Nonuniform reaction rates during CO and CO/H2 oxidation on coupled Pt electrodes

Article abstract of DOI:10.1021/jp0494943

The electro-catalytic oxidation of CO and CO/H₂ mixtures on polycrystalline platinum was studied on two electrodes with controllable degrees of coupling strength through experiments and numerical simulations. With strong positive coupling, large differences between the currents of the two almost-identical electrodes arose in a range of potential. The mean CO coverage on the two electrodes was significantly lower than the uncoupled case in a large potential region where the splitting occurred. Thus, coupling reduced the mean CO coverage. Similar effects were observed in OH coverage; one electrode in the bistable region had a higher OH coverage than in the uncoupled case, the other had a lower coverage; the mean OH coverage was increased due to coupling. Simulations also show that the total coverage of CO and OH is always lower (and the number of total free active sites higher) in the nonuniform states; this suggests the possibility of increased total reaction rate not only in the CO oxidation system but also in systems in which the CO electro-oxidation occurs in parallel with other chemical and electrochemical reaction steps.

Full text of DOI:10.1021/jp0494943

J. Phys. Chem. B 2004, 108, 14599-14608
14599
Nonuniform Reaction Rates during CO and CO/H2 Oxidation on Coupled Pt Electrodes†
Istva´n Z. Kiss, Andrew W. Brackett, and John L. Hudson*
Department of Chemical Engineering, 102 Engineers’ Way, UniVersity of Virginia,
CharlottesVille, Virginia 22904-4741
ReceiVed: February 4, 2004; In Final Form: April 20, 2004
The electro-catalytic oxidation of CO and CO/H2 mixtures on polycrystalline Pt has been investigated on two
electrodes with controllable degrees of coupling strength by means of experiments and numerical simulations.
With strong positive coupling, large differences between the currents of the two almost-identical electrodes
arise in a range of potential. Experiments on CO oxidation were carried out in three different electrolytes; all
three electrolytes support pattern formation to an extent in the following order: 0.05 mol/L sulfuric acid with
saturated sodium sulfate > 0.05 mol/L sulfuric acid > 0.1 mol/L perchloric acid. Experiments with 2% CO/
H2 mixtures also exhibit nonuniform states with coupling. Numerical simulations on CO electro-oxidation
confirmed the experimental findings: the current differences occur due to a symmetry breaking both with
identical electrodes (through a pitchfork bifurcation) and with electrodes with inherent heterogeneities (due
to a formation of an isola). The nonuniform reaction rates due to small inherent heterogeneities are greatly
amplified by coupling. Simulations also show that the total coverage of CO and OH is always lower (and the
number of total free active sites higher) in the nonuniform states; this suggests the possibility of increased
total reaction rate not only in the CO oxidation system but also in systems in which the CO electro-oxidation
occurs in parallel with other chemical and electrochemical reaction steps.
1. Introduction
and the activator species are weakly, coupled to neighboring
reacting sites. In electrochemical systems the interactions are
often due to the strong electrical coupling through the conducting
electrolyte;12 Turing patterns are expected to occur when the
electrode potential is the inhibitor and chemical species are the
activators.13,14 Such electrochemical systems can exhibit S-
shaped polarization curves on uniform surfaces and exhibit
electrode-size-independent patterns readily with strong electrical
interactions; this idea was first verified in the reduction of
periodate on Au electrodes.15 The electrocatalytic oxidation of
CO also exhibits an S-shaped polarization curve and thus is a
potential candidate for rich stationary pattern formation; non-
uniform stationary potential distributions during CO oxidation
on a rotating ring have been recently reported.7
The irreversible adsorption of CO on Pt and its electro-
oxidation have been extensively studied in several contexts
including the CO poisoning of low-temperature fuel cells.1 This
reaction has also exhibited kinetic and spatiotemporal dynamical
features that could have relevance to both catalyst and cell
design. A Langmuir-Hinselwood mechanism, in which adsorbed
CO reacts with adsorbed OH to form CO2, has been proposed
to model the kinetics of the reaction.2 The negative reaction
order of CO bulk concentrations3,4 implies that the reactant, CO,
self-inhibits CO2 formation, resulting in a chemical positive
feedback loopsan often necessary requirement for non-
trivial dynamical features such as bistability. Indeed, bi-
stability has been found in the electro-oxidation of CO: the
reaction rate can be high (mass-transfer controlled) or low5 at
a given electrode potential. Bistable (S-shaped) polarization
curves have been reported for various electrolytes in-
cluding sulfuric acid and perchloric acid on Pt single crystals.5,6
The coupling through the electric field in the electrolyte is
usually long range. Although both the strength and the length
scale of this coupling can be varied by changes in electrolyte
resistivity and cell geometry,12,16 these variations are difficult
to make without simultaneously altering the driving force of
the reaction. For example, changing the cell geometry changes
the potential drop through the electrolyte and thus also the
potential drop across the electrical double layer. Circuit
resistances also add a global coupling.12,16 We have been using
electrode arrays to explore the effect of coupling strength on
electrochemical pattern formation and spatiotemporal dy-
namics.17-19 The use of electrode arrays has several positive
features: the temporally varying current of each electrode in
the array can be easily followed with ammeters so that
spatiotemporal patterns are directly measured; furthermore, the
electrical interaction strength among the electrodes can be tuned
with external resistors. This allows variation in coupling strength
without concurrent changes in the reaction terms. Thus, the
arrays provide a convenient experimental tool to explore the
effect of coupling on electrochemical reaction systems.
6
Koper at al. constructed an ODE model based on charge
balance and mass balance equations for surface CO concentra-
tion and CO and OH coverages; the model reproduces the
experimentally observed bistability with an S-shaped polariza-
tion curve.
The CO oxidation system can also exhibit spatial Turing
patterns through symmetry breaking.7 Regular stationary patterns
8
predicted by Turing are far-from-equilibrium phenomena in
which differences in diffusion rates of reaction species de-
stabilize the uniform distribution and produce concentration
patterns.9-11 These patterns can occur in activator-inhibitor
systems in which the inhibitor diffuses faster than the activator.
Thus, patterns can form when the inhibitor species are strongly,
† Part of the special issue “Gerhard Ertl Festschrift”.
* Corresponding author. E-mail: hudson@virginia.edu.
10.1021/jp0494943 CCC: $27.50 © 2004 American Chemical Society
Published on Web 06/12/2004

14600 J. Phys. Chem. B, Vol. 108, No. 38, 2004
Kiss et al.
TABLE 1: Model Constants
constant
value
0.5
1
units
R
A
cCO,s
Cd
δ
D
F
kCO,ads
kOH,ads
kOH,des
kr
Butler-Volmer symmetry coefficient
unitless
cm2
electrode area
concentration of CO in the bulk solution
capacitance of double layer
diffusion layer thickness
diffusion coefficient
Faraday’s constant
rate constant for CO adsorption onto the surface
rate constant for OH adsorption onto the surface
rate constant for OH desorption from the surface
rate constant for CO reaction on the surface
gas constant
total catalyst sites available for reaction
OH maximum surface coverage
temperature
1 × 10-6
2 × 10-5
6.7 × 10-3
5 × 10-5
96485
mol/cm3
F/cm2
cm
cm2/s
C/mol
1/s
1 × 10-8
1 × 10-4
1 × 105
1 × 10-5
8.314
1/s
1/s
1/s
J/(mol K)
1/cm2
unitless
K
R
Stot
θOH
T
2.2 × 10-9
max
0.333
298
In this paper, symmetry breaking and stationary pattern
formation of electrocatalytic CO oxidation on polycrystalline
Pt are investigated in a two-electrode setup. The two-electrode
studies yield information on the effect of various degrees of
coupling strength on the symmetry breaking as well as the effect
of heterogeneities. The experimental parameters are chosen to
yield conditions where the positive feedback of CO is present
although the behavior of a single electrode is mono-stable. The
effects of positive coupling on stationary pattern formation are
investigated in both experiments and numerical simulations.
Conditions are chosen such that interactions through the
electrolyte are weak; coupling is added through variations in
parallel and series external resistors. The simple two-electrode
system elucidates many important features that occur in
distributed reacting systems such as structure formation, the
symmetry breaking, and variations in reaction rate and surface
coverage of adsorbed species. Furthermore, the effect of
systematic changes in coupling strength on the pattern formation
can be studied. The robustness and generality of the findings
are explored in three acidic electrolytes with different sulfate
content (0.05 mol/L sulfuric acid with sat. Na2SO4, 0.05 mol/L
sulfuric acid, and 0.1 mol/L perchloric acid). In the numerical
simulations the effect of pattern formation on total reaction rates
and fraction of free reacting sites are explored.
adsorbed CO and OH (step IV). The rates of steps III and IV
which involve charge transfer are dependent on potential. A
three-variable ODE model can be constructed 6 to describe the
variation of CO coverage (ΘCO), OH coverage (ΘOH), and the
surface concentration of CO (cCO,s):
dθ
CO ) VCO,ads - Vreact
(1a)
(1b)
(1c)
dt
dθ
OH ) VOH - Vreact
dt
dc
2Stot
2D
δ2
CO,s ) -
VCO,ads
+
(cCO,bulk - cCO,s)
dt
δ
where Vreact and VOH are the CO oxidation and OH adsorption
rates, respectively:
V
react ) krθCO
θ
OH exp(RFE/RT)
(2)
VOH ) kOH,ads exp(RFE/RT)[θmaxOH(1 - θCO) - θOH] -
kOH,des exp(- (1 - R)FE/RT)θOH (3)
VCO is the rate of CO adsorption:
CO,ads ) kCO,adscCO,s(0.99 - θCO - θOH
The patterns studied here are also expected to occur in
systems in which CO oxidation is a sub-process or a side
reaction. To explore this idea, patterns are investigated in
experiments with 2% CO/H2 mixtures.
V
)
for θCO + θOH e 0.99 (4a)
CO,ads ) 0 for θCO + θOH g 0.99 (4b)
The CO and OH coverages are limited to 0.99, and ΘOH
V
2. Simulations
max
Model. A detailed model describing the S-shaped polarization
curve of CO electro-oxidation on a single Pt electrode has been
proposed by Koper et al.6 The model is based on a dual site
Langmuir-Hinshelwood kinetics in which adsorbed CO reacts
with adsorbed OH to form CO2. The reaction takes place through
4 steps:
) 0.33, respectively; values for other kinetic constants are given
in Table 1.6 The potential drop across the double layer (E) is
an important quantity in the system: its value determines the
experimentally measurable Faradaic current density, jF:
jF ) FStot(VOH + Vreact
)
(5)
CObulk T COsurface
COsurface + Pt f CO - Pt
(I)
(II)
The model in its present form is meant only to give a
qualitative description of the experimental results. For example,
the effect of anions on the adsorption of OH and the rate of
CO oxidation is not included. A simplified mass transfer model
with a constant diffusion layer thickness is taken. Although such
approximations are commonly used, their effect on the detailed
behavior of the present system is not known. Nevertheless, as
we shall see below, the model does reproduce and help explain
the characteristics of pattern formation seen in the experiments.
Figure 1a shows jF as a function of E. A bistable region is
found in which CO oxidation can be fast (upper branch) or slow
H2O + Pt T OH - Pt + H+ + e-
(III)
CO - Pt + OH - Pt f CO2 + H+ + e-
(IV)
CO diffuses to the Pt surface (step I) and adsorbs quickly
(step II). Adsorbed OH is produced by a dissociative mechanism
through step III; CO2 is produced by the reaction between

Reaction Rates during CO and CO/H2 Oxidation
J. Phys. Chem. B, Vol. 108, No. 38, 2004 14601
Figure 1. Numerical simulations of the dynamics of a single electrode.
(a) Bifurcation diagram showing the current density (j) as a function
of the potential drop through the double layer (E). Solid line: stable
steady state. Dashed line: unstable steady state. SN: saddle-node
bifurcation. (b) Cyclic voltametry scans at R ) 1 Ω. Arrows indicate
the direction of the scan. (Scan rate: 50 mV/s) (c) Current vs fixed
values of potential at large resistance, R ) 1000 Ω. (d) Cyclic
voltammetry scan at R ) 1000 Ω. Scan rate: 50 mV/s. (e) Two-
parameter bifurcation diagram showing the bistable region (shaded area)
in the F vs V plane. A ) 1 cm2.
Figure 2. Schematics of two coupled electrodes. (a) Electrochemical
cell with a two-electrode array coupled through a combination of
collective (Rcoll) and individual (Rind) resistances. (b) Simplified
equivalent circuit.
(lower branch) at a given value of E. The bistability here is
due to the kinetics since E, the potential drop across the double
layer, is fixed. The two stable branches are connected by an
unstable branch that exhibits negative differential resistance. The
S-shaped curve in Figure 1a is a characteristic feature of CO
oxidation and a result of the chemical autocatalytic effect of
CO.
In an experiment the potential drop across the double layer
(E) cannot be controlled because of an unavoidable potential
drop in the electrolyte. Typically, either the overall applied
circuit potential (V) or the total current is controlled; here we
consider the former case. (A schematic showing the relationship
between the potentials V and E for a two-electrode system is
given in Figure 2b; the single-electrode case is similar.) The
two potentials V and E are related through a charge balance:
oxidation peak during the transition from the lower branch to
the upper branch.
Current at fixed values of V and with scans in V are shown
in Figures 1c and 1d, respectively, with a large circuit resistance
(1000 Ω); no bistability is observed at this large resistance and
the transient effects are smaller than in the case of small
resistance. The region of bistability in the resistivity (F ) RA)
- circuit potential (V) plane is shown in Figure 1e; there exists
a critical resistivity (in this case about 123 Ω cm2) above which
only a monostable state is seen.
We now consider sets of coupled electrodes. Well-controlled
electrical coupling of the electrodes can be implemented with
a combination of series (collective, Rcoll), and parallel (indi-
vidual, Rind) resistors (see Figure 2a).20 The coupling strength
is varied through changes in the collective resistance fraction
dE V - E
Cd
)
- jF
(6)
dt
RA
where R is the uncompensated resistance of the electrolyte and
the external circuitry, Cd is the double layer capacity, and A is
the surface area of the electrode. Figure 1b shows the current
density (j ) (V - E)/RA) as a function of the circuit potential
during cyclic voltammetry in which the circuit potential is
scanned up and down (dV/dt ) ( scan rate) at a small resistance
of 1 Ω. Bistability is also seen on the polarization scan; in
addition, some transient effects are observed such as the large
ꢀ ) Rcoll/Rtot
(7)
while keeping the total resistance constant:
Rtot ) Rcoll + Rind/N
(8)
where N is the number of electrodes. For convenient comparison
between arrays of different sizes an equivalent resistance Req

14602 J. Phys. Chem. B, Vol. 108, No. 38, 2004
Kiss et al.
Figure 3. Numerical simulations of forward polarization scans of two (identical) electrodes with coupling. (Top row) Effect of coupling strength,
ꢀ (K). Req ) 1000 Ω, scan rate ) 50 mV/s. (a) ꢀ ) 0.991 (K ) 0.11 Ω-1 cm-2). (b) ꢀ ) 0.995 (K ) 0.2 Ω-1 cm-2). (c) ꢀ ) 0.999 (K ) 1 Ω-1
cm-2). (Bottom row) Effect of scan rate and total resistance. (d) Scan rate ) 15 mV/s, Req ) 1000 Ω, ꢀ ) 0.999 (K ) 1 Ω-1 cm-2). (e) Req ) 500
Ω , scan rate ) 50 mV/s, ꢀ ) 0.998 (K ) 1 Ω-1cm-2). (f) Req ) 5000 Ω , scan rate ) 50 mV/s, ꢀ ) 0.9998 (K ) 1 Ω-1cm-2). Solid thick line:
electrode 1. Solid thin line: electrode 2. Dashed lines show the corresponding behavior without coupling, i.e., ꢀ ) 0 (K ) 0 Ω-1cm-2). Initial
conditions for the scans: {E, ΘCO, ΘOH, cCO} for electrode 1: {0.55 V, 0.99, 0.02, 1.1 × 10-6 mol/L}, for electrode 2 {0.45 V, 0.98, 0.01, 1 ×
10-6 mol/L }.
) NRtot is defined. A charge balance based on the simple
equivalent circuit shown in Figure 2b for a multi-electrode setup
is as follows:20
size of 0.01 s and an error tolerance of 10-3. Bifurcation
diagrams were obtained with the built-in AUTO 97 interface
of XPP.
Simulation Results. The polarization scan of two electrodes
without coupling (ꢀ ) 0) at Req ) 1000 Ω is identical to that
shown Figure 1d for a single electrode. The effect of coupling
on the polarization scan is demonstrated in three scans in the
top row of Figure 3; the scan rate (50 mV/s) is a value that can
be conveniently used in experiments. Up to ꢀ ) 0.991 (Figure
3a), the effect of coupling is negligible. At about ꢀ ) 0.995
(Figure 3b), the polarization scan shows that before reaching
the mass-transfer limited region the current of one electrode
suddenly increases while the current of the other electrode
decreases. At even stronger coupling (ꢀ ) 0.999, Figure 3c),
this splitting effect is stronger: it covers a larger potential range
and the differences between the currents are larger. The
overshoots seen in Figures 3b and 3c are due to transient effects.
In the overshoots (at about V ) 2.15 V in Figure 3c) the high
and low current states transiently switch positions. These
overshoots will also be seen in the experiments as will be seen
below. At a lower scan speed (15mV/s, Figure 3d) transient
effects are minimized, there are no overshoots just below the
mass transfer limited region, and the splitting window is larger.
(Decreasing the scan speed to even lower values does not have
a significant effect). The equivalent resistance also affects the
intensity of the splitting behavior. At lower (Figure 3e) and
larger (Figure 3f) resistances (with constant effective coupling,
K) the splitting intensity is weaker and stronger, respectively.
n
dEk V - Ek
Cd
)
- jF,k + K
(Eavg - Ek)
(9)
∑
dt
ReqA
k ) 1
where k ) 1...N, Eavg is the mean double layer potential drop,
and K is the effective positive coupling:
1
ꢀ
K )
(10)
ReqA 1 - ꢀ
The equations for the other variables are simply indexed
versions of eqs 1a-c. For two electrodes (N ) 2), the current
density of each electrode (jk) is
P - Ek
RindA
jk )
(11)
where P is the summed potential drop on the double layer and
the individual resistors:
P ) (1 - ꢀ)V + ꢀ Eavg
(12)
In this paper we investigate the effect of coupling strength ꢀ
on the dynamics of the coupled system with two electrodes at
sufficiently large resistances such that only a monostable state
exists on a single electrode or on sets of electrodes without
coupling.
Computational Methods. The software XPP was used in
integrating the ordinary differential equations of the model with
a Gear-based adaptive stiff method. This method provided
consistent convergence in the solutions to the ODEs with a step
The characteristics of the splitting behavior at strong coupling
(ꢀ ) 0.999) can be seen in the bifurcation diagrams (Figure 4)
that show both stable and unstable steady states of the system
as a function of fixed circuit potential V. Without interaction,
the behavior is the same as that for a single electrode (Figure
1c); the current density increases almost linearly until the mass-
transfer limited plateau is reached at large resistance. With

Reaction Rates during CO and CO/H2 Oxidation
J. Phys. Chem. B, Vol. 108, No. 38, 2004 14603
Figure 5. Numerical simulations: Bifurcation diagrams of two
(identical) electrodes with coupling: the effect of coupling strength
and total resistance. (a, b) Bifurcation diagram with Req ) 1000 Ω,
ꢀ ) 0.9091 (K ) 0.01 Ω-1 cm-2 ). Panel b is a zoom on the bi-
furcation region of panel a. (c, d) Bifurcation diagram with Req
)
250 Ω, ꢀ ) 0.996 (K ) 1 Ω-1 cm-2). Current of electrode one and
total current are shown as a function of circuit potential, V, in panels
c and d, respectively. Solid line: stable steady state. Dashed line:
unstable steady state. PF: Pitchfork bifurcation. SN: saddle-node
bifurcation.
Figure 4. Numerical simulations: Bifurcation diagrams of two
(identical) electrodes with coupling. Req ) 1000 Ω, ꢀ ) 0.999 (K ) 1
Ω-1 cm-2). (a) Bifurcation diagram showing current density of electrode
1 vs potential. (b) Total current density vs potential. (c) Bifurcation
diagram showing CO coverage of electrode 1 vs potential. (d) Mean
CO coverage of the two electrodes vs potential. (e) Mean OH coverage
vs potential. (f) Average of the sum of CO and OH coverages vs
potential. Solid line: stable steady state. Dashed line: unstable steady
state. PF: pitchfork bifurcation.
reduces the mean CO coverage. Similar effects are seen in OH
coverage; one electrode in the bistable region has a higher OH
coverage than in the uncoupled case, the other has a lower
coverage; the mean OH coverage is increased due to coupling
as seen in Figure 4e. The aggregate coverage of CO and OH is
shown in Figure 4f; the coupling decreases the total coverage
of ΘCO + ΘOH in the splitting window and therefore increases
the number of free active sites. The bifurcation diagrams in the
variables E1 and E2 are similar to those shown in Figure 4 except
that the differences between the high and low current states are
very small.
The bifurcation diagrams shown in Figure 4 were obtained
at strong coupling (ꢀ ) 0.999). For comparison a bifurcation
diagram at an intermediate coupling strength is shown in Figures
5a,b. The region of instability of the uniform state covers a
smaller potential range (1.86 V < V < 2.06 V) than at stronger
coupling and the current differences are smaller. In addition,
the lower pitchfork bifurcation is now subcritical; the stable
high and low current states are created with an additional saddle-
node bifurcation.
Circuit resistance also has a significant effect on the behavior.
Currents of the individual electrodes and the total current are
shown in Figures 5c and 5d, respectively, at lower resistance
(Req ) 250 Ω). The bifurcation structure is somewhat more
complicated than that obtained at Req ) 1000 Ω. The first
bifurcation point (at smaller V) is supercritical, but there are
two additional saddle-node bifurcations at which the stable high
and low current states are created; the bifurcation at large V is
subcritical (similar to that shown in Figure 5b). The behavior
seen here with smaller resistance differs in one significant aspect
from that obtained above with large resistance: under these
conditions the coupling produces large changes in the total
current. The total current with pattern formation (strong
coupling) differs from that of the uncoupled, uniform state. In
the lower potential region of the splitting window the total
current is increased, in the larger potential region it is decreased
(see Figure 5d).
coupling (Figure 4a) the same current dependence occurs
although the uniform state is unstable over a range of applied
circuit potential 1.36 V< V < 2.08 V; the stability is lost through
two supercritical pitchfork bifurcations. At the lower pitchfork
bifurcation the single stable steady state loses stability above
the bifurcation point and two new stable states (one with lower,
the other with larger, current density) emerge. The diagram
shown is for one of the electrodes. The diagram for the other is
identical except that the states are reversed; when one electrode
has a high current density in the bistable region, the other has
a low current. The splitting behavior seen in the scans of Figure
3 is a consequence of the stability loss of the uniform solution
due to the coupling. At these parameters the splitting has only
a small effect on the total current (Figure 4b); the total current
is slightly increased at low potentials in the bistable region and
slightly decreased at larger potentials.
Figures 4c-e show the dependence of two important chemical
quantities, ΘCO and ΘOH, on applied circuit potential. The CO
coverage without coupling is given by the monotonically
decreasing solid and dotted curve in Figure 4c; the coverage of
CO decreases with increasing potential due to the removal of
CO of the surface at larger potentials. With coupling, due to
the pitchfork bifurcation and the resulting unstable region, one
electrode is highly covered with CO (producing low CO
oxidation rates) while the other electrode is almost free of CO
(because CO is efficiently oxidized, producing a high oxidation
rate). The mean CO coverage on the two electrodes is
significantly lower than the uncoupled case in a large potential
region where the splitting occurs (see Figure 4d). Thus coupling

14604 J. Phys. Chem. B, Vol. 108, No. 38, 2004
Kiss et al.
Figure 6. Numerical simulations of forward polarization scans of two
nonidentical electrodes (σ ) 0.01): the effect of coupling strength, ꢀ
(or Κ). Req ) 1000 Ω cm-2, scan rate ) 50 mV/s. (a) ꢀ ) 0 (K ) 0
Ω-1 cm-2 ). (b) ꢀ ) 0.9091 (K ) 0.01 Ω-1 cm-2). (c) ꢀ ) 0.991 (K )
0.11 Ω-1 cm-2). (d) ꢀ ) 0.999 (K ) 1 Ω-1 cm-2). Dashed lines in
panels b-d represent the behavior of electrode 1 in the uncoupled case
[ꢀ ) 0 (K ) 0 Ω-1 cm-2)]. Solid thick line: electrode 1. Solid thin
line: electrode 2.
At large resistance (Req ) 5 kΩ) the bifurcation diagram is
similar to that shown with Req ) 1 kΩ (Figure 4a) but the region
of instability of the uniform state extends over a larger circuit
potential due to the increased potential drop on the external
resistors. The effect of the coupling on total current is, however,
almost negligible.
Effect of Heterogeneities. In laboratory experiments there
are always some heterogeneities on surfaces; in the present case
this arises as unavoidable differences between the electrodes.
Even small heterogeneities can affect the dynamical behavior
of the system. Heterogeneities are simulated in our model by
using slightly different CO adsorption rates of the two elec-
trodes: kCO,ads(1,2) ) kCO, ads (1 ( σ), where σ is a heterogeneity
parameter. Changes in CO adsorption rates can, for example,
model different compositions of the polycrystalline surface of
the two electrodes. Here we consider σ ) 0.01, i.e., the CO
adsorption rate for electrode one is 1% larger, for electrode 2
is 1% smaller than the nominal value.
Figure 7. Numerical simulations: Polarization scans and bifurcation
diagrams of two coupled electrodes: the effect of heterogeneities. (a)
Forward polarization scan of two identical electrodes (σ ) 0) with the
same conditions as in Figure 3c but with switched initial conditions
for the two electrodes. Solid thick line: electrode 1. Solid thin line:
electrode 2. (b) Forward polarization scan of two nonidentical electrodes
(σ ) 0.01) with the same conditions as in Figure 6d but with switched
initial conditions for the two electrodes. Solid thick line: electrode 1.
Solid thin line: electrode 2. (c) The same scan as in panel b, but at V
) 1.6 V (shown by the arrow) the variables for electrode 2 were
changed to conditions [{E, ΘCO, ΘOH, cCO} ) {0.45 V, 0.98, 0.01, 1
× 10-6 mol/L}] simulating a change to open circuit, i.e., close to those
obtained at V ) 0.6. (d) Bifurcation diagram of two nonidentical (σ )
0.01) electrodes showing the current of electrode 1 as a function of
circuit potential, V. Req ) 1000 Ω cm-2, (a) ꢀ ) 0.999 (K ) 1 Ω-1
cm-2). Solid line: stable steady state. Dashed line: unstable steady
state. SN: saddle-node bifurcation. Inset: a zoom on the SN bifurcation
at larger V. The size of the rectangle in the main panel corresponds to
the scaling of the inset. (e) Same as in panel d but for electrode 2.
In Figure 6 the effect of changes in the coupling parameter
ꢀ is investigated at a fixed value of the heterogeneity parameter
σ. The degree of heterogeneity is small such that without any
coupling, the small heterogeneity has a negligible effect on the
polarization scan with large resistance (see Figure 6a); electrode
one (with larger kCO) has about 0.1% smaller current throughout
the scan. As the coupling strength is increased, the effect of
the heterogeneity becomes more pronounced. At ꢀ ) 0.9091
(Figure 6b), a small split is seen and at somewhat larger coupling
strengths (ꢀ ) 0.991, Figure 6c; and ꢀ ) 0.999, Figure 6d) a
split with full intensity occurs. The heterogeneities play a major
role; under similar conditions (but without heterogeneities) splits
are either not observed (Figure 3a) or can only be obtained with
smaller scan speed (Figure 3d). There is also a difference in
the start of the split on the polarization scan: without hetero-
geneity the split is abrupt, with heterogeneity it is smoother.
of the ODEs) if initial conditions for electrode 1 and 2 are
switched, the electrodes following the high and the low current
path will be switched as well (compare Figures 3c and 7a).
However, with heterogeneities, such a switch does not affect
the current path of the electrodes (compare Figures 6d and 7b).
The electrode with larger value of kCO,ads has a tendency to
follow the low current path in the scan. However, with a well-
timed perturbation a switch between the low and large current
state can be initiated. In Figure 7c, at V ) 1.6 V the state of
electrode 2 (thin line) was set to its initial conditions; such a
change can simulate in the experiments a break of the current
circuit. As a result the large current of electrode 2 dropped and
after a short transient electrode one followed the low current
path in the scan.
These observations can be explained by analyzing the
bifurcation diagram of electrode 1 and 2, shown in Figures 7d
and e, respectively. Because of the loss of the symmetry in the
system, the pitchfork bifurcations seen in the nonheterogeneous
case disappear and an isola is formed. With increases in the
circuit potential, electrode one follows a low current branch
Additional effects of heterogeneities can be seen in Figures
7a-c (scans) and Figures 7d,e (fixed values of V). The
heterogeneities cause the electrodes to split toward the high or
low current state consistently, independently of the initial
conditions. Without heterogeneities (because of the symmetry

Reaction Rates during CO and CO/H2 Oxidation
J. Phys. Chem. B, Vol. 108, No. 38, 2004 14605
without any bifurcations. The large-current branch is an isola
that is formed by two saddle-node bifurcations. For electrode 2
(Figure 7e), the isola is a low current branch. Therefore, during
a scan electrodes 1 and 2 follow low and high current paths,
respectively; however, in the isola region the two states can be
switched by a proper perturbation.
3. Experiments
Procedures. The experiments were carried out in a three-
electrode electrochemical cell schematically shown in Figure
2a. Solutions of 0.05 mol/L H2SO4, 0.05 mol/L H2SO4 + sat.
Na2SO4, or 0.10 mol/L HClO4 were used as cell electrolytes. A
gas sparger was used to introduce CO (Messer, 99.99%) or 2%
CO/H2 (Messer, Scientific Grade) gases to the cell; the sparger
was positioned near the wall to minimize turbulence. The
counter electrode was a platinum-clad niobium expanded-mesh.
The reference electrode was a Hg/Hg2SO4/sat. K2SO4 electrode;
all potentials reported here are with respect to a standard
hydrogen electrode. Two polycrystalline platinum disks (ESPI
Inc, 99.99%) of 4.7625 mm diameter in 14.3 mm distance were
used as a working electrode; the electrodes were embedded in
epoxy and reaction takes place only at the ends. The potential
of the working electrode was controlled by a potentiostat (Pine
Model AFCBP1). The current was measured with zero-
resistance ammeters. The measured currents and the potential
were digitized at a rate of 100 Hz with a DAS-1802HC digital
analogue converter.
Figure 8. Experiments on CO oxidation: CV scans of a single
electrode in different electrolytes. (a) 0.05 mol/L H2SO4 + sat. Na2SO4.
(b) 0.05 mol/L H2SO4. (c) 0.1 mol/L HClO4. Scan rate: 50 mV/s, Req
) 0 Ω.
Before each set of experiments, the surfaces of the electrodes
were polished with 1 and 0.05 µm Buehler Micropolish alumina.
The electrodes were then sonicated for 15 min in distilled water
to remove any residual polishing material. The electrodes were
electrochemically cleaned for 20 min by 350 mV/s continuous
potential sweeps between -0.15 and 1.75 V in 0.05 mol/L
H2SO4. The cell electrolyte was purged with N2 gas for at least
20 min to remove dissolved oxygen. The solution was then
saturated with CO (or CO/H2) gas until open cell equilibrium
potentials reached a steady value, approximately 0.25 and 0.05
V, respectively. After the current level decreased below 0.1 µA
at these potentials (indicating that the surface was covered with
CO), the gas flow rate was minimized to reduce turbulence in
the system from bubbling and potential scans were carried out
at a scan speed of 50 mV/s.
Behavior of a Single Electrode. Cyclic polarization scans
of CO oxidation on a single polycrystalline Pt electrode in three
different electrolytes, 0.05 mol/L H2SO4 + sat. Na2SO4, 0.05
mol/L H2SO4, and 0.10 mol/L HClO4 solutions are shown in
Figures 8 a-c, respectively. In sulfuric acid and perchloric acid
electrolytes, bistability has been seen during CO oxidation on
Pt single crystals due to the S-shaped polarization curve.5,6 On
the polycrystalline electrodes used in this investigation, bi-
stability is most clearly seen in the 0.05 mol/L H2SO4 + sat.
Na2SO4 solution (Figure 8a). The forward and backward scans
are very similar to those of the numerical simulations (Figure
1b); they exhibit an oxidation peak at about 0.86-0.87 V and
bistability between about 0.78 and 0.86 V. The model does not
account for two details of the experiments. First, in the
experiments the current decreases above the oxidation peak
rather than leveling out on a mass-transfer limited current
plateau. The decrease of current is due to the combined effect
of oxide formation7,21 and sulfate adsorption.6 (Because of the
formation of this oxide a reduction peak appears in the backward
scan at about 0.5-0.6 V. This peak is typically small at a
reasonably high scan rate of 50 mV/s as in Figure 8.) Second,
a prewave occurs (very small in Figure 8) at about 0.65 V; this
prewave is due to CO oxidation through an alternative pathway
in which there is no self-inhibition of CO and in which the
reaction order in CO is positive.5 (We do not investigate the
effect of coupling in the prewave region and it is not included
in the model.) In sulfuric acid (Figure 8b), the bistability region
is smaller; in perchloric acid (Figure 8c) clear bistability was
not found. Thus in the three solutions with different sulfate
concentrations the extent of bistability is different. Sulfate and
bisulfate ions are known to interact strongly with a platinum
surface; they have the strongest interaction with Pt(111).1 The
anions change the resistivity of the electrolyte and also can affect
the kinetic parameters such as by changing the crystal config-
1
uration .
Experimental Results on Coupled Electrodes. We now
explore the effect of coupling in the two-electrode system with
the three electrolytes. Results are first given for the 0.05 mol/L
H2SO4 + sat. Na2SO4 solution in which the bistability without
added resistance is the strongest.
Polarization (forward) scans of two electrodes as a function
of coupling strength are shown in Figures 9a-e; the circuit
resistance is large (Req ) 4 kΩ, ꢀ ) 0). Figure 9a was obtained
without coupling in which case the two electrodes behave
similarly; there are small differences at low (below 0.9 V) and
large potentials (above 1.2 V). Differences between the two
curves are largely due to heterogeneities or differences between
the surfaces of the two electrodes. (The scans of the single
electrodes are practically identical to those shown in Figure 9a.)
The current remains low until about 0.9 V, above which it almost
linearly increases (ohmic region). There is no sudden change
of current indicating an absence of bistability; the forward
polarization scan is similar to those obtained in the simulations
except for the current decrease due to oxide formation at larger
potentials. A reduction peak (reduction of the oxides) occurs
in the reverse scan (not shown) at about 0.5 V.
Figures 9b through 9e show the effect of coupling, ꢀ. Up to
ꢀ ) 0.5 only small differences in the currents can be observed

14606 J. Phys. Chem. B, Vol. 108, No. 38, 2004
Kiss et al.
Figure 10. Experiments on CO oxidation in different electrolytes.
Forward CV scans of the two-electrode setup with maximum added
coupling, ꢀ ) 1. (a-c) 0.05 mol/L H2SO4, (a) Req ) 4 kΩ. (b) Req
)
40 kΩ. (c) Req ) 40 kΩ with perturbation. Electrode 1 (thick line)
was briefly disconnected during the scan (at about V ) 1.25 V denoted
by the arrow) while electrode 2 (thin line) remained connected. (d) 0.1
mol/L HClO4. Req ) 4 kΩ. Scan speed: 50 mV/s.
The reproducibility of the splitting is very good. In repeating
scans at a fixed coupling strength without repolishing the surface
or increasing the electrode potential to very large values into
the oxide formation region, the same electrodes always follow
the high and low current path and the shapes of the splitting
currents are similar. If these conditions are not satisfied (for
example, if the electrode is re-polished), however, the splitting
still occurs but the splitting intensity and waveform can be
different. Experiments at smaller equivalent resistance (results
not presented) show that in accordance with the numerical
simulations, the splitting intensity at the same coupling strength
and scan speed is smaller with smaller Req.
Representative experiments in 0.05 mol/L H2SO4 are shown
in Figure 10a-d. At Req ) 4 kΩ, the scans without coupling (ꢀ
) 0) are similar to those in 0.05 mol/L H2SO4 + sat. Na2SO4.
With maximum added coupling (ꢀ ) 1, Figure 10a) splitting
can be observed; however, its intensity is smaller than those in
electrolytes with large sulfate content seen in Figure 9e. With
a very large resistance (Req ) 40 kΩ, Figure 10b) the splitting
can be clearly seen; this indicates that the splitting will also
likely occur in galvanostatic operation since the galvanostatic
mode of operation is similar to running the cell at large Req and
ꢀ.
A perturbation experiment similar to that done in the
numerical simulations (Figure 7c) is shown in Figure 10c to
explore the capability of the system to switch between the high
and low current paths at strong coupling. Without perturbation
(Figure 10b) electrode 1 (thick line) initially follows the high
current path. A perturbation was introduced by breaking the
circuit path for electrode 2 in the splitting region. When the
perturbation is applied at the appropriate potential for long
enough time (Figure 10c), the states could be switched and the
currents of the electrodes followed the alternate current path.
(In Figure 10c the differences between the two electrodes caused
by coupling is smaller than in 10b, likely due to changes in
surface properties; nevertheless, the qualitative feature of
switching is the same as that seen in the simulations, Figure
7c.)
Figure 9. Experiments on CO oxidation: effect of coupling strength
on forward CV scans of two electrodes in 0.05 mol/L H2SO4-sat.
Na2SO4 electrolyte. Req ) 4 kΩ. (a) Without added coupling, ꢀ ) 0.
Thick line: electrode 1. Thin line: electrode 2. (b) ꢀ ) 0.5. (c)
ꢀ ) 0.75. (d) ꢀ ) 0.95. (e) Maximum added coupling, ꢀ ) 1. (f)
Total current during the forward scan. Thick line: ꢀ ) 1. Thin line:
ꢀ ) 0.
(Figure 9b). For somewhat larger values, ꢀ ) 0.75 and 0.95,
there are two changes; the currents of the two electrodes become
closer at large and small potentials but in an intermediate region
(0.9 V < V < 1.2 V) small differences begin to arise. With
maximum added coupling (ꢀ ) 1, Figure 9e) there is a dramatic
change in the polarization scans. In the ohmic region, where
without interactions the currents of the electrodes are identical,
a splitting is observed in which electrode one (thick line) follows
initially a large current path while electrode two follows a low
one. Above V ) 1.1 V, the positions are switched. These
experimental results show the same splitting behavior as in the
numerical simulations with small heterogeneities (see Figure
6d). In the experiments, the second, “overshoot splitting”, is
larger than in the simulations indicating stronger transient
effects. It seems that well-developed splitting can be experi-
mentally observed only for coupling strength ꢀ > 0.95. These
results are consistent with the simulation findings that showed
(Figure 6) that the splitting behavior develops at large coupling
strengths.
(The backward scans (not shown for clarity) do not exhibit
any splitting at these conditions but the split in the backward
scan does occasionally appear, particularly with the other
electrolytes. The simulations do show splits in both scan
directions. The chemistry is apparently very different in the
backward scan, perhaps due to the oxides.)
A comparison of the total currents at ꢀ ) 0 and ꢀ ) 1.0 is
shown in Figure 9f; only the potential window in which splitting
occurs is presented. At ꢀ ) 1.0, the total current is slightly
smaller than that without coupling above approximately V )
1.0 V; this is consistent with the numerical findings that the
effect of coupling on total current is small when the circuit
resistance is large (see, e.g., Figure 4b).
Experiments with 0.01 mol/L HClO4 are shown in Figure
10d with maximum added (ꢀ ) 1) coupling. Without coupling,

Reaction Rates during CO and CO/H2 Oxidation
J. Phys. Chem. B, Vol. 108, No. 38, 2004 14607
ref 22 and references therein). The presence of positive coupling
among the reaction sites (typically through the temperature,
pressure, or potential field) usually effectively reduces these
heterogeneities; the addition of positive coupling then results
in a more uniform spatial activity. For example, it has been
shown that coupling can synchronize the oscillation frequencies
of a heterogeneous population of electrodes.18 In this present
paper, the activity of two Pt electrodes during electrocatalytic
CO oxidation was investigated in laboratory experiments and
numerical simulations with tuned positive interactions. In the
presence of strong coupling, the interactions can initiate
nonuniform activities in which one electrode exhibits a high
reaction rate while the other is practically inactive. The different
activities of the two electrodes are remarkable since catalytic
activities are mostly influenced by surface structure, catalyst
material, temperature, applied driving force of the reaction, etc.,
each of which is similar in our case for the two electrodes as
confirmed by measurements without interactions. Although
patterns can develop on identical electrodes with interactions,
it is seen that small inherent heterogeneity has a major effect
on the resulting state; the nonuniform reaction rates due to
heterogeneities are greatly amplified by coupling.
Figure 11. Experiments on CO/H2 oxidation: Forward CV scans of
2% CO-98% H2 mixtures in a two-electrode setup with and without
coupling in 0.05 mol/L H2SO4. (a) Without added coupling, ꢀ ) 0, Req
) 10 kΩ. (b) Maximum added coupling, ꢀ ) 1, Req ) 10 kΩ. (a)
Without added coupling, ꢀ ) 0, Req ) 20 kΩ. (b) Maximum added
coupling, ꢀ ) 1, Req ) 20 kΩ. Thick line: electrode 1. Thin line:
electrode 2. Scan speed: 50 mV/s.
The experiments were carried out with carefully tuned
coupling strengths. The mechanism of the observed symmetry
breaking due to coupling is very similar to that in the formation
of Turing patterns in distributed systems. On the basis of our
results, we expect similar symmetry breaking transitions to be
seen in larger sets of reaction sites and also on distributed
systems. Experiments with eight globally coupled electrodes
show results similar to those obtained in this paper;23 although
the transitions are more complicated, symmetry breaking does
occur in a region of circuit potential in which sets of electrodes
exhibit large activities while others are practically inactive.
Turing structures have also previously been seen in a continuous
electrochemical system.7 A nonuniform potential distribution
was observed on a rotating polycrystalline Pt ring during CO
electro-oxidation in a dilute (2 × 10-3 mol/L) perchloric acid
solution. A dilute solution with low conductivity was used to
produce a large ohmic drop in the electrolyte so that an external
resistance was not required; long-range coupling is inherent in
the system and is determined by the cell geometry. The potential
distribution on the ring exhibited three peaks and rather small
amplitudes (about 15 mV) in a circuit potential window.
the scans are similar to those in the sulfuric acid experiments
but there is a larger prewave at about V ) 0.75 V. With
coupling, the intensity of splitting is weaker than that with
sulfate electrolytes. The current difference between the two
electrodes is smaller but a well-developed secondary overshoot
peak can be observed. These two features are characteristics of
the scans in perchloric acid in a wide range of the studied
equivalent resistance 1 kΩ < Req < 20 kΩ. Thus, even though
clear bistable behavior is not found on a single electrode, the
splitting is seen with two electrodes.
The splitting behavior can also be observed during the
simultaneous oxidation of CO and H2. H2 is oxidized very fast
on the surface sites not covered by CO or OH.1 Thus, when
patterns form on the electrode array due to CO oxidation, the
differences in currents can be intensified by large H2 oxidation
currents. The idea was tested on 2% CO/H2 gas in which (on
single crystals) an S-shaped polarization curve without added
resistance has been previously observed.2 In the two-electrode
configuration studied here, a larger equivalent resistance (Req
> 4 kΩ) was required compared to the pure CO case to obtain
an almost linear ohmic region on the scans without added
coupling (ꢀ ) 0, see Figures 11ac). With maximum added
coupling (ꢀ ) 1), splitting behavior does appear with both the
smaller (Req ) 10 kΩ, Figure 11b) and larger (Req ) 20 kΩ,
Figure 11d) equivalent resistances.
Our findings in the two-electrode systems support and
augment the results on Turing-type patterns on a ring. It was
shown that the patterns develop from the nearly uniform current
distribution with increased coupling. Our setup also enables us
to measure the currents directly on the electrodes; it was found
that although the amplitudes of the potential patterns are small,
variations in other observable variables including current and
concentrations (or coverages) of chemical species can be quite
large because of the coupling.
4. Discussion
It is seen through both experiments and simulations that large
differences in the currents on Pt electrodes occur during CO
electro-oxidation as the coupling strength between two elec-
trodes is increased. Furthermore, simulations show that such
differences can arise even on identical surfaces since variations
are produced by the symmetry breaking.
Inherent nonuniformity or heterogeneity, due to differences
of kinetic parameters, can also occur in surface reactions due
to variations in local surface properties. These may develop in
the course of an experiment by some pretreatment, or may be
due to a variation of the local density of the catalyst, porosity,
catalyst thickness, nonuniformities of the temperature distribu-
tion in the reactor, or imperfect mixing in the fluid phase (see
In general, the stronger the coupling, the larger the extent of
the pattern formation observed. Thus, in CO oxidation the extent
of stationary patterning can be tuned between the uniform and
large amplitude asymmetric case; the experimental setup enables
the creation of a structured active area with varying uniformity.
Patterns were also observed at very large resistances; since
running an electrochemical cell at large (series) resistance
simulates a galvanostatic mode of operation, the patterns are
also expected to form under galvanostatic control.
Simulations show that the symmetry breaking produces
patterned states in which the total coverage of CO and OH is
always lower and thus the number of total free active sites is

14608 J. Phys. Chem. B, Vol. 108, No. 38, 2004
Kiss et al.
higher than in the corresponding uniform state. Moreover, at
low total resistance and quasi-stationary circuit potential (low
scan rates), changes up to 20% in total current can occur. This
opens up a possibility of increased reactivity not only in the
CO oxidation system but also in systems in which CO electro-
oxidation occurs in parallel with other chemical and electro-
chemical reaction steps on the free sites. In these cases, running
the experiments under conditions favorable for pattern formation
could have a beneficial effect on the total reaction rate.
The experiments were carried out in three different electro-
lytes exhibiting different extent of S-shaped polarization curves;
all three electrolytes exhibited pattern formation with strong
coupling. The sulfate-saturated sulfate electrolyte exhibited both
the strongest bistability and the most pronounced pattern
formation; parallel tendencies in exhibited bistability and pattern
formation characteristics were seen in the three electrolytes,
sulfate-saturated sulfuric acid > sulfuric acid > perchloric acid.
(The sulfate ions affect the cell dynamics in several ways: they
induce surface changes and kinetic features responsible for
bistability as well as changes in electrolyte resistivity.) Since
stationary pattern formation requires bistability (S-shaped
polarization curve) at small ohmic drops, it is reasonable that
systems with stronger bistability would also show stronger
pattern formation.
We showed that electrical interactions (for example, due to
a load resistance) cause large differences in activities of Pt disks,
that otherwise have the same inherent catalytic activities, during
the electro-oxidation of CO and CO/H2 mixtures. The large
impact of coupling on local activities implies that care must be
taken in interpreting experiments in, for example, automated
catalyst design with arrays when coupling and positive feedback
kinetic mechanisms exist.
Acknowledgment. This work was supported in part by the
National Science Foundation (CTS-0317762). We thank Gerhard
Ertl for his many years of inspiration, support, and gracious
hospitality.
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