Hofstra Horizons Research

The BZ Reaction: An Oscillating Chemical System as a Model for Pattern Formation

Sabrina Sobel
Professor of Chemistry; Chair, Chemistry Department

Hand holding petri dish and swab

Discovery of a Chemical Oscillator

n the 1950s Boris P. Belousov, a Russian biochemist, was studying the chemistry of the citric acid cycle. The citric acid cycle is the way that our bodies obtain energy from the sugars and carbohydrates we eat. He mixed potassium bromate (KBrO3), cerium(IV) sulfate (Ce(SO4)2), malonic acid (HO2CCH2CO2H or MA) and citric acid in dilute sulfuric acid (H2SO4), and observed something really unexpected: the reaction jumped from yellow to clear, back and forth, as if it could not make up its mind which state to be in. In this case the catalyst indicator was cerium; cerium(IV) is clear, and cerium(III) is pale yellow. Well, the scientific community was not ready for what Dr. Belousov had discovered. The classical view of chemical reactions is that when the reaction is favorable, it proceeds to completion smoothly without jumping back and forth between two very different states. Prominent journals refused to publish Dr. Belousov’s work, and he was forced to publish in a more obscure journal, where his remarkable results were largely ignored.1

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Figure 1
Belousov (left) and Zhabotinsky (right).

In the 1960s Anatoli Zhabotinsky decided to try to reproduce Dr. Belousov’s work, and found that the reaction did oscillate as Belousov had reported.2 As is required in science, a new result is seen as more credible if it can be reproduced independently. Dr. Zhabotinsky has made a career of studying oscillating chemical reactions, finding many combinations of chemicals that form oscillating reactions. An oscillating chemical reaction is something that defies normal expectations, jumping between two states until the reactants are exhausted. They are often used in chemical demonstrations with color indicators/catalysts because they are so dramatic. A classic one is the iodine clock reaction in which the concentration of iodide oscillates between a low and a high value. Each time the concentration of iodide increases, some of it interacts with starch to make a deep blue starchiodide complex, thus the stirred solution flashes from clear to blue, then fades back to clear only to repeat the cycle again. The BZ reaction, named after B.P. Belousov and A. Zhabotinsky (Figure 1), can utilize ferroin/ferriin as a catalyst/indicator, oscillating between reddish-orange (ferroin) and pale blue (ferriin) states.

Description of the Chemistry

In 1972 Field, Köró´s and Noyes published a kinetic model that essentially captures the features of the BZ reaction,3 elucidating the necessary chemical components and their roles in creating the oscillating behavior. An oscillating chemical reaction must have a fast, auto-catalytic set of reactions that use up one component (Br) while oxidizing the indicator/catalyst (Processes A and B), followed by a slow, steady recovery step (Process C) that reduces the catalyst and regenerates the necessary reactant (Br) for the fast, auto-catalytic process to start again (Figures 2 and 3). It is sort of like the tortoise and the hare, but with the hare running in bursts, stopping periodically until the tortoise gets close, then sprinting ahead again.

Process A: Removal of Br
BrO3 + Br+ 2H+ → HBrO2 + HOBr (eqn. 1)
HBrO2 + Br + H+ → 2 HOBr (eqn. 2)
HOBr + Br + H+ ←→ Br2 + H2O (eqn. 3)
At a critical Br- concentration (~ 3.5 x 10-6[BrO3 ]), control switches to

Process B: Autocatalysis of HBrO2 and oxidation of Ce+3, or Fe+2 (as ferroin) or Mn+2 detected by color change of ferroin (red) to ferriin (blue)
BrO3 + HBrO2 + H+ → 2BrO2+ H2O (eqn. 4)
BrO2 + M+2 + H+ → HBrO2 + M+3 (eqn. 5)
2HBrO2 → BrO3 + HOBr + H+ (eqn. 6)

Then
Process C: Resetting the clock (reduction of M+3 and production of Br)
2M+3 + 2BrMA → Br + 2M+2 + other products (eqn. 7)

Bromination of MA to form BrMA
(occurs spontaneously, but not a ratelimiting reaction)

MA + Br2 → BrMA + Br + H+ (eqn. 8)

How Does It Get Started?

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Figure 2
The BZ reaction cycle with ferroin catalyst.

In the Hastings-Sobel group, we have studied the initiation phase of the ferroin-catalyzed BZ reaction, searching for clues as to how the oscillations start. When the solution is prepared with added bromide and continuously stirred, it starts out reddish-orange, then transitions into oscillations between blue and red every 40 seconds, which can last for up to an hour. This is in contrast to the Field-Köró´s-Noyes model, which predicts a blue initiation. By monitoring the concentration of bromide [Br] using a bromide ionselective electrode during the stirred reaction, we observed an interesting process – the concentration of bromide decreases, increases, then decreases to a threshold value that leads to oscillations (Figure 4). The solution stays red because Process B is never triggered. Such behavior is unexpected; according to Process A, bromide is only consumed, not produced. What we have concluded is that the bromination of malonic acid (eqn. 8) must occur very quickly during the initiation phase, thus temporarily raising the concentration of bromide for a short time. This makes sense based on two other factors: (1) bromomalonic acid (BrMA) is necessary for Process C and must be produced in situ, and (2) there is a strong smell of bromine (Br2) shortly after the reactants are mixed. We have modified the Field-Köró´s- Noyes model to account for the red initiation phase.4

Organized Patterns Out of Oscillating Events

One of the most aesthetically pleasing results of an oscillating chemical reaction is the capacity to make patterns when left unstirred in a Petri dish or other flat container (Figure 5). The ferroin-catalyzed BZ reaction starts out uniformly reddish-orange, then blue targets “spontaneously” appear in the solution over time. Waves of the blue state radiate out from the target center while the center recovers to the reddish-orange state. The center keeps oscillating over time, sending out new waves of blue color. We have determined that target distribution in the Petri dish is statistically clustered,5 and that target initiation can be explained by local, random, microscopic fluctuations in the concentrations of reactants.6 The capacity of an oscillating reaction to form patterns has been utilized by nature to produce patterns with which we are familiar: cheetahs and zebras.7 By sending out signaling molecules in an oscillating pattern over time, stripes are formed in the skin. Such processes are usually described as reaction-diffusion systems.

Excitability in the BZ Reaction and the Heart

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Figure 3
Simulation of one wave in the BZ reaction using a modified Field-Köró´s-Noyes (Oregonator) model by our group.

The ferroin-catalyzed BZ reaction can be prepared such that it is in an “excitable” state, essentially in the reddish-orange steady state, an aspect of the reaction that we have explored extensively.8 By reducing the initial concentrations of bromate, bromide and malonic acid, the reaction can be tuned to keep the concentration of bromide over time from falling below the threshold value that leads to oscillations. The reaction will not spontaneously oscillate, but can be perturbed to produce one blue wave by addition of silver ions, which tie up bromide ions, thus reducing the concentration of bromide below the threshold value.9 The excitable BZ reaction is essentially ready to go and only needs a trigger to get it started. Repeated perturbations by addition of silver ions are necessary to keep generating waves of blue color. This is very similar to the control system that creates heartbeats. In the heart, there is a cluster of cells called the sinus node that initiates a fast pulse of contraction that triggers contractions in nearby cells, thus creating a wave of contraction throughout the heart coordinated for efficient pumping of the blood, like a group of people in a stadium at a ball game creating a “wave” across the stadium. Before a heartbeat, the heart muscle cells are essentially in the excitable steady state, ready to contract, only waiting for the trigger from the sinus node.

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Figure 4
Plot of changes of bromide concentration over time in the BZ reaction measured with a bromide ion selective electrode.

The contraction/relaxation system of the heart and the oscillations of the BZ reaction share characteristics: a fast trigger followed by a slower recovery. Therefore, studies of the factors that affect the BZ reaction can be translated into insight about factors that may affect the heart. Both the excitable and the oscillatory BZ reaction are important in understanding oscillations in the heart. The unstirred oscillating BZ reaction, with “spontaneous” appearances of targets, can be thought of as similar to the action of “rogue” heart cells that spontaneously start waves of contraction in sites other than the sinus node. These atypical events can seriously compromise the pumping ability of the heart because the cells do not contract in synchrony. Instead, there is an anomalous contraction wave traveling through the heart along the wrong trajectory, which also occurs at the wrong time. As a result, the heart cells involved in the anomalous wave do not have enough time to recover before the next signal from the sinus node. Such anomalous behavior can lead to tachycardia (fast heartbeats), and possibly evolve into fibrillation as well.10 The state of the heart cells may be correlated to the state of the BZ reaction medium; the boundary between oscillatory and excitable behavior may be important since “rogue” waves in the heart could be caused by heart cells that have crossed into the oscillatory mode from the excitable mode. Simulation movies have been produced by the Hastings group (arrhythmia.hofstra.edu) take a look!

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Figure 5
The unstirred BZ reaction; ferroin-catalyzed (left and center), and manganese-catalyzed with ferroin indicator (right). Both center and right pictures photographed on grid paper. Picture on the left is from http://www.meta-synthesis.com/webbook/24_complexity/complexity3.html.

The Rewards of Research

This research has been carried out by Dr. Hastings, a team of talented undergraduates and high school students, and me. The students have been co-authors on papers and have presented at regional and national professional symposia. Our undergraduates have won the Best Undergraduate Poster award at the regional meeting of the American Physical Society two years in a row. “Graduates” of our research program have gone on to become high school physics teachers and a professional engineer, and to pursue Ph.D. programs in physics, math and chemistry. Two of our high school students have placed well in the Intel competition, one finalist and one semifinalist. All these students have gained first-hand experience in an interdisciplinary research project. It has been a satisfying experience for me, giving students valuable research experience that helps them mature into professional scientists.


Endnotes

1 Belousov, B.P.(1958). Sbornick Referatov po Radiatsionni Meditsine (A periodic reaction and its mechanism). Medgiz: Moscow.

2 Zhabotinsky, A.M. (1964). Periodic processes of the oxidation of malonic acid in solution (study of the kinetics of Belousov’s reaction). Biofizika. 9, 306

3 Field, R.J., Köró´s, E., and Noyes, R.M. (1972). Oscillations in chemical systems. II. Thorough analysis of temporal oscillations in the bromate-cerium-malonic acid system. J. Am. Chem. Soc. 94, 8649-64.

4 Sobel, S.G., Hastings, H.M., and Field, R.J. (2006). Oxidation state of BZ reaction mixtures. J. Chem. Phys. 110(1), 5-7.

5 Hastings, H.M., Sobel, S.G., Lemus, A., et al. (2005). Spatiotemporal clustering and temporal order in the excitable BZ reaction. J. Chem. Phys. 123, 064502.

6 Hastings, H.M., Field, R.J., and Sobel, S.G. (2003). Microscopic fluctuations and pattern formation in a supercritical oscillatory chemical system. J. Chem. Phys. 119(6), 3291-6.

7 Camazine, S. (2003). Patterns in nature. Natural History 112(5), 34-41.

8 Peralta C., Frank, C., Zaharakis, A., et al. (2006).Controlled excitations of the Belousov-Zhabotinsky reaction: Experimental procedures. J. Chem. Phys. 110(44), 12145-9.

9 Showalter, K., and Noyes, R.M. (1976). Oscillations in chemical systems. 15. Deliberate generation of trigger waves of chemical reactivity. J. Chem. Phys. Soc. 98(12), 3730-1.

10 Fenton, F.H., Cherry, E.M., Evans, S.J., and Hastings, H.M. (2002). Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity. Chaos 12, 852-892.


Acknowledgments

This work was partially supported by the National Science Foundation Grants DBI-0096692, MRI-0320865, and CHE-0515691. One undergraduate student was partially supported by NIH Grant R15 HL072816-01 to H.M.H. We thank Richard J. (Dick) Field for helpful discussions and critiques and Hofstra University for generous support for a visit by Professor Field.

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