Professor Zhabotinsky has prepared a very nice historical overview of the Belousov-Zhabotinsky reaction. It is meticulously done and treats the major contributors fairly. I have added a couple of historical citations.
In many places modern citations exist that would be informative to a reader interested in more than the BZ history or would add an informative dimension to the article. I have suggested a couple of such references.
However, in my opinion, this article suffers from not being as informative to a reader as it might be. Furthermore, some sections are not readily understood by me, are awkward to read, and in a few cases so obscure as to appear to be at least partially incorrect.
Thus I have attempted to polish the prose of the entire article. I believe that Professor Zhabotinsky's approach to the article is carefully preserved; the polished version is intended to follow his organization and tone as closely as possible. I believe only the technical presentation has been affected.
The polished version is below. The changes are so extensive that it did not seem reasonable to make them directly to the original version, which I have not touched. If Professor Zhabotinsky agrees with these changes, then I will be willing to help enter them into "Scholarpedia". It could well be useful for Anatol and I to enter into some discussion.
Finally, it seems to me that an article on the BZ reaction should have some kind of exhibition of the oscillations.
A Belousov-Zhabotinsky (BZ) reaction is a member of a group of chemical reactions occurring far-from-thermodynamic equilibrium and during which the concentrations of various intermediate and catalyst species may oscillate in time and space. The generic overall chemical reaction, whose negative ΔG drives the observed complex behavior in intermediate concentrations, is the metal-ion catalyzed oxidation by bromate ion (BrO3−) of various, usually organic, reductants in a strongly acidic (~ 1 M) aqueous medium. The BZ reactions are homogeneous in that their basic dynamical behavior is determined entirely by chemical reactions occurring in solution; super-saturation, surface, or precipitation phenomena are not critical to the appearance of oscillation. Each oscillation consumes only a very small fraction of the major driving reactants, BrO3− and reductant, thus preserving the initial far-from-equilibrium nature of the reaction through many cycles. The reaction is normally run in a closed batch system homogeneously distributed in space, with or without stirring. Oscillations occur in a well-mixed system, while spatial concentration patterns in catalyst and intermediate concentrations may develop in a distributed, initially spatially homogeneous, unstirred system. Oscillations and complex pattern formation may be observed by the naked eye on a convenient time scale of dozens of seconds and a spatial scale of a few millimeters. (Field and Burger, 1985; Epstein and Showalter, 1996, Epstein and Pojman, 1998; Taylor, 2002).
B. P. Belousov (1959, 1985) discovered the first member of the BZ class of oscillating reactions using the Ce4+/Ce3+ redox-couple as the catalyst and with citric acid as the reductant. He observed the color of the reaction solution to oscillate between colorless (Ce3+) and yellow (Ce4+), and the frequency of oscillation to increase with temperature. A. M. Zhabotinsky (1964a) replaced the citric acid with malonic acid (MA; CH2(COOH)2) to create a particularly well-behaved system that is now the most widely used BZ reaction. The ferriin/ferroin (Fe(phen)33+/Fe(phen)32+) redox couple is often used as the metal-ion catalyst in systems containing MA as the reductant.
Zhabotinsky (1964a,b) also showed that the oxidation of cerous ion (Ce3+) by BrO3− is autocatalytic, and that self-sustained BZ oscillations may occur only after accumulation of bromomalonic acid (BrMA; BrCH(COOH)2). He further demonstrated that bromide ion (Br−) is an inhibitor of the autocatalytic oxidation of Ce3+ by BrO3− and suggested that the BZ reaction consists of two main parts: the autocatalytic oxidation of Ce3+ by BrO3− and the reduction of Ce+4 by MA and its bromoderivatives, e.g., BrMA. In this scheme, the Ce4+ reduction is accompanied by the production of Br− from the MA-bromoderivatives. Bromide ion is a strong inhibitor of the autocatalytic Ce3+ oxidation because of its rapid reaction with the autocatalyst, presumably bromous acid (HBrO2).
A BZ oscillation cycle can be qualitatively described in the following way. Suppose the system starts with a relatively high concentration of Br− (~10−5 - 10−4 M) with the cerium ion catalyst (~10−4 M) essentially entirely in the Ce3+ form. The relatively high [Br−] at this point suppresses oxidation of Ce3+ to Ce4+. However, [Br−] must slowly decline via the reaction of Br− with BrO3− (~0 .1-0.5 M). Eventually [Br−] falls to a point such that it can no longer suppress the autocatalytic oxidation of Ce3+ to Ce4+, and a large fraction of the Ce3+ is oxidized to Ce4+. The [Br−] is simultaneously very rapidly driven to very low values (~ 10−7 M) by its reaction with the autocatalytic species, HBrO2.
However, after a delay while Ce4+ and perhaps various partially reduced bromine species, e.g., HOBr accumulate, sufficient Br− is produced by reactions of these species, especially Ce4+ with BrMA, to again inhibit the autocatalytic oxidation of Ce3+ to Ce4+. The [Br−] rises rapidly as Ce4+ is reduced back to Ce3+ by its reactions with MA (~0.1 - 0.5 M), BrMA and perhaps other brominated derivatives of MA. It is believed that this regenerated Br− comes mostly from BrMA and perhaps HOBr.
When the Ce4+ is essentially all reduced back to Ce3+, still in the presence of a relatively high [Br−], the cycle is complete. The next pulse occurs when [Br−] again falls below the concentration needed to suppress the autocatalytic oxidation of Ce3+ to Ce4+, and et cetera. This process occurs as long as the concentrations of BrO3− and MA remain high enough to maintain the necessary driving force, i.e., distance from chemical equilibrium.
Phase resetting experiments (Fig. 1) validate this scheme (Vavilin et al., 1973). One can see that pulsed injections of Br− or Ce4+ during a period of rising Ce4+ produces an immediate switch to the phase of Ce4+ decrease (Fig. 1a,c). An injection of silver ion (Ag+), which removes Br− by binding it into AgBr, switches the system from a declining to an increasing Ce4+ phase (Fig. 1b).
Vavilin and Zhabotinsky (1969) showed that HOBr is the final product of the oxidation of Ce3+ to Ce4+ by BrO3−. This observation suggested an important role for HBrO2 in this reaction (Vavilin and Zhabotinsky, 1969). Vavilin and Zaikin (1971) put forward the simplest mechanism for the autocatalytic oxidation of Ce3+, ferroin (Fe(phen)32+), etc. by BrO3− and its inhibition by Br−.
HBrO2 + HBrO3 → 2BrO2∙ + H2O (1)
2H+ + 2BrO2∙ + 2Fe(phen)32+ → 2Fe(phen)33+ + 2HBrO2 (2)
HBrO2 + H+ + Br− → 2 HOBr (3)
Adding to this mechanism the production of Br− during the reduction of Ce4+ results in a qualitative core scheme for the occurrence of oscillations in the BZ reaction.
Field, Koros and Noyes (FKN) (1972) presented a detailed and systematic mechanism for the BZ oscillations including the reactions discussed above as well as the additional reactions below that are necessary for oscillation to occur.
2H+ + BrO3− + Br− → HBrO2 + HOBr (4)
HBrO2 + HBrO2 → HOBr + BrO3− + H+ (5)
They also presented a detailed thermodynamic and kinetic analysis of the important quasi-elementary reactions, the reversibility of several of which must be considered. Edelson et al. (1975) showed the FKN mechanism reproduces in numerical simulation the major features of the BZ reaction with cerium catalyst and MA as reductant. The appearance of the FKN mechanism stimulated a great deal of study of the BZ reaction.
Field and Noyes (1974) developed (using basic approximations of chemical kinetics, especially the rate-determining step) a simple skeleton reduction of the FKN mechanism that retains its basic dynamic structure. This model is referred to as the Oregonator in recognition of its place of origin. The Oregonator variables are HBrO2, Br−, and Ce4+, and its structure is an extension of the scheme in Fig. 2 with the addition of reactions (4) and (5). It represents the mechanistic complexity of Br−-regeneration via the oxidation of MA and BrMA by Ce4+ by a simple stoichiometry including an expendable stoichiometric factor (f)defining the ratio of Br− ions produced per Ce4+ ion consumed.
The simple Oregonator properly models oscillations and excitability in the BZ reaction. Tyson (1977, 1979) reduced the Oregonator to two-variable systems with a fast (and thus subject to the steady-state approximation) variable being either Br− or HBrO2 coupled to the slow variable Ce4+. These systems are variants of the generalized Rayleigh-Van-der-Pol equation. They give an excellent interpretation of the BZ oscillations in terms of thresholds and switches in the Ce4+ vs. HBrO2 or Br− phase-plane. Figure 3 shows qualitative nullclines and relaxation limit cycles for each case.
However the original Oregonator is not a quantitative model of the BZ reaction. The total concentration of metal-ion catalyst is not incorporated into its parameters, it poorly reproduces the shape of the oscillations, and it does not reproduce the observed oscillatory domains in its parameter space. These deficiencies may be relieved some by taking into account reversibility of the reactions of the catalyst with the oxidant and reductant (Rovinsky and Zhabotinsky, 1984; Nagy-Ungvarai et al., 1989; Zhabotinsky et al., 1993; Vanag et al., 2000).
BZ reaction variants
The only irreplaceable BZ reagent is the oxidant, BrO3−. Cerium and Mn ions can be used as the catalyst, as well as complex ions of Fe, Ru, Co, Cr, Ag, Ni, and Os, each usually with two or more different ligands. A plethora of reductants may be used. (Zhabotinsky, 1964b; Field and Burger, 1985).
The first theoretical attempts to understand liquid-phase oscillating chemical reactions started with simple homogeneous chemical reactions. Hirniak (1910) proposed that cyclic reactions of the type A ⇄ B ⇄ C ⇄ A might exhibit oscillation. However, microscopic reversibility (Ki = kif /kir) and thermodynamics (ΔGo (cycle) = 0) put strong constraints on possible rate constant values, in fact excluding values that might lead to oscillation (Bak, 1963). It is known that the final approach to chemical equilibrium must be monotonic (Nicolis and Prigogine, 1977). These theoretical ideas made a strong impression on chemists, many of whom thus assumed that homogeneous (single-phase) oscillating chemical reactions were not possible.
Furthermore, many early oscillating chemical reactions involved metal-surfaces and gas evolution, e.g., dissolution of metals in acid (Ostwald, 1899). Upon the discovery by Bray (1921) of the first apparently homogeneous liquid-phase oscillating reaction, the iodate ion (IO3−)-catalyzed decomposition of hydrogen peroxide, efforts commenced to show that the observed oscillations in [I2] and intermittent release of O2 result from gas supersaturation, heterogeneous particles, or technical errors. Indeed, up until the mid-1960s, all chemical oscillators (including the BZ reaction) were ascribed to heterogeneous effects by many people. However, the experimental robustness of the BZ reaction coupled with the conceptual basis for the BZ oscillations offered by the FKN mechanism quieted doubters by the mid-1970s. Zhabotinsky (1991) experimentally demonstrated the homogeneity of the BZ oscillations by the lack of significant effect on them of variation of container surface type and surface/volume ratio.
Strong stirring effects noted in the BZ reaction and other homogeneous chemical oscillators suggest that inhomogeneities due to imperfect mixing do occur in oscillating chemical reactions (Epstein, 1995).
BZ reaction dynamics in well-stirred systems
BZ oscillations are found in large elliptical domains in the space of initial reactant concentrations: cerium ion, BrO3−, MA(BrMA). The long axes of the domain at constant [cerium ion] are directed approximately along the diagonal of the BrO3−-MA(BrMA) concentration plane, where the projections of the end points differ by about three orders of magnitude. The difference in [cerium ion] is almost four orders of magnitude in the MA system and about three in the BrMA system. Period-1 oscillations are normally observed in the BZ reaction; however, period-2 oscillations sometimes occur during evolution of the oscillations as the reaction proceeds (Zhabotinsky, 1964b, Vavilin et al., 1967a, 1967b). Excitability (Ruoff, 1982) and bistability (Ruoff and Noyes, 1985) appear outside of the oscillatory domain. Bistability requires continuous Br− production from a source other than reactions of Ce4+.
The BZ reaction may be run in a continuous-flow, stirred tank reactor (CSTR) in which true steady states may be established, new phenomena observed, and bifurcation lines among the various observed behaviors tracked. Bursting (Vavilin et al., 1968) and chaotic oscillations (Schmitz et al., 1977) have been observed. Various modes of complex periodic and dynamic behavior have been investigated (Epstein and Pojman, 1998).
Chemical waves and patterns
Zaikin and Zhabotinsky (1970) observed periodic propagation of concentric chemical concentration waves that are generated by the coupling of reaction and diffusion of intermediate species and surround centrally located pacemakers. These experiments used the ferroin-catalyzed BZ reaction run in a thin layer of reagent in contact with the atmosphere. These patterns are composed of trigger wave fronts consisting of a pulse of activation (oxidation) followed by a high-[Br−] refractory zone temporarily resistant to the propagation of another oxidation pulse. (Field and Noyes, 1972) Head-on collision of waves leads to their annihilation between the two following refractory zones. The velocity of wave propagation (5-10 mm/min) is roughly proportional (Field and Noyes, 1974) to (Dbromous acid [H+] [BrO3−])1/2.
If such waves are broken by physical disruption of the liquid medium, the excitation fronts curl around their refractory tails to form spiral patterns (Fig. 5) (Zhabotinsky and Zaikin, 1970, 1973; Winfree, 1972).
Two and even three dimensional patterns may form in thicker layers of BZ reagent. Breaking of such wave fronts may result in formation of three-dimensional scroll waves (Winfree, 1973). Concentric, spiral and scroll waves have attracted much attention (Field and Burger, 1985; Epstein and Pojman, 1998; Taylor, 2002; Mikhailov and Showalter, 2006).
Many other spatio-temporal patterns have been discovered in various BZ reaction-diffusion systems. Use of 1,4-cyclohexanedione as reductant may result in the appearance of an anomalous dispersion relationship in which multiple waves group into packets and sometimes merge (Manz et al., 2000; Hamik et al., 2001). The BZ reaction run in a microemulsion leads to a plethora of new pattern types, e.g., generating Turing and short-wave instabilities of the spatially uniform steady state, as well as Turing structures, standing waves, localized structures, waves propagating toward their source, and segmented waves (Vanag and Epstein, 2001a, b; Mikhailov and Showalter, 2006).
Bak, T. Contributions to the Theory of Chemical Kinetics, Benjamin, New York, 1963.
Edelson, D., Field, R. J., and Noyes, R. M. Mechanistic details of the Belousov-Zhabotinsky oscillations, Int. J. Chem. Kin. 7, 417-32 (1975).
Epstein, I. R. The consequences of imperfect mixing in autocatalytic chemical and biological systems, Nature, 374(6520) 321-7 (1995).
Field, R. J. and Noyes, R. M. Explanation of spatial band propagation in the Belousov Reaction, 237(5355), 390-392 (1972).
Field, R.J. and Noyes, R. M. Oscillations in chemical systems. Part 5. Quantitative explanation of band propagation in the Belousov-Zhabotinsky reaction, J. Amer. Chem. Soc. 96, 2001 - 2006 (1974)
Nicolis, G. and Prigogine, I. Self-Organization in Nonequilibrium Systems, Wiley, New York, 1977. Ostwald, W. Periodisch veraenderliche Reaktionsgeschwindigkeiten, Phys. Zeitsch. 8, 87-88 (1899).
User 2: BZ reactions and nanotechnology
Two recent articles describe the development of nanostructures in very high temperature BZ reactions.
1. J. A. Sekhar, H. P. Li and G.K. Dey, Decay-dissipative Belousov–Zhabotinsky nanobands and nanoparticles in NiAl, Acta Materialia, Volume 58, Issue 3, pp. 1056-1073, 2010
2. H. P. Li and J. A. Sekhar, Recognition of Belousov-Zhabotinsky-Type Oscillations in Autosynthetic Micropyretic Reactions, International Journal of Self-Propagating High-Temperature Synthesis, Volume 18, No. 4, pp. 219–234, 2009.
Micron size particle formation was previously described in the article "Frozen Chemical Waves in the Belousov Zhabotinsky Reaction", J. Phys. Chem., 99, pp. 980-983, 1995 by J. M. Köehler & S. C. Müeller.