Deuterium isotope effect on the induction period of the cerium catalyzed Belousov-Zhabotinsky reaction

Article abstract of DOI:10.1016/j.cplett.2009.01.042

In this work we present results about the deuterium isotopic effect on the global kinetics of a cerium catalyzed Belousov-Zhabotinsky reaction. A nonlinear dependence of the induction period upon the percentage of deuterated reactants was found in batch conditions. In order to understand this result, we investigated two reaction pathways responsible for the length of the induction period, namely: (a) the reaction between the enolic form of the malonic acid with molecular bromine and (b) the oxidation of malonic acid by the Ce(IV) ion. In both cases we obtained a linear dependence of the kinetic constants on the percentage of deuterated reactants. Nevertheless, by inserting the experimental values in the MBM (Marburg-Budapest-Missoula) model, we were able to qualitatively simulate the observed trend of the induction period.

Full text of DOI:10.1016/j.cplett.2009.01.042

Chemical Physics Letters 470 (2009) 147–150
Contents lists available at ScienceDirect
Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett
Deuterium isotope effect on the induction period of the cerium catalyzed
Belousov–Zhabotinsky reaction
a,*
b
b
b
Federico Rossi , Eugenio Simoncini , Nadia Marchettini , Enzo Tiezzi
a
Department of Physical Chemistry ‘F. Accascina’, University of Palermo, Viale delle Scienze Pad. 17, 90128 Palermo, Italy
Department of Chemistry, University of Siena, Via della Diana 2/a, Siena, Italy
b
a r t i c l e i n f o
a b s t r a c t
Article history:
In this work we present results about the deuterium isotopic effect on the global kinetics of a cerium cat-
alyzed Belousov–Zhabotinsky reaction. A nonlinear dependence of the induction period upon the per-
centage of deuterated reactants was found in batch conditions. In order to understand this result, we
investigated two reaction pathways responsible for the length of the induction period, namely: (a) the
reaction between the enolic form of the malonic acid with molecular bromine and (b) the oxidation of
malonic acid by the Ce(IV) ion. In both cases we obtained a linear dependence of the kinetic constants
on the percentage of deuterated reactants. Nevertheless, by inserting the experimental values in the
MBM (Marburg–Budapest–Missoula) model, we were able to qualitatively simulate the observed trend
of the induction period.
Received 21 November 2008
In final form 14 January 2009
Available online 21 January 2009
Ó 2009 Elsevier B.V. All rights reserved.
1
. Introduction
condition the oscillation frequency was found substantially inde-
2
pendent from D O dosage.
The Belousov–Zhabotinsky (BZ) reaction [1,2] is considered the
Isotopic effect due to the hydrogen substitution by deuterium,
is a subject of widespread interest in the frame of the chemical
kinetics discipline. The kinetic effect is termed primary if the deu-
terated bond is directly broken or formed by reaction; otherwise, a
smaller rate change (secondary isotope effect) can be observed [6].
prototype system for studying chemical oscillations and, in appro-
priate conditions, waves and patterns. It basically consists in the
catalytic periodic oxidation of an organic substrate with methylen-
ic hydrogens, generally malonic acid (MA), by bromate in acidic
aqueous solutions.
Recently [3], we investigated the behavior of the cerium cata-
lyzed BZ reaction in the presence of different percentages of deu-
terated reagents. The global kinetics of the reaction was found to
be slower and, even if the addition of deuterated reactants did
not alter the qualitative profile of the absorbance as a function of
time, it influenced some of the oscillatory parameters. This fact
was particularly evident from a markedly longer induction period,
The kinetics of the isotope exchange reactions of RCH(COOH)
2
(R = H, D, CH , etc.) in D H
3
2
O solutions was studied by using 1
NMR spectroscopy, and the implications for the BZ reaction were
discussed [7]. Hansen and Ruoff [8] estimated the enolization rate
constant of malonic and methylmalonic acid by an isotopic ex-
change reaction. Moreover, the kinetic isotope effect was used to
clarify the mechanism of the Bray–Liebhafsky reaction [9] and of
enzymatic oscillators [10]. Its influence on chemical waves was
also evaluated in a halogen-free oscillating system [11].
2 2
from 150 s in H O to 390 s in D O. Finally, we found a nonlinear
increment of the length of the induction period (IP) upon increas-
ing concentration of deuterium substituted reactants [3].
The influence of deuterated compounds on the global kinetics of
BZ reaction was also discussed in the past for the ruthenium cata-
lyzed system [4]. It was found that the substitution of H O by D O
2 2
as solvent caused a complete suppression of the oscillating regime.
A less dramatic effect was detected by Kreuels et al. [5] in cerium
The induction period (IP) is a distinctive feature of the cerium
catalyzed BZ reaction and it consists in a pre-oscillatory stage in
which [Br ] is increased and brominated organic species are accu-
mulated. According to the GTF (Györgyi–Turányi–Field) model [12]
the length of IP is determined by the concentration of bromoma-
lonic acid (BrMA). The crucial amount of BrMA necessary for the
onset of oscillations is produced through two main pathways: (a)
ꢀ
catalyzed systems. They found a linear D
2
O dosage dependence of
the bromination of the enol form of malonic acid by Br
2
and (b)
the oscillation frequency (OF) both at low (increased OF) and high
the reaction between Br
Ce–MA subsystem [13].
2
and the malonyl radical formed in the
(
decreased OF) catalyst concentration, but in our experimental
Recent studies [14,15] demonstrated that the oxidation of
malonic acid by ceric ions, when MA is in excess respect to the
Ce(IV), yields 1,1,2,2-ethanetetracarboxylic acid (ETA) and
monomalonyl malonate (MAMA) developing carbon dioxide.
*
Corresponding author. Fax: +39 091590015.
E-mail address: f.rossi@unipa.it (F. Rossi).
0
009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2009.01.042

1
48
F. Rossi et al. / Chemical Physics Letters 470 (2009) 147–150
It is known [16,17] that the oxidation process of MA is initiated
by a rate-determining unimolecular reaction of a Ce(IV) complex of
malonic acid. This process produces a malonyl radical that reacts
rapidly with more oxidant species by one-electron processes. The
final reaction products are obtained by the subsequent fast oxida-
tion of the organic radical. Moreover, several authors [17–22]
pointed out the differences between the aerobic and anaerobic sys-
tems, and in particular they showed how the presence of the oxy-
gen influences the reactivity of the organic radicals causing the
appearance of new products.
Due to the changes in the Ce–MA subsystem, also several oscil-
lating parameters, including the IP, of the BZ reaction, are affected
by the presence of molecular oxygen [23,24].
In this Letter we present results about the isotopic effect on the
induction period of a cerium catalyzed BZ reaction performed in a
closed stirred reactor and under aerobic condition. We extend our
previous results [3] by investigating the intermediate concentra-
tions of deuterated reagents in the bromine–malonic acid subsys-
tem, the pathway (a). We finally combine these results with
those coming from the cerium–malonic subsystem, the pathway
Fig. 1. Dependence of Induction period upon percentage of deuterated reactants at
20 °C
for
BZ
reactions
with
the
following
composition
(
b), to explain the observed IP trend.
MAꢂ ¼ 0:1 mol dm ; ½BrO ꢂ ¼ 3:0 ꢁ 10 mol dmꢀ3; ½H
ꢀ3
ꢂ ¼ 1:0 mol dmꢀ3 and
ꢀ
ꢀ2
½
2 4
SO
3
4+
ꢀ3
ꢀ3
[
Ce ] = 1.3 ꢁ 10 mol dm
.
2
. Experimental
age of the deuterated reactants in a nonlinear fashion (see Fig. 1)
3].
In our previous work, we investigated one of the reaction path-
way responsible for the IP length, namely the bromination of the
enolic form of malonic acid by molecular bromine
All reagents were of analytical grade (SIGMA) and they were
[
used without further purification except for MA, which was recrys-
tallized from 1:1 acetone–benzene solution, rinsed with CCl
and
dried in vacuum. Reagents were dissolved in double distilled water
and/or 99.98% D O (MERCK). The effective deuteration of the
4
2
1
methylenic group of MA was checked by H NMR measurements,
CH
2
ðCOOHÞ ꢀ ðCOOHÞCHCðOHÞ
ðE1Þ
ðE2Þ
2
2
! BrCHðCOOHÞ þ H þ Brꢀ
þ
which showed a signal at d = 3.388 ppm corresponding to the
ðCOOHÞCHCðOHÞ þ Br
2
2
2
CH
terated solutions. The intensity of the signal was proportional to
the percentage of D O used to dissolve MA. The substitution H–D
in the methylenic group of the malonic acid takes place in about
2
and a signal at d = 3.247 ppm corresponding to CHD for deu-
The halogen attack on the C@C double bond is very fast, there-
fore the determinant step in the bromination reaction is the enoli-
zation of the malonic acid. From the analysis of the pseudo-zero
order kinetics of the reactions E1 + E2 we found a primary isotopic
effect induced by the deuterated reagents on the enolization reac-
2
ꢀ
3
2
h at [MA]
0
= 0.1 mol dm [7].
The isotopic effect on the cerium–malonic acid reaction was
H
D
tion rate k
dependent on the amount of the deuterated malonic acid,
CD (COOD) , in solution. The linear response of k at different con-
e
(k =k ¼ 7:60) [3]. The value of the kinetic constant is
evaluated by following the change in the Ce(IV) concentration with
a double beam spectrophotometer (ULTROSPEC 2000 UV–Vis,
Pharmacia Biotech) at k = 320 nm, where Ce(IV) has an absorption
maximum. Measurements were performed in thermostatted
quartz cuvettes (1 ꢁ 1 ꢁ 4.5 cm) at 20 °C in aerobic conditions.
The spectrophotometer was connected to a PC for data storage
and treatment.
e
e
2
2
e
centrations of the deuterated reagent is shown in Fig. 2.
In order to understand the trend observed in Fig. 1, we need to
explore also the oxidation of malonic acid by ceric ions, i.e. the
Measurements of BZ induction period were performed with a
double beam spectrophotometer (Varian, 634 series), in thermo-
statted quartz cuvettes (1 ꢁ 1 ꢁ 4 cm) at 20 °C, by following the
absorbance of Ce(IV). BZ systems were prepared mixing normal
and deuterated reagents in different proportions, in order to get
ꢀ
3
ꢀ
ꢀ2
a final composition of ½MAꢂ ¼ 0:1 mol dm ; ½BrO ꢂ ¼ 3 ꢁ 10
f
3
f
ꢀ3
4þ
ꢀ3
ꢀ3
mol dm ; ½Ce ꢂ ¼ 1:3 ꢁ 10 mol dm
and [H
2
(D
2
4
)SO ]
f
= 1
f
ꢀ3
mol dm , where [X]
f
indicates the sum of deuterated and hydro-
genated reagents.
In order to minimize the variability due to the effect of the
atmospheric oxygen, we performed all the experiments with a con-
stant volume of the solution (1.5 ml). The stirring rate was 500 rpm
for all the experiments; in this conditions the solution was kept
homogeneous without the formation of vortexes.
Experimental details about the isotopic effect on the reaction
between Br
2
and malonic acid can be found in Ref. [3].
3
. Results and discussion
Fig. 2. Dependence of the malonic acid enolization rate constant upon percentage
As mentioned in the introduction, we found that the induction
period of a cerium catalyzed BZ reaction depends on the percent-
ꢀ3
of deuterated reactants at 20 °C. Solution composition was [MA] = 0.25 mol dm
,
] = 7.5 ꢁ 10ꢀ mol dm
3
ꢀ3
.
[Br
2

F. Rossi et al. / Chemical Physics Letters 470 (2009) 147–150
149
[
12,26,27]. In particular kobs calculated from the initial slope of
the semi-logarithmic plot of the full MA oxidation process is pro-
portional to [X], hence kobs = k
3
[X] ; k
0 3
representing the kinetic
constant of the process
k
3
4
þ
3þ
ꢁ
þ
Ce þ X ꢀ Ce þ X þ H
ð4Þ
Fig. 3. Structure of the six-member ring formed during the oxidation of organic
substrates by the ceric ions (Z = H, D, Br, CH , etc.).
k
ꢀ3
3
In anaerobic condition, the reverse constant kꢀ3 of the reaction
3
+
between the malonyl radical and Ce , depends on the kinetic con-
stant relative to the process where malonyl radicals react to give
ETA or MAMA. The final product depends on the mesomeric form
of the initial malonyl radical, which first react with the double
bond in the enol form of another malonic acid molecule and then
this new radical is oxidized further by Ce(IV) [14,15,28]. In aerobic
reaction pathway (b) responsible for the induction period of the
Ce-catalyzed BZ reaction.
The rate-determining step of the oxidation of MA is the forma-
tion of a six-member chelate ring (see the structure reported in
Fig. 3), and the mechanism is the same for malonic acid and for
its substituted compounds (bromomalonic acid, methylmalonic
acid, etc.) [17,25]. Therefore, we can suppose that the same mech-
anism is preserved in case of deuterium substituted malonic acid
ꢁ
condition MA reacts very fast with molecular oxygen to form the
3+
peroxymalonyl radical [19,22] and the reaction between Ce and
ꢁ
MA becomes negligible [26]. Fig. 4 shows the linear decrease
4
+
ꢀ4
ꢀ3
ꢀ3
CD
2
(COOD)
The formation of the malonyl radical can be described by a pseu-
do Michaelis–Menten reaction scheme [16]
2
.
of k
[
3
at [Ce ] = 5 ꢁ 10 mol dm , [H
2
SO
4
] = 1 mol dm
and
ꢀ3
MA] = 0.1 mol dm , when the concentration of deuterated re-
agents was increased in the reactor. As for the case of the bromin-
ation reaction, the kinetics was slower in the presence of
deuterated reagents and the kinetic constants were found to be
k
1
k
2
Ce þ X ꢀ ½Ce ꢀ ꢀ Xꢂ2þ ! Ce þ X þ H
4
þ
4þ
3þ
ꢁ
þ
ð1Þ
k
ꢀ1
H
ꢀ1
3
ꢀ1
D
k3 ¼ 0:26 ꢄ 0:015 mol dm
s
in 100% H
2
O and k3 ¼ 0:14 ꢄ
where X represents the organic substrate. In case of [X] ꢃ [ Ce4+]
ꢀ1
3
ꢀ1
0:011 mol dm
s
in 100% D O. In this case the isotopic effects
2
4
+
h d
the Ce decay shows a first order kinetics
on the reaction lies between a first and a second order ðk =k ¼
3
3
d½Ce4þꢂ
1:86Þ, because only one of the two steps of the reaction (1) involves
ꢀ
¼ kobs½Ce4þꢂ
ð2Þ
the break of a deuterated bond.
dt
e 3
Experimental values of k and k were finally used to perform
with
simulation of the BZ reaction in the presence of various percent-
ages of deuterated compounds and to evaluate the IP response to
these modifications. By using COPASI package [29], we performed
numerical integration of the MBM (Marburg–Budapest–Missoula)
model [27], where reactions (4), (E1) and (E2) in this Letter, corre-
spond to (R27), (R29) and (R30), respectively.
k
2
½Xꢂ
0
k
obs ¼ k
ð3Þ
m
þ ½Xꢂ
0
where k
m
= (kꢀ1 + k
2
)/k
1
and [X]
0
represent the analytic concentra-
tion of the organic substrate.
In our experimental condition, [Ce4+] = 5 ꢁ 10 mol dm
ꢀ4
ꢀ3
ꢀ3
,
Fig. 5 shows the trend of the IP upon changing the values of ke
ꢀ
3
[
H
2
SO
4
] = 1 mol dm
and 0.08 < [MA] < 0.5 mol dm , we found
ꢀ1
and k (the IP length along the Y-axis is normalized with respect to
3
H
H
ꢀ3
the simulated values for the system where deuterated reagents are
not present). We also tried to increase or decrease the value of kꢀ3,
but, as expected, the length of the induction period was not signif-
icantly influenced. In simulations we kept kꢀ3 constant using the
same value of the MBM model. The trend reported indicates a good
agreement between experimental and simulated results.
that
k
¼ 0:190 ꢄ 0:05 s ; k ¼ 0:312 ꢄ 0:04 mol dm
and k2 ¼ 0:052 ꢄ 0:01 s ; k ¼ 0:114 ꢄ 0:03 mol dm
in
in
2
H O
2
D
m
D
m
ꢀ1
ꢀ3
2
D O.
m 2
Both the decrease in k and k indicate that the D–H substitution
stabilize the transition complex; this is probably due to the higher
strength of the C–D bond.
In the context of the BZ modeling, the kinetics of the reaction
In our simulations, we only changed the values of reactions (4),
(
1) can be considered as a simple (or apparent) second order
(
E1) and (E2), according to the linear relationships showed in Figs.
Fig. 4. Dependence of the second order rate constant k
3
upon percentage of
SO ] = 1 mol dm
2 4
Fig. 5. Comparison between simulations (N) and experimental data (j) of the IP
length at different percentage of deuterated reactants. Experimental conditions are
the same of Fig. 1.
4
+
ꢀ4
ꢀ3
ꢀ3
deuterated reactants at 20 °C. [Ce ] = 5 ꢁ 10 mol dm , [H
ꢀ
3
and [MA] = 0.1 mol dm
.

1
50
F. Rossi et al. / Chemical Physics Letters 470 (2009) 147–150
[2] A.M. Zhabotinsky, Proc. Acad. Sci. USSR 157 (1964) 392.
2
and 4, leaving all the others unchanged; this fact can account for
[
[
3] F. Rossi, M. Rustici, C. Rossi, E. Tiezzi, Int. J. Mol. Sci. 8 (2007) 943.
4] A.D. Karavaev, V.P. Kazakov, G.A. Tolstikov, React. Kinet. Catal. Lett. 32 (1)
the quantitative discrepancies between numerical simulations and
experiments. Moreover, the MBM model itself, though very effec-
tive at low catalyst concentrations, generally shows some quanti-
tative deviations from experiments [27].
(
1986) 21.
[5] T. Kreuels, W. Martin, K. Brinkmann, Ber. Bunsenges. Phys. Chem. 84 (1980)
11.
4
[
[
[
[
6] K.B. Wiberg, Chem. Rev. 55 (4) (1955) 713.
7] M.C. Hsu, J.J. Jwo, Int. J. Chem. Kinet. 31 (6) (1999) 455.
8] E.W. Hansen, P. Ruoff, J. Phys. Chem. 92 (9) (1988) 2641.
9] D. Stanisavljev, N. Begovic, V. Vukojevic, J. Phys. Chem. A 102 (35) (1998) 6887.
4
. Concluding remarks
[
10] P. Rys, J. Wang, Biochem. Biophys. Res. Commun. 186 (2) (1992) 612.
The results presented in this Letter underline the role of the
[11] P. Rys, J. Wang, J. Am. Chem. Soc. 114 (1) (1992) 356.
[12] L. Gyorgyi, T. Turanyi, R.J. Field, J. Phys. Chem. 94 (18) (1990) 7162.
[
[
malonic acid oxidation by ceric ions, in the production of bromi-
nated species which, in turn, determine the length of the induction
period. The relevance of this reaction for the IP, was also pointed
out in the past by numerical simulations [13], which showed that
the kinetic constant k can be the only adjustable parameter to fix
3
some of the deviation of the GTF and MBM models with respect to
the experimental data.
By exploiting the deuterium isotope effect, we were able to
modify the reaction kinetics, thus influencing the oscillating
parameters, without altering the basic BZ mechanisms. Therefore,
it was possible to simulate our results with the MBM model. Final-
ly, we showed how the effective dependence of the IP length on the
reaction pathways (a) and (b) can be inferred by using kinetic con-
stants relative to reactions (4), (E1) and (E2) in numerical
simulations.
13] A. Cadena, N. Perez, J.S. Agreda, D. Barragan, J. Braz. Chem. Soc. 16 (2) (2005)
14.
2
14] Y. Gao, H. Foersterling, Z. Noszticzius, B. Meyer, J. Phys. Chem. 98 (34) (1994)
8377.
15] A. Sirimungkala, H.D. Forsterling, Z. Noszticzius, J. Phys. Chem. 100 (8) (1996).
16] G.J. Kasperek, T.C. Bruice, Inorg. Chem. 10 (2) (1971) 382.
17] J.J. Jwo, R.M. Noyes, J. Am. Chem. Soc. 97 (19) (1975) 5422.
[
[
[
[18] S. Barkin, M. Bixon, R.M. Noyes, K. Bar-eli, Int. J. Chem. Kinet. 10 (6) (1978) 619.
[
[
[
[
[
19] B. Neumann, S.C. Mueller, M.J.B. Hauser, O. Steinbock, R.H. Simoyi, N.S. Dalal, J.
Am. Chem. Soc. 117 (23) (1995) 6372.
20] B. Neumann, O. Steinbock, S.C. Muller, N.S. Dalal, J. Phys. Chem. A 101 (15)
(1997) 2743.
21] K. Butler, O. Steinbock, B. Steinbock, N.S. Dalal, Int. J. Chem. Kinet. 30 (12)
(
1998) 899.
22] L. Hegedus, H. Forsterling, M. Wittmann, Z. Noszticzius, J. Phys. Chem. A 104
(44) (2000) 9914.
23] J. Wang, F. Hynne, P.G. Sorensen, K. Nielsen, J. Phys. Chem. 100 (44) (1996)
17593.
[
[
24] L. Treindl, P. Ruoff, P. Kvernberg, J. Phys. Chem. A 101 (25) (1997) 4606.
25] P. Ruoff, G. Nevdal, J. Phys. Chem. 93 (23) (1989) 7802.
Acknowledgements
[26] H. Foersterling, R. Pachl, H. Schreiber, Z. Naturforsch, A: Phys. Sci. 42 (9) (1987)
63.
9
[
27] L. Hegedus, M. Wittmann, Z. Noszticzius, S.H. Yan, A. Sirimungkala, H.D.
Forsterling, R.J. Field, Faraday Discuss. 120 (2001) 21.
Thanks are due to Sandra Ristori (University of Florence) for
helping us to improve the quality of our manuscript. We are in
debt with anonymous referees which drove our attention to some
references and corrected many of our mistakes.
[28] L. Hegedus, H. Forsterling, L. Onel, M. Wittmann, Z. Noszticzius, J. Phys. Chem.
A 110 (47) (2006) 12839.
[
29] Co.pa.si. Homepage. <http://www.copasi.org/tiki-index.php?page=homepage>.
References
[
1] B.P. Belousov, A periodic reaction and its mechanism, in: Sbornik Referatov po
Radiatsonno Meditsine, Medgiz, Moscow, 1958, p. 145.