Belousov-Zhabotinsky oscillatory reaction"
Belousov & Zhabotinsky
Boris Belousov
Anatol Zhabotinsky
(1893-1970)
(1938-2008)
§  B. P. Belousov (1959). "Периодически действующая реакция и ее механизм"
[Periodically acting reaction and its mechanism]. Сборник рефератов по
радиационной медицине 147:145.
§  A. M. Zhabotinsky (1964). "Периодический процесс окисления малоновой кислоты
растворе" [Periodical process of oxidation of malonic acid solution]. Биофизика 9:
306–311.
Belousov-Zhabotinsky reaction
potassium bromate (KBrO3)
+cerium(IV) sulfate (Ce(SO4)2)
+malonic acid (HOOC-CH2-COOH)
+citric acid (C6H8O7)
in diluted sulfuric acid (H2SO4)
In a well stirring reactor (CSTR),
oscillations occur spontaneously
Oscillations of [Br-] and of the ratio [Ce4+]/[Ce3+]
Period ≈ 90 seconds
Belousov-Zhabotinsky reaction
potassium bromate (KBrO3)
+cerium(IV) sulfate (Ce(SO4)2)
+malonic acid (HOOC-CH2-COOH)
+citric acid (C6H8O7)
in diluted sulfuric acid (H2SO4)
Oscillations of [Br-] and of the ratio [Ce4+]/[Ce3+]
Period ≈ 90 seconds
https://www.youtube.com/watch?v=3OJCseEQg7Q
In a well stirring reactor (CSTR),
oscillations occur spontaneously
Belousov-Zhabotinsky reaction
potassium bromate (KBrO3)
+cerium(IV) sulfate (Ce(SO4)2)
+malonic acid (HOOC-CH2-COOH)
+citric acid (C6H8O7)
in diluted sulfuric acid (H2SO4)
In a well stirring reactor (CSTR),
oscillations occur spontaneously
Mechanism of the reaction
Belousov-Zhabotinsky reaction
Reaction scheme
(FKN mechanism)
§  Field RJ, Koros E, Noyes RM (1972) Oscillations in Chemical Systems. II, Journal of
the American Chemical Society 94:13
§  Noyes RM (1076) Oscillations in chemical systems. XII, J. Chem. Phys 64:15
§  Field RJ, Noyes RM (1974) Oscillations in chemical systems. IV., J. Chem. Phys 60:1
Belousov-Zhabotinsky reaction
Process A
Consumption of Br- when
[Br-] is high
Process B
Autcatalysis: HBrO2 activates its
own production (2 molecules
produced/1 molecule consumed)
Process C
Feedback loop
(regeneration
of Br-)
§  Field RJ, Koros E, Noyes RM (1972) Oscillations in Chemical Systems. II, Journal of
the American Chemical Society 94:13
§  Noyes RM (1076) Oscillations in chemical systems. XII, J. Chem. Phys 64:15
§  Field RJ, Noyes RM (1974) Oscillations in chemical systems. IV., J. Chem. Phys 60:1
Belousov-Zhabotinsky reaction
When the same
reaction is done in a
Petri dish, spatial
patterns (including
concentric and
spiral waves) occur
spontaneously.
https://www.youtube.com/watch?v=3JAqrRnKFHo
Brusselator
Brusselator
reactional
scheme
The Brusselator is an
hypothetical set of chemical
reactions which can produce
limit-cycle oscillations (Lefever
& Prigogine, 1968)
kinetic
equations
Prigogine (1917-2003),
Nobel Chemistry (1977)
limit-cycle
oscillations
This model is sometimes referred to as the
trimolecular model (indeed, the 3rd reaction
is trimolecular - which is a quite unrealistic
assumption). The name Brusselator was
coined by Tyson in 1973.
Oregonator
A 3-variable variant of the Brusselator was developed by Field and Noyes (1974) at the
University of Oregon. This model, named the Oregonator, is the simplest realistic model of
the chemical dynamics of the oscillatory BZ reaction. It is obtained by reduction of the
complex chemical mechanism of the BZ reaction suggested by Field, Korös and Noyes
(1974) and referred to as the FKN mechanism. The model contains both an autocatalytic step
and a delayed negative feedback loop. It is composed of 5 coupled reactions:"
Exercise
-  Write the kinetic equations for X, Y and Z (A and B are
supposed constant).
-  Write the jacobian matrix and identify the negative
feedback loop.
-  Simulate the system for the following parameter values:
A=0.06, B=0.02, k1=1.28, k2=2.4 106, k3=33.6, k4=2400,
k5=1, f=1, and the following initial condition: x0=y0=z0=1.
Use a method of integration for "stiff" systems and a time
span of at least 1000.
Spatial simulation
Computer simulation of the Belousov–Zhabotinsky
reaction occurring in a Petri dish
https://en.wikipedia.org/wiki/Belousov–Zhabotinsky_reaction