Chemical wave

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Chemical waves in the Belousov-Zhabotinsky reaction . The concentration waves appear in a thin layer of the reaction mixture. A wave front is marked in yellow.

Chemical waves are a phenomenon of non-equilibrium thermodynamics (or chemistry and biology ) and a special case of dissipative structures . In a medium (e.g. a reaction mixture or a colony of cells ) changes in concentration occur that move over time and space, which are generated and maintained by a self-reinforcing or positively fed back reaction in the medium. The energy for maintenance does not come from outside, as with classic waves (e.g. sound or electromagnetic waves), but from the medium itself (self-excited oscillations). Well-known examples of this are concentration waves in oscillating chemical reactions , such as the Belousov-Zhabotinsky reaction, and the propagation of excitation in the heart muscle .

In sub-areas of physical chemistry and theoretical biology , the abbreviation autowave is used and applied to other examples of structure formation in active media. The German attempt to translate Autowelle is unusual. Autowave was chosen in analogy to the English auto-oscillations , i.e. self-excited oscillations.

Physical description

Chemical waves occur in systems that are typically characterized by a non-linear, (positive) feedback reaction system with spatial coupling through a transport process. In many cases the transport process is normal diffusion . Such a system can be described mathematically by a reaction diffusion equation. Without the non-linearity and feedback, the system would strive towards a state of equilibrium without pattern formation. Without the spatial coupling, no spatial phenomena such as wave propagation would be possible and a maximum of temporal oscillations can be observed (e.g. when the reaction mixture of an oscillating reaction is constantly stirred). For the occurrence of chemical waves it is also necessary that the system is far from thermodynamic equilibrium . This means in particular that it contains energy that can be used for structure formation. This can be understood by considering entropy : Ordered structures, such as waves, lead to a local lowering of entropy. According to the 2nd law of thermodynamics , such a decrease in entropy is only possible if energy is used for it. In the case described here, this energy comes from the non-reversible approach of the system to the steady state of equilibrium (e.g. when non-reversible chemical reactions take place) at which energy is released. Typically, chemical waves in a closed system are therefore not stable and can only be observed for a certain period of time. The process ends when the system approaches an equilibrium state or when all of the reactants have been consumed. In an open system, based on a steady state , chemical waves are stable because energy is supplied from outside to maintain them (e.g. in the form of “fresh” reaction educts). Therefore the waves can be excited again and again and the system remains out of balance. In both cases, the energy for the structure formation comes from the medium itself.

Due to their self-reinforcing character, even small local disturbances, such as microscopic differences in concentration or temperature, for example heating the reaction mixture with a hot needle, are sufficient to trigger chemical waves. Therefore, there is often talk of the "spontaneous occurrence" of such structures. These disturbances act as excitation centers from which reaction fronts spread. In these, the reaction proceeds in a different phase than in the surrounding medium. For example, a first reaction step takes place at the beginning of the front, which leads to a color change. The products of this step react further later and are partially formed back again in the sense of an autocatalysis, which can lead to another color change. Different partial reactions therefore take place at different speeds at different points on the front.

The visibility of chemical waves is often due to local differences in the concentration of a colored component of the reaction mixture. Alternatively, indicators are added which react to the local concentrations with a color change.

Chemical waves are to be distinguished from other phenomena: B. purely temporal oscillations occur that do not represent a wave due to the lack of spatial propagation. Purely spatial, temporally stationary patterns, so-called Turing patterns, are also different. All of these phenomena are often summarized under the term dissipative structures, for the investigation of which Ilya Prigogine received the Nobel Prize in Chemistry in 1977 . Gerhard Ertl received the Nobel Prize for Chemistry in 2007, among other things, for studying chemical waves during the oxidation of carbon monoxide on platinum surfaces.


As a solution to a non-linear differential equation, chemical waves have some properties that distinguish them from common "linear waves" (e.g. water waves , light, and other electromagnetic waves ). They are similar in other properties:

  • Analogous to conventional waves, a wavelength , frequency and speed of propagation can usually be defined in these propagating patterns .
  • If two opposing chemical wave fronts meet, they often cancel each other out, while conventional waves superimpose one another undisturbed. The superposition principle does not apply, as the non-linear character of the descriptive differential equation shows.
  • For certain chemical waves, reflection and refraction phenomena have been observed, which differ in some points from analogous properties of linear waves.
  • Spiral waves , vortex waves or (in three-dimensional waves) also called scroll waves, are a special wave form.


Excerpts from a simulation of the Brusselsator model for chemical waves in two dimensions. Note the three time leaps between the different stages of the simulation (start, first waves are formed, propagation of the waves, waves + spiral waves everywhere)

Chemical waves can be observed in many systems:

  • non-homogenized (non-stirred) approaches of oscillating reactions, such as the Belousov-Zhabotinsky reaction or the oxidation of arsenic acid with iodate
  • solitonic waves are observed during the oxidation of carbon monoxide on platinum surfaces
  • biochemical transmission of impulses in the nervous system
  • Spread of the slime mold Dictyostelium discoideum
  • Excitation waves in the heart muscle
  • Models for pattern formation (e.g. color patterns on mussel shells) in biological organisms
  • A simple and often discussed theoretical example of an autocatalytic reaction system that shows wave propagation with a diffusion term is the so-called Brusselsator (see animation on the right).
  • Hantz reactions , a class of pattern-forming precipitation reactions in gels that implement a reaction diffusion system

There are some non-chemical processes that show a similar phenomenology and can be described by similar differential equations:

  • the "stadium wave" La ola (the fans are both pathogen and transmitter)
  • Traffic jams
  • many cellular automata exhibit wave phenomena corresponding to chemical waves, e.g. B. Conway's Game of Life or Wator

Individual evidence

  1. a b c Dilip Kondepudi, Prigogine : Modern Thermodynamics. From Heat Engines to Dissipative Structures. John Wiley & Sons, Chichester et al. 1998, ISBN 0-471-97393-9 .
  2. a b c A.M. Zhabotinsky , AN Zaikin: Autowave processes in a distributed chemical system . In: Journal of Theoretical Biology . 40, No. 1, July 1973, pp. 45-61. doi : 10.1016 / 0022-5193 (73) 90164-1 .
  3. a b c Jorge M. Davidenko, Arcady V. Pertsov, Remy Salomonsz, William Baxter, José Jalife: Stationary and drifting spiral waves of excitation in isolated cardiac muscle . In: Nature . 355, No. 6358, Jan. 23, 1992, pp. 349-351. doi : 10.1038 / 355349a0 .
  4. ^ Irving Robert Epstein, John Anthony Pojman: An Introduction to Nonlinear Chemical Dynamics. Oscillations, Waves, Patterns, and Chaos Oxford University Press , 1998, ISBN 0-19-509670-3
  5. AM Turing: The Chemical Basis of Morphogenesis . In: Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences . 237, No. 641, Aug. 14, 1952, pp. 37-72. doi : 10.1098 / rstb.1952.0012 .
  6. Mikhail Bushev: Synergetics: Chaos, Order, Self-Organization . World Scientific, 1994, ISBN 981-02-1286-0 , pp. 6 ( limited preview in Google Book search).
  7. a b c S. Jakubith, H. Rotermund, W. Engel, A. von Oertzen, G. Ertl: Spatiotemporal concentration patterns in a surface reaction: Propagating and standing waves, rotating spirals, and turbulence . In: Physical Review Letters . tape 65 , no. December 24 , 1990, pp. 3013-3016 , doi : 10.1103 / PhysRevLett.65.3013 .
  8. ^ Anatol M. Zhabotinsky, Matthew D. Eager, Irving R. Epstein: Refraction and reflection of chemical waves . In: Physical Review Letters . 71, No. 10, 1993, pp. 1526-1529. doi : 10.1103 / PhysRevLett.71.1526 .
  9. Joaquim Sainhas, Rui Dilao: Wave Optics in Reaction-Diffusion Systems . In: Physical Review Letters . 80, No. 23, August, pp. 5216-5219. doi : 10.1103 / PhysRevLett.80.5216 .
  10. Lingfa Yang, Irving R. Epstein: Chemical Wave Packet Propagation, Reflection, and spreading . In: Journal of Physical Chemistry A . 106, No. 47, 2002, pp. 11676-11682. doi : 10.1021 / jp0260907 .
  11. ^ Arthur T. Winfree: Spiral Waves of Chemical Activity . In: Science . 175, No. 4022, November 2, 1972, pp. 634-636. doi : 10.1126 / science.175.4022.634 .
  12. Adel Hanna, Alan Saul, Kenneth Showalter: Detailed studies of propagating fronts in the iodate oxidation of arsenous acid . In: Journal of the American Chemical Society . tape 104 , no. July 14 , 1982, p. 3838-3844 , doi : 10.1021 / ja00378a011 .
  13. M. Baer, ​​M. Eiswirth, H.-H. Rotermund, G. Ertl: Solitary-wave phenomena in an excitable surface reaction . In: Physical Review Letters . tape 69 , no. 6 , August 1992, p. 945-948 , doi : 10.1103 / PhysRevLett.69.945 .
  14. K. Tomchik, P. Devreotes: Adenosine 3 ', 5'-monophosphate waves in Dictyostelium discoideum: a demonstration by isotope dilution - fluorography . In: Science . tape 212 , no. 4493 , April 24, 1981, pp. 443-446 , doi : 10.1126 / science.6259734 .
  15. A. Gierer, H. Meinhardt: A theory of biological pattern formation . In: Biological Cybernetics . 12, No. 1, 1972, pp. 30-39. doi : 10.1007 / BF00289234 .
  16. Hans Meinhardt ; Przemyslaw Prusinkiewicz (Ed.): The algorithmic beauty of sea shells , Berlin, New York: Springer Verlag, 2003., ISBN 978-3-540-44010-9 (German edition: How snails throw themselves into shells ).
  17. ^ I. Farkas, D. Helbing, T. Vicsek: Social behavior: Mexican waves in an excitable medium . In: Nature . 419, No. 6903, September 12, 2002, pp. 131-132. doi : 10.1038 / 419131a .
  18. Takashi Nagatani: Density waves in traffic flow . In: Physical Review E . 61, No. 4, April 1, 2000, pp. 3564-3570. doi : 10.1103 / PhysRevE.61.3564 .
  19. ^ Jörg R Weimar: Simulation with cellular automata Berlin: Logos-Verlag, 2003., ISBN 3-89722-026-1 .