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
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