BZ History and Overview of
Chemical Oscillators at Brandeis
Irv Epstein
BZ boot camp 1

• Named for discoverer (Boris Belousov) and developer (Anatol Zhabotinsky)
• Bromination and oxidation of an organic substrate (e.g., citric acid, malonic acid) by bromate in acidic (usually sulfuric acid) solution in the presence of a metal ion catalyst (e.g., cerium, ferroin, Ru(bipy)
3
)
BZ boot camp 2

BZ boot camp 3

(as of 1991)
BZ boot camp 4

A + X  2X
X + Y  2Y
Y  P
• A = food, X = prey, Y = predator, P = dead
• With A fixed, gives periodic, antiphase oscillations of predator and prey for any set of rate constants
• Can be solved analytically
• Attractor is not a limit cycle, but a continuous set of orbits around a neutrally stable center (bad)
BZ boot camp 5

Do chemical oscillators violate thermodynamics?
• A serious question until the 1970’s
• A chemical oscillator is not a pendulum – it doesn’t pass through equilibrium
• Prigogine – irreversible thermodynamics – must be far from equilibrium
• In a closed system (beaker), oscillations must necessarily be transient
• Can maintain oscillations indefinitely in an open system (flow reactor, organism)
BZ boot camp 6

• Discovered by Belousov in the Soviet Union in
1951 accidentally while searching for a model of the Krebs cycle
• Unable to publish in refereed journals, B publishes 1-page abstract in 1958 conference proceedings, circulates recipe and manuscript to colleagues in Moscow
• In 1961, Zhabotinsky repeats experiments, goes on to develop mechanism, find chemical waves
BZ boot camp 7

• Zhabotinsky publishes papers in 1960’s in
Russian journals, but largely ignored
• In 1968, Zhabotinsky demonstrates reaction at Prague conference on biological and biochemical oscillators, catching the attention of Western scientists
• In 1971, Field, Koros and Noyes develop the FKN mechanism and F&N simplify it to the Oregonator model
BZ boot camp 8

• Can run for many (hundreds) of cycles in a closed system
• Reactants are cheap, easily obtainable (but not biocompatible)
• Convenient time scale (minutes)
• Oscillations easily monitored visually, spectrophotometrically, potentiometrically
• Can be controlled photochemically
• Rich variety of spatial and temporal phenomena
• Good mechanism/model (FKN/Oregonator)
BZ boot camp 9

Chemical Oscillators at Brandeis
• 1970’s – experiments with undergrads on perturbed and modified BZ reactions (Jacobs,
Kaner, Heilweil)
• 1980’s – first systematically designed chemical oscillators (Kustin, De Kepper, Orban), mechanistic studies
• 1990’s – increasing focus on spatiotemporal behavior (Lengyel), interaction with neuroscientists (Marder), Zhabotinsky arrives
• 2000’s – patterns in microemulsions (Vanag), coupled oscillators via microfluidics (Fraden)
BZ boot camp 10

BZ boot camp 11

M. F. Crowley and I. R. Epstein, "Experimental and Theoretical Studies of a Coupled Chemical Oscillator: Phase Death, Multistability and In- and
Out-of-Phase Entrainment," J. Phys. Chem. 93, 2496-2502 (1989)
12

I.
X
Hexagonal closed packing 2D arrays
0
II.
160
80
80
120
100
80
60
40
20
60
165 240
85
7
6
5
7
6 5
7
6
75
5
7
6 5
7
6
70
BZ boot camp 13
80 time
90 time (min)
100 110
drop number
2
3
4
120

dimer
100 m m tetrahedron time 70 min
BZ boot camp 14

BZ boot camp 15

Beyond the BZ –
Taxonomy of chemical oscillators
BZ boot camp 16

• Chlorite-iodide-malonic acid (chlorine dioxideiodine-malonic acid)
• Batch oscillator, discovered at Brandeis (IRE, De
Kepper, Orban) in 1982
• Used in first successful experiments on Turing patterns (Castets, De Kepper, 1990)
• Key is use of gel, starch indicator to get separation of effective diffusion coefficients
BZ boot camp 17

• Limitations of aqueous solution – convection, no chemomechanics, all D’s nearly equal, can’t make a flow reactor
• Instead use surfaces, membranes, beads, microemulsions, droplet arrays, gels
BZ boot camp 18