New experimental data and mechanistic studies on the bromate-dual substrate-dual catalyst batch oscillator

Article abstract of DOI:10.1021/jp0602575

The bromate-hypophosphite-acetone-Mn(II)-Ru(bpy)₃²⁺ batch oscillator was recently suggested for studying two-dimensional pattern formation. The system meets all major requirements that are needed for generation of good quality traveling waves in a thin solution layer. The serious drawback of using the system for studying, temporal and spatial dynamical phenomena is its unknown chemical mechanism. In order to develop a mechanism that explains the observed long-lasting batch oscillations the bromate-hypophosphite-acetone-Mn(II)-Ru(bpy)₃²⁺ oscillator was revisited. We studied the dynamics both in the total system and in some composite reactions, and kinetic measurements were carried out in three subsystems. From the new experimental results we concluded that the two oscillatory sequences observed in the full system are originated from two oscillatory subsystems, the Mn(II)-catalyzed bromate-hypophosphite-acetone and the Ru(bpy)₃²⁺-catalyzed bromate-bromoacetone reactions. Here we propose a mechanism which is capable of simulating the dynamical features that appeared in the complex system.

Full text of DOI:10.1021/jp0602575

J. Phys. Chem. A 2006, 110, 6067-6072
6067
New Experimental Data and Mechanistic Studies on the Bromate-Dual Substrate-Dual
Catalyst Batch Oscillator
Istva´n Szalai, Krisztina Kurin-Cso1rgei, Viktor Horva´th, and Miklo´s Orba´n*
Department of Inorganic and Analytical Chemistry, L. Eo¨tVo¨s UniVersity, P.O. Box 32,
H-1518 Budapest 112, Hungary
ReceiVed: January 13, 2006; In Final Form: March 17, 2006
The bromate-hypophosphite-acetone-Mn(II)-Ru(bpy)32+ batch oscillator was recently suggested for studying
two-dimensional pattern formation. The system meets all major requirements that are needed for generation
of good quality traveling waves in a thin solution layer. The serious drawback of using the system for studying
temporal and spatial dynamical phenomena is its unknown chemical mechanism. In order to develop a
mechanism that explains the observed long-lasting batch oscillations the bromate-hypophosphite-acetone-
2+
Mn(II)-Ru(bpy)3 oscillator was revisited. We studied the dynamics both in the total system and in some
composite reactions, and kinetic measurements were carried out in three subsystems. From the new experimental
results we concluded that the two oscillatory sequences observed in the full system are originated from two
oscillatory subsystems, the Mn(II)-catalyzed bromate-hypophosphite-acetone and the Ru(bpy)32+-catalyzed
bromate-bromoacetone reactions. Here we propose a mechanism which is capable of simulating the dynamical
features that appeared in the complex system.
Introduction
The reaction between bromate and hypophosphite ions in the
presence of a Mn(II) catalyst was reported long ago to show
oscillations in the redox potential and in the light absorbance,
if the bromine formed during the reaction was removed from
the system by an inert gas flow or by adding acetone.1 In a
typical experiment only a few (5-10) oscillations can be
observed (Figure 1a). These oscillations appear in a finite range
of gas flow rate or of acetone concentration. We found later
that introducing a small amount of a second catalyst (10-5
-
10-4 mol/dm3 Ru(bpy)3SO4, ferroin, or diphenylamine) into
the Mn(II)-catalyzed bromate-hypophosphite short-lived oscil-
latory system generates long-lasting oscillations.2 In most cases,
the long-lasting oscillations begin after an induction period
(Figure 1b). The bromate-hypophosphite-acetone-Mn(II)-
Ru(bpy)32+ system is ideally suited for studying pattern evolu-
tion. It exhibits long-lasting batch oscillations, it does not
produce gaseous product or precipitate, and it gives rises to color
oscillations in a stirred batch reactor and well visible patterns
in an unstirred solution layer. Both phenomena are maintained
for many (>5) hours.
To facilitate modeling of the rich temporal and spatial
dynamical behaviors observed in the title reaction requires a
simple but reliable chemical mechanism. Here we suggest a
mechanism based on our new experimental observations and
kinetic measurements performed in some subsystems of the
complex reaction.
Figure 1. Oscillations in the absorbance measured in the BrO3--H3-
PO2-acetone-Mn(II) system (a) in the absence and (b) in the presence
of 5 × 10-5 mol/dm3 Ru(bpy)32+. Initial concentrations: [BrO3-] )
0.02 mol/dm3, [H3PO2] ) 0.1 mol/dm3, [acetone] ) 0.1 mol/dm3, [H2-
SO4] ) 1.0 mol/dm3, [Mn(II)] ) 0.003 mol/dm3. The main absorbing
species at λ ) 480 nm: Mn(III) (ꢀ ) 120 mol-1 dm-3 cm-1) and Br2
(ꢀ ) 60 mol-1 dm-3 cm-1). At λ ) 450 nm: Ru(bpy)32+ (ꢀ ) 14 500
mol-1 dm-3 cm-1), Ru(bpy)3 (ꢀ ) 150 mol-1 dm-3 cm-1), and Br2
3+
Experimental Section
(ꢀ ) 120 mol-1 dm-3 cm-1). The color oscillates between pink and
colorless in panel a and between yellow and green in panel b.
H2SO4 (Chemolab 96%), NaH2PO2‚H2O (Sigma), KBr (Rea-
nal p.a.), NaBrO3 (Fluka p.a.), MnSO4‚H2O, Ru(bpy)3Cl2‚6H2O
(Aldrich), acetone (Fisher), and bidistilled water were used to
prepare the working solutions. Ru(bpy)3SO4 was obtained by
converting the chloride salt to the sulfato form using the recipe
suggested by Gao and Fo¨rsterling.3 Stock solutions of Ru-
* To whom correspondence should be addressed. E-mail: orbanm@
ludens.elte.hu.
2+
(bpy)33+ were prepared from the stock solutions of Ru(bpy)3
10.1021/jp0602575 CCC: $33.50 © 2006 American Chemical Society
Published on Web 04/15/2006

6068 J. Phys. Chem. A, Vol. 110, No. 18, 2006
Szalai et al.
by oxidation with solid PbO2 followed by filtration on a fritted
3+
glass. The Ru(bpy)3 solutions were stored in darkness and
used within 1 h. A Mn2(SO4)3 stock solution was prepared by
reacting a known amount of KMnO4 with a 50-fold excess of
MnSO4 in 2 mol/dm3 sulfuric acid.
The spectra for kinetic measurements were taken on Milton
Roy 3000 and Agilent 8452 diode array spectrophotometers
equipped with quartz cells (path length 1 cm, volume 2 mL).
In the cells the temperature was kept at 20.0 ((0.1) °C, and
the solutions were mixed by magnetic stirrer.
The simulations were done with the program XPPAUT.4 The
parameter estimations were carried out by the MULTIMRQ
program using the Marquardt method.5 Fitted parameters are
given at the 95% significance level.
Results
Effect of Stirring Intensity on the Dynamics of the
BrO3--H3PO2-Acetone-Mn(II) Oscillatory System. Poj-
man and co-workers6 observed a strong effect of stirring on
the behavior of the short-lived bromate-hypophosphite-Mn-
(II)-acetone oscillator. No oscillations occurred in the system
unless a gas/liquid interface was present. The absorption of the
bromine on the Teflon stirring bar or on the wall of the reactor
also influenced the dynamics. They concluded that the system
is extremely sensitive to the rate of removal of the volatile
species. They detected bromoacetone and bromine in the gas
phase above the reaction mixture using the GC/MS method.
In agreement with Pojman’s observations we found that the
number of the oscillations depends on the reactor geometry and
the stirring rate, and under similar conditions the number of
oscillations increases when the intensity of the stirring increases.
Surprisingly, applying quite intense stirring (high stirring rate
and relatively big Teflon coated stirrer bar) we observed long-
lasting oscillations in the absent of any second catalyst. The
oscillations in the bromate-hypophopshite-Mn(II)-acetone
system at a high stirring rate are presented in Figure 2.
This long-lasting batch oscillator cannot, of course, be utilized
for studying pattern formation due to its requirement of strong
stirring. However, the importance of bromine removal for
maintaining the sustained-like oscillations in the bromate-dual
substrate-dual catalyst system was considered in our mecha-
nistic studies.
Figure 2. Effect of stirring rate on duration of the oscillations in the
potential of a Pt vs Hg/Hg2SO4/saturated K2SO4 electrode pair in the
BrO3--H3PO2-acetone-Mn(II) system. Initial concentrations: [BrO3-
]
) 0.02 mol/dm3, [H3PO2] ) 0.075 mol/dm3, [acetone] ) 0.09 mol/
dm3, [H2SO4] ) 1.0 mol/dm3, [Mn(II)] ) 0.0036 mol/dm3. Stirring
rate: (a) 300 rpm, (b) 900 rpm.
-
Figure 3. Oscillations in the absorbance recorded in the BrO3
-
2+
acetone-Ru(bpy)3 system after perturbation with Br- ions. Initial
concentrations: [BrO3-] ) 0.02 mol/dm3, [acetone] ) 0.1 mol/dm3,
[H2SO4] ) 1.0 mol/dm3, [Ru(bpy)3]2+] ) 5 × 10-5 mol/dm3. In each
perturbation [Br-] ) 0.001 mol/dm3 was added at the times shown by
the arrows.
Dynamics in the BrO3--Acetone-Ru(bpy)32+ Subsystem.
In order to clarify the role of the second catalyst in the title
reaction, experiments were performed in the bromate-acetone-
2+
Ru(bpy)3 subsystem to check the possibility of BZ-type
(bromide-controlled) oscillations in this composite reaction. In
a BZ-type oscillator the reaction between the brominated organic
intermediate and the oxidized form of the catalyst produces
bromide ions, the inhibitor of the autocatalytic bromate-
bromous acid reaction in the oscillatory kinetics.
times indicated by the arrows produced elementary bromine in
the system, which brominated the acetone in a slow reaction.
The processes are described by eqs 1 and 2 and recorded in
Rastogi and Misra7 showed earlier that oscillations can occur
in the Ce(IV)- or Mn(II)-catalyzed bromate-acetone reaction
at high temperature (50 °C) and at high acetone concentration
(3.4 M). At room temperature or below (20 °C) we have not
found oscillations in the presence of any BZ catalyst including
Ru(bpy)32+. We supposed that at room temperature the bromi-
nation of the acetone is too slow to generate enough bromoac-
etone, the intermediate that is needed for production of a
sufficient amount of bromide in the oxidation reaction of the
bromoacetone. However, when additional bromoacetone was
produced by applying bromide ion perturbation in the bromate-
acetone-Ru(bpy)32+ system, oscillations appeared at 20 °C. The
result is shown in Figure 3. The bromide ions injected at the
BrO3- + 5Br- + 6H+ f 3Br2 + 3H2O
Br2 + Ac f BrAc + H+ + Br-
(1)
(2)
Figure 3 as the first peaks after the perturbations. The oscilla-
tions start after the bromine is consumed by acetone. The
increasing amount of added bromide yields more and more
bromoacetone, which results in longer and longer oscillatory
sequences. For example, when 7 × 10-3 M bromide was added
to the system in Figure 3, the oscillations lasted for 3 h.
We prepared bromoacetone in a separate experiment by
mixing a known amount of bromide and acetone with an excess

Bromate-Dual Substrate-Dual Catalyst Batch Oscillator
J. Phys. Chem. A, Vol. 110, No. 18, 2006 6069
The oscillations showed strong sensitivity to the stirring rate.
High amplitude potential oscillations (∼150 mV) appeared at
300-700 rpm, the amplitude decreased to half at 200 rpm, and
the oscillations stopped below 100 rpm.
The appearance of the oscillations in the bromide perturbed
2+
bromate-acetone-Ru(bpy)3 reaction mixture suggests that
the reaction between bromoacetone and Ru(bpy)33+ catalyst (eq
3) provides an effective source of bromide ions for generating
a BZ-type oscillatory behavior.
Ru(III) + BrAc f Br - + products
(3)
Kinetics of Some Composite Reactions. Oxidation of H3PO2
by Mn(III) Ions. The reaction was studied in [H2SO4] ) 1 mol/
dm3 at different initial concentrations of Mn(III) (1 × 10-3
-
Figure 4. Sustained-like oscillations in the bromate-bromoacetone-
2+
Ru(bpy)3 subsystem. Initial concentrations: [BrO3-] ) 0.073 mol/
5 × 10-3 mol/dm3) and NaH2PO2 (0.05-0.2 mol/dm3). In 1
mol/dm3 sulfuric acid the NaH2PO2 is present in the form of
H3PO2 (pKa ) 2.0). A typical absorbance vs time curve is shown
in Figure 5a. A similar mechanism as proposed by Caroll and
Thomas8 for the oxidation of H3PO2 with Ce(IV) was assumed
to exist in the Mn(III)-H3PO2 reaction. The mechanism is
represented by steps RI-RIII.
dm3, [acetone] ) 0.2 mol/dm3, [H2SO4] ) 1.16 mol/dm3, [Br-] ) 0.106
mol/dm3. Time of bromination: 4 h. Calculated concentrations after
bromination: [BrO3-] ) 0.02 mol/dm3, [bromoacetone] ) 0.16 mol/
dm3, [H2SO4] ) 1.0 mol/dm3, [Br-] ) 0 mol/dm3, [acetone] ) 0.04
mol/dm3 (this amount of acetone falls below the limit when oscillations
can occur in the bromoacetone-free system). The oscillations were
initiated by adding [Ru(bpy)3]2+] ) 5 × 10-5 mol/dm3. Stirring rate:
600 rpm. Temperature: 25 °C.
Mn(III) + H3PO2 / [MnH3PO2]3+
(RI)
VfI ) kfI [Mn(III)][H3PO2]
3+
VrI ) krI [MnH3PO2
]
[MnH3PO2]3+ f Mn(II) + H2PO2 + H+
(RII)
•
3+
VII ) kII[MnH3PO2
]
•
2H2PO2 + H2O f H3PO2 + H3PO3
(RIII)
• 2
VIII ) kIII[H2PO2 ]
The first step in the mechanism is the formation of a complex
between Mn(III) and H3PO2 (RI). Reduction of Mn(III) occurs
in RII, which is the rate determining step in the overall process.
•
RIII is the disproportion of H2PO2 radicals which yields reagent
H3PO2 and end product H3PO3.
We used nonlinear parameter estimation to evaluate kII and
KI ) kf /kr from the spectrophotometric measurements. If RIII
I
I
is assumed to be a fast reaction (kIII ) 3 × 109 mol-1 dm-3
s-1), then for KI and kII, 29((2) mol-1 dm-3 and 5.6((0.1) ×
10-3 s-1, respectively, are derived. These values are in good
agreement with the results of Zhang and Field.9 The sum of
the reactions RI-RIII is designated as R12 in our model
suggested to describe the oscillatory behavior in the total system.
Figure 5. The absorbance vs time curves in the oxidation of H3PO2
by (a) Mn(III) and (b) Ru(bpy)33+. Experimental conditions: (a) [H3-
PO2] ) 0.1 mol/dm3, [H2SO4] ) 1.0 mol/dm3, [Mn(III)] ) 0.002 mol/
dm3. At λ ) 480 nm the main absorbing species are Mn(III) and
MnH3PO23+ complex. (b) [H3PO2] ) 0.5 mol/dm3, [H2SO4] ) 1.0 mol/
dm3, [Ru(bpy)3]3+] ) 4 × 10-5 mol/dm3. At λ ) 450 nm the main
2+
3+
absorbing species are Ru(bpy)3 and Ru(bpy)3
.
2Mn(III) + H3PO2 + H2O f
2Mn(II) + H3PO3 + 2H+ (R12)
(and known amount) of bromate in the presence of 1 M H2-
SO4. The bromination of the acetone (the disappearance of the
brown color of bromine) was completed within 3-4 h. From
the stoichiometry of eqs 1 and 2 and using the initial concentra-
tions shown in Figure 4 the [BrAc] was calculated to be 0.16
mol/dm3. The concentration of BrO3- and H2SO4 in the mixture
after the bromination was close to the initial concentrations of
V12 ) k12K[Mn(III)]t[H3PO2]/(1 + K[H3PO2])
3+
[Mn(III)]t ) [Mn(III)] + [MnH3PO2
]
k12 ) kII, K ) KI
2+
Figure 3. When a small amount of Ru(bpy)3 catalyst was
3+
introduced into the mixture, oscillations in the potential of the
Pt electrode and in the color started, and the seemingly
undamped oscillations were recorded for 31/2 h (see Figure 4).
Oxidation of H3PO2 by Ru(bpy)3 Ions. The reaction was
studied in [H2SO4] ) 1 mol/dm3 at different initial concentra-
tions of H3PO2 (0.5-1 mol/dm3). A typical absorbance vs time

6070 J. Phys. Chem. A, Vol. 110, No. 18, 2006
TABLE 1: Model for the BrO3--H3PO2-Acetone-Mn(II)-Ru(bpy)3 Oscillatory Systema
Szalai et al.
2+
R1
R2
R3
R4
R5
R6
R7
R8
BrO3- + Br- + 2H+ f HBrO2 + HOBr
V1 ) k1[BrO3-][Br-]
V2 ) k2[HBrO2][Br-]
V3 ) k3[HBrO2][BrO3 ]
HBrO2 + Br- + H+ f 2HOBr
BrO3- + HBrO2 + 3H+ + 2Mn(II) f 2HBrO2 + 2Mn(III) + H2O
2HBrO2 f BrO3- + HOBr + H+
-
V4 ) k4[HBrO2]2
f
b
HOBr + Br- + H+ / Br2 + H2O
V
5 ) k [HOBr][Br-] - k5[Br2]
Br2 + H3PO2 + H2O f 2Br-+ H3PO3 + 2H+
BrO3- + H3PO2 + H+ f HBrO2 + H3PO3
HBrO2 + H3PO2 f HOBr + H3PO3
V6 ) k56[Br2][H3PO2]
V7 ) k7[BrO3-][H3PO2]
V8 ) k8[HBrO2][H3PO2]
V9 ) k9[HOBr][H3PO2]
V10 ) k10[Br2]
R9
HOBr + H3PO2 f Br- + H3PO3 + H+
Br2 f fBr-+ fBrAc
R10
R11
R12
R13
R14
Ru(III) + BrAc f Br-
V
V
V
V
11 ) k11[Ru(III)]
2Mn(III) + H3PO2 +H2O f 2Mn(II) + H3PO3 + 2H+
2Ru(III) + H3PO2 + H2O f 2Ru(II)+ H3PO3 + 2H+
Mn(III) + Ru(II)f Mn(II) + Ru(III)
12 ) k12K[Mn(III)][H3PO2]/(1+ K[H3PO2])
13 ) k13[Ru(III)][H3PO2]
14 ) k14([Ru]T - [Ru(III)])[Mn(III)]
a Abbreviations: BrAc ≡ bromoacetone, Ru(III) ≡ [Ru(bpy)3]33+, Ru(II) ≡ [Ru(bpy)3]32+, [Ru]T ) [Ru(II)] + [Ru(III)]. The variables in the
model are [BrO3-], [H3PO2], [Br-], [HBrO2], [HOBr], [Br2], [Mn(III)], [Ru(III)]. In [H2SO4] ) 1.0 mol/dm3 used in the experiments the [H+] )
1.29 mol/dm3.15 This value is included in the rate constants of V1, V2, V3, V5, and V7. k11 is a pseudo-first-order rate constant that includes [BrAc].
TABLE 2: Parameters Used in the Simulations
parameters
refs
R1
R2
R3
R4
R5
k1 ) 2.0 mol-1 dm-3 s-1
k2 ) 3.2 × 106 mol-1 dm-3 s-1
k3 ) 80 mol-2 dm-6 s-1
k4 ) 4.38 × 103 mol-1 dm-3 s-1
k5f ) 1 × 1010 mol-1 dm-3 s-1
kb5 ) 80 s-1
1
13
a
14
13
R6
R7
R8
R9
R10
R11
R12
R13
R14
k6 ) 1.04 mol-1 dm-3 s-1
k7 ) 1×10-5 mol-1 dm-3‚s-1
k8 ) 10 mol-1 dm-3 s-1
k9 ) 0.8 mol-1 dm-3 s-1
adjustable
9
9
9
9
Figure 6. Oxidation of Ru(bpy)3]2+ by Mn(III). Experimental condi-
tions: [H2SO4] ) 1.0 mol/dm3, [Ru(bpy)32+] ) 1.5 × 10-5 mol/dm3,
[Mn(III)] ) 1.0 × 10-4 mol/dm3 (.), [Mn(III)] ) 2.0 × 10-4 mol/
dm3(~).
adjustable
k12 ) 5.6 × 10-3 s-1, K ) 29 mol- 1 dm-3
k13 ) 2.1 × 10-3 mol-1 dm-3 s-1
k14 ) 360 mol-1 dm-3 s-1
b
b
b
curve is shown in Figure 5b. The reaction follows second-order
kinetics (eq R13).
a Adjusted here. b Measured here.
2Ru(bpy)33+ + H3PO2 + H2O f
in the bromate-H3PO2-acetone-dual catalyst system, consid-
ering that the dynamics is rather complex: it is sensitive to
stirring, and five input components (bromate, hypophosphite,
acetone, Mn(II), Ru(bpy)32+) and at least three volatile species
(bromine, acetone, bromoacetone) are involved. The model we
suggest is presented in Table 1. The parameters used in the
simulations are shown in Table 2.
Steps R1-R5 in the model represent the well-known Mn-
(II)-catalyzed oxybromine chemistry, which results in formation
of bromine in reactions of R1 + R2 + 3 × R5. Bromine is
consumed by hypophosphite in a slow process of R6 and by
reaction with acetone in step R19a (see below). The next three
steps (R7-R9) describe the oxidation of hypophosphite with
bromine species:
2Ru(bpy)32+ + H3PO3 + 2H+ (R13)
V13 ) k13[Ru(bpy)33+][H3PO2]
k13 ) 2.1((0.4) × 10-3 mol-1 dm-3 s-1
2+
Oxidation of Ru(bpy)3 by Mn(III) Ions. The oxidation of
Ru(bpy)3 by Mn(III) in [H2SO4] ) 1 mol/dm3 is a fast
2+
reaction. The reaction was studied at different initial concentra-
tions of Mn(III) (5 × 10-5 to 2 × 10-4 mol/dm3). In the
parameter estimation it was taken into account that the stock
solution of Mn(III) contained a high amount of Mn(II) ions. At
λ ) 450 nm the decrease in [Ru(bpy)3]2+ vs time was followed
(Figure 6). The equilibrium constant of the reaction was
calculated from redox potential data: E0 (Mn(III)/Mn(II)) )
1.51 V,10 E0 (Ru(bpy)33+/Ru(bpy)32+) ) 1.27 V.11 The fit
between the calculated curve and the measured data is good.
The reaction takes place as a second-order step (R14):
BrO3- + 3H3PO2 f Br - + 3H3PO3 (R7 + R8 + R9)
This overall process is a Landolt type clock reaction and
autocatalytic for hydrogen and bromide ions.
There are two main routes of bromine removal in the system,
a chemical and a physical route. Most important chemical
removal of bromine is its reaction with acetone:12
Mn(III) + Ru(bpy)32+ / Mn(II) + Ru(bpy)3
kf14 ) 360((5) mol-1 dm-3 s-1
K14 ) 1.1 × 104
(R14)
3+
Br2 + Ac f BrAc + H+ + Br-
V10a ) kkfE[Ac][Br2]/(kEb + k[Br2])
(R19a)
Mechanistic Model
Our aim was to build a relatively simple chemical model to
explain the major features of the dynamical behavior observed
where kfE and kbE are the forward and backward rate constants
of the enolization of acetone, and k is the rate constant of the

Bromate-Dual Substrate-Dual Catalyst Batch Oscillator
J. Phys. Chem. A, Vol. 110, No. 18, 2006 6071
reaction between bromine and the enol form of acetone. In the
experiments the bromine concentration is low and the concen-
tration of acetone is relatively high; therefore the rate equation
can be simplified as
V10a ) k10a[Br2]
k10a ) (kkfE/kbE)[Ac]
The second route implies the heterogeneous bromine removal
by inert gas flow, by evaporation, or by adsorption on the stirrer
bar and on the wall, etc. This process is expressed in step R19b:
Figure 7. Simulated oscillations in the BrO3--H3PO2-acetone-Mn-
(II) system (the second catalyst is absent) at different factors f. Initial
concentrations: [BrO3-] ) 0.02 mol/dm3, [H3PO2] ) 0.1 mol/dm3.
Parameters: [H+] ) 1.29 mol/dm3, k10 ) 0.16 s-1, f ) 1 (s) and f )
0.8 (- - -).
Br2 f V10b ) k10b[Br2]
(R19b)
In a typical experiment both routes are present. In the model,
reaction R10 represents the overall removal of the bromine:
Br2 f fBr- + fBrAc
(R19)
V
10 ) k10[Br2]
k10 ) k10a + k10b
We introduce factor f, which shows the ratio of the homo-
geneous chemical removal of bromine compared to the total
removal:
f ) V10a/(V10a + V10b
)
Figure 8. Simulated phase diagram of the bromate-H3PO2-acetone-
Mn(II) system in the f vs k10 plane. Parameters: [BrO3-] ) 0.02 mol/
dm3, [H3PO2] ) 0.1 mol/dm3, [H+] ) 1.29 mol/dm3.
In the absence of acetone V10a ) 0, f ) 0 (no extra bromide
formation can occur for lack of BrAc), and k10 ) k10b. In the
case of pure homogeneous bromine removal V10b ) 0, f ) 1,
and k10 ) k10a. In a real experiment with acetone present the
contribution of any heterogeneous process decreases the value
of f and the stoichiometry of the bromide production in R10
falls between 0 and 1.
Step R11 in the model is the reaction between bromoacetone
and Ru(bpy)33+. Since bromoacetone is not a variable of the
model, its concentration is included in the rate constant k11. The
next two reactions, R12 and R13, are the oxidation of hypo-
phosphite by the oxidized form of the catalyst, and the last one,
R14, is the reaction between the two catalysts. The overall
mechanism contains 14 reactions and 8 variables.
2+
Figure 9. Simulated oscillations in the bromate-acetone-Ru(bpy)3
subsystem. Initial concentrations: [BrO3-] ) 0.02 mol/dm3, [Br-] )
1 × 10-5 mol/dm3. Parameters: [H+] ) 1.29 mol/dm3, [Ru]T ) 5 ×
10-5 mol/dm3, k10 ) 0.5 s-1, k11 ) 2 s-1, and f ) 1.
Simulations and Discussions
The Effect of Bromine Removal on the Dynamics of the
BrO3--H3PO2-Acetone-Mn(II) System. The dynamics of
the bromate-hypophosphite-Mn(II) oscillatory reaction was
found to be very sensitive to the rate and the method of bromine
removal. In the experiments oscillations appeared in a finite
range of the acetone concentration, and the number of oscilla-
tions was highly sensitive to the rate of stirring (see Figure 2).
The number of oscillations predicted by the model strongly
depends on the actual values of f and k10. In Figure 7 the results
of simulations are shown at a given value of k10 when f ) 1.0
(solid line) and f ) 0.8 (dashed line). At f ) 1.0 (pure chemical
removal of bromine) only a few oscillations appear. A small
decrease in the value of f (contribution of physical processes to
the bromine removal) induces an increase in the number of
oscillations, similarly as in the experiments. By using bromate
and hypophosphite as pool components, we calculated a phase
diagram in the k10 vs f plane (Figure 8). The figure shows the
oscillatory domain simulated at a given rate of total bromine
removal (k10) when the ratio of the physical and chemical
removal (f) changes. At f ) 0, which means there is no acetone
in the system and just heterogeneous bromine escape occurs,
the range of oscillations is very narrow. The strong sensitivity
of the number of oscillations on the rate of bubbling N2 gas in
the bromate-hypophosphite-Mn(II) system was first demon-
strated by Adamcikova and Sevcik.1 When the relative rate of
the homogeneous bromine removal is increased by addition of
acetone (increasing the value of f), the range of oscillations
increases, as in the experiments.
2+
Oscillations in the BrO3--Acetone-Ru(bpy)3
Sub-
system. The model is capable of simulating the experimentally
found oscillations in the bromate-acetone-Ru(bpy)3 sub-
2+
system as well. The results are shown in Figure 9. In the absence
of hypophosphite our model works like an extended version of
the Oregonator. The necessary conditions for the oscillations
to occur are the removal of bromine and the appropriate rate of
the bromide ion production in reaction R11. In the model k11 is
a pseudo-first-order rate constant that includes the concentration

6072 J. Phys. Chem. A, Vol. 110, No. 18, 2006
Szalai et al.
concentration of the hypophosphite decreases, while BrAc starts
to accumulate and at a critical value of [BrAc] the bromate-
BrAc-Ru(bpy)32+ subsystem starts to oscillate (Osc. B). These
oscillations are maintained as long as BrAc is produced in the
Mn(II)-catalyzed reaction. The experimental observations and
the results of simulations support the conclusion that the
complex oscillatory pattern that was found in the bromate-
hypophosphite-acetone-dual catalyst system is the result of
an interaction between two internally coupled oscillators.
Acknowledgment. This work was financially supported by
grants from the Hungarian Academy of Sciences (HAS) (OTKA
No. T043743 and F034976).
Figure 10. Simulated phase diagram of the bromate-hypophosphite-
Mn(II)-Ru(bpy)32+ system in the k11 vs [H3PO2] plane. Here bromate
and hypophosphite are pool components. Parameters: [BrO3-]0 ) 0.02
mol/dm3, [H+]0 ) 1.29 mol/dm3, [Ru]T ) 5 × 10-5 mol/dm3, k10
)
References and Notes
0.5 s-1, f ) 1.
(1) Adamcikova, L.; Sevcik, P. Int. J. Chem. Kinet. 1982, 14, 735.
Sevcik, P.; Adamcikova, L. Collect. Czech. Chem. Commun. 1987, 52,
2125.; Quyang, Q.; Tam, W. J.; De Kepper, P.; McCormick, W. D.;
Noszticzius, Z.; Swinney, H. L. J. Phys. Chem. 1987, 91, 2181.
(2) Orba´n, M.; Kurin-Cso¨rgei, K.; Zhabotinsky, A. M.; Epstein, I. R.
Faraday Discuss. 2001, 120, 11.
(3) Gao, Y.; Fo¨rsterling, H. D. J. Phys. Chem. 1995, 99, 8638.
(4) Ermentrout, B. XPPAUT 5.41 Differential Equations Tool,
www.math.pitt.edu/∼bard/xpp/xpp.html (accessed 2005).
(5) Keszei, E. MULTIMRQ Multiple Nonlinear Fitting with Decon-
volution, http://keszei.chem.elte.hu/femto/fit/englishprog.html (accessed
2005).
(6) Pojman, J. A.; Dedeaux, H.; Forberry, D. J. Phys. Chem. 1992,
96, 7331.
(7) Rastogi, R. P.; Misra, G. P. Indian J. Chem. A 1990, 29A, 1205.
(8) Caroll, R. L.; Thomas, L. B. J. Am. Chem. Soc. 1966, 88, 1376.
(9) Zhang, Y. X.; Field, R. J. J. Phys. Chem. 1990, 94, 7154.
(10) CRC Handbook of Chemistry and Physics, 50th ed.; The Chemical
Rubber Co.: Cleveland, Ohio, 1970.
(11) Wayne, R. P. Principles and Applications of Photochemistry;
Oxford University Press: Oxford, 1988.
(12) Keeffe, J. R.; Kresge, A. J.; Schepp, N. P. J. Am. Chem. Soc. 1988,
110, 1993.
(13) Fo¨rsterling, H. D.; Mura´nyi, S.; Schreiber, H. Z. Naturforsch. 1989,
44a, 555.
(14) Fo¨rsterling, H. D.; Varga, M. J. Phys. Chem. 1993, 97, 7932.
(15) Robertson, E. B.; Dunford, H. B. J. Am. Chem. Soc. 1964, 86, 5080.
of bromoacetone. To accomplish the second condition, the
concentration of bromoacetone has to reach a critical value. This
is the reason why the appearance of the oscillations required
an induction time in the experiments.
Dynamics in the Total System. In the bromate-hypophos-
phite-acetone-dual catalyst system two sequences of oscilla-
tions were observed, a short-lived one which appeared shortly
after mixing the reagents and a long-lived oscillation sequence
which started after an induction time. The model in Table 1
simulates the two domains. In Figure 10 the two oscillatory
domains (Osc. A and Osc. B) were calculated in the [H3PO2]
vs k11 plane, where k11 ) k′11[BrAc]. We believe that the
substrate in the oscillator is H3PO2 in the part of Osc. A and
BrAc in the part of Osc. B. In the system at the start the value
of k11 is low (low concentration of BrAc), the [H3PO2] is high,
and the oscillatory domain simulated as Osc. A in Figure 10
corresponds to the short-lived oscillation in the bromate-
hypophosphite-acetone-Mn(II) system. The oscillations in
color between pink (from Mn(III)) and colorless are clearly seen
during this stage of the reaction. As the reaction proceeds, the