The Journal of
Physical Chemistry
0 Copyright, 1986, by the American Chemical Society
VOLUME 90, NUMBER 7 MARCH 27, 1986
LETTERS Heterogeneities and Stirring Effects in the Belusov-Zhabotinsky Reaction Michael Menzinger* and Peter Jankowski Department of Chemistry, University of Toronto, Toronto M5S l A I , Canada (Received: February 1 I , 1985)
Spatially distributed concentration fluctuations are found, using micro- and macroelectrodes, to occur over a wide range of reactant concentrations in a stirred-batch-reactor study of the Belusov-Zhabotinsky reaction. The noise spectrum as well as the period of the limit cycle depend sensitively on the rate of stirring. This is explained by the hydrodynamic control of the fluctuations and by noise-induced transitions (NIT) mediated through exchange at the gas/liquid interface.
In stirred-reactor studies of chemical instabilities, the concentrations are conventionally taken as spatially uniform and theoretical interpretations of the nonlinear effects (multistability, limit cycle oscillations, bifurcations) are generally based on homogeneous models, Le. ordinary differential equations1y2and iterative maps.2 Yet one encounters consistently reports of the dependence of the chemical instabilities on the rate of stirring, be it in batch reactor^^,^ or in C S T R k 5 This suggests that heterogeneities play a hitherto unsuspected role in the global dynamics and that their study constitutes a fruitful field of research. The purpose of this Letter is (1) to show that in a stirred batch reactor large concentration fluctuations indeed exist and appear ubiquitously in the ferroin-catalyzed Belusov-Zhabotinsky reaction and (2) to prove that they are spatially distributed rather than homogeneous. (3) Furthermore it is found that stirring not only ~~~
~
~~
~
(1) G . Nicolis and I. Prigogine, Self-organization in Nonequilibrium
Systems, Wiley, New York, 1977. (2) H. Haken, Advanced Synergefics, Springer, Berlin, 1983. (3) P. DeKepper, These d'Etat, Universite de Bordeaux, 1978. (4) P. Ruoff, Chem. Phys. Lett., 90, 76 (1982). (5) (a) J. C. Roux, P. DeKepper, and J. Boissonade, Phys. Lett., 97A, 168 (1983). (b) J. C. Roux, H. Saadaouii, P. DeKepper, and J. Boissonade, Experimental Studies of the Transition Between Stationary States in a Bistable Chemical System, in Fluctuations and Sensitivity in Nonequilibrium Systems, W. Horsthemke and D. K. Kondepuri, Ed.,Springer, Berlin, 1984.
0022-3654/86/2090-1217$01.50/0
affects the amplitude and spectrum of the fluctuations, but also the period and amplitude of the limit ~ y c l e . ~(4) , ~ Finally, an interpretation of this macroscopic stirring effect is advanced in terms of noise-induced transitions. The ferroin-catalyzed BZ reaction6 was studied in the stirred batch reactor shown in Figure 1 which is open to the atmosphere, by monitoring simultaneously the redox potentials in two sampling volumes of greatly differing size. The local dynamics was monitored by a microelectrode made from a 0.025-cm-diameter platinum wire which protruded 0.02 cm from a glass capillary. The macroelectrode consisted of a P t wire 0.05 cm in diameter and 2.5 cm long. The potential differences with respect to a common H g / H g S 0 4 electrode were recorded on a two-channel recorder. An upper limit of the microelectrode response time is given by the fastest observed fluctuation rise time of t = 0.15 s. Correspondingly, the fastest rise time observed with the macroelectrode was 0.6 s. The solution was stirred by a mechanically driven glass propeller (23 X 6 mm) a t a rate that was variable between 50 and 800 rpm and it was thermostated at 25 f 0.5 O C . Since our main interest is in fluctuations, stirring was somewhat slower than in some previous ~ t u d i e s ,but ~ . ~the fluctuations are (6) R.J. Field, Experimental and Mechanistic Characterization of Bromate Ion Driven Chemical Oscillations and Travelling Waves, in Oscillations and Travelling Waves in Chemical Systems, R.J. Field and M. Burger, Ed., Wiley, New York, 1985.
0 1986 American Chemical Society
1218 The Journal of Physical Chemistry, Vol. 90, No. 7, 1986
Letters
I
MOTOR
I
,
,
,
l
I
,
,
,
I
,
,
1.0 H Z
' 1 3 . l H r STIRRING RATE
RECORDER
reference
v+I
0
Figure 3. Effect of a change of stirring rate on the fluctuation amplitude
and on the macroscopic attributes (period and amplitude) of the limit cycle. Conditions were [BrO,-] = 0.19 M, [CH,(COOH),] = 0.18 M, others as in Figure 1. The solution was purged at a N2flow of 1.8 cm3 s-l. Without purging the noise amplitude and stirring effects were reduced to ca. one-half.
0.025cm Micro-electrode
Figure 1. The experimental arrangement. The thermostated batch reactor (45 mm i.d.) contains Pt macro- and microelectrodes, a motordriven propeller, and a fritted glass disk for optional N2purging. An enlarged view of the microelectrode is given in the insert.
1
T50mV
*
I
I
I
I
I
1
I
I
I
C
15r n ~ d
d
,
] 4 TIME (min) Figure 2. Noise portrait of a limit cycle (a, b) and of stationary steady states (c, d). Traces a and b were simultaneously recorded on Pt microand macroelectrodes, respectively. In traces a, b the initial composition was [BrOJ = 0.25 M, [CH,(COOH),] = 0.15 M, [H2S04]= 0.32 M, and [ferroin] = 0.0017 M. The solution was not purged. Stirring rate: 5.9 Hz. Note the pronounced noise on the microelectrode only, its dependence on the oscillation phase, and the irregularity of the period. The observed fluctuations in (a) translate' into absolute excursions of the (Red/Ox) ratio' of ca. 60%. Trace d shows similar noise in a stable steady state characterized by [BrO,-] = 0.013 M, [CH,(COOH),] = 0.61 M, others as above. The solution was N2 purged. Trace c is a control run demonstrating the absence of noise from a nonreactive solution similar to the one in d from which Br0,- is missing. I
0
10
T I M E (MINIJTESI
I-
a
5
I
2
I
I
I
I 6
I
I 8
expected to persist at stirring rates in excess of 1000 rpm albeit with diminished amplitude. In order to reduce the flux of oxygen from the atmosphere, the solution was in some instances purged by bubbling N2 through the solution from a fritted glass disk at the rate of 1.8 cm3/s, as specifically noted in the figure captions. An additional experiment was conducted to test the effect of excluding atmospheric oxygen altogether from the reactor. A Teflon plug which made a leaktight seal via an O-ring and whose lower surface had the shape of a n inverted funnel containing the appropriate electrical and stirrer feedthroughs was inserted into the top of the reactor which contained a previously purged solution until all air was displaced and a record similar to a and b in Figure 2 was taken. A typical record for the oscillating domain is shown in parts a and b of Figure 2. One notes the following: (1) The waveforms of the micro- and macroelectrode traces are alike except for the noise seen by the microelectrode during the decay phase of the potential. Fluctuation amplitudes as high as 22 mV (corresponding
to a more than twofold change of the Fe2+/Fe3+ratio) were observed.' Qualitatively similar noise portraits were found to persist over a wide range of control parameters (malonic acid and bromate concentrations, stirring, and purging rates). Noise similar to that of Figures 2, a and b, and 3 is also present in nonoscillating states, as Figure 2d shows, while it is practically absent (see Figure 2c) from a nonreactive mixture similar to the one in Figure 2, a and b, except for the lack of bromate. (2) Figure 2a and Figure 3 show that the fluctuation amplitudes and hence the system's noise susceptibility depend on the phase of the limit cycle: the maximum is reached shortly before the sudden upward jump of the potential and it is followed by a refractory interval of minimal noise activity. This demonstrates that the heterogeneitiesare not merely passively induced by stirring but that they reflect the local chemical dynamics along the limit cycle. (3) It should be noted that not only the local but also the global dynamics fluctuates in a random way. Figure 2, a and b, illustrates that the period of the limit cycle is not constant nor d e s it merely drift monotonically as one would expect from the slow approach to equilibrium in a deterministic oscillator, but it exhibits surprisingly large random fluctuations around a slowly drifting background. This can be seen clearly from the time series, Figure 2, a and b, where the successive periods are 46.8, 55.8, 58.1, 61.5, 52.4, 58.4, 55.3, and 51.7 s. (4) When studied in the closed reactor without free surface, a solution of the same composition as the one in Figure 2, a and b, produced fluctuations of redox potential and of oscillation period that were drastically reduced (to ca. 5-10% of their original values) but not completely eliminated and the limit cycle period increased by 6%. This shows that interfacial gas exchange is one of the principal causes of the fluctuations. ( 5 ) Figure 3 is intended to show the effect of a change in stirring rate on noise and global oscillations in a N, purged solution. We observe that the fluctuations'can be controlled hydrodynamically: decreased stirring leads to increased fluctuation amplitude and vice versa. Indeed the noise amplitude is enhanced by a factor of 5 in response to a 13-fold decrease of the stirring rate. It is very significant that at the same time the period of the limit cycle is shortened to 35% of its original value. The significance of the combined parts a and b of Figure 2 lies in the fact that the fluctuations are seen by the microelectrode only, while the large detector overlooks them due to spatial averaging. This is clear evidence for their heterogeneous nature. While the stirring dependence of the period of the limit cycle has been observed previously in batch reactor^,^^^^* the simultaneous observation of a stirring effect on both the deterministic dynamics and on the stochastic (noise) behavior suggests an intimate connection between the two. The irregularity of the oscillation period, Figure 2, a and b, illustrates how the deterministic limit cycle interacts with a (7) The Nernst equation yields 4%,4876, and 224% for the absolutechange in the (Red/Ox) ratio of the species determining the electrode potentials for fluctuation amplitudes of 1, 10, and 30 mV, respectively. (8) U. J. Farage and D. Jancic, Chimia, 35, 289 (1981).
J. Phys. Chem. 1986, 90, 1219-i222 4
a’
A
B Figure 4. The deterministic limit cycle (1234), governed by the S-shaped slow manifold, contracts to the stochastic cycle (1’2’3’4’) due to transitions at 1’ and 3’ induced by external noise (heavy arrows). fluctuating environment. This and the simultaneous effect of stirring on microscopic and macroscopic behavior can be understood in terms of the noise-induced transition (NIT) m g e l illustrated in Figure 4. The abscissa represents a slowly varying feedback parameter and the ordinate a fast response, in the present case the redox potential. The heavy line represents the slow manifold of the dynamical system.'^^*'^ Its dotted portion represents the locus of unstable states and the point USS is the unstable steady state around which the trajectory describes a determinstic limit cycle (1234) with jump points 1,3. In the presence of concentration fluctuations, indicated for the fast variable by the vertical arrows, transitions may be induced locally, whenever the representative point crosses the unstable manifold, from the new jump points 1’,3’, well before the system has drifted to the deterministic jump points. By avoiding the portions 1’-1 the and 3’-3 on the critically slowed part of the period of the stochastic limit cycle (1’2’3’4’) can be shortened considerably. The random Occurrence of supercritical fluctuations manifests itself in the irregularity of the oscillation period which in turn reflects the first passage time statistics. In addition to the noise-induced period shortening, the model also leads one to expect a decrease of the jump amplitudes 1’-2’, and 3’-4’, in agreement with Figure 3. The fact that the N I T model is admittedly very simple while being in qualitative accord with the observations would have pleased William Occam. Concerning the origin of the fluctuations, endogenous and exogenous causes have to be envisaged. Principal among the (9) J. Boissonade, Physica, 113A, 607 (1982). (10) K. Bar-Eli and S . Haddad, J. Phys. Chem., 83, 2952 (1979).
1219
former are the spontaneous, nucleation-induced fluctuations which have been believed onceg to be the source of stirring effects in C S T R s . At present their role and importance is still uncertain. Exogenous noise may arise in different ways. Particularly relevant here appears to be gas exchange at the liquid/gas interface. Loss of Br2, C 0 2 , and/or entrainment of atmospheric 02,all of which are known to play important kinetic r01es,~OJ~J’ can give tise, in the absence of stirring, to a vertical concentration gradient. This is the prerequisite for the production of fluctuations through the turbulent fragmentation of this gradient.I4 As Barkin et al.I3 noted for the Ce4+/BZ reaction, O2catalysis of the reaction betweeen Ce4+and malonic acid greatly increases the rate at which Ce3+ is formed. If similar kinetics holds for the ferroin/BZ system, ’~ and it can be shown from the known O2a b s o r p t i ~ n , diffusion, reaction rates6 that the (Fe(II)phen/Fe(III)phen) ratio near the air surface can exceed that in the bulk by a factor of the order of 10, as required. In this Letter we report the first direct evidence for the heterogeneous nature of large-scale concentration fluctuations, and we propose a new mechanism for the macroscopic irregularities of the BZ reaction based on noise-induced transitions.” The traditional interpretation of stirring effects is based on the notion of a global shift of the operating point of the dynamical system by the homogeneous intervention of reactive gases. It lacks, however, the ability of dealing with the kind of irregularities reported here. A contribution from a homogeneous mechanism cannot be excluded from the experiments reported here. However, heterogeneity induced transitions have recently been provedI6 to be responsible for the stirring effects in a CSTR.5 They arise from incomplete mixing of the separate reactor feedstreams. We shall report elsewhere on further examples of noise-induced transition phenomena.
Acknowledgment. This work was supported by NSERC. (1 1) W. Horsthemke and R. Lefever, Noise-Induced Tramitions, Springer, Berlin, 1984. (12) C. Zeemann, Di/ferential Equations for Heart Beat and Nerve Impulse in Towards a Theoretical Biologv, Vol. 4, Aldine & Atherton, Chicago,
1972. (13) S . Barkin, M. Bixon, R. M. Noyes, and K. Bar-Eli, Inr. J . Chem. Kinet., 10, 619 (1978). (14) J. 0. Hinze, Turbulence, McGraw-Hill, New York, 1975. (15 ) Gmelin’s Handbuch der Anorganischen Chemie, Systemnummer 3, 8th ed, Verlag Chemie, Weinheim, 1960-62: Lieferung 4, pp 921 ff;Lieferung 5 , pp 1642ff. (16) M. Menzinger, M. Boukalouch, P. DeKepper, J. Boissonade, J. C. Roux, and H. Saadaoui, J . Phys. Chem., 90, 313 (1986). (17) F. D’Alba and S . DiLorenzo, J . Chem. SOC.,Faraday Trans. I , 79, 39 (1983).
Cyclic Photocleavage of Water with the Intermediate Redox Couple Hg,O/Hg K. Tennakone*+ and S. Wickramanayaket Photochemistry Group, Institute of Fundamental Studies, 380172, Bauddhaloka Mawatha, Colombo 7 , Sri Lanka, and Department of Physics, University of Ruhuna, Matara, Sri Lanka (Received: August 15, 1985; In Final Form: January 10, 1986) It is found that water can be photodecomposed into oxygen and hydrogen by a cyclic two-photosystem process using TiO, as the sensitizer and the redox couple Hg20/Hg as the electron pool linking the two photosystems. At neutral pH an aqueous suspension of Ti02 and Hg20 photooxidizes water, reducing Hg,O to Hg. When the pH of the resulting solution is made strongly alkaline, water is photoreduced, oxidizing Hg back to Hg,O.
Introduction The search for catalytic systems that photodecompose water into oxygen and hydrogen has received much attention.’S2 It is ‘Institute of Fundamental Studies and University of Ruhuna. Address all correspondence to the University of Ruhuna. f Institute of Fundamental Studies.
well-known that aqueous dispersions of semiconductor particles possess the capacity to Photoreduce Or Photooxidize water in the (1) M. Gratzel, Ed., in “Energy Resources through Photochemistry and Catalysis”, Academic Press, New York, 1983. (2) J. Rabani, Ed., in “Photochemical Conversion and Storage of Solar Energy”, Weizmann Science Press of Israel, Jerusalem 1982.
0022-3654/86/2090-1219$01.50/00 1986 American Chemical Society
