Belousov-Zhabotinsky reaction
From Scholarpedia
Anatol M. Zhabotinsky (2007), Scholarpedia, 2(9):1435.
doi:10.4249/scholarpedia.1435
revision #46966 [link to/cite this article]
Curator: Dr. Anatol M. Zhabotinsky, Brandeis University, Waltham, MA
The Belousov-Zhabotinsky (BZ) reaction is a family of oscillating chemical reactions. During
these reactions, transition-metal ions catalyze oxidation of various, usually organic, reductants by
bromic acid in acidic water solution. Most BZ reactions are homogeneous. The BZ reaction makes
it possible to observe development of complex patterns in time and space by naked eye on a very
convenient human time scale of dozens of seconds and space scale of several millimeters. The BZ
reaction can generate up to several thousand oscillatory cycles in a closed system, which permits
studying chemical waves and patterns without constant replenishment of reactants (Field and
Burger, 1985; Epstein and Showalter, 1996; Epstein and Pojman, 1998; Taylor, 2002).
Basics
Oscillations can arise in a macroscopic medium if the system is sufficiently far from the state of
thermodynamic equilibrium (Nicolis and Prigogine, 1977). Oscillating chemical reactions have
been known for about three hundred years, but these were mainly heterogeneous reactions. By the
beginning of the 20th century, two excellent examples of heterogeneous oscillating reactions had
been discovered: the so-called "iron nerve"- the periodic dissolution of an iron wire in nitric acid,
and the "mercury heart" - the oscillatory decomposition of hydrogen peroxide on the surface of
metallic mercury (Zhabotinsky, 1991). On the other hand, the principle of detailed balance forbids
oscillations in the vicinity of thermodynamic equilibrium (Nicolis and Prigogine, 1977). The latter
result made a very strong impression on the majority of chemists, who interpreted it as forbidding
oscillations in all homogeneous, closed chemical systems. Therefore, the unfortunate custom
prevailed until the mid-1960s to ascribe all concentration oscillations observed in chemical and
biochemical systems to some undetermined but important heterogeneous processes or simply to
technical errors (Zhabotinsky, 1991). This situation has changed after the discovery and study of the
BZ reaction.
Belousov has discovered the first reaction of this class
with the Ce3+/Ce4+ couple as catalyst and citric acid as
reductant. He observed that the color of the reaction
solution oscillated between colorless and yellow and
found that the frequency of oscillations increased with
rise of temperature (Belousov, 1959; 1985).
Zhabotinsky replaced citric acid with malonic acid
(MA) to create the most widely used version of the BZ
Figure 1: Oscillations of concentration of Ce4+ and
reaction (Zhabotinsky, 1964a). He has shown that the
phase-shifting caused by pulsed injections of Br- (a),
oscillations in the solution color were due to
Ag+ (b), and Ce4+ (c).
oscillations in concentration of Ce4+ (Fig. 1). He further
found that oxidation of Ce3+ by HBrO3 was an autocatalytic reaction and self-sustained oscillations
of Ce4+ concentration arose after accumulation of bromomalonic acid (BMA). He demonstrated that
Br- ion was an inhibitor of the autocatalytic oxidation of Ce3+. He suggested that the BZ reaction
consisted of two main parts: the autocatalytic oxidation of Ce3+ by HBrO3 and the reduction of Ce4+
by MA and its bromoderivatives, which were produced during the overall reaction. In his scheme,
1
the Ce4+ reduction is accompanied by the production of Br- from the bromoderivatives of MA. Br- is
a strong inhibitor of the autocatalytic oxidation of Ce3+ because of its rapid reaction with the
autocatalyst, which is presumably HBrO2 (Zhabotinsky, 1964a,b).
An oscillatory cycle can be qualitatively described in the following way. Suppose that a sufficiently
high Ce4+ concentration is present in the system. Then, Br- will be produced rapidly, and its
concentration will also be high. As a result, autocatalytic oxidation of Ce3+ is completely inhibited,
and the [Ce4+] decreases due to its reduction by MA and BMA. The Br- decreases along with that of
[Ce4+]. When [Ce4+] reaches its lower threshold, the bromide ion concentration drops abruptly. The
rapid autocatalytic oxidation starts and raises [Ce4+]. When [Ce4+] reaches its higher threshold [Br-]
increases sharply and inhibits the autocatalytic oxidation of Ce3+. The cycle then repeats. The reader
can check this description by tracing a limit cycle generated by the Oregonator model and shown in
Fig. #F3a. Phase resetting experiments (Fig. 1) validate this scheme (Vavilin et al., 1973). One can
see that pulse injections of Br- or Ce4+ during the rising of [Ce4+] produces an immediate switch to
the phase of the [Ce4+] decrease (Fig. #F1a, c). An injection of Ag+ , which removes Br- by forming
AgBr, switches the system from a declining to an increasing [Ce4+] phase (Fig. #F1b).
Vavilin and Zhabotinsky (1969) showed that HOBr was the
final product of the oxidation of Ce3+ to Ce4+ by HBrO3.
Vavilin put forward the simplest mechanism of the
autocatalytic oxidation of Ce3+ or ferroin by bromate and its
inhibition by bromide ion (Vavilin and Zaikin, 1971):
Addition of production of Br- during oxidation of BMA by
Ce4+ to this mechanism results in the core scheme of the BZ
reaction with cerium ions as catalyst and BMA as reductant
(Fig. 2).
Field, Koros and Noyes (1972) performed systematic
and detailed thermodynamic and kinetic analysis of the
basic quasi-elementary reactions involved in the BZ
reaction and suggested a detailed mechanism of the
reaction responsible for oscillations. This meticulous
paper stimulated numerous chemists to study the BZ
reaction. On the basis of the FKN mechanism, Field
and Noyes (1974) have developed a mathematical
model of the BZ reaction named Oregonator. The
variables of Oregonator are concentrations of HBrO2,
Br-, and Ce4+. The relevant scheme is an extension of
the scheme in Fig. 2. It includes additionally reaction
of HBrO3 with Br- that produces HBrO2, and
disproportionation of HBrO2. It replaces complexity of
production of Br- via the oxidation of MA and its
bromoderivatives by Ce4+ with a quasi-stoichoimetric
factor, which is the ratio of the rate of Br- production
2
Figure 2: A core scheme of the BZ reaction with Ce
and BMA.
Figure 3: Phase portraits of the two-variable Oregonator models,
which show nullclines and trajectories of relaxation limit cycles.
H is the higher [Ce4+] switching threshold, L is the lower one.
to that of Ce4+ consumption. Oregonator properly models oscillations and excitability in the BZ
reaction. Tyson (1977, 1979) reduced Oregonator to two two-variable versions with the fast
variable being [Br-] or [HBrO2], and the slow variable [Ce4+]. These versions are variants of the
generalized Rayleigh-Van-der-Pol equation. They give excellent presentation of thresholds and
switches in the phase plane. Figure 3 shows qualitative drawings of nullclines and relaxation limit
cycles for both models.
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 can be corrected by taking into account reversibility of
reactions of the catalyst with the reductant or oxidant (Rovinsky and Zhabotinsky, 1984; NagyUngvarai et al., 1989a,b; Zhabotinsky et al., 1993; Vanag et al., 2000). In particular, the correct
shape of the [Ce4+] oscillations shown in Fig. 1 has been obtained with the improved version of
Oregonator developed by Nagy-Ungvarai et al. (1989b).
The BZ reaction variants
The only irreplaceable initial reagent is the oxidant bromate. Ce and Mn ions can be used as the
catalysts as well as complex ions of Fe, Ru, Co, Cu, Cr, Ag, Ni, and Os; each usually with two or
more different ligands. A plethora of various reductants give rise to oscillations (Zhabotinsky,
1964b; Field and Burger, 1985).
The BZ dynamics in well-stirred systems
Closed systems
Oscillations have been found in large ellipsoidal domains in the space of initial reactant
concentrations: cerium, bromate, and MA or BMA. The long axes of the domain sections at
constant concentrations of total Ce are directed approximately along the diagonal of the bromateMA(BMA) concentration plane, where the values of projections of the end points differ about three
orders of magnitude. The difference in [Ce] is almost four orders of magnitude in the MA system
and about three orders in the BMA system. The period-1 oscillations were mostly observed in the
BZ reaction, while period-2 oscillations can arise during evolution of oscillations (Zhabotinsky,
1964b; Vavilin et al., 1967a, 1967b). Excitability (Ruoff, 1982) and bistability (Ruoff and Noyes,
1985) arise outside the oscillatory domain. Bistability requires continuous Br - production from a
source other than reactions of Ce4+.
Open systems
Stationary oscillations can continue indefinitely in a continuous-flow, stirred tank reactor (CSTR).
More complex regimes such as bursting (Vavilin et al., 1968) and chaotic (Schmitz et al., 1977)
oscillations have been found when the BZ reaction was run in CSTR. Later various modes of
complex periodic and chaotic BZ oscillations have been studied. The CSTR allows fine tuning of
parameters of a chemical oscillator that makes it possible to trace bifurcation sequences, which
connect such regimes (Epstein and Pojman, 1998).
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Chemical waves and patterns
Concentration waves can propagate in
reaction-diffusion
systems
with
oscillatory or excitatory local chemical
kinetics (Field and Burger, 1985;
Epstein and Pojman, 1998; Taylor,
2002). Using a thin layer of unstirred
solution with the ferroin-catalyzed BZ
reaction, Zaikin and Zhabotinsky
(1970) observed periodic propagation
of
concentric
chemical
waves
generated by point pacemakers, which
formed target patterns ( Fig. 4). These
trigger waves are composed of pulses
of excitation followed by refractory
zones (Field and Noyes, 1974).
Collision of such waves leads to
mutual annihilation due to the presence
of non-excitable refractory zones ( Fig.
#F4c, d) and ( Fig. #F4f, g).
Figure 4: Generation of concentric waves by pacemakers and entrainment by the fastest
pacemaker resulting in a single target pattern in the BZ reaction-diffusion system.
If such waves are broken the excitation fronts curl around their refractory tails forming spiral waves
(Fig. 5) (Zhabotinsky and Zaikin, 1971, 1973; Winfree, 1972).
Figure 5: Development of spiral waves after hydrodynamic
breaking of a concentric wave (Zhabotinsky and Zaikin, 1971).
Two-dimensional wave fronts can propagate in
thicker layers of solution. Breaking such fronts
results in formation of three-dimensional scroll
waves (Winfree, 1973). Concentric, spiral and scroll
waves 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 1,4cyclohexanedione as reductant leads to emergence
of negative dispersion of the wave speed. As a
result, multiple chemical waves group into packets
(Manz et al., 2000; Hamik et al., 2001). The BZ
reaction run in a microemulsion leads to emergence
of a plethora of new patterns. It generates Turing
and short-wave instabilities of the spatially uniform
steady state, and produces Turing structures,
standing waves, localized structures, waves
propagating towards their sources, and segmented
waves (Vanag and Epstein, 2001a, b; Mikhailov and
Showalter, 2006)
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