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Spatial patterns in the Briggs-Rauscher reaction
Volume 156, number 5
CHEMICAL PHYSICS LETTERS
I4 April 1989
SPATIAL PATTERNS IN THE BRIGGS-RAUSCHER REACTION
Zs. NAGY-UNGVARAI, S.C. MULLER and B. HESS Max-Planck-InstitutJiir Erntirungsphysiologie, Rheinlanddamm 20 I, D-4600 Dortmund 1, Federal Republic of Germany
Received 26 January 1989
Different spatial patterns form in thin layers of the Briggs-Rauscher reaction maintained at a temperature between 5 and 15°C and are investigated by two-dimensional spectrophotometry. There are close similarities with wave propagation in the BelousovZhabotinskii reaction. However, quite different behaviour is observed when a wave encounters a gas bubble or when two waves approach a collision process.Already at a distance of some millimeters the wave fronts are deformed, attracted towards each other, and merge rapidly.
1. Introduction
2. Materials and methods
In thin unstirred layers of chemical reactions that show oscillations in closed batch systems, e.g. in a beaker, chemical waves might be observed because they contain a repeated kinetic feedback (autocatalysis) [ 11. Spatial chemical reactions have been reported so far only in the Belousov-Zhabotinskii (BZ) reaction [ 2,3 1, in some uncatalyzed BrOy oscillators [ 4 ] and in the ClO? + I- + malonic acid reaction [ 5 1. Further oscillating batch reactions, for example the Bray reaction [ 61, the Briggs-Rauscher (BR) reaction [ 7 1, some other gas-evolution oscillators [ 8 1, the copper (II )-catalyzed H202 + KSCN and H,O,+S,O:reactions [9,10] and the Jensen oscillator [ 111 are probable further candidates for the occurrence of chemical waves. Here we report on different spatial patterns in the Briggs-Rauscher reaction which is the oxidation of malonic acid by iodate and hydrogen peroxide catalyzed by the manganous ion [ 7,121. The waves resemble in many respect those described in the wellknown BZ reaction, but we also observe unusual behaviour in some diffusion-dependent processes, for example when waves are moving across gas bubbles or during wave collision. The observation of structures in this new system extends our knowledge about the properties of chemical waves.
The reagents malonic acid (MA), KI09, MnS04.4H20, HClO,,, H,O, and starch were of analytical reagent grade. The measurements were carried out in unstirred solution layers of the BR reaction with the following ranges of composition: 0.72-1.20 M Hz02, 0.06-0.08 M RIO, or NaI03, 0.05 M HClO.,, 0.05 M MA, 0.06 M MnSO* and 0.05% starch. All reactant solutions were thermostatted to 5, 10 or 15 “C. The temperature of the laboratory was lowered to 15’C. The humidity of the air in the laboratory was kept at 30% to reduce water condensation. The solutions were mixed and placed in an optically flat Petri dish with a layer thickness of 0.5-O-7 mm. The dish was then covered with a glass plate leaving an air gap of about 10 mm between the solution surface and the cover plate. Further tests were carried out in a cold room kept at 5°C. Spatial patterns in the layer were observed by twodimensional (2D) spectrophotometry [ 131 at 300, 350, 450 and 560 nm corresponding to the absorption maxima of the Iz/Kl/H+/starch system. Solutions prepared without starch show very little change in I2 absorption because of the small extinction coefficient of iodine. In such solutions chemical waves can barely be detected. However, using 0.05% starch as indicator, distinct patterns are observed. Pictures with the best contrast were obtained at 560 nm. The sample layer was illuminated by the parallel
0 009-2614/89/$ 03.50 Q Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
433
Volume 156, number 5
CHEMICAL PHYSICS LETTERS
light beam of a 300 W xenon short arc lamp (Cermax). The wavelength was selected by interference filters. The 2D distribution of the light transmitted through a 5 x 5 or 10 x 10 mm2 layer area was imaged by a photolens (UV-Nikon, Nikkor) on the target of a video camera system (Hamamatsu ClOOO)
14 April 1989
resulting in a 5 12X 512 array of picture elements with 256 digital units intensity resolution. The digitalized video signal was stored on the magnetic disc of a computer system (Perkin-Elmer 3230) for further processing and evaluation.
Fig. 1. Different waves in ii BR solution with an initial composition of 1.1 M H,O,, 0.06 M KI02, 0.05 M HCIO, and 0.05 M MA, 0.06 M MnS04 and 0.05% starch, thermostatted to lO.O”C.Layer thickness 0.5 mm. Image area 9.0x 9.0 mm’. Room temperature IS.O'C.
Volume 156, number 5
CHEMICAL PHYSICS LETTERS
14 April 1989
3. Results and discussion At 25”C, BR solutions spread out in thin layers exhibit bulk oscillations. By decreasing the temperature of the solution temporal oscillations can be almost suppressed. When the sample layer is prepared at 10°C or below, one or two waves with irregular shape are observed, probably due to small temperature or phase differences in the solution which, at this temperature, exhibit little bulk oscillations (fig. la). Such waves can also be produced by initially imposing temperature gradients of 2-4” C/cm. After this initial period of some minutes trigger waves appear. Sometimes they originate from an irregularly shaped, spatially extended region (OS-1 mm*, fig. lb) and quite often from' dust particles. However, there are also waves starting from small circular spots devoid of any macroscopically visible heterogeneous particles (fig. 1c ) . Afrera certain time every trigger wave becomes circular in shape (fig. 1d ) , a feature commonly explained by curvature effects [ 141. The velocity of these waves varies between 2.0 and 4.0 mm min-‘, depending on temperature and initial composition of the solution, whereas the speed of the irregular waves at the beginning of the reaction is up to 5 times greater. Because of the relatively broad wave fronts (6-8 mm) it is extremely hard to break wave fronts to cause curling up to spiral waves. Only the beginning of such a process can be observed in our systems, but spiral waves never have enough time to develop fully because of their short lifetime. At the concentrations studied, the BR reaction terminates after IO- 15 min. Similar to oscillations in the stirred BR reaction, chemical waves cease after a certain amount of iodine has formed. At increased iodate or decreased hydrogen peroxide concentrations iodine even precipitates and characteristic precipitation patterns can be observed as shown in fig. 2. The patches in this pattern are the result of convective flow in the solution layer, As in the BZ reaction there is a strong gas evelution in the BR reaction. Such gas bubbles may influence the diffusion of the autocatalytic species in the wavefront and thus affect its propagating velocity. The behaviour of the waves moving across gas bubbles is different in the two systems. In the BZ reaction CO, is formed which is chemically inert in the
Fig. 2. Precipitation patterns in the BR reaction with an initial composition of 1.O M H202, 0.08 M IUO,, 0.05 M HCIO,, 0.05 M MA, 0.06 MnSO, and 0.1% starach, thermostatted to lO.O”C. Room temperature: 25.O”C. Layer thickness 1.0 mm. Image area 9.0x9.0 mm?.
reaction. Therefore, CO2 bubbles behave like me chanical obstacles in the solution layer. A wave front, when arriving at a CO1 bubble, attains on both sides of the bubble a large negative curvature with respect to the propagation velocity because of hindered diffusion into areas occupied by the bubble. This leads to increased velocities [ 14,151. During its motion across the obstacle, formerly “closed” directions of propagation become accessible again, that is, the wave attains a large positive curvature on both sides of the bubble causing a decrease in the velocities [ 14,15 ] and when detached from the bubble a waveform like the wall of a constricted cell (fig. 3a). In extreme cases this can lead to the disruption of the wave front [ 151. In contrast, wave fronts in the 02-producing BR reaction “overflow” the 0, bubbles immediately after having reached them, causing a protruding bump in the wave front (fig. 3b). This behaviour is possibly related to I2 production connected with the 0, formation in the BR reaction [ 121. As described in stirred systems, I-&O2reduces iodate, while oxygen is produced, and the concentration of iodine rises to 435
Volume 156, number 5
CHEMICAL PHYSICS LETTERS
I 4 April 1989
Fig. 3. Motion of a wave front across gas bubbles (a) in a BZ reaction solution with initial composition of 0.3 M NaBrO,, 0.4 M MA, 0.09 M bromomalonic acid, 0.41 M HZSOI, 0.006 M Ce (IV) at 25.O”C. Layer thickness 0.6 mm, and (b) in a BR reaction solution under identical experimental conditions as in tig. 1,but with a H202 concentration of 0.8 M.
a maximum. Subsequently, the iodine concentration decreases as H202 oxidizes much of the iodine back to iodate. In fact, we observe at places where bubbles are formed locally higher .iodine concentrations, which become visible as dark patches after bubbles have burst (indicated by A in fig. 3b). Just as bubbles accelerate wave propagation such patches induce the same behaviour, that is waves “overflow” them. A further difference between the BZ and the BR reaction is observed during collision processes. Shortly before the collision of two wave fronts the respective autocatalytic species diffuse from two opposite directions into the same region. This changes the regular circular form of the two wave fronts even before the collision of the circular geometries. The distance at which the two wave fronts begin to interact with each other; thereby changing their previous regular form; is about 0.02 mm in the BZ reaction as can be calculated from the figures of ref. [ 161. In the BR reaction waves are deformed, or “attracted” by each other in a much more pronounced fashion. Their mutual influence starts at a 436
Fig. 4. Wave collision in the BR reactionunder the same experimental conditions as in fg_ 3b.
Volume 156, number 5
14Aprill989
CHEMICAL PHYSICS LETTERS
distance some 500-600 times higher than in the BZ reaction. For the example shown in fig. 4 this distance is z 5 mm. What is the source of this large difference between the two systems? It cannot be the difference between the diffusive properties of the two autocatalytic species alone. More probably substantial differences in the whole reaction-diffusion processes are involved. In particular, the steepness of the concentration fronts and their dependence on the specific reaction kinetics should be considered. Furthermore, what role does lowering of the temperature play? In order to answer these questions further experimentation is needed.
Acknowledgement Thanks are due to M. Orban who focused our interest on the BR reaction and to I. Wilms for technical assistance. References
[2] A. Zaikin and A.M. Zhabotinskii, Nature 225 ( 1970) 535. {3] J. Ross, SC. Miiller and C. Vidal, Science 240 (1988 ) 460. [4] M. Orbin, J. Am. Chem. Sot. 102 (1980) 431 I. [ 51 P. de Keppcr, LR. Epstein, K Kustin and M. Orb&n,J. Phys. Chem. 86 (1982) 170. [6] WC. Bray, J.Atn. Chem. Soc.43 (1921) 1262. [7] T.S. Brings and W.C. Rauscher, J. Chem. Ed. 50 (1973) 496. [8] P.G. Bowers and R.M. Noyes. in: Oscillationsand traveling waves in chemical systems, eds. RJ. Field and M. Burger ( Wiley-Interseience, New York, 1985 ) p. 473. [9] M. Orban, J. Am. Chem. Sot. 108 ( 1986) 6893. [ 101 M. Orb&n and LR. Epstein, J. Am. Chem. Sot. 109 ( 1987) 101. [ 111J.H. Jensen, J. Am. Chem. Sot. 105 (1983) 2639. [ 121 SD. Furrow, in: Gscillations and traveling waves in chemical systems, eds. R.J. Field and M. Burger ( Wiley-Interscience, New York, 1985) p. 171, and references therein. [ 131 SC. Milller, Th. Plesser and B. Hess, Physica D 24 (1987) 71. [ 141 J.P. Keener and J.J. Tyson, Physica D 21 (1986) 307. [ 151 Zs. Nagy-Ungvarai, S.C. MiIller and B. Hess in: Spatial inhomogeneities and transient behaviour in chemical kinetics, eds. G. Nicolis and P. Gray (Manchester Univ. Press, Manchester), in press. [ 161 P. Foerster, S.C. Miiller and B. Hess, Science 241 (1988) 685.
[ I ] A. Hanna, A. Saul and K. Showalter, J. Am. Chem. Sot. 104 (1982) 3838.
.
437
CHEMICAL PHYSICS LETTERS
I4 April 1989
SPATIAL PATTERNS IN THE BRIGGS-RAUSCHER REACTION
Zs. NAGY-UNGVARAI, S.C. MULLER and B. HESS Max-Planck-InstitutJiir Erntirungsphysiologie, Rheinlanddamm 20 I, D-4600 Dortmund 1, Federal Republic of Germany
Received 26 January 1989
Different spatial patterns form in thin layers of the Briggs-Rauscher reaction maintained at a temperature between 5 and 15°C and are investigated by two-dimensional spectrophotometry. There are close similarities with wave propagation in the BelousovZhabotinskii reaction. However, quite different behaviour is observed when a wave encounters a gas bubble or when two waves approach a collision process.Already at a distance of some millimeters the wave fronts are deformed, attracted towards each other, and merge rapidly.
1. Introduction
2. Materials and methods
In thin unstirred layers of chemical reactions that show oscillations in closed batch systems, e.g. in a beaker, chemical waves might be observed because they contain a repeated kinetic feedback (autocatalysis) [ 11. Spatial chemical reactions have been reported so far only in the Belousov-Zhabotinskii (BZ) reaction [ 2,3 1, in some uncatalyzed BrOy oscillators [ 4 ] and in the ClO? + I- + malonic acid reaction [ 5 1. Further oscillating batch reactions, for example the Bray reaction [ 61, the Briggs-Rauscher (BR) reaction [ 7 1, some other gas-evolution oscillators [ 8 1, the copper (II )-catalyzed H202 + KSCN and H,O,+S,O:reactions [9,10] and the Jensen oscillator [ 111 are probable further candidates for the occurrence of chemical waves. Here we report on different spatial patterns in the Briggs-Rauscher reaction which is the oxidation of malonic acid by iodate and hydrogen peroxide catalyzed by the manganous ion [ 7,121. The waves resemble in many respect those described in the wellknown BZ reaction, but we also observe unusual behaviour in some diffusion-dependent processes, for example when waves are moving across gas bubbles or during wave collision. The observation of structures in this new system extends our knowledge about the properties of chemical waves.
The reagents malonic acid (MA), KI09, MnS04.4H20, HClO,,, H,O, and starch were of analytical reagent grade. The measurements were carried out in unstirred solution layers of the BR reaction with the following ranges of composition: 0.72-1.20 M Hz02, 0.06-0.08 M RIO, or NaI03, 0.05 M HClO.,, 0.05 M MA, 0.06 M MnSO* and 0.05% starch. All reactant solutions were thermostatted to 5, 10 or 15 “C. The temperature of the laboratory was lowered to 15’C. The humidity of the air in the laboratory was kept at 30% to reduce water condensation. The solutions were mixed and placed in an optically flat Petri dish with a layer thickness of 0.5-O-7 mm. The dish was then covered with a glass plate leaving an air gap of about 10 mm between the solution surface and the cover plate. Further tests were carried out in a cold room kept at 5°C. Spatial patterns in the layer were observed by twodimensional (2D) spectrophotometry [ 131 at 300, 350, 450 and 560 nm corresponding to the absorption maxima of the Iz/Kl/H+/starch system. Solutions prepared without starch show very little change in I2 absorption because of the small extinction coefficient of iodine. In such solutions chemical waves can barely be detected. However, using 0.05% starch as indicator, distinct patterns are observed. Pictures with the best contrast were obtained at 560 nm. The sample layer was illuminated by the parallel
0 009-2614/89/$ 03.50 Q Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
433
Volume 156, number 5
CHEMICAL PHYSICS LETTERS
light beam of a 300 W xenon short arc lamp (Cermax). The wavelength was selected by interference filters. The 2D distribution of the light transmitted through a 5 x 5 or 10 x 10 mm2 layer area was imaged by a photolens (UV-Nikon, Nikkor) on the target of a video camera system (Hamamatsu ClOOO)
14 April 1989
resulting in a 5 12X 512 array of picture elements with 256 digital units intensity resolution. The digitalized video signal was stored on the magnetic disc of a computer system (Perkin-Elmer 3230) for further processing and evaluation.
Fig. 1. Different waves in ii BR solution with an initial composition of 1.1 M H,O,, 0.06 M KI02, 0.05 M HCIO, and 0.05 M MA, 0.06 M MnS04 and 0.05% starch, thermostatted to lO.O”C.Layer thickness 0.5 mm. Image area 9.0x 9.0 mm’. Room temperature IS.O'C.
Volume 156, number 5
CHEMICAL PHYSICS LETTERS
14 April 1989
3. Results and discussion At 25”C, BR solutions spread out in thin layers exhibit bulk oscillations. By decreasing the temperature of the solution temporal oscillations can be almost suppressed. When the sample layer is prepared at 10°C or below, one or two waves with irregular shape are observed, probably due to small temperature or phase differences in the solution which, at this temperature, exhibit little bulk oscillations (fig. la). Such waves can also be produced by initially imposing temperature gradients of 2-4” C/cm. After this initial period of some minutes trigger waves appear. Sometimes they originate from an irregularly shaped, spatially extended region (OS-1 mm*, fig. lb) and quite often from' dust particles. However, there are also waves starting from small circular spots devoid of any macroscopically visible heterogeneous particles (fig. 1c ) . Afrera certain time every trigger wave becomes circular in shape (fig. 1d ) , a feature commonly explained by curvature effects [ 141. The velocity of these waves varies between 2.0 and 4.0 mm min-‘, depending on temperature and initial composition of the solution, whereas the speed of the irregular waves at the beginning of the reaction is up to 5 times greater. Because of the relatively broad wave fronts (6-8 mm) it is extremely hard to break wave fronts to cause curling up to spiral waves. Only the beginning of such a process can be observed in our systems, but spiral waves never have enough time to develop fully because of their short lifetime. At the concentrations studied, the BR reaction terminates after IO- 15 min. Similar to oscillations in the stirred BR reaction, chemical waves cease after a certain amount of iodine has formed. At increased iodate or decreased hydrogen peroxide concentrations iodine even precipitates and characteristic precipitation patterns can be observed as shown in fig. 2. The patches in this pattern are the result of convective flow in the solution layer, As in the BZ reaction there is a strong gas evelution in the BR reaction. Such gas bubbles may influence the diffusion of the autocatalytic species in the wavefront and thus affect its propagating velocity. The behaviour of the waves moving across gas bubbles is different in the two systems. In the BZ reaction CO, is formed which is chemically inert in the
Fig. 2. Precipitation patterns in the BR reaction with an initial composition of 1.O M H202, 0.08 M IUO,, 0.05 M HCIO,, 0.05 M MA, 0.06 MnSO, and 0.1% starach, thermostatted to lO.O”C. Room temperature: 25.O”C. Layer thickness 1.0 mm. Image area 9.0x9.0 mm?.
reaction. Therefore, CO2 bubbles behave like me chanical obstacles in the solution layer. A wave front, when arriving at a CO1 bubble, attains on both sides of the bubble a large negative curvature with respect to the propagation velocity because of hindered diffusion into areas occupied by the bubble. This leads to increased velocities [ 14,151. During its motion across the obstacle, formerly “closed” directions of propagation become accessible again, that is, the wave attains a large positive curvature on both sides of the bubble causing a decrease in the velocities [ 14,15 ] and when detached from the bubble a waveform like the wall of a constricted cell (fig. 3a). In extreme cases this can lead to the disruption of the wave front [ 151. In contrast, wave fronts in the 02-producing BR reaction “overflow” the 0, bubbles immediately after having reached them, causing a protruding bump in the wave front (fig. 3b). This behaviour is possibly related to I2 production connected with the 0, formation in the BR reaction [ 121. As described in stirred systems, I-&O2reduces iodate, while oxygen is produced, and the concentration of iodine rises to 435
Volume 156, number 5
CHEMICAL PHYSICS LETTERS
I 4 April 1989
Fig. 3. Motion of a wave front across gas bubbles (a) in a BZ reaction solution with initial composition of 0.3 M NaBrO,, 0.4 M MA, 0.09 M bromomalonic acid, 0.41 M HZSOI, 0.006 M Ce (IV) at 25.O”C. Layer thickness 0.6 mm, and (b) in a BR reaction solution under identical experimental conditions as in tig. 1,but with a H202 concentration of 0.8 M.
a maximum. Subsequently, the iodine concentration decreases as H202 oxidizes much of the iodine back to iodate. In fact, we observe at places where bubbles are formed locally higher .iodine concentrations, which become visible as dark patches after bubbles have burst (indicated by A in fig. 3b). Just as bubbles accelerate wave propagation such patches induce the same behaviour, that is waves “overflow” them. A further difference between the BZ and the BR reaction is observed during collision processes. Shortly before the collision of two wave fronts the respective autocatalytic species diffuse from two opposite directions into the same region. This changes the regular circular form of the two wave fronts even before the collision of the circular geometries. The distance at which the two wave fronts begin to interact with each other; thereby changing their previous regular form; is about 0.02 mm in the BZ reaction as can be calculated from the figures of ref. [ 161. In the BR reaction waves are deformed, or “attracted” by each other in a much more pronounced fashion. Their mutual influence starts at a 436
Fig. 4. Wave collision in the BR reactionunder the same experimental conditions as in fg_ 3b.
Volume 156, number 5
14Aprill989
CHEMICAL PHYSICS LETTERS
distance some 500-600 times higher than in the BZ reaction. For the example shown in fig. 4 this distance is z 5 mm. What is the source of this large difference between the two systems? It cannot be the difference between the diffusive properties of the two autocatalytic species alone. More probably substantial differences in the whole reaction-diffusion processes are involved. In particular, the steepness of the concentration fronts and their dependence on the specific reaction kinetics should be considered. Furthermore, what role does lowering of the temperature play? In order to answer these questions further experimentation is needed.
Acknowledgement Thanks are due to M. Orban who focused our interest on the BR reaction and to I. Wilms for technical assistance. References
[2] A. Zaikin and A.M. Zhabotinskii, Nature 225 ( 1970) 535. {3] J. Ross, SC. Miiller and C. Vidal, Science 240 (1988 ) 460. [4] M. Orbin, J. Am. Chem. Sot. 102 (1980) 431 I. [ 51 P. de Keppcr, LR. Epstein, K Kustin and M. Orb&n,J. Phys. Chem. 86 (1982) 170. [6] WC. Bray, J.Atn. Chem. Soc.43 (1921) 1262. [7] T.S. Brings and W.C. Rauscher, J. Chem. Ed. 50 (1973) 496. [8] P.G. Bowers and R.M. Noyes. in: Oscillationsand traveling waves in chemical systems, eds. RJ. Field and M. Burger ( Wiley-Interseience, New York, 1985 ) p. 473. [9] M. Orban, J. Am. Chem. Sot. 108 ( 1986) 6893. [ 101 M. Orb&n and LR. Epstein, J. Am. Chem. Sot. 109 ( 1987) 101. [ 111J.H. Jensen, J. Am. Chem. Sot. 105 (1983) 2639. [ 121 SD. Furrow, in: Gscillations and traveling waves in chemical systems, eds. R.J. Field and M. Burger ( Wiley-Interscience, New York, 1985) p. 171, and references therein. [ 131 SC. Milller, Th. Plesser and B. Hess, Physica D 24 (1987) 71. [ 141 J.P. Keener and J.J. Tyson, Physica D 21 (1986) 307. [ 151 Zs. Nagy-Ungvarai, S.C. MiIller and B. Hess in: Spatial inhomogeneities and transient behaviour in chemical kinetics, eds. G. Nicolis and P. Gray (Manchester Univ. Press, Manchester), in press. [ 161 P. Foerster, S.C. Miiller and B. Hess, Science 241 (1988) 685.
[ I ] A. Hanna, A. Saul and K. Showalter, J. Am. Chem. Sot. 104 (1982) 3838.
.
437