Electrocatalysis under Conditions of High Mass Transport Rate: Oxygen Reduction on Single Submicrometer-Sized Pt Particles Supported on Carbon

3262

J. Phys. Chem. B 2004, 108, 3262-3276

Electrocatalysis under Conditions of High Mass Transport Rate: Oxygen Reduction on

Single Submicrometer-Sized Pt Particles Supported on Carbon

Shengli Chen and Anthony Kucernak*

Department of Chemistry, Imperial College London, London SW7 2AZ, U.K.

ReceiVed: September 22, 2003; In Final Form: January 12, 2004

The effect of the mass transport coefficient of reactant and product species during the oxygen reduction

reaction, orr, on platinum in an acidic electrolyte has been experimentally examined and kinetically modeled.

By using carbon electrodes having electroactive radii on the nanometer scale it is possible to produce single

Pt particles having effective radii ranging from several micrometers to several tens of nanometers. As the

mass transport coefficient is directly related to the size of these platinum particles, it is possible to examine

the effect of mass transport on the orr in regions inaccessible to other experimental techniques. At the smallest

of these Pt particles, mass transport coefficients equivalent to a rotating disk electrode at rotation rates (ω)

of greater than 10⁸rpm are obtainable. Under low mass transport conditions equivalent to those obtainable

using the normal rotating disk technique (i.e, ω < 10 000 rpm), oxygen reduction is seen to proceed via a

four-electron reduction to water as has been reported in the general literature. Under high mass transport

conditions about 75% of reactant oxygen molecules are reduced to water with the balance being only reduced

as far as hydrogen peroxide. The production of peroxide which this result implies may be an important aspect

within the cathode catalyst layer of solid polymer electrolyte fuel cells, as these layers are inherently designed

to provide high mass transport coefficients. The oxygen reduction reaction on single catalyst particles is

modeled according to the parallel reaction mechanism originally introduced by Wroblowa et al. [Wroblowa,

H. S.; Pan, Y. C.; Razumney, J. J. Electroanal. Chem. 1976, 69, 195]. A general expression is derived to

predict the effects of the mass transport rate, surface blockage, and potential on the effective electron-transfer

number, n_eff, which reflects the average number of electrons produced during the reduction of each dioxygen

molecule. It is shown that a pure series (or indirect) reaction mechanism for the four-electron reduction of

oxygen on Pt electrodes in sulfuric acid solution is consistent with the experimental results. The kinetics of

the orr is analyzed using both Tafel plots and the half-wave potential method. The kinetic parameters extracted

from the half-wave potential method are in very good agreement with those extrapolated from the Tafel

curves with a -120 mV per decade slope. The complexities involved in the orr kinetics are discussed according

to the results obtained on these small single-particle electrodes. Specifically, the effect of the double-layer

structure and the role of anion adsorption are considered. It is argued that the electrocatalytic reduction of

oxygen involves inner-sphere electron-transfer steps and that its kinetics are affected by the potential profile

within the compact double layer, especially inside the inner Helmholtz plane (IHP). Anion adsorption may

perturb the orr in a way much more complex than simply blocking the surface sites and may significantly

change the potential near the IHP, thereby changing the effective driving potential that the reactant and reaction

intermediates experience. This may be partly responsible for the variable apparent values of the transfer

coefficient of the orr in different potential regions. A new mechanism for the size effects of catalyst nanoparticles

on their electrocatalytic properties toward oxygen reduction is proposed in terms of the particle size tunable

structure of the double layer.

1. Introduction

oxygen reduction leads to a more than 300 mV voltage loss in

polymer electrolyte fuel cell under typical operation conditions.³

The oxygen reduction reaction, orr, has been the focus of

electrochemical studies over many years especially because of

its critical role in fuel cells and its complex reaction mecha-

nism.^1-3The efficiency of fuel cells is limited on the cathode

side by the orr in terms of both the mechanism and its kinetics.

In mechanism, the formation of the two-electron reduction

product, H₂O₂, will reduce the effective electron-transfer number

(n_eff) of the orr. This product may also significantly increase

the degradation rate of any organic materials present, for

example, the proton conducting solid polymer electrolyte present

within a solid polymer electrolyte fuel cell. Poor kinetics of

The rotating ring-disk electrode (RRDE) technique has often

been used in studies of the orr because it provides the possibility

of probing the formation of H₂O₂accompanying oxygen

reduction and therefore of determining the effective electron-

transfer number, n_eff. In addition, the rotating electrode technique

allows kinetic analysis under steady-state mass transport condi-

tions. The RRDE results have been obtained either on bulk

electrodes made of polycrystalline materials,^4-6single-crystal

electrodes,^7-12or from electrodes decorated with small par-

ticles.^13-16The results obtained from these studies of oxygen

reduction on platinum and platinum-based alloy electrodes have

been used to support a parallel reaction mechanism with pre-

dominantly direct four-electron reduction to water. The forma-

* Corresponding author. E-mail: a.kucernak@imperial.ac.uk. Phone:

+44(0)20 75945831. Fax: +44(0)20 75945804.

Published on Web 02/12/2004

Oxygen Reduction on Pt Particles

J. Phys. Chem. B, Vol. 108, No. 10, 2004 3263

However, extremely high mass transport rates can be attained

at electrodes of reduced size. For example, the mass transport

rate would be about 0.2 cm s^-1at an electrode of 1 µm radius.

To attain such high mass transport rates, rotation rates of almost

10⁶rpm would be required, which is impossible using the

rotating electrode technique. Moreover, the mass transport rate

increases proportionally with the reciprocal of the electrode

radius. Recently, the RRDE technique has been used to study

the orr on carbon-supported Pt nanoparticles to investigate the

size effect of catalyst particles on the product distribution during

oxygen reduction.^13-16The model electrodes used in these

studies were prepared by coating a carbon RRDE disk with a

Nafion film containing carbon-supported Pt particles. The

steady-state diffusion behavior of such electrodes is actually

similar to that of a “normal” disk electrode made of platinum

in a normal RRDE experiment. Therefore, it is not possible to

study the effect of rapid diffusion away from individual particles

under steady-state measurements in such model electrode

configurations. These studies also suffer from the interference

of diffusion through the surrounding Nafion film. In addition,

the formation fraction of H₂O₂may be significantly underes-

timated in RRDE measurements at the Pt ring electrode because

catalytic decomposition of H₂O₂at this electrode occurs

simultaneously and is unseen as a ring current.

It has been suggested that the ideal model electrode system

for investigating the size effects of supported electrocatalysts

could be produced by deposition of platinum nanocrystals on

well-defined substrate surfaces.^30-32To obtain catalyst particles

of uniform size and shape and to keep particles well separated

from each other, the loading of Pt catalyst has to be rather

low.^30-32For instance, a pulsed electrodeposition method may

be used.³¹However, measurement of the electrocatalytic

response of such very low loading electrodes is difficult because

of the relatively large background interference from the un-

catalyzed substrate. Attempts to increase the Pt loading typically

result in a loss of monodispersity and an overlap of adjacent

catalyst particles.³⁰Recently, we have shown that carbon

electrodes having very small electroactive areas with effective

radii of only a few nanometers may be prepared by electro-

chemically etching carbon fibers followed by electrophoretic

deposition of paint to insulate the body of the etched fibers.³³

With the use of these very small electrodes as substrate, it is

possible to limit formation during Pt electrodeposition to only

one nucleus during the deposition process, thus forming a single

catalyst particle supported on a carbon substrate.³⁴Such carbon-

supported Pt particle electrodes may act as model catalyst

particles in the study of fuel cell relevant reactions without the

complication of the presence of other nearby catalyst particles

allowing measurements under conditions of defined mass

transport and kinetics. The effective Pt loading for these elec-

trodes is high even though only a very small catalyst particle is

deposited as the electroactive area of the supporting substrate

is extremely small. In this paper we conduct a study of the orr

in an aqueous acid medium employing such carbon-supported

individual Pt particle electrodes. The particle size effects on

the reaction pathways and kinetics are explored. It is shown

that the catalyst particle size may alter the orr pathway via

changing the mass transport rate, even though the particle sizes

studied are much larger than those typically used in fuel cell

systems. The apparent kinetics of the orr also appear to be

affected by the particle size via double-layer effects.

Figure 1. Wroblowa scheme for the pathways of the oxygen reduction

reaction.

tion of H₂O₂during the orr at Pt-based electrodes in acid

medium is presumed to occur through an alternative, parallel

mechanism and is negligible at potentials outside the hydrogen

adsorption region. The reaction scheme proposed by Wroblowa

et al.^1,2,17has been generally accepted as the mechanism of this

parallel reaction (Figure 1). The k’s and a’s in Figure 1 are the

overall rate constants for the corresponding reaction or adsorp-

tion steps, each of which may contain several elementary steps.

The superscripts b, s, and * refer, respectively, to species which

are in bulk solution, in the vicinity of the electrode surface,

and which are adsorbed on the electrode surface. Also, it has

been generally accepted that the rate-determining step in the

orr is the first electron-transfer step and that the real reaction

rate is an overall result of the coupling of this step with the

diffusion and adsorption of oxygen molecules.^1,2,18-20

Pt particles of nanometer size supported on carbon are the

most widely used catalyst in polymer electrolyte fuel cells. There

has been great interest in the relationship between the activity

of such catalysts toward the orr and the size of the supported

Pt particles.^21-29Although great efforts were made, the conclu-

sions varied among the different researchers. The inconsistent

results and conclusions are most probably caused by the

structural complexity of the electrodes employed. The electrodes

used in these studies were prepared by deposition of Pt colloidal

particles onto porous graphitic carbon. The catalyst particles

produced in this way usually have a layer of stabilizing organic

ligand on surface. In addition, other additives, for example,

binding materials, have to be used in the production of the elec-

trode.²³Thus, the results may be modified by such complex-

ities as porous diffusion, particle size distribution, and the

presence of additives. A study by Watanaba et al.²³suggested

that the distance between adjacent Pt particles plays a key

role in the catalytic activity of the supported Pt nanoparticles

electrodes toward the orr. According to this suggestion, the

activity of a given mass of Pt particles is controlled by both

particle size and particle separation. At constant loading of

platinum on carbon, the average particle separation distance

decreases with particle size, and thus, even though absolute

surface area of the platinum increases, each particle has a greater

probability of influencing the diffusion field of adjacent particles.

However, the high mass transport rate around individual

nanoparticles may lead to formation of H₂O₂, resulting in loss

of activity. It is clear from the reaction scheme shown in Figure

1 that the two-electron reduction to H₂O₂would become more

pronounced when the transport rate of H₂O₂away from the

vicinity of the electrode surface is increased, as this provides a

continuous driving force to move the equilibrium toward pro-

duction of hydrogen peroxide. Although the rotating electrode

technique can increase the mass transport rate, the rotation rates

used in RRDE studies of the orr (all below 10 000 rpm, limited

by cavitation of the electrolyte) might be too low to produce

high enough mass transport rates to affect the reaction pathways

of the orr.

2. Experimental Section

Carbon fibers (PANEX33 CF, 95% carbon, Zoltek Corpora-

tion, MO) were used as received, as was the cathodic electro-

3264 J. Phys. Chem. B, Vol. 108, No. 10, 2004

Chen and Kucernak

phoretic paint solution (Clearclad HSR, LVH Coating Ltd.,

U.K.). Solutions containing H₂SO₄(Merck, Aristar), K₂PtCl₄-

(Aldrich, 99.9%), Ru(NH₃)₆Cl₃(Aldrich, 98%), KCl(BDH

Analar) were made with Milli-Q water (19 MΩ cm). All

experiments are conducted at room temperature. Ultrahigh purity

gases were used, with the hydrogen being “CO-free”.

Ltd., Cambridge U.K.) into a tapered glass tube using a resistive

heating coil made from Nichrome wire (Advent, Ni80/Cr20,

0.5 mm in diameter). This sealing method can completely seal

the metal wires into the glass. The Pt disk was exposed by

polishing the electrode on 30 µm alumina paper (Buehler). After

the Pt was exposed, the electrodes were then polished with

successive grades of alumina paper (9 µm, 1 µm, and 0.3 µm,

respectively). Before each use the Pt microdisk electrode was

polished with 0.3 µm alumina paper and rinsed in Milli-Q water

in an ultrasonic bath. After this, the electrodes were immersed

in acidified potassium permanganate solution for 30 min; this

treatment was followed by sonication and then a rinse in

acidified dilute H₂O₂solution and then in Milli-Q water.

2.2. Electrochemical Measurement. An AutoLab PG-

STAT20 potentiostat with the ECD module (Eco Chemie BV,

Netherlands) was used in all electrochemical experiments, and

a two-electrode configuration was employed. A calomel refer-

ence electrode was employed during electrodeposition of

platinum and in the experiments in which the electroactive radii

of the carbon electrodes were determined. A large Pt sheet was

used as a quasi-reference electrode in the experiments on oxygen

reduction and hydrogen oxidation because it is easily cleaned.

All potentials are reported with respect to RHE, unless otherwise

stated. The glass electrochemical cell and the Pt quasi-reference

electrode were immersed in acidified potassium permanganate

solution overnight and rinsed with acidified dilute H₂O₂solution

and then Milli-Q water before use.

After rinsing with Milli-Q water, the Pt/carbon electrode

assemblies were transferred into the electrochemical cell

containing 0.1 mol dm^-3H₂SO₄saturated with high-purity argon

and subjected to potential cycling between 0.05 and 1.5 V at a

scan rate of 100-500 mV s^-1until a reproducible and well-

defined cyclic voltammogram (CV) was obtained. The solution

was then replaced by fresh 0.1 mol dm^-3H₂SO₄and oxygenated

with high-purity oxygen for at least 15 min. The electrodes were

then subjected to several potential scans (0.05-1.5 V) to check

the reproducibility of the voltammograms. Immediately after

this cycling, a steady-state current-potential curve (1.05 to 0.25

to 1.05 V) was recorded. After measurement on the Pt particle

electrodes, steady-state CVs were recorded on two Pt microdisk

electrodes in the same solution. The solution was then saturated

with research grade CO-free hydrogen by bubbling for 15 min

using the same experimental protocol as described above. During

the experiments an atmosphere of the corresponding gas was

kept in the cell above the solution.

2.1. Electrodes Preparation. 2.1.1. Carbon-Supported Single-

Pt-Particle Electrodes. The preparation of nanometer-sized

carbon electrodes has been previously described.^33,35The

electroactive radii of the prepared carbon electrodes were

determined from the steady-state limiting current obtained in

0.01 mol dm^-3Ru(NH₃)₆Cl₃+ 0.5 mol dm^-3KCl. In this study

only the carbon electrodes having effective electroactive radii

less than 10 nm are used as substrates to prepare the carbon-

supported Pt particle electrodes so that single Pt particles are

formed.³⁴The Pt electrodeposition solution was composed of

0.1 mol dm^-3H₂SO₄+ 1 × 10^-3mol dm^-3H₂PtCl₄. Argon

gas was bubbled into the electrodeposition solution for 15 min

to remove any oxygen prior to electrodeposition of platinum.

During the deposition, an argon atmosphere was maintained

above the solution. The Pt was deposited at a constant potential

of -0.15 V vs SCE at which potential the deposition process

occurs under pure diffusion control.³⁴The size of the resulting

Pt particle was controlled by terminating the deposition either

after a specific deposition charge had been consumed or when

the magnitude of the current exceeded a predetermined value.

Before and after deposition of Pt, the electrodes were rinsed

with large amounts of Milli-Q water. SEM images of several

typical Pt particle electrodes obtained by this method are shown

in refs 34 and 36. In these images it can be seen that the Pt

particles sit at the very end of the insulated carbon tips and

have an approximately hemispherical shape. These particles are

almost uniformly accessible for diffusion of reactants, and the

corresponding diffusion geometries around such particles are

between hemispherical and spherical. In the following we will

assume that the diffusion field around these particle electrodes

is uniform. Under such conditions the mass transport coefficient

of the electroactive species i (m_i) on these particles can be

defined as^37,38

D_i

m_i)

(1)

r_eff

where D_iis the diffusion coefficient of the corresponding

electroactive species and r_effis the effective electroactive radius

of the catalyst particle. We use the term “effective radius”

because the radius values are determined from the steady-state

limiting diffusion current by assuming that the particles possess

a hemispherical shape. In reality, the particles may not have a

perfect hemispherical shape, although as will be shown below

such deviations have no effect on our analysis.

These particles are large enough so that their surface can

effectively be considered as being composed of polycrystalline,

bulk platinum. We do not expect any formation of faceting, or

changes in the predominance of different crystal facets with

particles size, as has been shown to occur for much smaller

particles.³⁹Indeed, work in the literature suggests that the

specific activity of platinum particles due to changes in surface

structure does not occur until particles are less than 15 nm in

size,⁴⁰and so we can be confident that the specific activity of

our particles and the reaction mechanism remains independent

with particle size over the range of particles sizes which we

study.

The effective electron-transfer number n_efffor the orr is

calculated from the limiting current I_Lof the steady-state

voltammograms in the presence of oxygen. The steady-state

limiting diffusion current obtained on a microelectrode is

I_L) Bn_effFD_ic^b_ir_eff

(2)

where B is a factor that depends on the geometric shape of the

electrode and c^b_iis the bulk concentration of the electroactive

species. Glass-sealed Pt microdisk electrodes (25 µm diameter)

have a well-defined disk shape, so the values of D_ic^bcan be

i

determined from the limiting current values determined during

the steady-state voltammograms of the Pt microdisk electrodes

according to eq 2 using B ) 4, r_eff) 12.5 µm, n_eff) 4 for

oxygen reduction and n_eff) 2 for hydrogen oxidation. It is

reasonable to assume that n_eff) 4 for orr on a Pt microdisk

electrode of 12.5 µm radius because an electrode of this size

has a mass transport rate close to that of a rotating electrode at

4000 rpm, a typical value used in RRDE experiments. Under

2.1.2. Pt Microdisk Electrodes. Pt microdisk electrodes were

made by sealing Pt microwire (12.5 µm radius, Goodfellows

Oxygen Reduction on Pt Particles

J. Phys. Chem. B, Vol. 108, No. 10, 2004 3265

4Fk₁c^b_O

2Fk₂c^b_O

2Fk₃â₂c^b_O

2

such conditions four-electron reduction occurs provided the

potential is not within the hydrogen adsorption region. Use of

the limiting current from the steady-state CVs obtained on each

Pt particle electrode for hydrogen oxidation (n_eff) 2) and the

known values of D_Hc^bdetermined in the same solutions

2

j )

+

(9)

â₁

Similarly, if water was the only species produced from the

reduction of O₂then the current density expected would be

2

H₂

using the Pt microdisk electrodes of known diameters allows

determination of Br_efffor that Pt/C catalyst particle. The n_eff

values for oxygen reduction on each Pt particle can then be

determined from the limiting current in the steady-state CV

obtained for oxygen reduction according to eq 2, by substituting

the values of D_Oc^bdetermined from the CVs of the Pt

k₁+ k₂

â₁

j_4e) 4F

c_O^b

(10)

2

Expressions for θ₁, θ₂, â₁, and â₂are given in Appendix I.

Both â₁and â₂are functions of the particle size and the reaction

rate constants k_iand a_i, which are potential dependent. The

current-potential variation can be obtained by substituting the

potential dependence of each of the rate constants into eqs 9

and 10.

3.2. Effective Electron-Transfer Number n_eff. The effective

electron-transfer number accompanying the orr when H₂O₂is

produced and diffuses away from electrodes into solution can

be derived from eqs 9 and 10

2

O₂

microdisk electrodes in the same solution and the values of Br_eff

determined from the CVs for the hydrogen oxidation reaction

on the same particle electrodes.

3. Modeling the orr on Single Catalyst Particles

3.1. Current-Potential Behavior. According to the reaction

scheme shown in Figure 1, the current density accompanying

oxygen reduction can be expressed as

j ) 4FV₁+ 2FV₂+ 2FV₃) 4Fk₁θ₁+ 2Fk₂θ₁+ 2Fk₃θ₂

j

j_4e

2

k₁

n_eff

)

4 ) 4 -

(11)

(3)

1 + (1 + x)

(

)

k₂

where V_irepresents the overall reaction rate of the ith reaction

step. θ₁and θ₂are the coverage of adsorbed oxygen and

hydrogen peroxide species, respectively. Under steady-state

conditions we have the following mass balance equations for

adsorbed and soluble species

where

k₃

a₂

k₃

a₂r_eff

x )

1 +

)

1 +

(12)

(

)

(

)

a_2-

m

a_2-

D

H₂O₂

dθ₁

) a₁c^s_O(1 - θ) - a_1-θ₁- k₁θ₁- k₂θ₁) 0 (4)

It is clear that the value of n_effwill decrease with an increased

mass transport coefficient of H₂O₂, that is, with decreased radius

of the catalyst particle when the values of the rate constants

involved in eqs 11 and 12 remain constant. It is also implied

by eqs 11 and 12 that the mass transport rate-induced change

in the value of n_effis significant only when the value of r_effis

in a certain range. When the radius of the catalyst particle (r_eff)

is small enough so that 1 + a₂r_eff/D_{H O}≈ 1, the n_effvalue will

2

dt

dθ₂

) k₂θ₁- k₃θ₂+ a₂c^s_{H O}(1 - θ) - a_2-θ₂) 0 (5)

2

dt

dc^s

dc

s

O₂

) D_O

- a₁c^s_O(1 - θ) + a_1-θ₁) 0 (6)

(

)

2

dt

dr

become almost invariant with r_effand is determined by the value

s

of (1 + k₁/k₂)(1 + k₃D_Ha_2-). When r_effis large enough so that

2

s

dc

H₂O₂

+ a_2-θ₂- a₂c^s_{H O}(1 - θ) ) 0 (7)

2/(1 + k₁/k₂)(1 + x) , 4, the value of n_effwill be very close to

4 and also independent of the value of r_eff, that is, independent

of the mass transport rate.

) D_{H O}

(

)

2

2 2

dt

dr

where θ represents the total surface coverage of all the possible

adsorbed species and 1 - θ represents the fraction of surface

sites available for adsorption. It is reasonable to assume that

the value of 1 - θ stays constant at a defined potential when

steady-state has been reached. Thus, we can incorporate the 1

- θ term into the corresponding adsorption rate constant, that

is, replace a_i(1 - θ) with a_iin the above equations. In results,

the corresponding adsorption rate constant a_iwill depend on

Thus, at certain values of the mass transport coefficient, the

value of n_effis determined by the ratio of k₁/k₂, which represents

the competition between the so-called direct four-electron

pathway and the series reduction (or indirect) pathway, and the

ratio of k₃/a_2-, which represents the competition between the

electroreduction of absorbed peroxide species and its desorption.

The value of n_effwill decrease with the value of these two ratios.

Furthermore, n_effwill be a function of electrode potential because

these rate constants are potential dependent. The detailed

relationship between n_effand electrode potential might be a quite

complex function that requires knowledge of the dependence

of each rate constant on the potential. As well as the rate

constant, the potential can affect the surface coverage of various

adsorbed species. This will result in a change of the 1 - θ term

that for simplicity has been incorporated into a₂. It can be seen

from the above expression of n_effthat the effective electron-

transfer number accompanying the orr decreases with the value

of 1 - θ, that is, the adsorption of species other than the reactant

or reaction intermediates may result in enhanced formation of

hydrogen peroxide.

the total coverage of adsorbed surface species. The c^sand (dc_i/

i

dr)^sterms are the concentration and concentration gradient of

soluble species i (i ) O₂or H₂O₂) in the vicinity of the electrode

surface. The concentration gradients in the vicinity of the

electrode can be obtained by solving the steady-state diffusion

equations. The solution is given as^38,41

s

dc_i

m_i

D_i

)

(c^b_i- c^s_i)

(8)

( )

dr

where m_iis the mass transport coefficient defined in eq 1.

Solving eqs 4-8 gives the steady-state values of θ₁and θ₂. An

expression for the current density is then obtained by substituting

the values of θ₁and θ₂into eq 3

It should be pointed out that the n_efffor the orr can also be

affected by the chemical decomposition of H₂O₂into O₂and

3266 J. Phys. Chem. B, Vol. 108, No. 10, 2004

Chen and Kucernak

Figure 2. Typical steady-state cyclic voltammograms obtained on a

12.5 µm radius Pt microdisk electrode in either O₂- or H₂-containing

0.1 mol dm^-3H₂SO₄solution. (dV/dt): 100 mV s^-1

.

H₂O without net electron transfer. This paper mainly deals with

the effect of the catalyst particle size on the orr reaction

mechanism and kinetics. So, we do not include this possible

decomposition reaction of H₂O₂in the reaction scheme and

model because this effect would be similar on electrodes of

different size. In the above derivations we did not include the

concentration of hydrogen ions in the rate equations. Even if

the proton is involved in the reaction steps that control the

overall reaction rate, the concentration of protons can be

considered a constant and included in the rate constants of the

corresponding reaction steps. It is also worth mentioning that

each reaction step shown in Figure 1 may contain a number of

elementary steps. In addition, the reaction intermediates may

not necessarily have the exact form as that shown in Figure 1

and might even have multiple forms. However, this will not

affect the basic form of the expressions for the current density

and n_eff. In these alternate cases, the rate constants involved in

the above equations have to be replaced by rather more

complicated expressions consisting of the rate constants of the

elementary steps.

Figure 3. Steady-state cyclic voltammograms obtained on Pt single-

particle electrodes of effective electroactive radii of 49 nm (a) and 3.6

µm (b) in either O₂- or H₂-containing 0.1 mol dm^-3H₂SO₄solution.

(dV/dt): 100 mV s^-1. The measured values of the effective electron-

transfer number for the orr on each of those particles are displayed in

the diagrams.

10^-11mol cm^-1s^-1and D c ) 2.24 × 10^-11mol cm^-1s^-1

H₂H₂

calculated from D ) 1.8 × 10^-5cm²s^-1and c ) 1.12 ×

O₂

10^-6mol cm^-3(both from ref 42) and D ) 3.8 × 10^-5cm²

H₂

s^-1and c ) 0.59 × 10^-6mol cm^-3(both from ref 43), with

H₂

the slight variation due to the different conditions under which

the measurements were made. For comparison, D

is 1.45

H₂O₂

× 10^-5cm²s^-1under similar conditions.⁴⁴

Figure 3 shows the steady-state cyclic voltammograms

obtained on two Pt particle electrodes of different radii. The

CVs obtained on larger particles are very similar to that in Figure

2. On small particles, however, the CVs for the oxygen reduction

reaction are obviously drawn out because of the irreversibility

of the orr under accelerated mass transport. The limiting current

value is still readable from the negative limit of the CVs when

r_effis larger than 50 nm. It is more difficult to get CVs for

oxygen reduction having well-defined limiting currents when

the effective radii of particles is smaller than this value, as these

limiting currents do not occur until within the hydrogen

adsorption region.

The expression for n_effderived above is not limited to the

orr on small particles. It could also be applied to the orr in

rotating electrode experiments, but in those cases the mass

transport coefficient m_ihas to be replaced by 0.620D_i^2/3V^-1/6ω^1/2

.

The effect of the rotation rate on the value of n_effmight not be

seen with rotating electrode techniques as discussed in the

Introduction. However, this model may be useful in analyzing

the results from rotating electrode experiments investigating the

effect of surface blockage, such as oxide formation, hydrogen

adsorption, anions adsorption, and so on, on the formation of

H₂O₂during the orr.

It can be seen that for these steady-state CVs the orr current

on the positive-going I-E curves are always larger than those

on the negative-going scans. This is a common characteristic

for steady-state CVs for oxygen reduction and has also been

obtained on bulk Pt electrodes while using rotating electrode

techniques. The orr activity is always higher during the positive-

going scan because of the orr taking place on an oxide-free

surface. The numbers inserted in Figure 3 indicate the values

of the effective electron-transfer number calculated from the

limiting current values using eq 2. On the larger particle

electrode (3.6 µm effective Pt particle radius), the value of n_eff

is close to 4, whereas the calculated n_effvalue is about 3.5 at

the Pt particle of effective radius of ∼50 nm.

4. Results and Discussion

4.1. Particle-Size-Dependent n_effand the Mechanism of

orr. Figure 2 shows the typical steady-state cyclic voltammo-

grams obtained on a 12.5 µm radius Pt microdisk electrode for

oxygen reduction and hydrogen oxidation. Well-defined limiting

current plateau can be found in both I-E curves. The steady-

state CVs obtained on two Pt microdisk electrodes of the same

diameter are almost identical to each other within an experiment.

There was some variation in the limiting current values of the

CVs of the Pt microdisk electrodes in different experiments,

but this deviation is below 5%. The values of D_Oc_Oand D_Hc_H

Figure 4 shows the variation of n_effat a potential of 0.4 V

(RHE), that is, within the double-layer region, with the effective

radius of the Pt particle (r_eff) obtained from the steady-state CVs

on electrodes having a range of particle sizes. This potential

was chosen because it is outside the hydrogen adsorption region

2

determined from these experiments are (2.41 (²0.06) × 10^-11

mol cm^-1s^-1and (2.9 ( 0.1) × 10^-11mol cm^-1s^-1

,

respectively. These values compare well to D_Oc_O) 2.03 ×

2

Oxygen Reduction on Pt Particles

J. Phys. Chem. B, Vol. 108, No. 10, 2004 3267

) 2.2, a₂) 0.4 cm s^-1, respectively. In all cases, a D_{H O}of

2

1.45 × 10^-5cm²s^-1was used.⁴⁴

From the experimental data and the model curves, it is clear

that the variation of n_effmainly occurs on particle having sizes

ranging from 50 nm to 5 µm. On particles larger than 5 µm,

the n_effvalue is larger than 3.97 and hardly changes with the

particle size, that is, the fraction of hydrogen peroxide produced

is less than about 2%. This is in good agreement with the

conclusion obtained from the RRDE measurements on large

electrodes. When the radius of particles is less than 50 nm, the

value of n_effappears to also tend toward a constant. This is

because the diffusion of H₂O₂is so rapid at small particles that

the local concentration of H₂O₂adjacent to the electrode is

effectively zero and the rate of loss of H₂O₂is controlled by

the a_2-desorption process. Thus, the formation rate of H₂O₂is

mainly governed by the competition between the so-called direct

four-electron pathway and the series or indirect pathway (k₁/

k₂) and the competition between the electroreduction steps of

reaction intermediates H₂O_2adand its desorption steps. The Pt

particles used in fuel cell catalytic electrodes usually have radii

less than 5 nm. The data and the model curves in Figure 4

indicate that changes in particle size over this range should have

little effect on the formation fraction of hydrogen peroxide

resulting from the mass transport effect. Of course, other effects

at such small particles, for instance, variations in the prevalence

of different crystallite facets, may play an important part in the

reactions occurring.

Figure 4. Variation of the value of n_effwith the effective radius of

single carbon-supported Pt particles for the orr at 0.4 V (RHE) in O₂-

saturated 0.1 mol dm^-3H₂SO₄. The lines represent simulations of the

curves using eq 11 utilizing the following parameters: k₁/k₂) 1.0,

k₃/a_2-) 0.72, a_2-) 0.4 (solid curve); k₁/k₂) 0.0, k₃/a_2-) 2.2, a_2-

) 0.4 (dashed curve), respectively. The top x-scale shows the equivalent

mass transport coefficient assuming a diffusion coefficient of 1.6 ×

10^-5cm²s^-1, a value intermediate between that of hydrogen peroxide

and oxygen. Set within the figure is an indication of the equivalent

rotation rates required to achieve the same mass transport conditions

utilizing a rotating electrode in aqueous electrolyte.

Another aspect which will have a significant effect in real

fuel cell systems is the fact that other particles will exist in

close proximity to each other. They will tend to form diffusion

spheres that collide and interact to greater or lesser extent de-

pending upon the interparticle separation and diffusion coef-

ficient of the reactant. The net effect will be to lower the local

mass transport coefficient. The extent to which this occurs will

be highly geometry dependent. Indeed, in agreement with our

work, Watanaba et al.²³have suggested that a large separation

between adjacent particles should be able to increase the overall

oxygen reduction activity on supported Pt nanoparticles. In other

words, not only the particle size but the Pt loading plays a key

role in determining the specific mass activity of the carbon-

supported Pt particle electrodes toward oxygen reduction.

but provides a point at which a limiting current is seen on the

smallest Pt particles examined. If a higher potential is used,

the diagram is exactly the same as that shown in Figure 4 except

for the exclusion of points from the smallest electrodes, as these

do not show a limiting current at that higher potential. Thus,

the reason for choosing the lower potential is to provide the

widest range of accessible mass transport rates, and the

conclusions drawn from the plots are generally applicable to

oxygen reduction at any potential above the hydrogen adsorption

region.

The top x-scale in Figure 4 corresponds to the mass transport

coefficient at the equivalent electrode radius assuming a

diffusion coefficient of 1.6 × 10^-5cm²s^-1, that is, a value

intermediate between those of oxygen and hydrogen peroxide.

Also displayed in Figure 4 is a scale representing the equivalent

disk rotation rates under the same conditions. It can be seen

that the value of n_effshows a continuous decrease with r_effin

the range from 3 micrometers down to 100 nanometers. When

the radii of particles are below 100 nm, the decrease of n_eff

becomes less obvious, although the value of n_effappears to start

leveling out at a value less than 3.5. An n_effvalue of 3.5

corresponds to a situation in which 75% of oxygen molecules

are reduced to water and 25% are reduced to H₂O₂. As

mentioned above, measurement of the n_effvalues on particles

smaller than about 50 nm is problematic, as the limiting oxygen

reduction current does not occur until the hydrogen adsorption

region, and as has already been discussed, we expect there to

be enhanced H₂O₂production within that potential range.

According to eq 11 and considering that 1 + k₃/a_2-is always

larger than 1, the value of k₁/k₂has to be less than 2.5 to allow

such small n_effvalues to occur. Obtaining more accurate values

is difficult although we find reasonable fits to the data with

restricted sets of parameters. A reasonable fit to the whole set

of data in Figure 4 with the model equations can only be

achieved by setting k₁/k₂< 1.5 and a₂to 0.4. Two fitting curves

are shown in Figure 4 using the following parameters values:

k₁/k₂) 1, k₃/a_2-) 0.72, a₂) 0.4 cm s^-1and k₁/k₂) 0, k₃/a_2-

Another interesting conclusion obtained from examining the

fitting curves for Figure 4 is that our results do not exclude a

pure series (i.e., indirect) reaction mechanism for oxygen

reduction on Pt electrodes in sulfuric acid solution, that is,

exclusively following the lower branch in Figure 1. When k₁/

k₂) 0, the model curve still well fits the experimental data.

Within Figure 4 we see that, even for the pure series mechanism,

approximate four-electron reduction of oxygen occurs provided

the particle is not very small, for example, provided it is >5

µm in size. The corresponding mass transport coefficient is about

0.04 cm s^-1, equivalent to a rotation rate of about 25 000 rpm.

Thus, our present study shows that the series pathway (i.e.,

indirect hydrogen peroxide pathway) plays an important role

in the orr, rather than a negligible role as generally believed.

Within the general electrochemistry literature, the conclusion

that the direct four-electron reduction pathway is the predomi-

nant pathway in orr on Pt is generally based on several facts

obtained in RRDE experiments. For instance, little ring current

due to the oxidation of peroxide is generally detected^4-10,12-15

and pronounced formation of H₂O₂is only observed when

strongly adsorbed surface species are present, for example,

strongly adsorbed anions such as Br^-, Cl^-, and so on^{1,2,7,9-12,15}

or some surface UPD (underpotential deposition) atoms such

3268 J. Phys. Chem. B, Vol. 108, No. 10, 2004

Chen and Kucernak

as H, Pb, Cu, and so on^{2,7,8,10-12,45-49}It is shown in the present

study that the small values of ring current may be due to the

low mass transport rate accessible using typical RRDE experi-

ments. Under such mass transport conditions, the nearly com-

plete four-electron reduction is possible following the pure series

(indirect) mechanism. The effect of a blocking species on the

formation of H₂O₂has been generally attributed to the inhibition

of the dissociative adsorption of the oxygen molecule on the Pt

surface, a process that is considered to be the initial step of the

direct four-electron reduction pathway. Thus, the increased rate

of H₂O₂production in the presence of strongly adsorbed species

has been considered as being indirect evidence of the direct

four-electron reduction pathway.^1,2However, the enhancement

of H₂O₂formation induced by surface adsorption of spectator

species might not be a unique indicator for the direct pathway

reaction mechanism. If we set k₁/k₂) 0 and separate the 1 -

θ term from the adsorption rate constant, the expression for

n_effthen becomes

occurs, which has been explained as a rate-determining first

electron-transfer process for which the corresponding transfer

coefficient is close to 0.5.^{1,5,7-12,18-20}The slopes of Tafel curves

in the high-potential region (low current density region) are

typically around -60 mV per decade of current density on Pt

electrodes in pure sulfuric or perchloric acid solutions. A

transition in slope occurs at potentials between 0.8 and 0.85 V.

Such changes in slope of the Tafel plots for the orr have been

attributed to a change of the adsorption mode of the reactant

and reaction intermediates on the electrode surface, for example,

from Langmuirian adsorption to Temkin adsorption,^5,18-20or

has been explained in terms of the potential-dependent coverage

of surface oxide like PtOH which inhibits the adsorption of O₂

and reaction intermediates.^{1,2,7-12,50-52}The inhibitory mechanism

seems to be more reasonable and has been supported by some

indirect evidence.^1,2,7-12Such inhibition effects of surface oxide

on the rate of oxygen reduction can be shown by expressions

for the apparent rate constant k_appof orr, that is

- RF(E - E⁰)

-∆G_θ

2

k_app) k⁰(1 - θ) exp

exp

(14)

n_eff) 4 -

(13)

(

)

[

]

k₃

a₂(1 - θ)

RT

1 +

a_2-

[

m_{H O}

]

This equation is straightforwardly derived from eq A9 (shown

in Appendix II) by replacing the adsorption equilibrium constant

a₁/a_1-with its equivalent in terms of the adsorption free energy

∆G_θand separating the 1 - θ term from a₁. It can be seen that

the surface oxide may affect the reaction rate in two ways. First,

it reduces the number of surface sites available for oxygen

adsorption, that is, decreases the value of 1 - θ. Second, it

modifies the free energy for oxygen adsorption. Furthermore,

not only the surface oxide but also other surface-adsorbed

species may affect the orr rate in a similar way and can thus be

described using eq 14. Such a rate equation has been used by

Markovic et al.^2,9for oxygen reduction on Pt single-crystal

electrodes. This expression is different from that given by

Damjanovic et al.^18-20in which the 1 - θ term is not included.

The slopes of the Tafel plots depend on the value of the transfer

coefficient R of the first electron-transfer step, the potential

dependence of the total coverage of all adsorbed species, and

the potential dependence of ∆G_θ, the latter depending on the

interaction between neighboring adsorbed species. It should be

pointed out that eq 14 is only valid when the electron-transfer

step is very slow compared to the adsorption step, that is, the

electron transfer between the electrode and the adsorbed reactant

determines the overall reaction rate and the surface coverage

of oxygen is approximately determined by the adsorption/

desorption equilibrium. This is more likely the case at low

overpotentials. At very high overpotential, the electron-transfer

step may become rather rapid and is thus no longer the slowest

step in the overall reaction pathway. Thus, the reaction becomes

diffusion or adsorption controlled. In most of the kinetics studies

of the orr by rotating electrode techniques, mixed kinetic/

diffusion control is mostly observed at potentials above 0.7 V

in sulfuric or perchloric acid solution. At lower potentials

limiting diffusion behavior usually occurs. In the present study

we use single-particle electrodes having effective radii down

to the submicrometer scale. The rapid mass transport at such

small particles can compensate for reactant consumption so that

a higher overpotential is required to reach limiting diffusion

conditions. Figure 5 shows a series of steady-state polarization

curves for oxygen reduction on Pt particles of different sizes.

A number of interesting features are obvious from this plot.

The first is that, as the particle size is decreased, the current

density for oxygen reduction increases, as might be expected

from the increased mass transport coefficient of the smaller

2

It is very clear that a decrease in the value of 1 - θ will

result in a decline in the n_effvalue when the mass transport

coefficient and rate constants are invariant. This indicates that

surface blockage by the strongly adsorbed species can signifi-

cantly increase the formation fraction of H₂O₂during oxygen

reduction while exclusively following the pure series (indirect)

mechanism. In studies of the orr on Pt low-index single-crystal

faces in aqueous acid solution by Markovic et al.,^7,11it was

found that O₂almost completely undergoes a two-electron

reduction to H₂O₂on a Pt(111) electrode in the H UPD region.

Separate experiments in oxygen-free H₂O₂-containing solution

showed that the reduction of H₂O₂is almost totally inhibited in

this potential region on the Pt(111) electrode. The authors

believed that the two experiments confirmed the speculation

that the pronounced formation of H₂O₂induced by adsorption

of blocking species is due to a loss of surface sites for the O-O

bond cleavage that is the initial step of the direct four-electron

reduction pathway. It seems to us that a counter argument could

be made that the hydrogen peroxide pathway plays an important

role in the oxygen reduction reaction (i.e., that the indirect

pathway in Figure 1 is the dominant pathway). In our approach,

we would argue that the adsorption equilibrium of hydrogen

peroxide involved in the series (indirect) pathway of the orr is

probably also the initial step in the reduction of H₂O₂. The

adsorption of hydrogen can inhibit the H₂O₂adsorption step

and favors the desorption of the peroxide species. This might

be the common reason for the enhanced formation of hydrogen

peroxide accompanying orr and the inhibition of H₂O₂reduction

in the H UPD region. In contrast, if a pronounced rate of H₂O₂

formation occurs during the orr in the presence of strong surface

adsorption while the reduction of H₂O₂is not obviously inhibited

under the same conditions, one may conclude that the hydrogen

peroxide pathway plays a minor role in the O₂reduction

reaction; yet this case is not observed.

4.2. Kinetics of Oxygen Reduction on Carbon-Supported

Pt Single Particles. The kinetics of the orr is generally analyzed

using a Tafel relationship between the current and potential.

Frequently, two slopes can be found in Tafel plots obtained

during the orr on Pt. In the low-potential region (generally called

the high current density region or high-overpotential region), a

Tafel slope of around -120 mV per decade of current density

Oxygen Reduction on Pt Particles

J. Phys. Chem. B, Vol. 108, No. 10, 2004 3269

Figure 7. Tafel plots of the kinetic current in the potential region

between 0.4 V and 0.7 V obtained from the steady-state I-E curves

for the orr in 0.1 mol dm^-3H₂SO₄on Pt single-particle electrodes.

The radii of the particles and the slope of the fitted Tafel lines are

indicated in the figure.

Figure 5. Steady-state |j|-E profiles obtained during positive-going

scans for the orr in O₂-saturated 0.1 mol dm^-3H₂SO₄on carbon-

supported Pt particle electrodes. Inset: Data in the main figure

normalized by the corresponding limiting j values at the negative

potential limit. The numbers in the figure indicate the radii of Pt

the hydrogen adsorption-desorption process in CVs obtained

in oxygen-free 0.1 mol dm^-3H₂SO₄. The current density values

are those obtained from the steady-state I-E curves obtained

during the positive-going scan where the reaction takes place

on a prereduced electrode surface.

particles. Scan rate: 100 mV s^-1

.

It can be seen from Figures 6 and 7 that the Tafel curves

obtained on particles of different size have similar slopes to

each other in the potential range below 0.85 V although the

kinetic current density is slightly larger on smaller particles.

For example, the kinetic current density obtained at particles

having radii around 50 nm is about 1.5 times larger than those

obtained on particles having radii larger than 500 nm when the

potential is below 0.85 V. The Tafel curves obtain at particles

larger than 500 nm almost overlap each other once the potential

is below 0.85 V. In general, a slope of around -120 mV per

decade can be fitted to the Tafel plots over the potential region

between 0.85 and 0.75 V, as shown by the lines c and d in

Figure 6. The Tafel plots in the potential region above 0.85 V

obtained on particles having radii larger than 500 nm have low

values of slope close to -60 mV per decade of current density,

as indicated by line a. This indicates that the Tafel behavior of

these large particles is identical to that on bulk Pt electrodes.

However, as the radius of the Pt particle becomes smaller than

500 nm, the slope of the Tafel plots in this high-potential region

shows a general increase with decreasing particle size. In these

results only one single slope of -120 mV per decade can be

found for the Tafel curves at particles having an effective radius

of less than or equal to 55 nm over the entire potential region

above 0.7 V (line d in Figure 6). This single Tafel slope be-

havior is different to that reported by Markovic et al.^2,7-9,11for

the orr on Pt(111) single-crystal electrodes in bisulfate- or halide-

ion-containing media. In their studies, the single-slope behavior

on Pt(111) electrodes is always accompanied by significant

inhibition of the orr, which was attributed to the loss of sur-

face sites for both oxygen and its reduction intermediates due

to anion adsorption. No inhibition of the orr occurs at the

smallest electrodes which we studied even though they show a

single slope. Indeed, we see an enhanced kinetic current density

at smaller particles. The authors explained the single Tafel slope

behavior in terms of a delay in PtOH formation due to strong

adsorption of anions on the Pt(111) surface.^2,7The formation

of PtOH on this crystal plane occurs only when the potential is

more positive than 1.0 V in bisulfate-containing solution. So,

it is expected that the Tafel slope of -120 mV covers the entire

potential region below 1.0 V. As the oxygen reduction process

Figure 6. Tafel plots of the kinetic current in the potential region above

0.7 V obtained from the steady-state I-E curves for the orr in 0.1 mol

dm^-3H₂SO₄on Pt single-particle electrodes. The radii of the particles

and the slope of the fitted Tafel lines are indicated in the figure.

electrodes. It is interesting to see that these effects are present

even at potentials as high as 0.95 V indicating that mass trans-

port effects still have a significant effect on catalyst performance

at such high potentials. The increased current density seen on

the smaller Pt particles at high potentials at which mixed kinetic

and mass transport control exists suggests that poisoning or deac-

tivation of the catalyst surface is not significant and should have

no effect on the validity of the results presented in this paper.

Inset into Figure 5 are the normalized steady-state I-E

profiles of the data provided in the main diagram. The current

is normalized to the corresponding limiting value at the negative

potential limit. It can be seen that the steady-state I-E curves

obtained at relatively large particles (e.g., r_eff> 1 µm) have

well-defined S shapes. The I-E curve becomes gradually less

reversible with decreased particle size, and the limiting diffusion

behavior occurs at a more negative potential. This enables us

to investigate the kinetics of the orr within the higher overpo-

tential regions.

4.2.1. Tafel Plots. The Tafel plots for the kinetic current

density (j_K) of the orr obtained on a set of particle electrodes

are given in Figure 6 and Figure 7 for different potential regions.

The j_Kvalues are determined from the measured current density

j and the limiting diffusion current density j_Lon the steady-

state I-E curves using eq A7. The effective active area of the

particle electrodes is determined from the charge involved in

3270 J. Phys. Chem. B, Vol. 108, No. 10, 2004

Chen and Kucernak

In the low-potential region from 0.4 to 0.7 V, we observe

Tafel slopes on these small particles of around -240 mV per

decade (Figure 7). According to eq 14, deviation of the Tafel

slope from -120 mV per decade may be due to a potential

dependence of the 1 - θ term or of the adsorption energy.

Indeed, both of these parameters are affected by the potential-

dependent change of the total surface coverage of adsorbed

species. In this potential region the main adsorbed species may

be anions as the electrode surface is free of surface oxide.

Because the anion coverage should increase with increasing

potential in this region, it is expected that the Tafel slope would

be less than the -120 mV per decade as seen in the oxide region.

Such large Tafel slopes might be due to the rate-determining

step for the orr being different from that in the potential region

above 0.7 V. For instance, the initial adsorption of oxygen

becomes the rate-determining step at high overpotential where

the electron-transfer step becomes rather fast so that the rate

equation changes from eq A9 to A10. The slope of -240 mV

per decade indicates an apparent value of 0.25 for the symmetry

factor. This value could result from a coupling between the

potential dependence of the bisulfate coverage and a potential

dependence of the adsorption rate constant a₁. As will be

discussed below, such a low transfer coefficient value might

also be related to a double-layer effect.

The exchange current density j⁰can be obtained by extrapo-

lating the Tafel line. Two sets of j⁰values can be obtained from

the Tafel plots in the potential region where the reaction rate is

determined by the electron-transfer step. Only one set of j⁰

values can be obtained from the Tafel plots obtained on Pt

particles of 50 nm radius or less because those Tafel plots only

show a single slope. From the j⁰values, the apparent values of

the standard rate constant can be determined using

Figure 8. Cyclic voltammograms obtained on electrodes of carbon-

supported single Pt particles in 0.1 mol dm^-3H₂SO₄saturated with

high-purity Ar. The effective radii of the particles are 49 nm (a) and

1.3 µm (b), respectively.

is strongly inhibited by anion adsorption, the corresponding

reduction current is too low to conduct kinetic analysis in the

positive potential region (low-overpotential region); thus, the

Tafel behavior for the orr on Pt(111) electrodes in 0.05 mol

dm^-3H₂SO₄seems only to extend as far positive as 0.85 V

rather than the entire region of E < 1.0 V.^7,11,12In fact, the

Tafel plots obtained on the other two low-index single-crystal

electrodes Pt(100) and Pt(110) also have a single slope of

approximately -120 mV per decade over the entire potential

region below 0.85 V.⁷In another research paper by Markovic

et al. dealing with the effect of Br^-addition on the orr on

Pt(111) in 0.1M HClO₄, it was reported that the Tafel slope

changes from -76 to -118 mV per decade as the amount of

Br^-is increased.⁷However, the Tafel plots shown for the

solution with and without Br^-are in totally different potential

regions. The Tafel plot for pure 0.1M HClO₄is in the range of

0.4-0.6 V vs SCE, whereas for the Br^--containing solution it

is below 0.4 V where in bromide-free HClO₄the Tafel slope

would be expected to be close to -120 mV per decade. Thus,

it seems that there is no direct correlation between the single-

slope behavior on Pt(111) with the delay of surface oxide

formation. Instead, the single Tafel slope behavior might be

due to the significant depression of reduction current in the high-

potential region where the low Tafel slopes occur. As shown

in Figure 6, the single Tafel slope of approximately -120 mV

per decade extends to the potential region above 1.0 V for the

orr on small particles. However, no obvious delay in oxide

formation can be seen on these small particles, as shown in the

CVs for different-sized particles in Ar-saturated 0.1 mol dm^-3

H₂SO₄(Figure 8).

j⁰) 4Fk_app⁰c^b_O

(15)

2

The results are listed in Table 1.

4.2.2. Particle-Size-Dependent Half-WaVe Potential. As

shown in Figure 5, the electrode reaction becomes more

irreversible as the particle size decreases. Furthermore, the half-

wave potential (E_1/2, the potential at which the current reaches

half the value of the limiting diffusion current) in the steady-

state I-E curves shifts toward lower potentials (i.e., higher

overpotentials). Figure 9 summarizes the size dependence of

the half-wave potential values obtained from the steady-state

I-E curves for the orr obtained in our experiments. It can be

seen that there is a reasonable linear relationship between the

values of E_1/2and the values of log(r_eff). The fitted line has a

slope of 119 ( 11 mV per decade of r_eff.

A theoretical relationship between E_1/2and r_effis straight-

forward from the relationship between the current and the

1

particle size, that is, eq A5. Setting j ) /₂j_L, we have

k_1/2,app) m_O

(16)

2

where k_1/2,appis the rate constant at the half-wave potential, that

is, E ) E_1/2. Substituting m_O) D_O/r_effand eq A8 into eq 16

2

leads to

0

k_appr_eff

RT

RF

E_1/2) E⁰+

ln

(17)

So, it would appear that in our system increased Tafel slopes

in the high-potential region are not directly linked to a delay of

the formation of surface oxide (or adsorption of OH). This seems

to imply that the transition in Tafel slopes is not necessarily

due to surface oxide formation. Instead, we propose an alterna-

tive mechanism below.

(

)

D_O

2

The significance of the symbols in this equation are given in

Appendix II. A similar expression to eq 17 has been given by

Oldham et al. for a simple redox reaction at a hemispherical

Oxygen Reduction on Pt Particles

J. Phys. Chem. B, Vol. 108, No. 10, 2004 3271

0

TABLE 1: Apparent Values of the Standard Rate Constant k_appand Exchange Current Density j⁰Extracted from the

Steady-state I-E Profiles of the Oxygen Reduction Reaction in 0.1 mol dm^-3H₂SO₄on Electrodes of Single Pt Particles of

Different Size

k_app⁰/cm s^-1

j⁰/A cm^-2

r_eff(µm)

Tafel plot^a

Tafel plot^b

half-wave^c

Tafel plot^a

Tafel plot^b

half-wave^c

3.60

0.56

0.28

0.15

0.05

1.2 × 10^-6

1.3 × 10^-6

2.5 × 10^-6

2.7 × 10^-6

3.7 × 10^-6

5.5 × 10^-9

6.5 × 10^-9

1.8 × 10^-8

1.4 × 10^-7

3.7 × 10^-6

2.2 × 10^-6

2.4 × 10^-6

2.3 × 10^-6

3.0 × 10^-6

5.6 × 10^-6

5.0 × 10^-7

5.6 × 10^-7

1.1 × 10^-6

1.2 × 10^-6

1.6 × 10^-6

2.4 × 10^-9

2.8 × 10^-9

8.0 × 10^-9

6.5 × 10^-8

1.6 × 10^-6

1.0 × 10^-6

1.3 × 10^-6

2.4 × 10^-6

^aFrom Tafel plots of 120 mV slope region. ^bFrom Tafel plots of 60 mV region. ^cFrom half-wave potential values.

density region) in Figure 6 also show some variation at r_eff

<

500 nm, this change is much less than that seen in the high-

potential region. The values calculated for j⁰in this potential

region are mostly around 1 × 10^-6A cm^-2and increase slightly

with decreasing particle size. It can be seen that the values of

0

k_appand j⁰obtained from the half-wave potential method are

very close to those obtained from the Tafel plots in the low-

potential region where slopes of around -120 mV per decade

of current density occur. In addition, both the slope of the Tafel

plots in the low-potential region and the slope of the E_1/2

∼

log(r_eff) give an apparent transfer coefficient (R) value of about

0.5. This implies that the same kinetic processes are behind these

two measurements. For a simple redox process this would be

easy to understand as both the Tafel relationship and the E_1/2

∼ log(r_eff) relationship are derived from the expression relating

the current density to the particle size, that is, eq A5. But the

orr is a multistep reaction involving surface adsorption of a

reactant and reaction intermediates. The overall reaction rate

constant is a complex expression of the electron-transfer rate

constant and adsorption rate constant, for example, eq A6. Even

when the electron-transfer step is the rate-determining step, the

potential dependence of the apparent rate constant is affected

by surface adsorption, for example, eq A9. Because surface

adsorption varies with potential, the reaction rate should show

a variation in its potential dependence within the different

potential region as indicated by changes in the slope of the Tafel

plots. The E_1/2values determined from the steady-state polariza-

tion curves occur mostly below 0.8 V (Figure 9) where the Tafel

plots in Figure 6 have a slope of about -120 mV per decade.

So, the kinetics revealed by the E_1/2∼ r_effrelationship is similar

to that behind the Tafel behavior in the -120 mV per decade

region. When the E_1/2point occurs at potentials above 0.85 V,

we expect that the kinetic constants determined from the E_1/2

∼ r_effplot would be close to those extrapolated from the 60

mV per decade Tafel plots. In order for E_1/2> 0.85 V we require

that the radius of the particle is larger than 50 µm according to

eq 17. In reality, the radius of the particle has to be larger than

1.5 mm since the slope of the E_1/2∼ log(r_eff) would be 60 mV

instead of 120 mV in the potential region above 0.85 V. On

such large electrodes, steady-state measurement is impossible

under stationary electrode conditions.

Figure 9. Variation of the value of the half-wave potential for the

steady-state j-E curve (Figure 5, inset) with particle size during the

orr in 0.1 mol dm^-3H₂SO₄at Pt single-particle electrodes.

microelectrode.⁵³To obtain eq 17, an assumption that the

apparent reaction rate constant k of the four-electron oxygen

reduction has a Butler-Volmer type dependence on the potential

E has to be made (see Appendix II). The linear relationship

between E_1/2and log(r_eff) shown in Figure 9 indicates that this

assumption is reasonable.

The 119 mV per decade slope of the E_1/2∼ log(r_eff) plot

indicates that the apparent transfer coefficient R is close to 0.5,

which is similar to the transfer coefficient values usually

obtained from the Tafel plots of oxygen reduction in the high

current density region (when E < 0.85 V). From eq 17, the

apparent standard rate constant (k_app⁰) can be determined using

E⁰) 1.23 V; therefore, the exchange current density j⁰can be

determined using eq 15. The values of k_app⁰and j⁰calculated in

this way are given in Table 1.

4.2.3. Kinetic Parameters. Table 1 gives the values of the

0

apparent standard rate constant k_appand the exchange current

density determined using the Tafel method and half-wave

potential method, respectively. On particles having effective radii

larger than 500 nm, the j⁰values determined from the Tafel

plots in the low current density region (approximately -70 mV

per decade slope region) are around 2.5 × 10^-9A cm^-2

(corresponding to k_app⁰values of around 6 × 10^-9cm s^-1). Such

values are close to those normally obtained on bulk Pt electrodes

in sulfuric acid solutions.^18-20The j⁰and k_app⁰values evaluated

from the Tafel plots in this potential region increase significantly

upon decreasing the particle size once r_effbecomes less than

500 nm. This is because of the slope of the Tafel plots in this

potential region becoming larger on smaller particle, as shown

The kinetics parameters obtained from the Tafel plots with

-120 mV per decade slopes and those obtained from the

particle-size-dependent half-wave potentials should represent the

real kinetics of the orr governed by the electron-transfer step

since they exclude any possible interference from surface oxide.

The Tafel plots with -60 mV per decade slopes provide

information about the orr influenced by the presence of oxide,

which modifies the transfer coefficient and the reaction rate

constant via changing the effective surface site availability and

the free energy of adsorption. In fact, even the kinetic parameters

estimated from the half-wave potentials and the Tafel plots with

-120 mV per decade slope are not the real kinetics of the orr

0

in Figure 6. Although the values of j⁰and k_appextrapolated

from the Tafel plots in the low-potential region (high current

3272 J. Phys. Chem. B, Vol. 108, No. 10, 2004

Chen and Kucernak

on Pt electrodes, as these results are affected by the adsorption

of anions such as bisulfate. The real kinetic parameters for the

orr on bare Pt electrodes may be obtained under conditions

where no anion adsorption occurs, for example at the Pt/Nafion

membrane interface. The -120 mV per decade slope of the

Tafel plots and 120 mV per decade slope of the E_1/2∼ log(r_eff)

line suggest that the rate-determining step is a one-electron

transfer with R ≈ 0.5, seemingly indicating that the orr kinetics

is not affected by the adsorption of anions. Slopes close to -120

mV per decade in the high current density region have also

been observed on Pt single-crystal electrodes in halide-ion-

containing solution.^7-12The authors of that work believed that

the adsorption of halide ions would only affect the 1 - θ term

and not the free energy of oxygen adsorption(∆G_θ). However,

it is rather hard to accept that the adsorption of OH affects the

free energy of oxygen adsorption but that the adsorption of

anions does not. The most likely reason for the observed almost

pure electron-transfer kinetics in this potential region might be

that the adsorption of anions reaches saturation coverage and

then changes little with potential. Thus, both the term 1 - θ

and ∆G_θremain approximately constant over this potential

region. Under such conditions, the measured transfer coefficient

value would be that of the pure electron-transfer reaction. In

is known as the Frumkin effect.^54,55,65In some electrochemical

reactions the electron-transfer process may occur in the inner

part of the compact double layer near the inner Helmholtz plane

(IHP). These processes are then called inner-sphere electron-

transfer reactions. For example, the electrochemical reaction

involving adsorption of reactants or those involving reactants

that have a very short closest approach distance may belong to

such cases. The double-layer structure will show a larger affect

on the kinetics of inner-sphere electron-transfer reactions

regardless of whether the electrolyte is dilute or not, since there

always is a potential drop across the compact double layer. The

real potential at the reaction plane, ψ_r, for an inner-sphere

reaction may be significantly different from that at the OHP,

ψ_o, the latter being close to the potential in bulk solution when

there is excess of electrolyte present. The difference between

ψ_rand ψ_odepends on a number of factors, such as the applied

electrode potential, the presence of surface charge on the

electrode surface, the ionic environment around the IHP, and

so on.^56-60It is a rather complex task to evaluate the value of

ψ_rand its effects on the reaction kinetics. To do so requires a

full understanding of the double-layer structure, as reviewed

recently by Fawcett.⁵⁶The overall results of the potential

difference between ψ_rand ψ_omight be that the observed transfer

coefficient and reaction rate constant deviate significantly from

their intrinsic values and may even be potential dependent.^56-64

It is well established that the adsorption of oxygen molecules

on the electrode surface is an essential step prior to electron

transfer in the reduction of oxygen on catalytic materials like

Pt, although the initial adsorption state of oxygen at the solid/

electrolyte interface is still controversial. The adsorbed oxygen

and subsequent reaction intermediates have to replace surface-

bound water molecules that form the first layer of the compact

double layer. So, the electron-transfer processes involved in the

electrocatalytic reduction of oxygen occur near the inner

Helmholtz plane (IHP), that is, it is an inner-sphere electron-

transfer reaction. Thus, it seems unreasonable to ignore the role

of the structure of the double layer on the kinetics of the orr.

Concerning possible double-layer effects, several factors have

to be considered when analyzing the kinetics of the orr. First,

the real driving potential value that the reactant and intermedi-

ates experience is different from the applied potential. This may

result in a low apparent value of the transfer coefficient. Second,

the adsorption of anions would not only block surface sites as

is commonly stated but might also significantly change the

potential near the IHP and the potential distribution in the entire

double layer.

0

our experiments, the k_appmeasured is the rate constant of

electron-transfer reaction modified by the 1 - θ and exp-

(-∆G_θ/RT) terms. The role of anion adsorption may be much

more complicated than simply that of surface blockage, as will

be discussed in the next section.

The kinetics analysis and discussion addressed above are all

based on the assumption that any oxygen is fully reduced to

water. The effects of hydrogen peroxide formation are ignored.

This is because the effect of hydrogen peroxide formation on

the current density is rather small. Even at very small electrodes,

the current density deviation due to hydrogen peroxide formation

is only ∼10%. At larger particle electrodes, this deviation is

much less. The correction to the current density in considering

the formation of hydrogen peroxide results in only negligible

changes to the Tafel slopes and exchange current density values.

At small particle electrodes, the reaction is highly irreversible

and the limiting current density is much larger than the kinetic

current density over virtually the entire potential range so that

1/j_K. 1/j_L, and the latter parameter may be ignored in the

kinetic equations.

4.2.4. Possible Effects of the Electric Double Layer on the

orr Kinetics on Single Catalyst Particles. The activation energy

barrier for the electron-transfer process in an electrochemical

reaction is overcome by the potential difference between the

electrode and the electrolyte solution, as indicated in the

exponential term of the Butler-Volmer equation.^54,55This

potential difference distributes itself in the electric double layer

formed at the electrode/electrolyte interface. It has been long

realized that the location of the electron-transfer site in the

double layer and the corresponding double-layer structure have

significant effects on the kinetics of an electrode reaction.^56-64

In most electrochemical theories, it is supposed that the electron-

transfer site is near the outer Helmholtz plane (OHP). The

electron-transfer reaction is thus called an outer-sphere electron-

transfer reaction. One may ignore the effect of any potential

drop beyond the OHP on the reaction kinetics of an outer-sphere

electron-transfer reaction unless the reaction occurs in very dilute

electrolyte solution in which case some of the potential drop

occurs in the diffuse double layer: the region between the OHP

and the bulk solution. The effect of the potential drop in the

diffuse double layer on an outer-sphere electron-transfer process

The Tafel slopes observed in the different potential regions

during the orr may contain some contribution from these double-

layer effects. Slopes of around -240 mV per decade in the

potential region below 0.7 V suggest an apparent transfer

coefficient value of 0.25. Although this low transfer coefficient

value can be explained as a change of the rate-determining step

from the electron transfer to the initial adsorption of oxygen, it

is also possible that the rate-determining step is still the electron-

transfer step and that the low transfer coefficient value observed

is due to the double-layer effect previously mentioned. Because

the electron-transfer site is located within the inner Helmholtz

plane, the potential difference between the electrode surface and

the reaction plane would be E - ψ_rwhich may be only a

fraction, γ, of the applied potential E:

E - Ψ_r) γE

(18)

Thus, the apparent transfer coefficient would be γR, a value

smaller than the real value of R since γ is smaller than 1. The

Oxygen Reduction on Pt Particles

J. Phys. Chem. B, Vol. 108, No. 10, 2004 3273

the compact double layer around particle electrodes of various

radii calculated according to eq 19 using a hard sphere diameter

of the water molecule of 0.29 nm⁶⁸and assuming that the ion

radius is 0.1 nm. The derivation of eq 19 assumes that the

dielectric permittivity is uniform in the compact double layer

and that no specific adsorption occurs. In reality, the dielectric

permittivity inside the IHP is much lower than that outside of

it, and the dielectric permittivity varies with distance from the

electrode surface because of the variable interaction between

water molecules and the electrode.^54,57Thus, the potential drop

between the electrode surface and the IHP should be larger than

that shown in Figure 10. For example, the average value of the

dielectric constant of water between the IHP and the electrode

surface might be only 6, whereas the average value between

the IHP and OHP is about 40.⁵⁴Correspondingly, the potential

drop in the region inside of the IHP will be much larger than

that predicted by eq 19. In addition, the adsorption of anions

will significantly shift the potential near the IHP toward more

negative values. This will further increase the potential drop

inside the IHP when the electrode potential is positive of the

PZC.

Figure 10. Potential profile inside a compact double layer formed at

a catalyst particle having a radius of 500 nm (solid curve), 10 nm (short-

dashed curve), and 1 nm (long-dashed curve) calculated using eq 19

(see text).

adsorption of bisulfate anions can shift the potential near the

IHP negatively. This will tend to increase the value of γ. When

the potential is much more positive than the PZC (potential of

zero charge), the coverage of anions is so high that the potential

drop occurs mainly in the inner Helmholtz layer; the γ value

thus would be close to one. Under these circumstances the

observed transfer coefficient becomes close to the intrinsic value

of 0.5. Such effects of anion adsorption on reaction kinetics

may also occur in other electrocatalytic systems involving

surface adsorption of reactants or reaction intermediates. For

example, the nonlinear dynamical responses obtained during the

electrocatalytic oxidation of small organic molecules were found

to change dramatically upon changing the anions present in

solution, a result which cannot be explained by a simple surface-

blocking mechanism.^66,67These nonlinear dynamical phenomena

may become easier to understand when considering the variable

potential profile across the double layer due to adsorption of

different anions.

In the double layer around a particle of spherical geometry,

the charges on the solution side (carried by the electrolyte ions)

reside mainly on a spherical surface that is concentric with the

particle and located at the distance of closest approach of the

hydrated ion. The compact double layer formed thus is like a

concentric spherical capacitor. If we assume that the potential

drop in the diffuse double layer is negligible, then the poten-

tial profile ψ(r) inside the compact layer around a particle

electrode is

It can be seen that a size dependence of the potential profile

in the double layer appears as the particle size shrinks to below

20 nm. At particles with radii larger than 20 nm the potential

distribution is almost linear and independent of the electrode

size. Such a potential distribution is identical to that in the double

layer formed on a large planar electrode. When the particle

radius is less than 20 nm, the potential profile gradually deviates

from linear distribution and the potential drop in the inner part

becomes larger. Thus, an effect of particle size on the kinetics

of the electrocatalytic reduction of oxygen is expected, that is,

the apparent rate constant and transfer coefficient may change

with particle size. As well as the heterogeneity of dielectric

permittivity and anion specific adsorption, eq 19 also ignores

the effects of the flow of current on the double-layer structure.

The potential profiles shown in Figure 10 depict those in an

equilibrium and stationary double layer. When there is current

flowing through the electrochemical cell, the double-layer

structure undergoes dynamic changes.^69-71At small particle

electrodes the current density could be very high since the

current density is scaled with the reciprocal of the electrode

size (e.g., see Figure 5). This may enhance the double-layer

effects and cause the size effect to arise at larger particles. For

example, a digital simulation by Smith et al.⁷²indicated that

the double-layer effect on microelectrode voltammetry can arise

when the electrode radius is below 0.1 µm even in the presence

of excess supporting electrolyte.

r₀r₀+ µ - r

ψ(r) )

E

(19)

(

)

It has been suggested that the rate-determining step of the

orr might be an electron-transfer process coupled with proton

transfer.^18-20The difference between ψ_rand ψ_ocan affect the

concentration of protons at the reaction plane, and this change

in concentration may change the apparent rate constant and

transfer coefficient of the orr. The potential drop occurring inside

the IHP becomes larger at smaller particle. At potentials more

positive than the PZC, this means a shift of the potential at the

IHP toward more negative values, resulting in an increase in

the concentration of protons and giving a larger apparent rate

constant. This seems to be consistent with the larger kinetic

current density observed at smaller electrodes.

µ

r

where r is the radial distance from the center of the particle

electrode, r₀the radius of the particle, and µ the thickness of

the compact double layer. This equation has been derived by

solving the Poisson equation with assumptions that the dielectric

permittivity is uniform and that there is no charge inside the

compact layer, that is, that no specific adsorption occurs. The

thickness of the compact layer can be approximately estimated

using^54,68

x

µ ) 2r_w+ 3r_w+ r_i

(20)

In the analysis above we have provided only a rather approx-

imate description of the double-layer effects on orr kinetics.

To clarify the situation requires an accurate understanding of

the dynamic structure of the double layer during anion adsorp-

tion, oxide formation, and at high current densities, an area

where r_wis the radius of water molecules bound to the electrode

surface forming the first layer of the compact double layer and

r_iis the radius of the ions that carry the charges to compensate

the electrode charge. Figure 10 shows the potential profile inside

3274 J. Phys. Chem. B, Vol. 108, No. 10, 2004

Chen and Kucernak

which still challenges modern electrochemistry. Furthermore,

one has to consider the effects of the size-induced changes in

the intrinsic properties of catalyst particles on the double-layer

structure once the particle size is below 20 nm. A direct re-

sult of the decrease in particle size is that more metal atoms

will be confined on the catalyst surface, which would cause a

change of the electronic properties of metal particles. For par-

ticles in the nanoscopic or mesoscopic range, electronic proper-

ties such as the density of state (DOS) profile and electron

distribution are expected to be significantly different from bulk

metals. All these properties could result in dynamic changes

on the structures of the double layer at the catalyst particle/

electrolyte interface. We are pursuing this work with measure-

ments using electrodes down to nanometer sizes with a defined

geometry conducted at the interface between Pt and perfluori-

nated polymer electrolytes where the absence of specific anion

adsorption may help to understand the double-layer effects on

the orr kinetics.

Alternatively, providing some mechanism to increase the

adsorption strength of the peroxide on the catalyst surface or

increase its subsequent decomposition may also be beneficial.

Such an approach could be accomplished by alloying the Pt

with other compounds, for instance, transition metals.

5. Conclusion

A new approach to study the effects of mass transport on

electrochemical reactions of relevance to fuel cells has been

demonstrated. We show how it is possible to investigate the

oxygen reduction reaction using single-Pt-particle electrodes of

submicrometer dimensions. The particle size effects on the

reaction pathways and kinetics have been characterized and

explored. Contrary to the size effects typically reported for

experiments performed using dispersed high surface area

catalysts, we see size effects occurring at much larger particle

sizes. It is shown that the oxygen reduction pathway may be

altered by the catalyst particle size because of variation of the

mass transport rate, an area which has hitherto not received

significant research. Such an effect of particle size on reaction

mechanism occurs when the particle size is between 50 nm and

5 µm. These effects have not been reported before because of

the inability of rotating disk measurements to access such high

mass transport conditions. At potentials outside the hydrogen

adsorption region on platinum when the particle is larger than

5 micrometers (mass-transfer coefficient for hydrogen peroxide

or oxygen ∼0.04 cm s^-1, equivalent to ∼25 000 rpm), the

formation of hydrogen peroxide is negligible and virtually all

oxygen molecules undergo a complete four-electron reduction

to water. At particles smaller than this, progressively larger

amounts of hydrogen peroxide are produced. At particles smaller

than 50 nm the formation rate of hydrogen peroxide appears to

become independent of the particle size since mass transport is

very high and the formation rate of hydrogen peroxide is

governed by the adsorption/desorption equilibrium. In this mass

transport regime (mass-transfer coefficient for hydrogen per-

oxide or oxygen ∼4 cm s^-1), about 75% of oxygen molecules

reacting at the surface are reduced to water and 25% are reduced

to hydrogen peroxide. The comparison between the experimental

results and a theoretical model suggests that a pure series or

indirect mechanism is possible for oxygen reduction on Pt

electrodes in sulfuric acid solution. The kinetics of the orr is

rather more complex than usually believed. Anion adsorption

may affect the orr not only by blocking surface sites but also

by changing the potential profile within the double layer. The

orr strongly depends on the potential profile in the double layer

since inner-sphere electron-transfer steps are involved. The size

of the catalyst particle may affect the oxygen reduction kinetics

via double-layer effects as there is a dependency of the potential

distribution within the double layer around a catalyst particle

on that particles radius.

4.3. Relevance to Fuel Cell Catalyst Layers. Our results

have shown that under conditions of sufficiently high mass

transport significant amounts of hydrogen peroxide may be

produced during the reduction of oxygen. This has been shown

to occur at platinum particles much larger than those typically

used as catalyst particles within fuel cells. It is certainly true

that the mass transport coefficient for an individual isolated

nanometer-sized fuel cell type catalyst particle would be much

larger than even the smallest of the particles we have looked

at, and that as a result we would expect a smaller value of n_eff

for that individual particle and thus a larger amount of hydrogen

peroxide produced. However, as can be seen from Figure 4 and

eq 11, we expect the value of n_effto asymptotically approach

some limiting value and become independent with mass trans-

port coefficient. Furthermore, within a fuel cell catalyst layer

we do not have individual catalyst particles separated by signifi-

cant distances. Rather, all of the catalyst particles exist in

close proximity. This close proximity means that the diffusion

spheres around each of the particles will collide, and this

will reduce the local mass transport coefficient. The degree to

which this happens is rather complicated and will probably

vary with position within the catalyst layer. Nonetheless, for a

given catalyst layer, it should be possible to calculate an

“average” mass transport coefficient for hydrogen peroxide

under the operating conditions of the catalyst layer. With the

use of this mass transport coefficient and Figure 4, it would

then be possible to read off the expected value of n_efffor that

particular catalyst layer and from this determine the amount of

hydrogen peroxide which is expected to be formed in the catalyst

layer.

The production of hydrogen peroxide would probably not

significantly effect the efficiency of the fuel cell because any

free peroxide will probably eventually undergo autocatalytic

decomposition to water and oxygen; rather, hydrogen peroxide

in the presence of transition metals may react to produce

hydroxyl radicals (OH^•) which in turn may lead to the

degradation of the solid polymer electrolyte due to oxidative

attack. Variations in the local value of D_{H O}due to, for instance,

Acknowledgment. Financial support of this research from

the Leverhulme trust is kindly acknowledged. We thank Mr.

Peter Hope from LVH for kindly providing the electrophoretic

paint solution. Mr. Simon Turner and Mr. Steve Atkins at the

Chemistry Department of this college are thanked for their

technique supports.

2

changes in the amount of hydrating water in the solid polymer

electrolyte, may effect changes in the local rates of production

of H₂O₂, and through this the local production rates of OH^•

lead to variations in membrane degradation rate.

Appendix I. Expressions for θ₁, θ₂, â₁, and â₂.

To reduce the production of H₂O₂, it would seem necessary

to reduce the average mass transport coefficient of the fuel cell

catalyst layer. Unfortunately, this approach may also have the

effect of reducing the performance of the fuel cell cathode.

c^b

O₂

θ₁)

(A1)

â₁

Oxygen Reduction on Pt Particles

â₂c^b_O

J. Phys. Chem. B, Vol. 108, No. 10, 2004 3275

the same potential dependence as that of an adsorption or

desorption process (i.e., the same symmetry factor), although

there are other possibilities in which a simple Butler-Volmer

dependence of k_appwith potential may occur. For instance

(making reference to Figure 1), when k ) k₁+ k₂, a_1-, the

expression for k_appbecomes

2

θ₂)

(A2)

(A3)

â₁

k₁+ k₂a_{1 -}k₁+ k₂

â₁)

+

a₁

m_O

2

a₁

k₂

k_app) k

(A9)

â₂)

(A4)

a_1-

a_2-

a₂

k₃+

or when k ) k₁+ k₂. a_1-

k_app) a₁

1 +

m

H₂O₂

(A10)

Appendix II. Kinetics Equations for the Four-Electron

Reduction of Oxygen on Single Particles.

The term a₁/a_1-in eq A9 is actually the equilibrium constant

of the adsorption/desorption of oxygen molecules. The kinetic

interpretation of eq A9 is that the coverage of the adsorbed

oxygen is determined mainly by the adsorption/desorption

equilibrium and the electron-transfer step is the rate-determining

step. The kinetic interpretation of eq A10 is that the reaction

rate is governed by the rate of adsorption of oxygen.

Eq 10 in the model section describes the current density for

the four-electron oxygen reduction and may be rewritten as

1

j

1

)

+

(A5)

(A6)

4Fk_appc^b_O

4Fm_Oc^b_O

2

where

References and Notes

(1) Adzic, R. Recent Advances in the Kinetics of Oxygen Reduction.

In Electrocatalysis; Lipkowski, J., Ross, P. N., Eds.; Wiley-VCH: New

York, 1998; p 197.

(2) Markovic, N. M.; Schmidt, T. J.; Stamenkovic, V.; Ross, P. N.

Fuel Cells 2001, 1, 105.

k₁+ k₂

k_app

)

k₁+ k₂a_1-

+

a₁

(3) Gottesfeld, S.; Zawodzinsk, T. A. Polymer Electrolyte Fuel Cells.

In AdVances in Electrochemical Science and Engineering; Alkire, R. C.,

Gerischer, H., Kolb, D. M., Tobias, C. W., Eds.; Wiley-VCH: Weinheim,

1997; Vol. 5, p 195.

(4) Hsueh, K. L.; Chin, D. T.; Srinivasan, S. J. Electroanal. Chem.

1983, 153, 79.

(5) Damjanovic, A.; Genshaw, M. A.; Bockris, J. O. M. J. Phys. Chem.

1964, 45, 4057.

(6) Paulus, U. A.; Wokaun, A.; Scherer, G. G.; Schmidt, T. J.;

Stamenkovic, V.; Markovic, N. M.; Ross, P. N. Electrochim. Acta 2002,

47, 3787.

is the apparent rate constant for four-electron oxygen reduction,

representing an overall rate consisting of a number of intermedi-

ate reaction steps. It is obvious that the second term on the right-

b

O₂

hand side of eq A5, 1/(4Fm_O2c ) is the reciprocal of the

steady-state limiting diffusion current density (j_L) of oxygen

reduction, whereas the first term is the reciprocal of the current

density for oxygen reduction when no concentration polarization

occurs, that is, the kinetic current density, j_K. So, an equivalent

expression to eq A5 is

(7) Markovic, N. M.; Gasteiger, H. A.; Ross, P. N. J. Phys. Chem.

1995, 99, 3411.

(8) Markovic, N. M.; Ross, P. N. In Interfacial Electrochemistry:

Theory, Experiment and Application; Wieckowski, A., Ed.; Marcel Dek-

ker: New York, 1999; p 131.

(9) Markovic, N. M.; Gasteiger, H. A.; Grgur, B. N.; Ross, P. N. J.

Electroanal. Chem. 1999, 467, 157.

1

j

1

)

+

(A7)

j_Kj_L

This eq has the same form as the current density expression

on a rotating disk electrode. In fact, eq A7 is a general current

density expression for steady-state measurement methods, but

the j_Lterm has different formulations depending on the

experimental method. Although k_apphas a complex form, we

can assume it has a Butler-Volmer type of potential depen-

dence, that is,

(10) Stamenkovic, V.; Markovic, N. M.; Ross, P. N. J. Electroanal.

Chem. 2001, 500, 44.

(11) Markovic, N. M.; Gasteiger, H. A.; Ross, P. N. J. Electrochem.

Soc. 1997, 144, 1591.

(12) Grgur, B. N.; Markovic, N. M.; Ross, P. N. Can. J. Chem. 1997,

75, 1456.

(13) Antoine, O.; Durand, R. J. Appl. Electrochem. 2000, 20, 839.

(14) Paulus, U. A.; Schmidt, T. J.; Gasteiger, H. A.; Behm, R. J. J.

Electroanal. Chem. 2001, 495, 134.

(15) Schmidt, T. J.; Paulus, U. A.; Gasteiger, H. A.; Behm, R. J. J.

Electroanal. Chem. 2001, 508, 41.

(16) Paulus, U. A.; Wokaun, A.; Scherer, G. G.; Schmidt, T. J.;

Stamenkovic, V.; Radmilovic, V.; Markovic, N. M.; Ross, P. N. J. Phys.

Chem. B 2002, 106, 4181.

RF

RT

k_app) k_app⁰exp - (E - E⁰)

(A8)

[

]

where E⁰is the standard equilibrium potential and k_appand R

are the apparent standard rate constant and apparent transfer

coefficient of the orr, respectively. We say “apparent” because

these parameters are not those for a simple electron-transfer

reaction. They represent the overall results from several reaction

steps including electron-transfer and adsorption steps. The

assumptions required for eq A8 are that each of the individual

rate constants involved in the expression of k_appshould have a

simple Butler-Volmer type dependence on the potential and

that the symmetry factors (called transfer coefficients for a

simple electron-transfer reaction) in the exponential term of these

Butler-Volmer equations are all same. Otherwise, eq A8 does

not hold. It seems unlikely that an electron-transfer process has

0

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Article Doi

Electrocatalysis under Conditions of High Mass Transport Rate: Oxygen Reduction on Single Submicrometer-Sized Pt Particles Supported on Carbon

DOI: 10.1021/jp036831j

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Full text of DOI:10.1021/jp036831j

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