classical two-step indirect inser-
tion of hydrogen into iron in competition with a direct entry of
hydrogen in the iron electrode of absorbed monoatomic hydro-
gen in sites in a sublayer is proposed.
These experiments on the hydrogen/iron system allow the
behaviour of iron to be compared, at least qualitatively, to the
behaviour of palladium concerning its interaction with hydro-
gen when the metal is deposited in thin films on a gold substrate.
However, it is necessary to keep in mind that for iron, hydro-
gen is evolving under bubble form in the whole cathodic range
whereas there is solely absorption in the potential range of the ␣-
phase for palladium. A variation of the charge transfer resistance
with respect to the thickness of the film is observed for the two
metals. This feature is highly surprising as the charge transfer
resistance is generally related to surface phenomena and not to
volume processes. This special behaviour has been explained by
Two other types of adsorbed hydrogen are also considered:
HUPD and HOPD in [26,27], HUPD being right on the metal
surface and HOPD adsorbed on the second layer. The second
type is sometimes considered as due to the direct absorption
as it “undergoes direct interfacial transfer to a subsurface site,

N. Amokrane et al. / Electrochimica Acta 53 (2007) 700–709
709
a “trapping” of the absorbed hydrogen in a sublayer just below
the surface of the electrode and, for palladium, a direct desorp-
tion of this “trapped” hydrogen in the solution [31]. However,
for palladium, the charge transfer resistance decreases when the
thickness of the film increases whereas for iron this resistance
increases with the thickness of the film, which was explained
by a direct absorption of hydrogen on the sites in the sublayer.
Therefore, the involvement of a one-step Frumkin mechanism
of direct hydrogen absorption is responsible for the observed
interaction of hydrogen with palladium and iron. At the end,
a possible explanation of such a deep penetration of the direct
hydrogen absorption in the metal is proposed. It is based on
the imperfections of the first layers of the deposited metals on
polycrystalline gold.
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The authors gratefully acknowledge the financial support of
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