Chemical Physics Letters 470 (2009) 147–150

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Chemical Physics Letters

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Deuterium isotope effect on the induction period of the cerium catalyzedBelousov–Zhabotinsky reaction

Federico Rossi a,*, Eugenio Simoncini b, Nadia Marchettini b, Enzo Tiezzi b

a Department of Physical Chemistry ‘F. Accascina’, University of Palermo, Viale delle Scienze Pad. 17, 90128 Palermo, Italyb Department of Chemistry, University of Siena, Via della Diana 2/a, Siena, Italy

a r t i c l e i n f o a b s t r a c t

Article history:Received 21 November 2008In final form 14 January 2009Available online 21 January 2009

0009-2614/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.cplett.2009.01.042

* Corresponding author. Fax: +39 091590015.E-mail address: f.rossi@unipa.it (F. Rossi).

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, weinvestigated two reaction pathways responsible for the length of the induction period, namely: (a) thereaction between the enolic form of the malonic acid with molecular bromine and (b) the oxidation ofmalonic acid by the Ce(IV) ion. In both cases we obtained a linear dependence of the kinetic constantson the percentage of deuterated reactants. Nevertheless, by inserting the experimental values in theMBM (Marburg–Budapest–Missoula) model, we were able to qualitatively simulate the observed trendof the induction period.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

The Belousov–Zhabotinsky (BZ) reaction [1,2] is considered theprototype system for studying chemical oscillations and, in appro-priate conditions, waves and patterns. It basically consists in thecatalytic periodic oxidation of an organic substrate with methylen-ic hydrogens, generally malonic acid (MA), by bromate in acidicaqueous 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 tobe slower and, even if the addition of deuterated reactants didnot alter the qualitative profile of the absorbance as a function oftime, it influenced some of the oscillatory parameters. This factwas particularly evident from a markedly longer induction period,from 150 s in H2O to 390 s in D2O. Finally, we found a nonlinearincrement 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 ofBZ reaction was also discussed in the past for the ruthenium cata-lyzed system [4]. It was found that the substitution of H2O by D2Oas solvent caused a complete suppression of the oscillating regime.A less dramatic effect was detected by Kreuels et al. [5] in ceriumcatalyzed systems. They found a linear D2O dosage dependence ofthe oscillation frequency (OF) both at low (increased OF) and high(decreased OF) catalyst concentration, but in our experimental

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condition the oscillation frequency was found substantially inde-pendent from D2O dosage.

Isotopic effect due to the hydrogen substitution by deuterium,is a subject of widespread interest in the frame of the chemicalkinetics discipline. The kinetic effect is termed primary if the deu-terated bond is directly broken or formed by reaction; otherwise, asmaller rate change (secondary isotope effect) can be observed [6].The kinetics of the isotope exchange reactions of RCH(COOH)2

(R = H, D, CH3, etc.) in D2O solutions was studied by using 1HNMR spectroscopy, and the implications for the BZ reaction werediscussed [7]. Hansen and Ruoff [8] estimated the enolization rateconstant of malonic and methylmalonic acid by an isotopic ex-change reaction. Moreover, the kinetic isotope effect was used toclarify the mechanism of the Bray–Liebhafsky reaction [9] and ofenzymatic oscillators [10]. Its influence on chemical waves wasalso evaluated in a halogen-free oscillating system [11].

The induction period (IP) is a distinctive feature of the ceriumcatalyzed BZ reaction and it consists in a pre-oscillatory stage inwhich [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 theonset of oscillations is produced through two main pathways: (a)the bromination of the enol form of malonic acid by Br2 and (b)the reaction between Br2 and the malonyl radical formed in theCe–MA subsystem [13].

Recent studies [14,15] demonstrated that the oxidation ofmalonic acid by ceric ions, when MA is in excess respect to theCe(IV), yields 1,1,2,2-ethanetetracarboxylic acid (ETA) andmonomalonyl malonate (MAMA) developing carbon dioxide.

Fig. 1. Dependence of Induction period upon percentage of deuterated reactants at20 �C for BZ reactions with the following composition½MA� ¼ 0:1 mol dm�3

; ½BrO�� ¼ 3:0� 10�2 mol dm�3; ½H SO � ¼ 1:0 mol dm�3 and

148 F. Rossi et al. / Chemical Physics Letters 470 (2009) 147–150

It is known [16,17] that the oxidation process of MA is initiatedby a rate-determining unimolecular reaction of a Ce(IV) complex ofmalonic acid. This process produces a malonyl radical that reactsrapidly with more oxidant species by one-electron processes. Thefinal 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 theappearance 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 affectedby the presence of molecular oxygen [23,24].

In this Letter we present results about the isotopic effect on theinduction period of a cerium catalyzed BZ reaction performed in aclosed stirred reactor and under aerobic condition. We extend ourprevious 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 withthose coming from the cerium–malonic subsystem, the pathway(b), to explain the observed IP trend.

3 2 4

[Ce4+] = 1.3 � 10�3 mol dm�3.

2. Experimental

All reagents were of analytical grade (SIGMA) and they wereused without further purification except for MA, which was recrys-tallized from 1:1 acetone–benzene solution, rinsed with CCl4 anddried in vacuum. Reagents were dissolved in double distilled waterand/or 99.98% D2O (MERCK). The effective deuteration of themethylenic group of MA was checked by 1H NMR measurements,which showed a signal at d = 3.388 ppm corresponding to theCH2 and a signal at d = 3.247 ppm corresponding to CHD for deu-terated solutions. The intensity of the signal was proportional tothe percentage of D2O used to dissolve MA. The substitution H–Din the methylenic group of the malonic acid takes place in about2 h at [MA]0 = 0.1 mol dm�3 [7].

The isotopic effect on the cerium–malonic acid reaction wasevaluated by following the change in the Ce(IV) concentration witha double beam spectrophotometer (ULTROSPEC 2000 UV–Vis,Pharmacia Biotech) at k = 320 nm, where Ce(IV) has an absorptionmaximum. Measurements were performed in thermostattedquartz cuvettes (1 � 1 � 4.5 cm) at 20 �C in aerobic conditions.The spectrophotometer was connected to a PC for data storageand treatment.

Measurements of BZ induction period were performed with adouble beam spectrophotometer (Varian, 634 series), in thermo-statted quartz cuvettes (1 � 1 � 4 cm) at 20 �C, by following theabsorbance of Ce(IV). BZ systems were prepared mixing normaland deuterated reagents in different proportions, in order to geta final composition of ½MA�f ¼ 0:1 mol dm�3

; ½BrO�3 �f ¼ 3� 10�2

mol dm�3; ½Ce4þ�f ¼ 1:3� 10�3 mol dm�3 and [H2(D2)SO4]f = 1

mol dm�3, where [X]f indicates the sum of deuterated and hydro-genated reagents.

In order to minimize the variability due to the effect of theatmospheric oxygen, we performed all the experiments with a con-stant volume of the solution (1.5 ml). The stirring rate was 500 rpmfor all the experiments; in this conditions the solution was kepthomogeneous without the formation of vortexes.

Experimental details about the isotopic effect on the reactionbetween Br2 and malonic acid can be found in Ref. [3].

Fig. 2. Dependence of the malonic acid enolization rate constant upon percentageof deuterated reactants at 20 �C. Solution composition was [MA] = 0.25 mol dm�3,[Br2] = 7.5 � 10�3 mol dm�3.

3. Results and discussion

As mentioned in the introduction, we found that the inductionperiod of a cerium catalyzed BZ reaction depends on the percent-

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 theenolic form of malonic acid by molecular bromine

CH2ðCOOHÞ2� ðCOOHÞCHCðOHÞ2 ðE1ÞðCOOHÞCHCðOHÞ2 þ Br2 ! BrCHðCOOHÞ2 þHþ þ Br� ðE2Þ

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-zeroorder kinetics of the reactions E1 + E2 we found a primary isotopiceffect induced by the deuterated reagents on the enolization reac-tion rate ke (kH

e =kDe ¼ 7:60) [3]. The value of the kinetic constant is

dependent on the amount of the deuterated malonic acid,CD2(COOD)2, in solution. The linear response of ke at different con-centrations of the deuterated reagent is shown in Fig. 2.

In order to understand the trend observed in Fig. 1, we need toexplore also the oxidation of malonic acid by ceric ions, i.e. the

Fig. 3. Structure of the six-member ring formed during the oxidation of organicsubstrates by the ceric ions (Z = H, D, Br, CH3, etc.).

F. Rossi et al. / Chemical Physics Letters 470 (2009) 147–150 149

reaction pathway (b) responsible for the induction period of theCe-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 inFig. 3), and the mechanism is the same for malonic acid and forits substituted compounds (bromomalonic acid, methylmalonicacid, etc.) [17,25]. Therefore, we can suppose that the same mech-anism is preserved in case of deuterium substituted malonic acidCD2(COOD)2.

The formation of the malonyl radical can be described by a pseu-do Michaelis–Menten reaction scheme [16]

Ce4þ þ X �k1

k�1

½Ce4þ � � X�2þ !k2 Ce3þ þ X� þHþ ð1Þ

where X represents the organic substrate. In case of [X]� [ Ce4+]the Ce4+ decay shows a first order kinetics

�d½Ce4þ�dt

¼ kobs½Ce4þ� ð2Þ

with

kobs ¼k2½X�0

km þ ½X�0ð3Þ

where km = (k�1 + k2)/k1 and [X]0 represent the analytic concentra-tion of the organic substrate.

In our experimental condition, [Ce4+] = 5 � 10�4 mol dm�3,[H2SO4] = 1 mol dm�3 and 0.08 < [MA] < 0.5 mol dm�3, we found

that kH2 ¼ 0:190� 0:05 s�1; kH

m ¼ 0:312� 0:04 mol dm�3 in H2O

and kD2 ¼ 0:052� 0:01 s�1; kD

m ¼ 0:114� 0:03 mol dm�3 in D2O.Both the decrease in km and k2 indicate that the D–H substitutionstabilize the transition complex; this is probably due to the higherstrength of the C–D bond.

In the context of the BZ modeling, the kinetics of the reaction(1) can be considered as a simple (or apparent) second order

Fig. 4. Dependence of the second order rate constant k3 upon percentage ofdeuterated reactants at 20 �C. [Ce4+] = 5 � 10�4 mol dm�3, [H2 SO4] = 1 mol dm�3

and [MA] = 0.1 mol dm�3.

[12,26,27]. In particular kobs calculated from the initial slope ofthe semi-logarithmic plot of the full MA oxidation process is pro-portional to [X], hence kobs = k3[X]0; k3 representing the kineticconstant of the process

Ce4þ þ X �k3

k�3

Ce3þ þ X� þHþ ð4Þ

In anaerobic condition, the reverse constant k�3 of the reactionbetween the malonyl radical and Ce3+, depends on the kinetic con-stant relative to the process where malonyl radicals react to giveETA or MAMA. The final product depends on the mesomeric formof the initial malonyl radical, which first react with the doublebond in the enol form of another malonic acid molecule and thenthis new radical is oxidized further by Ce(IV) [14,15,28]. In aerobiccondition MA� reacts very fast with molecular oxygen to form theperoxymalonyl radical [19,22] and the reaction between Ce3+ andMA� becomes negligible [26]. Fig. 4 shows the linear decreaseof k3 at [Ce4+] = 5 � 10�4 mol dm�3, [H2SO4] = 1 mol dm�3 and[MA] = 0.1 mol dm�3, 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 ofdeuterated reagents and the kinetic constants were found to bekH

3 ¼ 0:26� 0:015 mol�1 dm3 s�1 in 100% H2O and kD3 ¼ 0:14 �

0:011 mol�1 dm3 s�1 in 100% D2O. In this case the isotopic effectson the reaction lies between a first and a second order ðkh

3=kd3 ¼

1:86Þ, because only one of the two steps of the reaction (1) involvesthe break of a deuterated bond.

Experimental values of ke and k3 were finally used to performsimulation of the BZ reaction in the presence of various percent-ages of deuterated compounds and to evaluate the IP response tothese modifications. By using COPASI package [29], we performednumerical 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.

Fig. 5 shows the trend of the IP upon changing the values of ke

and k3 (the IP length along the Y-axis is normalized with respect tothe simulated values for the system where deuterated reagents arenot present). We also tried to increase or decrease the value of k�3,but, as expected, the length of the induction period was not signif-icantly influenced. In simulations we kept k�3 constant using thesame value of the MBM model. The trend reported indicates a goodagreement between experimental and simulated results.

In our simulations, we only changed the values of reactions (4),(E1) and (E2), according to the linear relationships showed in Figs.

Fig. 5. Comparison between simulations (N) and experimental data (j) of the IPlength at different percentage of deuterated reactants. Experimental conditions arethe same of Fig. 1.

150 F. Rossi et al. / Chemical Physics Letters 470 (2009) 147–150

2 and 4, leaving all the others unchanged; this fact can account forthe quantitative discrepancies between numerical simulations andexperiments. Moreover, the MBM model itself, though very effec-tive at low catalyst concentrations, generally shows some quanti-tative deviations from experiments [27].

4. Concluding remarks

The results presented in this Letter underline the role of themalonic acid oxidation by ceric ions, in the production of bromi-nated species which, in turn, determine the length of the inductionperiod. The relevance of this reaction for the IP, was also pointedout in the past by numerical simulations [13], which showed thatthe kinetic constant k3 can be the only adjustable parameter to fixsome of the deviation of the GTF and MBM models with respect tothe experimental data.

By exploiting the deuterium isotope effect, we were able tomodify the reaction kinetics, thus influencing the oscillatingparameters, 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 thereaction pathways (a) and (b) can be inferred by using kinetic con-stants relative to reactions (4), (E1) and (E2) in numericalsimulations.

Acknowledgements

Thanks are due to Sandra Ristori (University of Florence) forhelping us to improve the quality of our manuscript. We are indebt with anonymous referees which drove our attention to somereferences and corrected many of our mistakes.

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