Reconsideration of the quantitative characterization of the reaction intermediate on electrocatalysts by a rotating ring-disk electrode: The intrinsic yield of H2O2 on Pt/C

Article abstract of DOI:10.1016/j.electacta.2010.11.086

To solve the problem of the catalyst-loading-effect on quantifying the reaction intermediates on the surface of electrocatalysts with a rotating ring-disk electrode, we studied the formation of hydrogen peroxide in the oxygen reduction reaction on Pt/C with various sample loadings and then proposed an extrapolation model for measuring the intrinsic yield of H₂O ₂, which can quantitatively reflect the characteristics of the surface of a given catalyst. In the extrapolation model, the catalyst loading effect can be compensated by taking the catalyst loading-dependent probability of the re-adsorption + further reaction of the desorbed H₂O ₂ into consideration. The core concept in this extrapolation model is that the probability of the re-adsorption + reaction of the desorbed H ₂O₂ becomes zero if there is no other active site available (i.e., at the extrapolated hypothetical point of zero catalyst loading) for re-adsorption of the desorbed H₂O₂. The intrinsic yield of H₂O₂ by extrapolation was much higher than that measured by the conventional model, in which the re-adsorption + reaction of the desorbed H₂O₂ is not considered, and thus the catalyst loading-dependent apparent yield of H₂O₂ does not properly reflect the intrinsic characteristics of the surface of a given catalyst.

Full text of DOI:10.1016/j.electacta.2010.11.086

Electrochimica Acta 56 (2011) 2098–2104
Contents lists available at ScienceDirect
Electrochimica Acta
journal homepage: www.elsevier.com/locate/electacta
Reconsideration of the quantitative characterization of the reaction
intermediate on electrocatalysts by a rotating ring-disk electrode:
The intrinsic yield of H O on Pt/C
2
2
∗
Ke Ke, Tatsuya Hatanaka, Yu Morimoto
Toyota Central R&D Labs., Inc., 41-1, Yokomichi, Nagakute, Nagakute-cho, Aichi 480-1192, Japan
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 12 July 2010
Received in revised form
To solve the problem of the catalyst-loading-effect on quantifying the reaction intermediates on the
surface of electrocatalysts with a rotating ring-disk electrode, we studied the formation of hydrogen
peroxide in the oxygen reduction reaction on Pt/C with various sample loadings and then proposed
an extrapolation model for measuring the intrinsic yield of H2O2, which can quantitatively reflect the
characteristics of the surface of a given catalyst. In the extrapolation model, the catalyst loading effect
can be compensated by taking the catalyst loading-dependent probability of the re-adsorption + further
reaction of the desorbed H2O2 into consideration. The core concept in this extrapolation model is that the
probability of the re-adsorption + reaction of the desorbed H2O2 becomes zero if there is no other active
site available (i.e., at the extrapolated hypothetical point of zero catalyst loading) for re-adsorption of
the desorbed H2O2. The intrinsic yield of H2O2 by extrapolation was much higher than that measured by
the conventional model, in which the re-adsorption + reaction of the desorbed H2O2 is not considered,
and thus the catalyst loading-dependent apparent yield of H O does not properly reflect the intrinsic
2
4 November 2010
Accepted 26 November 2010
Available online 3 December 2010
Keywords:
Oxygen reduction
RRDE
Hydrogen peroxide
Quantitative analysis
Extrapolation model
2
2
characteristics of the surface of a given catalyst.
©
2010 Elsevier Ltd. All rights reserved.
1
. Introduction
In developing electrocatalysts for polymer electrolyte fuel cells
PEMFCs) [4,9–11], it is known that H O tends to attack the mem-
(
2
2
In fundamental studies of catalytic processes, quantifying the
branes [12–15] and accelerate the dissolution of Pt, leading to a
deterioration of the durability. Therefore, ORR electrocatalysts with
high selectivity for the four-electron pathway are desired. In con-
reaction intermediates can provide some key hints concerning the
reaction mechanism [1–4]. In corresponding applied research, the
yield of the intermediate could be used as a criterion for evaluating
the performance of the catalyst [5,6].
It is widely known that, in the oxygen reduction reaction (ORR)
on platinum, the predominant reaction proceeds via a four-electron
pathway [7] (Eq. (1) [8]) with a two-electron side reaction (Eq. (2))
trast, in developing electrocatalysts for H O2 production [16,17],
2
high selectivity for the two-electron pathway is desired. In either
case, it is important to understand the intrinsic characteristics of
the surface of a given catalyst by quantifying the yield of H O2
2
(referred to as XH2O2 , the molar ratio of produced H O2 to the total
2
[
8]. Even for the two-electron reaction, hydrogen peroxide (H O )
of all reduced oxygen).
2
2
can be further reduced according to Eq. (3) [8]. A disproportion reac-
tion could also occur, as shown in Eq. (4). The disproportion reaction
is generally electrochemically undetectable and is thus neglected.
The rotating ring-disk electrode (RRDE) technique is widely
used to characterize the intermediates or side-products. XH2O2 has
been conventionally derived as below (from Eq. (5) to Eq. (11)) for
decades [18–21]. An underlying assumption for the conventional
quantification model is that no further reaction occurs on the disk
+
−
0
O + 4H + 4e = 2H O
E = 1.229 V
(1)
(2)
(3)
(4)
2
2
+
−
0
for the desorbed H O2 before it reaches the ring.
O + 2H + 2e = H O
E = 0.67 V
2
2
2
2
The definition of XH2O2 is expressed in Eq. (5) by the reaction rate
+
−
0
H O + 2H + 2e = 2H O
E = 1.77 V
con
2
2
2
of the oxygen molecule reduced via a two-electron pathway (v2
)
−
e
con
and a four-electron pathway (v4e ) assumed in the conventional
−
2
H O = 2H O + O
2
2
2
2
model. In the conventional model, one actually cannot distinguish
the two reaction pathways (Eq. (1) or Eq. (2) + Eq. (3)) from each
other and treats both as four-electron pathways. One is the real
four-electron pathway occurring on the same active site, and the
other is first a reduction of O2 to H2O2 via a two-electron path-
∗ Corresponding author. Tel.: +81 561 717207; fax: +81 561 634120.
E-mail addresses: kekeicpm@hotmail.com (K. Ke), morimoto@mosk.tytlabs.co.jp
Y. Morimoto).
(
0
013-4686/$ – see front matter © 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2010.11.086

K. Ke et al. / Electrochimica Acta 56 (2011) 2098–2104
2099
way on one active site and then a desorption, re-adsorption and
reduction of the produced H O2 to H O2 on a different active site.
To the best of our knowledge, however, there is no report on a
quantitative model for characterizing reaction intermediates with
the characteristics of the surface distinguished from the catalyst
loading-dominated structure of the electrode.
2
2
con
con
v
v
−
−
2
e
2e
XH
2O2
=
=
(5)
reduced
O
2
con
con
v
v
−
+ v
−
In this work, we reconsider the quantification model by
taking the probability of the re-adsorption + reaction of the
H O into consideration and then establish an extrapolation
4e
2e
By combining the Faraday’s Law-based equations (Eqs. (6) and
2
2
(
7)) with Eq. (5), one can express XH2O2 with the reduction current
model in which the catalyst loading (essentially, the num-
ber of active sites, referred as nas hereinafter) effects can be
compensated for to achieve the XH2O2 intrinsic to a given
con
due to the assumed two-electron pathway (I2 ) and the four-
electron pathway (I4e ), as shown in Eq. (8).
−
e
con
−
surface (as illustrated in the schematic diagram shown in
Fig. 1).
con
con
I
I
−
= 4Fv4e
−
(6)
(7)
4
e
con
con
−
= 2Fv2e
−
2e
con
2
I
−
2e
2. Experimental
XH
=
(8)
2O2
con
con
I
+ 2I
−
−
2e
4
e
2.1. Controlling nas on thin-film electrodes
In RRDE evaluation, there are only two current values experi-
mentally obtainable, disk current (I ) and ring current (Ir). In the
conventional quantification model, Id and Ir can be expressed as
given in Eqs. (9) and (10), respectively:
d
For carbon-supported platinum (Pt/C), nas can be expressed
by the electrochemically active surface area (ECSA) of Pt (i.e.,
nas = ECSA).
con
con
By using an in-house-developed automated thin-film-electrode
preparation system [25], we controlled nas by homogeneously coat-
ing a glassy carbon (GC: 5 mm dia.) disk with various Pt loadings
Id = I2e
−
+ I
−
(9)
4e
con
Ir = I2e
−
× N
(10)
(
(
␮gPt/cm2GC: 11.7, 7.83, 5.2, 3.91, 2.61, 1.31) of a commercial Pt/C
where N stands for the collection efficiency of the RRDE. By com-
bining Eqs. (9) and (10) with Eq. (8), one generally expresses XH2O2
as Eq. (11).
Tanaka Kikinzoku, 46.1 wt% Pt, 2.7 nm mean diameter of Pt parti-
cles).
2
Ir
2
N
X
H2O2
=
= I
(11)
2.2. Controlling the structure of the thin-film electrode
I
N
r
d
I +
× N + 1
d
Ir
In order to obtain structure-reproducible thin films of catalyst
nano-particles homogeneously distributed on the GC and highly
dispersed, with minimal agglomeration, an ultrasonicated sus-
pension of the catalysts in ethanol was transferred to controlled
positions (∼1 ␮m precision) on the GC surface in tiny droplets
Up to now, XH2O2 has been derived according to the conven-
tional model (Eq. (11)) with the experimentally obtainable Ir, I , and
d
electrode-geometry-determined N [20]. N is also experimentally
measurable [21].
In both applied and fundamental research, XH2O2 has been
widely recognized as a characteristic parameter for a given cata-
lyst. Therefore, XH2O2 is supposed to have a constant value under
certain conditions (such as potential, temperature, electrolyte and
so on) for the surface of a given catalyst. The XH2O2 values obtained
according to Eq. (11), however, are reported to depend signifi-
cantly on the catalyst loading [19,22–24]. XH2O2 tends to decrease
with increasing catalyst loading, and this was attributed to fur-
(
∼3 nL in volume). As a result of the electrode preparation pro-
cess, the particles could be homogeneously distributed on the GC
surface in the form of micro-islands (less than 2–3 ␮m in thick-
ness even for the thickest part for the heaviest loading in this
study) or submicro-islands. Compared with the slow mass trans-
port through the overall diffusion layer (on the order of 10 ␮m
in thickness at rotation rates used in this study [20]) via one-
dimensional diffusion, mass transport within such micro-islands
or submicro-islands can proceed quickly via three-dimensional
quasi-hemispherical diffusion. This fast quasi-hemispherical dif-
fusion makes the effect of the mass transport-limit within the
micro-islands or submicro-islands negligible, and thus the thin-
film electrode behaves like a smooth bulk electrode. Further details
about the thin-film electrodes will be systematically reported
elsewhere [25].
ther reaction of the produced H O2 on active sites different from
2
those where they are produced [19]. As to the further reaction, a
mechanism of ‘desorption + re-adsorption + reaction’ was reported
in the literature [24]. In this mechanism, the probability for the
re-adsorption + reaction of the desorbed H O2 depends on the cat-
2
alyst loading and electrolyte flow in a thin-layer flow cell [24]. The
higher the loading or the lower the electrolyte flow, the higher is
the probability for re-adsorption.
The dependence of the conventionally-derived XH2O2 on catalyst
loading clearly indicates that the value of the conventional XH2O2
does not realistically or quantitatively reflect the intrinsic charac-
teristics of the surface for a given electrode in terms of the reaction
2
.3. Electrochemical measurements
−
The 0.1 M HClO4 electrolyte was prepared from high-purity
rate of the 2e pathway, because it is dominated not only by the
Grade reagent (Ultrapur, Kanto Chemicals). The glass cell was
treated in hot concentrated nitric acid and then rinsed with high
purity Milli-Q water. A platinum mesh was used as the counter
electrode and a reversible hydrogen electrode (RHE) was used as
the reference electrode.
surface properties of a given catalyst but also by the structure of
the electrode (essentially determined by catalyst loading), as illus-
trated in Fig. 1. Although both factors are important for a real fuel
cell electrode, it is important to distinguish them from each other
for a clear understanding, and then a reliable design, of the catalysts
and electrodes. In particular, a parameter such as XH2O2 that can
quantitatively reflect the intrinsic characteristics of the surface of
a given catalyst is critical in investigating the reaction mechanism
and comparing the surfaces of different catalysts.
Cyclic voltammograms (CV) of the electrodes were obtained at
◦
3
0 C from argon-deaerated electrolyte to characterize the ECSA
of Pt and then from oxygen-saturated electrolyte to quantitatively
characterize the H O2 formation.
2

2
100
K. Ke et al. / Electrochimica Acta 56 (2011) 2098–2104
Fig. 1. Schematic diagram for detecting hydrogen peroxide formation in oxygen reduction on the RRDE and models for deriving the yield of hydrogen peroxide.
3
. Results and discussion
With Id and Ir shown in Fig. 3 and N = 0.474, one can derive
according to the conventional model, as shown in Eq. (11).
XH
2O
2
3
.1. Confirmation of the problem in the conventional model:
Fig. 4 clearly shows that the conventionally-derived XH2O2 depends
on the ECSA (i.e., nas). The higher is nas, the lower is XH2O2 . This
trend agrees well with that reported in the literature [19,22–24]
and can be qualitatively explained, as shown below, by the re-
dependence of XH
on nas
O
2
2
The voltammograms are shown in Fig. 2 (in argon-deaerated
electrolyte) and Fig. 3 (in oxygen-saturated electrolyte). The ECSA
of Pt was calculated from the hydrogen underpotential deposition
charge.
adsorption + reaction of the desorbed H O before it is finally swept
2
2
completely away from the disk. A higher nas means a higher proba-
bility for the H O to re-adsorb on other reaction active sites, with a
2
2

K. Ke et al. / Electrochimica Acta 56 (2011) 2098–2104
2101
3
.2. Development of an extrapolation model by considering the
Ar-100mV s-1
re-adsorption + reaction probability
2
00
In order to obtain a value of XH2O2 intrinsic to the surface of a
given catalyst and free from the loading effect, we first introduce
the probability of the further reaction into the quantification model
as below. As illustrated in Fig. 1, if oxygen molecules are reduced
0
1
.62
reduced
−1
on the surface of a given catalyst at a rate of vO2
the real two-electron pathway proceeding at v2e
mol s , clearly, the
mol s , with
E
1
.01
−
1
-
200
400
0
.631
−
mol s and the
−
1
ECSA/cm2
0.544
real four-electron pathway proceeding at v4e
−
0
0
.278
.138
yield of hydrogen peroxide can be defined in Eq. (12). One should
note that this yield is only governed by the intrinsic characteristics
of the surface of the catalyst. Therefore, this yield could be used as
-
0
.0
0.2
0.4
0.6
0.8
1.0
1.2
E/V(vs RHE)
a characteristic parameter for the surface and we refer to this yield
int
as XH
hereinafter.
2O
2
Fig. 2. Voltammograms in Ar-deaerated electrolyte. (Note: the potential sweeping
−1
v2e
−
v2e
−
between 0 V and 1.2 V was conducted at 500 mV s for 50 cycles to pre-condition
the surface before obtaining the voltammograms in this figure).
int
X
=
=
(12)
H
2O
2
reduced
v
v4e
−
+ v2e
−
O
2
According to the re-adsorption + reaction mechanism [24], the
0
.0
0.2
0.4
0.6
0.8
1.0
produced hydrogen peroxide molecule can desorb from the site
where it is produced and may re-adsorb at some other site for
further reduction. One can imagine that the percentage of the
desorbed peroxide for re-adsorption + reaction (referred as Pre) is
proportional to the probability of re-adsorption + reaction. Then,
1
.62
1.01
.631
0.544
.278
.138
4
0
Ering =1.2V
0
ECSA/cm 2
2
0
0
0
0
0
re−ad
the reaction rate of further reduced hydrogen peroxide, v2e− , can
-1
1
10 0mm VV s/ s (O :0.1MPa, 900rpm)
be expressed in Eq. (13).
2
re−ad
-
500
v
−
2e
= Pre
v
2e− 0 ≤ Pre ≤ 1
(13)
Edisk
According the Faraday’s Law, one can express the reduction
current for the real two-electron reaction (I2e ) in Eq. (14), the
reduction current for the real four-electron reaction (I4e ) in Eq.
-
1,000
−
0
.0
0.2
0.4
0.6
0.8
1.0
−
Edisk/V (vs RHE)
(15), and the reduction current due to re-adsorption + reaction
re−ad
) in Eq. (16).
(I
−
e
2
Fig. 3. Voltammograms in an O2-saturated electrolyte. (Note: the voltammograms
shown in this figure were obtained by holding Edisk at 0.06 V for 30 s and then sweep-
ing Edisk between 0.06 V and 1.0 V. Data shown are the positive-going sweep of the
second cycle).
I2e
−
= 2Fv2e
−
(14)
(15)
(16)
I4e
−
= 4Fv4e
−
re−ad
re−ad
I
= 2Fv
−
−
2e
2e
concomitant higher probability to be consumed (Eq. (3)), and thus
One obtains Eq. (17) by combining Eqs. (14) and (13).
makes the overall reaction appear as if less H O2 forms (Eq. (2)).
2
re−ad
I
= PreI2e
−
(17)
−
e
2
This indicates that the conventional model for deriving XH
can
2O
2
−
underestimate the reaction rate of the 2e pathway on the surface
of a given catalyst. Therefore, the parameter XH2O2 derived from the
conventional model, may lead to misleading results in discussing
the difference in surface characteristics of different catalysts, par-
ticularly in calculating the kinetic parameters for fundamental
research.
r
Furthermore, Id and I can be expressed by Eqs. (18) and (19),
respectively. I2e
(19).
−
can be expressed in Eq. (20) by rearranging Eq.
re−ad
Id = I4e
Ir = (1 − Pre) I2e
−
+ I2e
−
+ I
= I4e
−
+ (1 + Pre)I2e
−
(18)
(19)
−
2e
−
N
1
I2e
−
=
× Ir
(20)
N(1 − Pre)
ECSA=0(extrapolation)
50
40
30
20
10
ECSA=0.138
ECSA=0.278
ECSA=0.544
ECSA=0.631
ECSA=1.01
ECSA=1.62
2
Pt
One can express I4e
−
by Eq. (21) by replacing I2e
−
in Eq. (18) with
(ECSA:cm )
the right hand side of Eq. (20) and then rearranging.
1
+ Pre
Ir
I4e
−
= I −
×
(21)
d
1 − Pre
N
int
X
H O2
int
2
One can express XH
with Id and Ir, as shown in Eq. (22), by
2O
2
by extrapolation model
combining Eqs. (17)–(21) with Eqs. (12), (14)–(16).
0
1
2
int
X
=
×
(22)
by conventional model
H
2O2
1 − Pre
Id
Ir
2
XH O2
×
N + 1
0
.0
0.2
0.4
0.6
0.8
1.0
Because the conventionally derived XH2O2 actually depends on
nas (Fig. 4), one can clearly see from Eq. (11) that, it is the current
Edisk/V (vs RHE)
ratio of I /Ir that depends on catalyst loading (i.e., nas). From Eq.
d
Fig. 4. Relation of the yield of hydrogen peroxide (XH2O2 ) versus disk potential (Edisk)
derived from the conventional model (Eq. (11)) and the extrapolation model (Eq.
(
22), one can naturally see that Pre should also be a function of nas,
int
(
23)).
because both XH
and N are independent of nas.
2O
2

2
102
K. Ke et al. / Electrochimica Acta 56 (2011) 2098–2104
In order to obtain Xint , one needs to know the specific values
-2
H
2O
Pt loading/µg .cm
2
Pt
GC
for both Pre and I /Ir. I /Ir is experimentally available. Pre, however,
d
d
0
.0
3.8
7.6
11.5
15.3
is not directly experimentally obtainable.
100
8
6
4
0
0
0
Edisk
1
500
400mV
int
20
0
3
.3. Extrapolation of XH
O
2
2
0
.0
0.1
0.2
0.3
For obtaining a specific value for Pre, one must re-examine
the mechanism [24] of the re-adsorption + reaction of the des-
orbed H O . Oxygen is reduced on some active sites, partially
producing hydrogen peroxide. The produced hydrogen peroxide
desorbs from where it is produced and is transported to another
location (neighboring to or away from the production site) to re-
adsorb. Therefore, it is not difficult to imagine that the probability
for re-adsorption on other active sites is dominated by two fac-
1000
500
0
300mV
2
2
200mV
100mV
65mV
0
.0
0.5
1.0
1.5
2.0
tors: (i) the mass transport rate for the H O2 (i.e., the rate of
2
2
escape of the hydrogen peroxide before it has absolutely no fur-
ther opportunity to be captured by the working electrode), and
nas(=ECSA of Pt)/cm
Fig. 5. Voltammograms derived results: linear relation of the current ratio (Id/Ir) at
various Edisk versus the number of the active sites (nas) or the catalyst loading.
(
ii) the number of active sites within the domain accessible by the
peroxide.
As to the effect of the rate of escape of the hydrogen perox-
ide, there are already detailed reports available. According to a
study with nanostructured model electrodes in a thin-layer flow
cell, under a condition with a given number of active sites (cata-
lyst loading), the higher was the electrolyte flow rate, the greater
was the opportunity for the desorbed H O to escape into the elec-
(
Eq. (23)).
1
2
int
H2O2
X
=
× lim
I
1
− limnas→0Pre
d
(
) × N + 1
nas→0
I
r
2
2
trolyte and the lower the opportunity for re-adsorption + reaction
24]. Therefore, one can imagine that if the rate of escape of
the hydrogen peroxide is infinitely fast, the opportunity for re-
2
= lim
(23)
[
Id
(
) × N + 1
nas→0
I
r
adsorption + reaction might be negligible (i.e., Pre = 0 at infinite
I
Ir
d
int
The specific value for limnas→0( ) is obtainable by extrapolat-
rate of escape). Therefore, theoretically, XH
is measurable if the
2O
2
ing the relation of I /Ir versus nas to nas = 0. Interestingly, a linear
relation was experimentally obtained for I /Ir versus nas (Fig. 5),
making the extrapolation very convenient. The linear relation can
be described by Eq. (24):
d
electrolyte flow rate is infinitely fast. This hypothesis is experi-
mentally supported by an interesting study on micro-electrodes
and ultramicro-electrodes of single carbon-supported Pt parti-
cles [26]. On the micro-electrodes or ultramicro-electrodes, a high
rate of escape of the hydrogen peroxide is realized by particle
diameter-determined hemispherical diffusion. When the size of
d
Id
=
A + A nas
(24)
0
1
Ir
the Pt particle is less than 50 nm, the H O2 formation rate is the
2
highest (XH2O2 = 25% at 0.4 V [26]) and appears to become inde-
where, A1 stands for the slope and A0 for the intercept at nas = 0.
Reasonably, A0 can be mathematically described by Eq. (25).
pendent of the size, and, however, a size-dependence of H O
2
2
formation is observed between 50 nm and 5 ␮m. We believe that
the value for the yield of hydrogen peroxide obtained at a diam-
eter of 50 nm is the intrinsic value to the Pt surface and is nearly
free from the re-adsorption reaction due to the high rate of escape
of the hydrogen peroxide. To achieve such a high rate of escape
of the hydrogen peroxide, however, is clearly not feasible for a
flow cell or an RRDE cell. Neither is it feasible to evaluate and
compare all catalysts with the single particle micro-electrode or
ultramicro-electrode due to the difficulty in the experimental
handling.
Id
A0 = limnas→0
(
)
(25)
Ir
Id
Eq. (23) becomes Eq. (26) by replacing lim
shown in Eq. (25).
(
) with A , as
nas→0 Ir
0
2
int
X
=
(26)
H
2O2
A0 N + 1
From Eq. (26), one can obtain the specific value for X Hi nt at a
2O
2
As to the effect of the number of active sites, one can imagine
that, at a given rate of escape, the fewer are the available active
sites, the lower will be the re-adsorption probability for the des-
orbed hydrogen peroxide before escaping from the disk. Therefore,
if there are close to zero active sites available for the desorbed
hydrogen peroxide, the probability for the re-adsorption of the per-
oxide also tends to approach zero. Consequently, the probability
for the further reaction (Eq. (3)) tends to approach zero. In other
words, all of the desorbed hydrogen peroxide can survive, with no
possible further reaction when there are no other active sites (i.e.,
under the condition of close to zero catalyst loading) on the disk
electrode.
certain potential. This value reflects the intrinsic characteristics of
the surface for a given catalyst in terms of the formation rate of
the H O2 intermediate, because the nas-dependent consumption
2
on the disk of the desorbed H O2 has been compensated by the
2
extrapolation.
The extrapolated X Hi nt values are shown in Fig. 4. By compar-
2O
2
int
H2O2
ing the X
extrapolated values with the conventionally-derived
XH
values, one can clearly see that the H O2 formation rate on
2O
2
2
the surface of a catalyst can be greatly underestimated (up to about
0-fold) if the re-adsorption + reaction of the H O2 are not taken
1
2
into consideration.
The high value of the extrapolated Xint agrees with the value
With the hypothetical boundary value at zero catalyst-loading
H2O2
int
obtained at a high rate of escape of the hydrogen peroxide on a
(
nas → 0) for Pre, one can derive X
from Eq. (22) if the value
H2O2
5
0 nm Pt particle [26], strongly supporting the extrapolation model.
of I /Ir at the boundary condition (i.e., nas → 0) is also available
d

K. Ke et al. / Electrochimica Acta 56 (2011) 2098–2104
2103
value of the slope A1 will be and the higher the probability of the
re-adsorption + reaction. This can be explained by a larger attrac-
tive force of the oxygen atoms in the peroxide at more positive
potentials. A larger attractive force obviously indicates an easier re-
adsorption + reaction at a single re-adsorption opportunity, hence
a higher Pre. Therefore, we believe that, the slope A1 is a parameter
related to the reaction probability of the peroxide during its one
opportunity for re-adsorption.
In this work, we first establish an extrapolation model for deriv-
ing the intrinsic yield of the hydrogen peroxide on the basis of the
thin-film of real catalyst particles. We expect that this extrapolation
model could promote the analysis of oxygen reduction mechanism
in a more accurate way and that applying the model into some
model electrode system [27] may clarify some unknown points for
the well known Pt/Co and Pt/Ni alloy catalysts, [5] as well as for
particle size effects and inter-particle distance effects.
In characterizing a given nano-sized catalyst with complicated
structure (for example, core-shell particles supported on some
difficult-to-process material) realized by some unique technique
or difficult process, it is quite challenging to study with a model
electrode due to the difficulty in fabricating an equivalent catalyst.
Thus, the thin-film electrode method in this work is clearly advan-
tageous, because the real catalyst material can be evaluated as it
is.
Roughness factor(=ECSA/area of GC)
0
.0
2.6
5.1
7.7
10.2
1
00
80
60
40
20
Edisk
400mV
300mV
200mV
100mV
65mV
0
0
.0
0.5
1.0
1.5
2.0
2
nas(=ECSA)/cm
Pt
Fig. 6. Voltammogram-derived results: Percentage of the desorbed hydrogen per-
oxide further reduced via re-adorption + reaction (Pre) versus the number of active
sites (nas).
3
.4. Specific expression of Pre in the extrapolation model
Rearranging Eq. (26) further, A0 can be expressed by Eq. (27).
int
4. Conclusions
2
− X
X
A0 = 1
×
H2O2
(27)
int
H2O2
N
In the quantitative characterization of the reaction intermedi-
ates on electrocatalysts with the RRDE method, if further reactions
of the intermediate occur before it reaches the ring, the yield of the
intermediate derived from the conventional model, in which there
is an underlying assumption that no further reaction occurs for the
produced intermediate, tends to be underestimated and does not
correctly reflect the intrinsic characteristics of the surfaces of the
electrocatalysts. For a proper quantitative analysis, the probability
for the further reactions of the desorbed intermediate should be
taken into consideration.
int
X
in Eq. (22) can be further expressed as Eq. (28) by com-
H
2O
2
bining Eqs. (24) and (27).
1
2
int
X
=
×
(28)
H
2O
int
2
1 − Pre
2−X
1
N
H2O2
(
×
+ A × nas) × N + 1
int
2
1
X
H
O
2
Rearranging Eq. (28), one can express Pre by Eq. (29).
2
Pre = 1 −
(29)
By studying the formation of H O in oxygen reduction on highly
2
2
int
2
+ A X
N nas
2O2
1
H
dispersed Pt/C thin-layer electrodes with various sample loadings,
we first propose a quantitative model (Eq. (22)) to compensate for
int
Because A > 0 (as shown in Fig. 5), 0 ≤ X
≤ 1, N > 0 and
1
H
2O
2
the re-adsorption + reaction of the desorbed H O2 and to extrap-
2
nas ≥ 0, one easily estimate from Eq. (29) the value range of Pre, i.e.,
olate the intrinsic yield of H O2 on the surface of a given catalyst
2
0
(
(
≤ Pre ≤ 1. This result satisfies the condition for Pre shown in Eq.
(shown in Eq. (23)). This model is based on the core concept that,
22). Also, from Eq. (29), one can obtain the two boundary values
if there are few active sites available (i.e., nas → 0, or ECSA → 0,
or zero loading) for the re-adsorption + reaction, nearly all of the
desorbed reaction intermediate can escape from the disk without
further consumption by its re-adsorption + reaction.
The high value obtained by extrapolation for the yield of hydro-
gen peroxide on Pt/C agrees well with that obtained at high rate of
escape of the hydrogen peroxide on an ultramicro-electrode of a Pt
single particle (50 nm in diameter) [26], on which we believe that
for nas → 0, and nas → ∞) of Pre, respectively: lim
(Pre) = 0 and
nas→0
limn →∞ (Pre) = 1. The experimentally derived boundary condition
as
value at zero-loading equals the hypothetical boundary condition
value. In contrast to zero-loading, at infinite loading (nas → ∞),
the value of Pre is 1, indicating that 100% of the desorbed hydro-
gen peroxide can be consumed due to the high probability for
re-adsorption + reaction. These results strongly support the extrap-
olation model.
the high rate of escape also ensures the desorbed H O2 to survive
2
Pre can be rearranged into Eq. (30) by combining Eqs. (22) and
26).
with little re-adsorption + reaction on other active sites.
(
A N + 1
A0 N
(A + A nas) N + 1
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