J . Chem. SOC., Faraday Trans. I , 1984,80, 1415-1424 Oscillatory Phenomena Application of the D’ Alba-Di Lorenzol Model to the Bray-Liebhafsky2 System and Others Derived from it BY FRANCESCA D’ALBA* Istituto di Ingegneria Chimica, Wale delle Scienze, 90100 Palerrno, Italy AND SERGIO DI LORENZO Istituto Tecnico Commerciale ‘ Bortolo Belotti’, Via Azzano, 24100 Bergamo, Italy Received 13th June, 1983 The model proposed by D’ Alba and Di Lorenzo, which explains oscillations by supersaturation and phase exchange, has been applied to the Bray-Liebhafsky system (hydrogen peroxide, potassium iodate and sulphuric acid), the Briggs-Rauscher system (hydrogen peroxide, potassium iodate, sulphuric acid, manganous sulphate and malonic acid) and the arsenite- iodate-chlori te sys tem. The mechanisms of these reactions and the roles of the phase exchanges have been elucidated.The role of the catalyst and of some of the organic substrates is discussed, along with an interpretation of some of the experimental results. Studies concerning oscillating chemical systems are of increasing interest because they may provide experimentally tractable models of some endogenous rhythms in living systems. Only three different non-biological oscillating systems, the Bray- Liebhafsky,2 the Belousov-Zhabotinskii3 and the Morgan4 systems, have been identified, others (e.g. the Briggs-Rauscher5 system) being derived from them. There have been many attempts to develop a mode16-18 capable of explaining the behaviour of these systems using only the kinetics of the reactions. OSCILLATORY MODEL BASED UPON SUPERSATURATION AND PHASE EXCHANGE We do not agree with the application of these kinetic models to the Bray-Liebhafsky, Belousov-Zhabotinskii and Morgan systems and have presented1 a new theoretical model based upon phase exchange and pulsating supersaturation of the solution. We consider a stirred batch reactor.An irreversible chemical reaction takes place (1) inside the solution with kinetics given by (2) B is a gas at the temperature and pressure of the reaction and hence phase exchange B(so1.) -+ B(gas) (3) -dl\r,/dt(p.e. 1,l) = K2S[B] (4) A(so1.) -+ B(so1.) - d[A]/dt = d[B]/dt(chem.) = &[A]. occurs on going from the solution to the gas above it with kinetics given by if the gas is renewed continuously. 14151416 OSCILLATORY PHENOMENA It is possible to obtain the function B(t) using Vd[B]/dt(overall) = Vd[B]/dt(chem.) + dNB/dt(p.e.1,l) ( 5 ) with the boundary conditions if t = to, then [A] = [A], and [B] = [B],. This function increases up to the value oft, obtained at d[B]/dt(overall) = 0, which gives [B],,,, the maximum value of [B], on substituting it in eqn (5). If [BImax is lower than the value of saturation [B],,,., then [B],ax is obtained and [B] decreases. If [B]m,x > [B]sat., [B],ax cannot be obtained and the concentration of B increases until it reaches [B],,,.. The thermodynamics would prescribe that the system creates a new phase of pure B(gas) as bubbles inside the solution. However, the saturated solution is not in equilibrium with the bubbles and they cannot be nucleated. Hence the concentration of B increases up to a value [Bib allowing nucleation, with kinetics given by - The balance is Vd[B]/dt(overall) = Vd[B]/dt(chem.) + dNB/dt(p.e.1,1) + dNB/dt(p.e. 2). (7) We may have d[B]/dt(overall) $0. If d[B]/dt(overall) < 0, the concentration of B becomes less than that allowing nucleation and we have no new nucleation. However, the presence of the bubbles alters the system, because they can vary in mass and volume; in fact the solution becomes supersaturated with respect to the bubbles. Phase exchange then takes place from the solution to the bubbles. With some simplifications1 we have -dNB/dt(p.e. 1,2) = K3sb V[n,-Cf(f-?b)] ([BI-[B],) (8) and Vd[B]/dt(overall) = Vd[B]/dt(chem.)+ d%/dt(P.e. 1,1) +dN~/dt(P.e.1,2)- (9) When the bubbles have left the solution the phenomenon is repeated and the physical system is governed by the mathematical system This gives oscillations in the concentration of B. We have demonstratedl that this model is capable of explaining the oscillations in the Belodsov-Zhabotinskii, Bray-Liebhafsky and Morgan systems. The influence of the rate of stirring is definitive and unmistakable evidence for discriminating between our modell and that of Noyes, who also agrees about the Morgan system, contrary to his previous work.20 APPLICATION OF THE MODEL TO THE BRAY-LIEBHAFSKY REACTION PRELIMINARY REMARKS In this work we detail the application of our model to the Bray-Liebhafsky system and to the systems derived from it. We explain the mechanisms of the reactions and the role of the catalyst and some of the organic substrates.Since our model freed the kinetics of oscillating reactions from the constraints imposed by models such as the ' Oregonator ',14 it is no longer possible to invoke these constraints to justify some unlikely steps and to neglect other more plausible steps.F. D'ALBA AND S. DI LOREN20 141 7 SETTING UP THE KINETIC MODEL Bray2? 21 has shown that the potassium iodate, hydrogen peroxide and sulphuric acid system has oscillating behaviour at 333 K in a range of concentrations of sulphuric acid. He considered the reactions 5H20, + I, + 2HI0, + 4H20 H,O, -+ H,O + 40, (10) (1 1) (12) 5H,O, + 2HI0, -+ 5 0 , + I, + 6H,O and demonstrated the possibility of a catalytic role for the redox couple 10;/1, in the decomposition of hydrogen peroxide.The oscillations can be explained by the following mechanism. Both reactions (10) and (1 1) are overall reactions that may be derived by bimolecular steps. Reaction (1 1) is derived from the following steps, some demonstrated for a Briggs-Rauscher subsystem by Furrow and Noyes,, by their tests with phenol. Steps A 1 0 , + H+ f HIO, (13) HId, + H+ f +IO, + H,O (14) '-10, + H20, 3 + I 0 + H,O + 0, (15) + I 0 + H20 f HIO, + H+ (16) HIO, f 1 0 , + H+ (17) + I 0 + H,O, -+ I+ + H,O + 0, (18) I+ + H,O f HIO+H+ (19) HI0 f 1 0 - + H+ (20) I++H,O, -+ I-+2H++02 (21) I+ +I- f I, (22) +IO, + I- f I++ 1 0 , (23) + I 0 + I- $ I++ 1 0 - . (24) We do not consider other components because they are not necessary, although this may be incorrect.At the same time, there occur steps giving reaction (10) (though we have no evidence about them) which can be hindered by the removal of iodine2T 21 as soon as it is formed. Steps A are divided into steps B with hydrogen peroxide, considered also by Peard and Cullis22 (who demonstrated that it is possible to obtain the experimental kinetic law, by applying the steady-state method to steps B) and not confuted by N O Y ~ S , , ~ ~ 25 and steps C with iodide. Steps B with hydrogen peroxide [+IO, + H,O, -+ + I 0 + H,O + O,] x 2 [ + I 0 + H,O, + +I + H,O + O,] x 2 +I + H,O, + I- + 2H+ + 0, I+ + I- $ I, 47 F A R 1141 8 OSCILLATORY PHENOMENA which give 2+10,+ 5H202 -+ I,+ 4H20 4- 5 0 2 + 2H+. This gives reaction (1 1) on the addition of two reactions (14).Steps C with iodide +IO, + I- e I+ + 10, + I 0 + I- e I++ IO- (23) (24) (22) Steps C do not alter the stoichiometries of reaction (11). The kinetics and equilibrium parameters of these steps are not available, but we can say that steps C are faster than steps B since iodate reduction by iodide is faster than iodate reduction by hydrogen peroxide. has a dissociation constant2, Hence reaction (- 19) has an equilibrium constant This allows us to assume I+ to be the prevailing form of hypoiodous acid. Reaction (22) has an equilibrium constant,' in aqueous medium K,, = (1.2 x 10-l1)-l. Reaction (22) is faster than both reactions (23) and (24) if reaction (22) is far from its equilibrium, whilst both reactions (23) and (24) become faster than reaction (22) when reaction (22) is reaching its equilibrium and reactions (23) and (24) are not reaching theirs.I+ + I- s I,. HI0 e If +OH- (26) (27) (28) The reaction K,, = 3.2 x 10-l'. K( - 19) = [I+]/[HIO] [H+] = 3.2 x lo4. DERIVING GOVERNING EQUATIONS Equations expressing the kinetics of phase exchange in this system are more complicated than those in the theoretical model. We must consider phase exchange of oxygen from the solution to the gas above it, expressed by (29) where dN,,/dt(p.e. 1,l) is the molar discharge of oxygen from the solution to the gas above it, Kl is the coefficient of phase exchange, expressed by the penetration theory, [O,] is the concentration of oxygen inside the solution, [O,], is the concentration of oxygen inside the solution which would be in equilibrium with that in the gas above it, and S is the surface area available for phase exchange.We must next consider phase exchange of oxygen caused by continuous nucleation of some bubbles, as noted by Bray., This is expressed by -dNo2/dt(p.e* 191) = K1([0,1- [OJe) S where po,,mol is the molar density of oxygen inside a bubble, V, is the volume of a bubble, Vis the volume of the solution, no is the specific nucleation (number of bubbles generated per unit volume) per unit time when the homogeneous concentration of oxygen inside the solution has a value that allows equilibrium with bubbles at nucleation and pO2[0,] is the probability of nucleation expressed as the product of the concentration of oxygen and the coefficient of probability at that concentration. We must also consider phase exchange of oxygen from the solution to the bubbles. This is expressed by (31) -dNo2/dt(~-e* 1 9 3 ) = K3 %([02l- [02le, b) noh ~ ~ 0 , [ 0 2 1 / 2 ~F.D’ALBA AND s. DI LORENZO 1419 where K3 is the coefficient of phase exchange expressed by the penetration theory, [O,] is the concentration of oxygen inside the solution, [O,],.b is the concentration of oxygen equilibrating with that in the bubbles and nohpoz[02]/2v is the average number of bubbles per unit volume, where v is the average ascensional velocity of the bubbles and h is the thickness of the solution. Phase exchange of iodine is represented by several terms. We consider phase exchange of iodine as gas from the solution to the gas above it, expressed by - where the symbols are analogous to those of eqn (29).We next consider phase exchange of iodine as gas from the solution to the bubbles of oxygen, expressed by We also consider phase exchange due to the nucleation of crystals of solid iodine, where the symbols are analogous to those of eqn (30) and [I2], is the concentration of iodine allowing generalizated nucleation. We finally consider phase exchange of solid iodine from the solution to the crystals; this exchange is pulsating since crystals are never present inside the solution. Hence we can writel - dNIZ/dt(p.e* 2,4) = K5 S,([I21 - [I21~) v{ncp[lzlc - a(t - lh)) (35) where K5 is the coefficient of phase exchange, S, is the surface area of a crystal, a is the number of crystals per unit volume that have gone out of the solution per unit time and th is the time of nucleation of the crystals.QUALITATIVE EXPLANATION OF OSCILLATIONS To obtain concentration against time functions we would have to write the balance with respect to oxygen and iodine and the chemical rates of every component that can be derived easily from steps B and C . A computer would be required to resolve the system obtained, putting values in place of the symbols, but this is not possible as most of them are unknown. Hence we attempt to give a qualitative interpretation. At the beginning we have steps with hydrogen peroxide, which are slow but produce iodide by reaction (22). At this time, we have no nucleation of bubbles of oxygen, because reactions (18) and (21) are slow owing to the low concentration of both + I 0 and I+.This is the first part of the induction period, as observed by Bray.2 We then have the steps with iodide. At the start, when the concentration of iodine is low and reaction (22) is far from equilibrium, it is faster than reactions (23) and (24). At this time only reactions (15), (18), (21) and (22) take place. This is the second part of the induction period and there is as yet no nucleation of oxygen bubbles or iodine crystals. Reaction (22) then approaches equilibrium. Reactions (23) and (24) become faster than it and hinder reactions (15) and (18), whilst reaction (21) may become faster. At this time production of oxygen and iodine is very slow, but [+I01 and [I+] are increasing because of reactions (23) and (24). This is the third part of the induction period.The iodine concentration reaches the value [I2], and a generalized nucleation of crystals takes place, suddenly lowering the concentration of iodine. Reaction (22) again becomes faster than reactions (23) and (24), which cannot take place because the iodide concentration is too low to sustain reactions (22), (23) and (24) at the same time. Hence reactions (1 5), (1 8) and (2 1) can take place and are faster than they were 47-21420 OSCILLATORY PHENOMENA in the induction period because of the high values of [+I01 and [I+]. The rate of oxygen production allows the concentration to reach a value where nucleation can take place. The induction period of the iodine oscillations ends at the first nucleation, but the induction period observed by Bray ends shortly after it, because he observed the evolution of bubbles of oxygen.This mechanism explains why Bray2 and Peard22 observed an increase in oxygen evolution shortly after the concentration of iodine reaches its maximum. Peard2, thought that iodine initiates a process producing oxygen, whereas our model shows that the decrease of iodine concentration hinders some processes inhibiting oxygen production. The decrease of iodine concentration allows reaction (22) to occur and the phenomenon starts again. INFLUENCE OF X- (X = C1, Br OR F) ON THE OSCILLATIONS CONSIDERED The influence of halogenides on the oscillations is good evidence for the validity of our model. Degn28 found that increasing concentrations of chloride and bromide ions decrease both the maximum concentration of iodine at the beginning of every oscillation and the induction time, whilst an increasing concentration of fluoride ion increases both the maximum concentration of iodine at the beginning of every oscillation and the induction time.We believe that the hydrogen peroxide oxidizes chloride to chlorine and bromide to bromine: 2C1-+ H,O, + 2H+ + C1, + 2H,O 2Br-+ H,O, + 2H+ -+ Br, + 2H,O. (36) (37) Both the nucleation of gas bubbles of chlorine and liquid bubbles of bromine are faster than that of solid crystals of iodine, since several steps are required to produce iodine. Oscillations in the concentration of chlorine or bromine take place according to our model and a pulsating phase exchange of iodine occurs from the solution to the bubbles of chlorine or bromine, allowing oscillations in the concentration of iodine.This does not allow the iodine concentration to increase to the value allowing its nucleation and hence the concentration of iodine, at the beginning of every induced oscillation, is lower. The induction time decreases because the nucleation of both bromine and chlorine are faster than that of iodine. Fluoride cannot be oxidized by hydrogen peroxide and cannot give analogous phenomena. It remains unchanged inside the solution and we may have I, + F- + 12F- (38) or other absorption phenomena, which hinder the formation crystallization nuclei because of electrostatic repulsion, and we have a higher supersaturation for nucleating crystals. APPLICATION OF THE MODEL OF THE BRIGGS-RAUSCHER5 SYSTEM The Briggs-Rauscher5 system, consisting of hydrogen peroxide + malonic acid + potassium iodate + manganous sulphate and sulphuric or perchloric acid, is derived from the Bray system.The latter oscillates at 333 K because of d[I,]/dt(chem.) is not capable of leading to [I2], at room temperature, but it is possible to obtain a value of d[I,]/dt(chem.) capable of leading to [I2], by using a catalyst. Manganous ion is not capable of producing oscillation^^^ without malonic a~id,~O-~* which must therefore be present if there are to be oscillations.F. D’ALBA AND s. DI LORENZO 1421 THE NOYES AND FURROW MODEL At first Furrow and NoyeP proposed a model, similar to that proposed by Noyes,ls to explain oscillations in the Belousov-Zhabotinskii system, in accordance with De Kepper31 and C~oke.~,-,~ The results of some of their tests23 obliged them to propose the following scheme:30 The overall reaction 10; + 2H,O, + RH + H+ -+ RI + 20, + 3H,O 10; + 2H,O, + H+ + HI0 + 20, +2H,O HI0 + RH -, RI + H,O.(39) (40) (41) where R is an organic radical, is generated by the process Step (42) is generated by the reaction H+ HIO+I-eI,+H,O RH e enol (43) (44) I, +en01 t RI + I- + H+. Process (41) is generated by two chains. The non-radical chain is H+ 10; +I- t 10; + HI0 H+ HIO, + I- s 2HI0 (45) 2 x (HI0 + H,O, + I- + 0, + H+ + H,O). (47) The radical chain is H+ 2 x (10; + HIO, e 2 * 1 0 , + H,O) 4 x [ 1 0 , + Mn2+ + H,O t HIO, + Mn(OH),+] (49) (50) (51) (52) Furrow and Noyes thought that reactions (41) and (44) decreased the sum H[IO]+2[12]+[I-], but these reactions may serve to increase the value of [I-], which passes through a critical value allowing the system to switch between the radical and the non-radical chains.4 x [Mn(OH),+ + H,O -+ Mn2+ + H,O + HOO .] 2 x [2H00 - -+ H,O, + O,] 2HI0, -+ 10; + HI0 + H+. We do not agree with this scheme. EXPERIMENTAL RESULTS AND DISCUSSION We recorded the potential difference of the galvanic chain Pt(so1.) I Agar-Agar + KNO, I KCl,,,,., I Hg,Cl, I Hg, Pt from the beginning to the end of the oscillations. Fig. 1 shows the curves for the maxima and minima of the potential, referred to the standard hydrogen electrode, as functions of time for different systems. Considering that the range of potentials,1422 OSCILLATORY PHENOMENA 0.90 0.80 0 5 tlmin 10 Fig. 1. Curves of the maxima and minima of the potential, referred to the standard hydrogen electrode, as functions of time.[KIO,] = 7.02 x mol drn-,, [H,O,] = 9.9 x 10-1 mol dm-3, [MnSO,] = 3.47 x lo-, mol dm-3, [H2S0,] = 0.692 x mol drn-,, 0, [malonic acid] = 2.62 x mol dm-3 and ., [malonic acid] = 10.47 x lo-, mol dm-3. referred to the standard hydrogen electrode, measured by us goes from 0.76 to 0.92 V and considering the initial concentrations- of reagents, we can relate the measured potential to the redox couple 12/1-. The maxima of the potential are almost steady, but the minima are not, demonstrating that the system does not have cyclical limiting behaviour, as the Noyes theory requires. The maxima are almost steady because they are related to [I2Ic, which is steady within the probability limit, whilst the minima have no specific significance. INFLUENCE OF ORGANIC SUBSTRATES The tests of Furrow and Noyes with organic Tests with the following system: [IO;] = 0.025 mol drn-,, [H+] = 0.1 rnol dm-,, [H,O,] = 0.1 rnol dm-,, [Mn2+] = 0.002 mol dm-3 and [C6H,0H] = 1 x low4 mol dm-, exhibited an extreme induction period such that over 4 h only 1 cm3 of oxygen was evolved.Then, in a few minutes, the rate of oxygen production increased by two orders of magnitude. A naphth-2-01 concentration of 1 x mol dm-3 causes a 10 min induction period. Their tests with trans-CH,-CH=CH-COOH showed a change in the stoichio- metry from reaction (1 1) to are very interesting. Mn2+ 10; + 2H,O, + H+ + C4H60, --* C,H,O,I + 20, + 2H,O (53) with the production of an iodohydrin.The tests with the aromatics showed the importance of +IO,, which reacts with them instead of hydrogen peroxide, preventing oxygen evolution. The tests with crotonic acid showed the importance of I+, which is the prevailing form of hypoiodous acid under these reaction conditions. A test with acrylamide is fundamental to a challenge of the Furrow and Noyes mechanism. They observed that acrylamide reacts with I+ and does not react with radicals, although it is a specific radical trap. Thus no radical is present in this system.F. D’ALBA AND s. DI LORENZO 1423 INFLUENCE OF MALONIC ACID Because of the absence of radicals, oxidation of malonic acid by iodate must occur Malonic acid and the manganous ion can give a complex, although we do not know by a two-electron process.how many malonates are bonded: An analogous complex with cerium was considered by Iwo and no ye^^^ for the Belousov-Zhabotinskii system. The complex can react with anionic iodine compounds in the following way: 10; + 10; + coz + Mn I L O J I I I I (55) [+IO], [I+] and [I-] increase and d[I,]/dt(chem.) increases, leading to a value of [I2Ic capable of causing nucleation. COMMENTS ON THE AsO;/IO;/ClO; SYSTEM De Kepper et al.36 have demonstrated that the arsenite, iodate and chlorite system shows oscillating behaviour. They considered the following reactions : 3H,As03 + 10; + 3H3As0, + I- 4H’ + C10; + 41- +2H,O + C1- + 21, (56) (57) and thought that these reactions explained the oscillations, whilst the arsenite and iodate subsystem does not oscillate. We think that reaction (57) is necessary to obtain d[I,]/dt(chem.) capable of leading to [I2Ic.F. D’Alba and S. Di Lorenzo, J . Chem. SOC., Faraday Trans. I , 1983,79, 39. W. C. Bray, J . Am. Chem. SOC., 1921, 43, 1262. B. P. Belousov, J . Res. Radiat. Med., 1959, 1958, 145. J. S. Morgan, J . Chem. SOC., 1916, 109; 274. T. S. Briggs and W. C. Rauscher, J. Chem. Educ., 1973,50, 496. A. Lokta, J. Phys. Chem., 1910, 14, 271.1424 OSCILLATORY PHENOMENA A. Lokta, Proc. Natl Acad. Sci. USA, 1920, 6,410. A. Lokta, J. Am. Chem. SOC., 1920,42, 1395. A. M. Turing, Philos. Trans. R. SOC. London, Ser. 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