Formation of spontaneous patterns Belousov reaction. What is self-organization? Spiral Wave Tip Trajectory Control
The Belousov-Zhabotinsky self-oscillatory reaction is very widely known not only in the scientific world. She is known both by schoolchildren and students, and just inquisitive people. A glass of red-purple liquid suddenly turns bright blue, and then again red-purple. And blue again. And when the liquid is poured in a thin layer, waves of color change propagate in it. Complex patterns are formed, circles, spirals, vortices, or everything takes on a completely chaotic appearance.
This reaction has been known for over 40 years. It was opened in 1951 by Boris Pavlovich Belousov.
Anatoly Markovich Zhabotinsky made a decisive contribution to the study of this reaction, to the fact that this remarkable phenomenon has become a common scientific property. The reaction is named honorably with two initials: BZ-reaction (Belousov-Zhabotinsky).
Discovery of B.P. Belousov almost completed almost 150 years of searching for oscillatory regimes in chemical processes. Periodic processes in general are one of the foundations for constructing theories in a wide variety of industries. Periodicity - the regular repetition of something in time and (or) space convinces us of the cognizability of the world, of the causality of phenomena. In essence, periodicity is the basis of the worldview of determinism. Understanding its nature allows you to predict events, say, eclipses or the appearance of comets. And such predictions are the main proof of the power of science.
The history of the Belousov-Zhabotinsky reaction is a vivid illustration of the old riddle: what came first, the chicken or the egg? What comes first: a phenomenon that requires a theoretical explanation, or a theory that predicts the appearance of a previously unknown phenomenon? In fact, it is a "vicious circle". We notice and declare as a phenomenon only what we understand, for which there is already a theory. But to build a theory, there must be an "order" - the presence of an unexplained phenomenon.
Breaking this vicious circle requires enormous intellectual and moral efforts of the pioneer researcher. The inertia of "common sense" is the cause of many tragic destinies, the sad "tradition of posthumous glory", when remarkable discoveries turn out to be premature, not recognized during the lifetime of their authors.
Belousov's discovery in this series. It vividly demonstrates this difficulty in perceiving "obviousness", what is literally visible to the eye and, nevertheless, not seen by others.
HISTORY OF THE REACTION DISCOVERY
Old Moscow, the end of the last century. The family of a bank employee: father, Pavel Nikolaevich, and mother, Natalya Dmitrievna, raising six sons. The eldest, Alexander, aged 17, is already a revolutionary. Exciting plans: blow up, shoot, hide. He is imbued with Marx and studies him stubbornly.
Sasha Belousov, inspired by the idea of world justice, found an excellent audience in his brothers, involved everyone in revolutionary work, including 12-year-old Boris. And the revolutionary work, obviously, was connected with chemistry. Chemistry - the best science for overthrowing the existing system teaches how to make bombs. The laboratory was built right in the attic of a Moscow house on Malaya Polyanka. The brothers were truly passionate. Making bombs at 12 is a delight! And test them too! And so that my mother did not know!
In 1905, during the 1st Russian Revolution, Sasha Belousov, associated with the top of the Bolshevik faction, led a brigade of militants. When the revolution was crushed, Alexander managed to escape. He was arrested a year later, but managed to escape from Siberian exile.
Mothers soon suggested: either we will send everyone to Siberia, or go into exile. Naturally, she preferred Switzerland. We left for a Bolshevik colony, because my brother was a Bolshevik. Boris found himself surrounded by the Bolsheviks, where "in the difficult conditions of emigration" they prepared what they later arranged.
Alexander Pavlovich became an economist. During the war, he completed work on a book on economics while staying in Leningrad. And he died in the blockade, and his book perished.
In Zurich, Boris had to pay tuition. There was another opportunity to study for free, but without a diploma, with a certificate of the courses taken. No documentary evidence has been preserved, but, as I understand it, at that time his main hobby was still chemistry. When the World War began, he came to Russia to volunteer for the army. But they did not take it - there was not enough weight.
There was chemistry. Now they say that there were three great chemists in Russia: Lomonosov, Mendeleev and Ipatiev. Ipatiev, the creator of the theoretical foundations of industrial chemistry, in the 30th year, anticipating the arrest, managed to go abroad and settled in the United States. In America, works, symposiums, and so on are devoted to him. In Russia, he is almost unknown. Belousov went to work in the chemical laboratory of the Goujon metallurgical plant (in Soviet times, the Hammer and Sickle plant), ideologically led by Ipatiev. Entering Ipatiev's laboratory meant doing military chemistry. Boris Pavlovich improved his education there and became a real military chemist.
Even before the revolution, he developed ways to deal with toxic substances, thought about special compositions for gas masks. After the revolution, he became a military man, from the age of 23, on the recommendation of Academician P.P. Lazarev, he taught chemistry to the commanders of the Red Army at the Higher Military Chemical School of the Red Army, reads a course of lectures on general and special chemistry at the School of Improvement of the Command Staff of the Red Army, and in 1933 becomes a senior lecturer at the Military Chemical Academy named after K.E. Voroshilov. However, the main content of his life is scientific research. He is the author of many scientific works. But due to their specificity, not a single line of Belousov's works, even their summary, has ever been published anywhere. Everything went in the form of closed instructions, orders marked "top secret". In a secret review by Academician Alexander Nikolaevich Terenin, it is noted that: "... B.P. Belousov initiated a completely new direction in gas analysis, which consists in changing the color of film gels during the sorption of active gases by them. The task was to create specific and universal indicators for harmful gaseous compounds, with the detection of them in extremely low concentrations... This task was brilliantly accomplished ... a number of optical instruments were developed that allow automatic or semi-automatic qualitative analysis of air for harmful gases ... In this group of works, B.P. Belousov proved himself as a scientist who poses the problem in a new way and solves it in a completely original way.In addition to these studies, B.P. Belousov owns a number of equally original and interesting scientific works, which leave no doubt that he certainly deserves to be awarded the degree of Doctor of Chemical Sciences without defending a dissertation.
He was promoted to brigade commander, a high military rank for a chemist, equivalent to the rank of major general. During the period of mass repressions of 1937-38, many military personnel in the ranks of major and above were arrested and killed, many colleagues and friends of Belousov were killed. He was not arrested, perhaps because back in 1935 he left the army for a long-term leave, and after 1938 he retired?
Boris Pavlovich began to work at a secret medical institute, where they were mainly engaged in toxicology. At first he was the head of the laboratory. Then they realized that there was no university diploma, and they transferred him to the position of a senior laboratory assistant, without releasing the head of the laboratory from his duties. In many respects he remained a military man. Irritated by the new environment, complex relationships, with emotions, feelings, resentments. His character has always been difficult, and over the years it has become quite complex.
The director of the institute, however, understood who he was dealing with. Now this cannot be comprehended, but then all the main, and not very important, papers had Stalin's signature. Blue thick pencil. A letter was written to the same name stating that an honored person works in our secret institution, his salary is low, like that of a senior laboratory assistant, since he does not have a diploma of higher education, but in fact he is in charge of the laboratory. On this letter, Stalin wrote: "Pay, as the head of the laboratory, a doctor of sciences, while he is in office." Thick blue pencil. Enemies fell silent: Stalin himself orders to pay. This did not last long, however, Stalin soon died. During these years, the radiation problem, anti-radiation agents, became the main one. Belousov had remarkable discoveries in the field of anti-radiation drugs.
At this time, cyclic reactions were discovered in biochemistry: one substance turns into a second, a second into a third, a third into a fourth, then into a fifth, and the first is formed from it again. Boris Pavlovich thought that this was a wonderful thing and that it should be studied, that it would be good to make a chemical analogy of biochemical cycles.
This is where the "chemistry of childhood" begins. This is only a "live" chemist can immediately come up with. Recall that in 1905 he took Berthollet's salt, that its analogue is KBrO3: there is chlorine, and here is bromine. It is possible to arrange a reaction in which the starting component of the Krebs cycle, citric acid, will be oxidized by this analogue of Berthollet's salt. Bromine is colored so it will be visible when released during the reaction. It was luck.
To speed up the reaction, Boris Pavlovich added catalytic amounts of cerium salt to the solution. Cerium is an element of variable valence, it catalyzes oxidation, passing from the four to the trivalent state. In a solution, in rather concentrated sulfuric acid, at first a yellow color really appeared, but then for some reason it disappeared and suddenly appeared again, and then disappeared again ... Thus, an oscillatory chemical reaction in solution was discovered. (And the yellow color, as Zhabotinsky later showed, is not from bromine, but from cerium).
SIGNIFICANCE OF THE BELOUSSOV REACTION
Was B.P. Belousov the first to discover chemical oscillatory reactions? Nobel Prize winner I.Prigozhin considers the work of Boris Pavlovich a scientific feat of the twentieth century. To some authors, the popularity of BZ-reaction seems unfair, and the role of Belousov is exaggerated.
All cases of fluctuations in chemical reactions observed so far could be explained by spatial effects, for example, a temperature drop on the walls of the flask or diffusion limitations of reaction rates.
But the main obstacle was... knowledge of equilibrium thermodynamics. An educated person could not imagine macroscopic orderliness in the random thermal motion of a huge number of molecules, all the molecules now in one state, then in another! As if to recognize the existence of a perpetual motion machine. This cannot be. And indeed it cannot be. It cannot be near the equilibrium state, but only it was considered by the thermodynamics of those years. However, there are no restrictions on complex, including oscillatory, modes for non-equilibrium chemical systems, when the reactions have not yet been completed, and the concentrations of the reagents have not reached the equilibrium level. But this circumstance escaped the attention of chemists.
It is clear to everyone that thermodynamics is not just a branch of physics. The triumph of equilibrium thermodynamics, created by the giants Carnot, Mayer, Helmholtz, Boltzmann, Planck, Gibbs, Nernst, determined the worldview of several generations of researchers.
It took extreme intellectual effort to break out of the "iron fetters of complete knowledge" and explore the behavior of systems far from equilibrium in order to create a thermodynamics of non-equilibrium processes. This is the feat of life of Onsager and Prigogine. By this time, there was already a general proof of the possibility of oscillations in a homogeneous, homogeneous system, when spatial inhomogeneities are insignificant. In 1910, A. Lotka came up with a system of equations describing fluctuations in the concentrations of reagents in a complete mixing system, where autocatalysis is possible. In this first Lotka model, the oscillations were damped. Ten years later, he proposed a system with two successive autocatalytic reactions, and in this model the oscillations could already be undamped. This means that oscillations in a homogeneous solution are in principle possible. A situation typical for the life of new knowledge has developed: there is a strict Lotka-Volterra theory (fluctuations in homogeneous chemical systems are possible), and there is a general opinion that they are impossible, since they contradict the foundations of science. That is why the experimental, indisputable proof of the existence of oscillatory regimes in homogeneous solutions, in systems of complete mixing, has acquired such great importance. Here we should note the fundamental difference between the positions of physicists and chemists. One of the most striking achievements of physics and mathematics of the 20th century was the creation of the theory of oscillations. Great, universally recognized merits here belong to the Soviet physicists of the school of Academician L.I. Mandelstam. In the 28th year, Mandelstam's graduate student A.A. Andronov spoke at the congress of Russian physicists with a report "Poincaré limit cycles and the theory of self-oscillations". He did not doubt the possibility of chemical oscillatory reactions and was the initiator of a directed search for such reactions in the experiment.
In the early 1930s, fluctuations in luminescence in "cold flames" similar to the vibrational luminescence of phosphorus vapor were discovered at the Institute of Chemical Physics of the Academy of Sciences, which interested the remarkable physicist D.A. Frank-Kamenetsky. In 1939, he explained these fluctuations on the basis of Lotka's 2020 kinetic model. In 1941, in an article in the journal Advances in Chemistry, he specifically considered the possibility of oscillatory regimes in homogeneous chemical systems, although "cold flames", strictly speaking, cannot be attributed to homogeneous chemical reactions. The reasons are the same: temperature drops and spatial concentration gradients.
The mechanism of oscillations in this complex system, together with Frank-Kamenetsky, was taken up by a graduate of the Andronov school, I.E. Salnikov, and in 1947 he submitted a dissertation to the Institute of Chemical Physics, which was called "On the Theory of the Periodic Flow of Homogeneous Chemical Reactions." But the dissertation was rejected! Who was the most implacable guardian of unshakable truths, the most educated person in the audience? Unknown. The "inertia of previous knowledge" worked. The barrier of "common sense" of chemists was not overcome.
Salnikov successfully defended this dissertation the following year in Gorky at the Institute of Physics, headed by A.A. Andronov.
In 1951, General Belousov sent an article about the oscillatory reaction discovered by him to the Journal of General Chemistry. And he received an offensive negative review: "this cannot be." The article described an easily reproducible process. All reagents are readily available. But if you are firmly convinced that the result is impossible, then checking it is a waste of time. The grandson of Boris Pavlovich, Boris Smirnov, persuaded his grandfather: "Take the reagents, go to the editorial office and show them ..." The general considered all this insulting, inconsistent with the norms of scientific ethics, and did not go.
And Belousov continued to study his wonderful reaction. Fluctuations - yellow-colorless were not very bright. A student and collaborator of Boris Pavlovich A.P. Safronov advised him to add an iron complex with phenanthroline to the solution. The coloring has changed dramatically. Lilac red faded to bright blue. This was great.
A remarkable feature of the work of Zhabotinsky and the group of collaborators that formed around him was the combination of a chemical experiment, methods of physical registration, and the construction of mathematical models. In these models of systems of differential equations, the kinetic constants were substituted from experimental data. After that, it was possible to compare the experimental recordings of vibrations with the curves that were obtained by computer simulation.
Computers then were bulky and inconvenient, data was entered on punched tapes or punched cards. But this did not dampen the enthusiasm.
By 1963, the main qualitative stage of studying the Belousov reaction was completed. PhD student Zhabotinsky had to write an article. And he wrote a wonderful first article. A natural question arose about the authors.
The article was published under the signature of one Zhabotinsky. The article produced such an unexpected effect that admiring humanity named the reaction after Belousov and Zhabotinsky.
The "scientific community" was gradually imbued with the realization that oscillatory regimes are not only possible, but even obligatory and fairly common in chemistry and biochemistry. I especially wanted to find them in biochemistry in order to explain the phenomenon of the biological clock with them.
With the substantiation of the high probability of oscillatory biochemical reactions from the point of view of the theory of oscillations at a seminar at the Physical Institute of the USSR Academy of Sciences in 1959, post-graduate student I.E. Tamma D.S. Chernavsky spoke. Now a situation has already arisen when theory, understanding, are ahead of phenomenology. The discovery of oscillations in biochemical systems was expected.
In the autumn of 1964, Chance published an article on the vibrational kinetics of the phosphofructose kinase reaction. A boom in studies of oscillatory regimes began in biochemistry. The number of such publications has been growing year by year.
In 1966, in March, the first All-Union Symposium on Oscillatory Processes in Chemistry and Biochemistry was convened. This is a completely historic event in science. Because oscillatory processes in biology: the biological clock, all sorts of processes such as cardiac activity, intestinal peristalsis, and even population size are all the same differential equations. Physicists considered this one of the main achievements of our Pushchino Center and the Institute of Biophysics. D.A. Frank-Kamenetsky took an active part in the work of the symposium, I.E. Salnikov and B.V. Voltaire made presentations, D.S. Chernavsky and his colleagues Yu.M. his first works E.E. Selkov. The reports of A.M. Zhabotinsky and his co-authors M.D. Korzukhin, V.A. Vavilin occupied the central place. Boris Pavlovich Belousov refused to participate in the symposium.
Already in January 1967, the book Oscillation Processes in Chemical and Biological Systems was published.
Long before the symposium another significant event took place. The president of the USSR Academy of Sciences, Mstislav Vsevolodovich Keldysh, wanted to know more about Belousov's reaction. He was known as a man of very special speeds of perception, phenomenal erudition. Concentrated, gloomy, face in such leonine wrinkles.
Zhabotinsky briefly stated the essence: Keldysh became furious if they spoke for a long time. There were fluctuations in the glass, we thought that this was enough for Keldysh, but he looked angrily at the glass and said: "Are you hiding the most important thing from me?" And the most important were the colored waves that started at the bottom and went up. Keldysh was a specialist in the spatial effects of vibrations. Zhabotinsky, of course, noticed spatial waves, but he had not figured it out yet and decided not to tell Keldysh about them. But it was not there! The President was terribly angry, believing that they simply did not want to tell him ... The remark was of extreme importance. And then we found out that Belousov also saw it. Even called the flask "zebra". And I thought it was the most important thing.
After the symposium, Zhabotinsky focused on the study of wave propagation. The work was made very difficult by the low optical density of the solution. At this time, A.N. joined the group. Zaikin, and they decided to use a television set capable of accumulating a weak signal through repeated scanning. It was not possible to get an industrial television installation. Work has stalled. And no one remembered the iron-phenanthroline complex.
Spatial effects, wave propagation in an active medium have opened up new remarkable possibilities and analogies. Excitation spreads in a similar way in the nerve, in the cardiac syncytium, in general in "active media". The BZ-reaction "came into operational space", entered the textbooks and became one of the brightest objects of the new science of synergetics.
CONCLUSION
So, is the significance of the reaction discovered by Belousov exaggerated? Not at all. Is his posthumous fame fair? Without a doubt. And it does not in the least detract from the merits of many researchers who have been studying these problems for almost three centuries.
It remains to be said that while humanity was learning about Boris Pavlovich Belousov, he was expelled from the institute ... "because he is old and often sick." He was indeed old, but his creative activity remained very high. He could not bear to live without a laboratory and died on June 12, 1970.
When Zhabotinsky defended his doctoral dissertation in 1974, his opponent, a great man, academician Rem Viktorovich Khokhlov, said: "By analogy with self-oscillations, the process of wave propagation in an active medium can be called autowave." Khokhlov's term stuck. This new part of science, devoted mainly to spatial effects, was combined with studies of the propagation of excitation waves in the heart and in general in the "active media" of Krinsky-Ivanitsky. A closely interacting team was formed: Zhabotinsky, Krinsky, Ivanitsky, Zaikin. And these four moved things further.
The idea of the Lenin Prize was born. Belousov was not on the list of applicants. But the Lenin Prizes, unlike the Nobel Prizes, were also given posthumously. Boris Pavlovich was awarded the Lenin Prize posthumously. This was in 1980, ten years after his death.
BIBLIOGRAPHY
- M. Zhabotinsky. A history of chemical oscillations and waves, CHAOS 1(4), 1991, 379-385
Salnikov IE, "At the origins of the theory of chemical self-oscillations", in Sat. "Dynamics of systems. Dynamics and optimization". Interuniversity collection of scientific papers. Nizhny Novgorod, 1992
Belousov B.P., "Periodically acting reaction and its mechanism" in the Collection of abstracts on radiation medicine for 1958. - M. Medgiz, 1959, pp. 145-147.
Belousov B.P., "Periodic reaction and its mechanism" in Sat. "Autowave processes in systems with diffusion" Sat. scientific tr. Ed. M.T. Sinful. Gorky. state un-t, Gorky, 1981. pp. 176-186.
Zhabotinsky A.M. "The periodic course of the oxidation of malonic acid in solution (a study of the kinetics of the Belousov reaction)", Biophysics, 1964, vol. 9 pp. 306-311.
"Oscillatory processes in biological and chemical systems". Proceedings of the All-Union Symposium on oscillatory processes in biological and chemical systems. Pushchino-on-Oka, March 21-26, 1966, Ed. Science, M. 1967
Zhabotinsky A.M., "Concentration self-oscillations" M. Nauka, 1974, 178 p.22.
Wolter B.V. "Legend and true story about chemical vibrations", Knowledge-Power, 1988, No. 4, pp. 33-37.
Shnol S.E., V.A.Kolombet, N.V.Udaltsova, V.A.Namiot, N.B.Bodrova "On regularities in discrete distributions of measurement results. (cosmophysical aspects)" Biophysics, 1992, volume 34 , issue 3, pp. 467-488.
The Belousov–Zhabotinsky reaction is a self-oscillatory catalytic oxidation of various reducing agents with bromic acid HBrO 3 . In this case, fluctuations in the concentrations of the oxidized and reduced forms of the catalyst and some intermediate products are observed. The reaction takes place in an acidic environment, in an aqueous solution; as catalysts, metal ions of variable oxidation state, such as cerium or manganese, are used. Malonic acid, acetylacetone, etc. act as reducing agents.
Reagents
- iron(II) sulfate heptahydrate FeSO 4 ∙7H 2 O (crystalline)
- cerium(III) nitrate hexahydrate Ce(NO 3) 3 ∙6H 2 O (crystalline)
- an aqueous solution of potassium bromide KBr (2 mol / l, or 12 g in 50 ml of solution)
- potassium bromate KBrO 3 (crystalline) and a saturated solution of potassium bromate (about 10 g per 100 ml of water)
- sulfuric acid H 2 SO 4 concentrated and diluted (1: 3 by volume).
- an aqueous solution of malonic acid CH 2 (COOH) 2 (5 mol / l, or 52 g in 100 ml of solution)
- o-phenanthroline (phen) C 12 H 8 N 2
- citric acid CH (OH) (CH 2 COOH) 2
- cerium(III) sulfate octahydrate Ce 2 (SO 4) 3 ∙8H 2 O
- distilled water.
Equipment
Projector, 30 x 30 cm glass plate, Petri dish, 100 ml volumetric flask, 250 ml Erlenmeyer flask with ground stopper, six pipettes, burette, glass rod, washer, filter paper.
1 variant of the experiment (Zhabotinsky variant)
Experience preparation
To demonstrate the experiment, prepare two solutions - A and B.
A – solution of ferroin (iron(II) complex) with o-phenanthroline (phen).
0.70 g of iron(II) sulfate heptahydrate and 1.49 g of o-phenanthroline are added to a 100 ml volumetric flask, the volume of the solution is adjusted to the mark with water and mixed. The solution should have a red color due to the formation of a phenanthroline complex of composition 2+:
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it can be prepared in advance.
B - bromomalonic acid solution (prepared immediately before the demonstration). 3.3 ml of potassium bromide solution (2 mol/l), 5 ml of malonic acid solution (5 mol/l) and 5 ml of concentrated sulfuric acid are introduced into an Erlenmeyer flask with a ground stopper using pipettes.
The resulting solution is titrated from a burette with a saturated solution of potassium bromate, thoroughly mixing it after each regular portion of the titrant, achieving the disappearance of the brown color characteristic of bromine released in the parallel switching reaction:
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The total volume of potassium bromate solution used for titration should be about 7.5 ml. The resulting bromomalonic acid is unstable, but it can be stored at a low temperature for some time.
Conducting experience
To directly demonstrate the experiment, a Petri dish is placed on a glass plate placed on a projector mirror, into which 10 ml of a saturated potassium bromate solution, 4 ml of a bromomalonic acid solution and 1.5 ml of a ferroin solution are successively added using pipettes. Within a few minutes, blue areas appear on a red background in the cup; this is due to the formation of another complex - 3+ during the redox reaction of the 2+ complex with bromate ions:
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The liberated bromide ions are inhibitors of the oxidation of the iron(II) complex by bromate ions. Only when the concentration of 2+ becomes high enough, the inhibitory effect of bromide ions is overcome, and the reactions of obtaining bromomalonic acid and the oxidation of the complex begin to proceed again. The process is repeated again, and this is reflected in the color of the solution. Concentric circular red-blue “waves” of coloring diverge in all directions from the blue areas in the cup.
If the contents of the cup are mixed with a glass rod, the solution will become monochromatic for a short time, and then the periodic process will be repeated. Eventually the reaction stops due to the release of carbon dioxide.
You can add to the Petri dish, in addition to all the listed reagents, a few crystals of cerium(III) nitrate hexahydrate; then the range of colors will expand: a yellow color will appear due to cerium (IV) derivatives, green - due to the superposition of blue and yellow colors:
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When heated, the oscillatory reaction cycle is shortened, the color change occurs faster.
Notes
- In the reaction equations, the cerium(IV) derivative of the composition Сe(OH) 2 2+ is conditionally written; more accurately, its composition is reflected by the formula (4 - x) + .
- Instead of iron (II) sulfate heptahydrate, it is possible to use Mohr's salt - crystal hydrate of iron (II) sulfate - ammonium composition (NH 4) 2 Fe (SO 4) 2 ∙ 6H 2 O in the amount of 0.99 g for the same volume to prepare a solution A water.
2 variant of the experiment (Belousov's variant)
Experience preparation
For the experiment, take 2 g of citric acid (HOOC) C (OH) (CH 2 COOH) 2, 0.16 g of octahydrate cerium (III) sulfate Ce 2 (SO 4) 3 ∙ 8H 2 O and 0.2 g of potassium bromate KBrO 3 . Samples are dissolved in 2.0 ml of sulfuric acid solution (1:3 by volume). Then the volume of the solution was adjusted to 10 ml by adding distilled water.
Conducting experience
For a direct demonstration of the experiment, a Petri dish is placed on a glass plate placed on a projector mirror, into which the prepared mixture of citric acid, cerium salt and potassium bromate in dilute sulfuric acid is poured. Within a few minutes, the color of the solution in the cup changes from whitish to bright yellow and vice versa.
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Belousov-Zhabotinsky experiments
Self-oscillating reactions
A special type of redox reactions is oscillatory reactions. They occur in rather complex reaction systems, and for such reactions, the kinetic factor turns out to be a very important factor. In such systems, a number of successive reactions are possible, which are characterized by different rates. Mutual superposition of several such reactions, the products of which can have a catalytic or inhibitory effect, leads to the fact that one or the other component alternately accumulates in the reaction medium. In the case of intensely colored substances in significant concentrations, oscillatory reactions are easy to observe. The most famous and applicable for demonstration under normal conditions, oscillatory reactions were first observed by Boris Pavlovich Belousov in 1958, studying the system citric acid - cerium (III) sulfate - potassium bromate in an acidic medium.
Historical information
The first descriptions of fluctuations in concentration systems date back to the 19th century. This is a study of the oscillations of an electrochemical reaction (1828) and a catalytic heterogeneous reaction (1833) M. Rosenskiöld in 1834 accidentally noticed that a small flask containing a little phosphorus emits a rather intense light in the dark, and this glow was regularly repeated every seventh second. M. Joubert in 1874 observed the periodic formation of "luminous clouds" in a test tube with white phosphorus vapor. Later, A. Tsentnershwer studied the effect of air pressure on periodic flashes of phosphorus: he found that the frequency of flashes starts from 20 seconds and increases with decreasing pressure. At the same time, T. Thorpe and A. Tatton observed periodic flashes of the oxidation reaction of phosphorus trioxide in a sealed glass vessel. In 1896, the German chemist R. Liesegang, while experimenting with photochemicals, discovered that if a silver nitrate solution is dropped onto a glass plate coated with gelatin containing potassium dichromate, the reaction product, precipitating, is located on the plate in concentric circles. Liesegang became fascinated with this phenomenon and studied it for almost half a century. It also found practical applications. In applied art, “Liesegang rings” were used to decorate various products with imitation of jasper, malachite, agate, etc. Liesegang himself proposed the technology for making artificial pearls. F. Runge's book (1855) collected numerous examples of such experiments.
Later, oscillatory reactions were discovered at the interface between two phases. Of these, the most well-known are the reactions at the metal-solution interface, which received specific names - "iron nerve" and "mercury heart". The first of them - the reaction of dissolving iron (wire) in nitric acid - got its name because of the external similarity with the dynamics of an excited nerve, noticed by V.F. Ostwald. The second is the decomposition reaction of H 2 O 2 on the surface of metallic mercury. In the reaction, periodic formation and dissolution of an oxide film on the mercury surface occurs. Fluctuations in the surface tension of mercury cause rhythmic pulsations of the drop, reminiscent of the beating of the heart.
For a long time there was no explanation for ongoing periodic processes in chemistry. Only in the second half of the XIX century. thermodynamics and chemical kinetics arose, which laid the foundation for a specific interest in oscillatory reactions and methods for their analysis. At the same time, the development of equilibrium thermodynamics served at first as a brake on the study of such processes. The point, apparently, was in the "inertia of previous knowledge." It was impossible to imagine a macroscopic order in the random thermal motion of a huge number of molecules. And in fact, this cannot be - but only near the state of equilibrium, which was considered by the thermodynamics of those years. However, there are no restrictions for complex, including oscillatory, modes for nonequilibrium chemical systems, when the reactions have not yet been completed and the concentrations of the reagents have not reached the equilibrium level.
The modern history of research on oscillatory chemical reactions in the liquid phase began in 1951 with the discovery of Belousov, although for the author himself, everything did not go so smoothly. His paper describing the oscillatory reaction was twice rejected by the editors of academic chemical journals. Only in 1958 was its abridged version published in the little-known Collection of Abstracts on Radiation Medicine. Obviously, the main reason for the rejection of this phenomenon by chemists was the widespread opinion that such reactions are "forbidden" by the second law of thermodynamics. However, in 1952, an article by the English scientist A.M. Turing "Chemical Foundations of Morphogenesis", in which he reported that the combination of chemical vibrations with the diffusion of molecules can lead to the appearance of stable spatial structures, the regions of high and low concentrations of which alternate. Turing, solving the theoretical problem of whether stable configurations of intermediate products can form in a reactor under the conditions of a chemical reaction, created a mathematical model of this process.
In 1955, the author of the theory of thermodynamics of irreversible processes, I.R. Prigogine showed that chemical fluctuations are possible in an open system near a stationary state, far enough from chemical equilibrium, drew the attention of the scientific community to the work of Soviet scientists. As a result, some oscillatory heterogeneous chemical reactions, discovered as early as the end of the 19th century, have received wide recognition. It was they who began to be considered as analogues of a number of periodic processes, for example, "biological clocks".
It became clear to researchers that the second law of thermodynamics is not violated in living systems and does not interfere with their complex behavior and evolution. But for the existence of life or any of its physical or chemical models, it is necessary that the system be away from thermodynamic equilibrium for a sufficiently long time. And homogeneous chemical systems could become a convenient model for studying such processes.
Later, these works were continued in the Laboratory of Physical Biochemistry of the Institute of Biological Physics of the USSR Academy of Sciences. The ease of reproducing the results and the beautiful visual effects observed in the Belousov reaction contributed to its wide popularity (later it was called the Belousov–Zhabotinsky reaction, or BZ reaction). Similar oscillations in a liquid-phase chemical system were discovered in 1921 by W. Bray while studying the reaction of hydrogen peroxide with potassium iodate, which is accompanied by periodic release of oxygen from the system. The periodic Brey reaction was later called the Brey–Libawski reaction.
The discovery and study of self-oscillations and self-waves in the course of the Belousov reaction is one of the most brilliant pages of fundamental Russian science in the post-war period.
BELOUSOV Boris Pavlovich
(19.II.1893-12.VI.1970)
BELOUSOV Boris Pavlovich - Soviet chemist. Born in Moscow in the family of a bank employee, the sixth child in the family. Together with his brothers, he was early involved in revolutionary activities and was arrested at the age of 12. His mother was offered a choice: either Siberian exile or emigration. The family ended up in Switzerland in a Bolshevik colony. In Zurich, his passion for chemistry began, but there was no opportunity to get an education, since he had to pay tuition. At the beginning of the First World War, Boris returned to Russia, wishing to voluntarily join the army, but for health reasons he was not accepted.
Belousov goes to work in the chemical laboratory of the Guzhon metallurgical plant (now the Hammer and Sickle plant), which was headed by the famous Russian chemist V.N. Ipatiev. This predetermined the direction of research of the future scientist: the development of methods for combating poisonous substances, compositions for gas masks. Becoming a military chemist, Belousov from 1923 taught chemistry at the Higher Military Chemical School of the Red Army (Workers 'and Peasants' Red Army, 1918-1946), lectured on general and special chemistry at the School for the Improvement of Command Staff of the Red Army, then at the Red Banner Military Academy chemical defense named after S.K. Timoshenko.
The military chemist Belousov had the rank of brigade commander, but in 1935 he took a long leave, and in 1938 he resigned. This, perhaps, explains the fact that Belousov himself did not suffer during the period of mass repressions of 1937-1938. However, the loss of many colleagues and friends left an indelible imprint on his character.
The specificity of Belousov's scientific activity was such that none of his scientific works has ever been published anywhere. Despite his huge contribution to the creation of the "chemical shield" of the USSR and brilliant reviews of the work, in which it was indicated that "B.P. Belousov owns a number of equally original and interesting scientific works, which leave no doubt that he certainly deserves to be awarded the degree of Doctor of Chemical Sciences without defending a dissertation, ”he never received any degree. The difficult character of Boris Pavlovich manifested itself here too, he "did not want any diplomas." The assessment of his contribution to the creation of drugs that reduce the effects of radiation was high: without having a higher education, the scientist was in charge of the laboratory and received the salary of a doctor of science.
After analyzing the cyclic reactions discovered in the postwar years by biochemists, Belousov decided to make a chemical analogy of biological cycles. Investigating the oxidation of citric acid with bromate in the presence of a catalyst, he discovered concentration fluctuations of the reagents - this is how the oscillatory reaction was discovered. In 1951 and 1955, Belousov made attempts to publish his discovery in the journals "Kinetics and Catalysis" and "Journal of General Chemistry". The comments on his articles were categorically negative and, as it turned out later, just as categorically erroneous. It is known that this influenced the scientist so much that he simply threw out the laboratory recipe for the reaction and forgot about it.A few years later, when biochemists became interested in Belousov's discovered reaction, he had to restore the results obtained by sequential enumeration.We can say that the discovery was made by Belousov twice - the first time by accident , the second time as a result of a system search.
But he no longer wanted to actively participate in the work of the scientific team. All that colleagues managed was to persuade Belousov to try to publish his article again. As a result, the only lifetime publication of the scientist appeared in the "Collection of Abstracts on Radiation Medicine" for 1958.
B.P. Belousov left work at the Institute shortly before his death, in 1970, and in 1980 he was awarded the Lenin Prize in Chemistry.
Experience Description
The Belousov-Zhabotinsky reaction is self-oscillatory catalytic oxidation of various reducing agents with HB bromic acid rO 3 . In this case, fluctuations in the concentrations of the oxidized and reduced forms of the catalyst and some intermediate products are observed. The reaction takes place in an acidic environment, in an aqueous solution; as catalysts, metal ions of variable oxidation state, such as cerium or manganese, are used. Malonic acid, acetylacetone, etc. act as reducing agents.
Reagents
· iron(II) sulfate heptahydrate FeSO 4 7 H 2 O (crystalline)
· cerium(III) nitrate hexahydrate Ce (NO 3) 3 . 6 H 2 O (crystalline)
· an aqueous solution of potassium bromide KBr (2 mol / l, or 12 g in 50 ml of solution), a saturated solution of potassium bromate KBrO 3 (about 10 g per 100 ml of water)
· concentrated sulfuric acid H 2 SO 4
· an aqueous solution of malonic acid CH 2 (COOH) 2 (5 mol / l, or 52 g in 100 ml of solution)
· o-phenanthroline (phen) C 12 H 12 N 2
· distilled water.
Crockery and cutlery
Projector, 30 x 30 cm glass plate, Petri dish, 100 ml volumetric flask, 250 ml Erlenmeyer flask with ground stopper, six pipettes, burette, glass rod, washer, filter paper.
Experience preparation
To demonstrate the experiment, prepare two solutions - A and B.
A - a solution of ferroin - an iron (II) complex with o-phenanthroline (phen).
0.70 g of iron(II) sulfate heptahydrate and 1.49 g of o-phenanthroline are added to a 100 ml volumetric flask, the volume of the solution is adjusted to the mark with water and mixed. The solution should have a red color due to the formation of a phenanthroline complex of composition 2+:
Fe 2+ + 3phen= 2+
and can be prepared ahead of time.
B - a solution of bromomalonic acid (prepared immediately before the demonstration). 3.3 ml of potassium bromide solution (2 mol/l), 5 ml of malonic acid solution (5 mol/l) and 5 ml of concentrated sulfuric acid are introduced into an Erlenmeyer flask with a ground stopper using pipettes. The resulting solution is titrated from a burette with a saturated solution of potassium bromate, thoroughly mixing it after each regular portion of the titrant, achieving the disappearance of the brown color characteristic of bromine released in the parallel switching reaction:
BrO3 - + 5Br - + 6 H + \u003d 3 Br 2 + 3 H 2 O
3 Br 2 + 10 CH 2 (COOH) 2 + 38 H 2 O \u003d 6 BrCH (COOH) 2 + 4 HCOOH + 8 CO 2 + 30 H 3 O +
The total volume of potassium bromate solution used for titration should be about 7.5 ml. The resulting bromomalonic acid is unstable, but it can be stored at a low temperature for some time.
Conducting experience
For a direct demonstration of the experiment, a Petri dish is placed on a glass plate covering the polylux light window, into which 10 ml of a saturated potassium bromate solution, 4 ml of a bromomalonic acid solution and 1.5 ml of a ferroin solution are successively added using pipettes. Within a few minutes, blue areas appear on a red background in the cup; this is due to the formation of another complex - 3+ during the redox reaction of the 2+ complex with bromate ions:
6 2+ + 6 H 3 O + + BrO 3 - = 6 3+ + 9 H 2 O + Br -
This process is auto-accelerating.
Then the resulting complex 3+ oxidizes bromomalonic acid with the formation of bromide ions:
4 3+ + BrCH(COOH) 2 + 7 H 2 O = 2 CO 2 +5 H 3 O + + Br - + HCOOH + 4 2+
The liberated bromide ions are inhibitors of the oxidation of the iron(II) complex by bromate ions. Only when the concentration of 2+ becomes high enough, the inhibitory effect of bromide ions is overcome, and the reactions of obtaining bromomalonic acid and the oxidation of the complex begin to proceed again. The process is repeated again, and this is reflected in the color of the solution. Concentric circular red-blue “waves” of coloring diverge in all directions from the blue areas in the cup.
If the contents of the cup are mixed with a glass rod, the solution will become monochromatic for a short time, and then the periodic process will be repeated. Eventually the reaction stops due to the release of carbon dioxide.
You can add to the Petri dish, in addition to all the listed reagents, a few crystals of cerium (III) nitrate hexahydrate; then the range of colors will expand: a yellow color will appear due to derivatives of cerium (IV), green - due to the imposition of blue and yellow colors.
6 Ce 3+ + 6 H 3 O + + BrO 3 - \u003d 6 Ce (OH) 2 2+ + 9 H 2 O + Br -
4 C e(OH) 2 2+ + BrCH(COOH) 2 + 7 H 2 O = 2 CO 2 +5 H 3 O + + Br - + HCOOH + 4 Ce 3+
When heated, the oscillatory reaction cycle is shortened, the color change occurs faster.
Notes
· In the reaction equations, the derivative of cerium (IV) of the composition Сe (OH) 2 2+ is conditionally written; its composition is more accurately reflected by the formula (4 - X )+ .
· Instead of iron (II) sulfate heptahydrate, you can use Mohr's salt to prepare a solution A - iron (II) -ammonium sulfate crystalline hydrate of composition (NH 4) 2 Fe (SO 4) 2 6 H 2 O in an amount of 0.99 g for the same water volume.
Chemistry seems to most of us to be a very boring science. It's like calculations, but instead of numbers - letters. It takes a unique psycho to get excited about solving alphabet math problems. But search YouTube for the word "chemistry" and you will see some truly amazing things that will surely blow your mind.7. Hypnotizing Bromic Acid
Is your dealer out of town and you miss your daily dose of LSD? No problem. All you need is two simple substances and a Petri dish in order to create with your own hands not a virtual, but a real lava lamp. It’s a joke, otherwise they’ll run in, close the site ...
According to science, the Belousov-Zhabotinsky reaction is an “oscillatory chemical reaction” in which “transition group metal ions catalyze the oxidation of various, usually organic, reducing agents with bromic acid in an acidic aqueous medium,” which allows “to observe with the naked eye the formation of complex space-time structures." This is the scientific explanation for the hypnotic phenomenon that occurs when a little bromine is thrown into an acidic solution.
The acid turns the bromine into a chemical called bromide (which takes on a completely different hue), in turn, the bromide quickly turns back into bromine because the scientific elves that live inside it are overly stubborn assholes. The reaction repeats itself over and over again, allowing you to endlessly watch the movement of incredible undulating structures.
6. Transparent chemicals turn black instantly
Q: What happens when you mix sodium sulfite, citric acid and sodium iodide? Correct answer below:
When you mix the aforementioned ingredients in certain proportions, you end up with a moody liquid that is initially transparent in color and then abruptly turns black. This experiment is called "Iodine Clock". Simply put, this reaction occurs when specific components are combined in such a way that their concentration gradually changes. If it reaches a certain threshold, the liquid becomes black.
But that is not all. By changing the proportion of ingredients, you have the opportunity to get a feedback:
In addition, with the help of various substances and formulas (for example, the Briggs-Rauscher reaction) you can create a schizophrenic mixture that will constantly change its color from yellow to blue.
5. Creating plasma in the microwave
Do you want to do something fun with your friend but don't have access to a bunch of obscure chemicals or the basic knowledge needed to mix them safely? Do not despair! All you need for this experiment is grapes, a knife, a glass and a microwave. So, take a grape and cut it in half. Divide one of the pieces again with a knife into two parts so that these quarters remain bound by the peel. Put them in the microwave and cover with an inverted glass, turn on the oven. Then take a step back and watch the aliens steal the cut berry.
In fact, what is happening before your eyes is one way to create a very small amount of plasma. From school you know that there are three states of matter: solid, liquid and gaseous. Plasma, in fact, is the fourth type and is an ionized gas obtained by superheating ordinary gas. Grape juice, it turns out, is rich in ions, and therefore is one of the best and most affordable means for conducting simple scientific experiments.
However, be careful when trying to create a plasma in the microwave, because the ozone that forms inside the glass can be toxic in large quantities!
4. Laminar flow
If you mix coffee with milk, you end up with a liquid that you are unlikely to ever be able to separate into its component components again. And this applies to all substances that are in a liquid state, right? Right. But there is such a thing as laminar flow. To see this magic in action, just place a few drops of multi-colored dyes in a transparent container with corn syrup and gently mix everything ...
... and then mix again at the same pace, but now in the opposite direction.
Laminar flow can occur in all conditions and with different types of liquids, but in this case, this unusual phenomenon is due to the viscous properties of corn syrup, which, when mixed with dyes, forms multi-colored layers. So, if you just as carefully and slowly perform the action in the opposite direction, everything will return to its original place. It's like time travel!
3. Lighting an extinguished candle through a smoky trail
You can try this trick at home without the risk of blowing up the living room or the whole house. Light a candle. Blow it out and immediately bring fire to the smoky trail. Congratulations: you succeeded, now you are a real master of fire.
It turns out that there is some love between fire and candle wax. And this feeling is much stronger than you think. It doesn't matter what state the wax is in - liquid, solid, gaseous - the fire will still find it, overtake it and burn it to hell.
2. Crystals that glow when crushed
Here is a chemical substance called europium-tetrakis, which demonstrates the effect of triboluminescence. However, it is better to see once than to read a hundred times.
This effect occurs during the destruction of crystalline bodies due to the conversion of kinetic energy directly into light.
If you want to see all this with your own eyes, but you don’t have europium tetrakis on hand, it doesn’t matter: even the most ordinary sugar will do. Just sit in a dark room, put some sugar cubes in the blender and enjoy the beauty of fireworks.
Back in the 18th century, when many people thought that ghosts or witches or the ghosts of witches caused scientific phenomena, scientists used this effect to play a trick on "mere mortals" by chewing sugar in the dark and laughing at those who ran from them like from fire. .
1. Infernal monster emerging from a volcano
Mercury thiocyanate (II) is a seemingly innocent white powder, but as soon as it is set on fire, it immediately turns into a mythical monster, ready to devour you and the whole world entirely.
The second reaction, pictured below, is caused by the combustion of ammonium dichromate, resulting in a miniature volcano.
Well, what happens if you mix the above two chemicals and set them on fire? See for yourself.
However, do not attempt these experiments at home, as both mercury(II) thiocyanate and ammonium dichromate are highly toxic and can cause serious harm to your health if burned. Take care of yourself!
Self-organization as an elementary process of evolution
According to modern ideas, the elementary process of evolution is self-organization. We can say that, in essence, evolution consists of an endless sequence of processes of self-organization. In the broad sense of the word self-organization is understood as the tendency of the development of nature from less complex to more complex and ordered forms of organization of matter. In a narrower sense self-organization is a spontaneous transition of an open non-equilibrium system from simple and disordered forms of organization to more complex and ordered ones. Self-organizing systems must meet certain requirements: 1) they must be non-equilibrium or be in a state far from thermodynamic equilibrium; 2) they must be open and receive an influx of energy, matter and information from the outside. According to G. Haken, a system can be called self-organizing if it acquires some kind of spatial, temporal or functional structure without specific external influence. A specific external influence is understood as one that imposes a structure or functioning on the system.
Recently, the essence of self-organization in open systems has been studied in a new area of natural science - synergetics, which covers all the problems associated with the formation of ordered structures in complex systems as a result of the correlated behavior of subsystems. Its main ideas go back to E. Schrödinger, A.M. Turing, L. von Bertalanffy, I. Prigogine, M. Eigen and G. Haken. It is believed that the development and development of the methodology of the following disciplines was of decisive importance for the creation of synergetics: thermodynamics of irreversible processes in open systems; nonlinear mechanics, electrophysics and laser physics; chemical kinetics of strongly nonequilibrium processes; evolution of populations in ecology; nonlinear theory of regulation, cybernetics and system analysis. The above list confirms the interdisciplinary nature of synergetics. In order to understand the essence of self-organizing systems, which are considered by synergetics, let us recall that they distinguish closed systems that do not exchange matter, energy and information with the environment. Let's consider some simple examples of ordering (self-organization) in open systems.
Example1. Convective instability, or Benard instability. Let the liquid layer be heated from below, while the temperature is kept constant from above. With a small temperature difference, heat is transferred due to thermal conductivity and the liquid remains at rest. As the heated regions of the liquid expand, they have a lower density and float to the top, cool, and sink back to the bottom. This movement is in order. In this case, either cylindrical or hexagonal cells are formed.
Example 2. In the reaction of Belousov - Zhabotinsky, spatial, temporal or space-time structures are also formed. For its implementation, mix Ce2 (SO4) 3, KBrO3, CH2 (COOH) 2, H2SO4 and add a few drops of ferroin (redox indicator). The resulting homogeneous mixture is poured into a test tube, where temporal oscillations immediately begin. The solution periodically changes color - from red, indicating an excess of Ce3+, to blue, corresponding to an excess of Ce4+. Since the reaction proceeds in a closed system, it eventually comes to a homogeneous equilibrium state.
Example 3 Spiral Waves
Belousov-Zhabotinsky reaction
The Belousov-Zhabotinsky self-oscillatory reaction is very widely known not only in the scientific world. She is known both by schoolchildren and students, and just inquisitive people. A glass of red-purple liquid suddenly turns bright blue, and then again red-purple. And blue again. And when the liquid is poured in a thin layer, waves of color change propagate in it. Complex patterns are formed, circles, spirals, vortices, or everything takes on a completely chaotic appearance.
This reaction has been known for over 40 years. It was opened in 1951 by Boris Pavlovich Belousov.
Color change of the reaction mixture in the Belousov-Zhabotinsky reaction with ferroin. In the system (test tube) shown, the oscillations decay rapidly.
At a small time of stay, it is not allowed to equalize the rates of forward and reverse reactions. Wherein the behavior of the system will be non-equilibrium.
With a long residence time in the system, a homogeneous stationary state is reached - the concentrations remain constant in time. This is a state of chemical equilibrium - an analogue of the thermal conductivity mode (∆Т<Т с) в системе Бенара.
Experiment
In a closed vessel with intensive stirring, after a short inductive period, fluctuations in the concentrations and occur. Typical experimental curves are shown in Fig.1. The beginning of oscillations has the character of "hard excitation". In the system it passes through a subcritical Andrionov-Hopf bifurcation. Fluctuations in the concentration of ions registered on the platinum electrode have a constant amplitude. The bromide electrode registers an increase in amplitude, its maximum value corresponds to the difference in ion concentrations by two orders of magnitude, the shape of the oscillations changes somewhat with time, the period increases to 2 minutes after 1.5 hours. After that, the amplitude of oscillations gradually decreases, they become irregular, and disappear very slowly.
Fig. 1. Experimentally observed readings, taken from a platinum electrode, (a) and an electrode that records the current of fordide ions (b)
The first model of the observed processes was proposed by A.M. Zhabotinsky. The reaction cycle considered by him consists of two stages (I) - the oxidation of trivalent cerium with bromate: Ce 3+ BrO 3 Ce 4+ (I)
The second stage (II) is the reduction of tetravalent cerium with malonic acid:
Ce 4+ + CHBr(COOH) 2 Ce 3+ + Br - + other products (II)
The bromate reduction products formed in step I are brominated. The resulting bromo derivatives are destroyed with isolation. Bromide is a strong inhibitor of the reaction. The scheme of the self-oscillating reaction can be qualitatively described as follows. Let there be ions in the system. They catalyze the formation of stage (II), which interacts with the Y particles of reaction I and is removed from the system. If the concentration is high enough, reaction I is completely blocked. When the concentration of ions as a result of reaction II decreases to a threshold value, the concentration falls, thereby removing the blocking of reaction I. The rate of reaction I increases, and the concentration increases. When the upper threshold value is reached, the concentration also reaches high values, and this leads to blocking of the reaction. Etc.
Benard cells
Consider an example of the emergence of a spatial structure called "Benard cells" (Fig. 2).
Benard cells arise at a critical temperature difference that occurs between the upper and lower layers of the liquid when it is heated (the liquid is in the cuvette).
As long as the temperature difference has not reached a critical value, heat spreads by conduction, the surface of the liquid is stationary.
Rice. 2. Regular hexagonal pic. 3. Complete dependencies
Cells on the liquid surface of the heat flux J per unit
(Benard cells) of time on the temperature difference
As the critical value of the temperature difference is approached, convection (circulation) occurs and hexagonal cells appear on the surface of the liquid. Inside the cell, the liquid moves up, and along the edges - down (Fig. 3). The emergence of cells is a self-organized process.
An example of a time structure is the Belousov-Zhabotinsky reaction. The reaction is observed in a reaction mixture consisting of bromate (KBr), bromomalonic acid, cesium sulfate (Ce).
The mixture must be dissolved either in citric or sulfuric acid. After 4 minutes, the color of the solution will change from blue to red (and vice versa). This occurs in connection with the reduction of cerium ions.
The alternation of the color of the solution is a self-organized process that develops over time.
An example of a space-time structure is the glycolytic cycle, the absorption of sugar by a living organism.
spiral waves
A technique was developed in the laboratory that allows one to "bring" the tip of one of the waves beyond the border of the Petri dish, and subsequently observe the evolution of a single spiral wave, the "tip" (tip) of which performs complex spatial movements, the trajectory depends on the illumination mode (Grill et al. , 1995).
Under constant illumination, the tip describes a cycloid with four "Petals" (Fig. 4). The effect of light pulses on the trajectory of the tip of a spiral wave was studied. The pulses were applied at the moment when the wave front reached a certain point (in Fig. marked with a cross), or with a certain specified delay.
Rice. 4 Two types of spiral wave tip trajectories obtained in the experiment for the photosensitive BZ reaction.
Two types of modes were observed. In the case when the “measurement point” was close to the center of the unperturbed trajectory, after some time the movement of the tip came to an asymptotic trajectory with the center at the “measurement point”, while the distance between the position of the tip and the measurement point did not exceed the dimensions of the cycloid loop (Fig. 4 a) The presence of feedback led to synchronization - the period of pulsed light exposure was set equal to the time during which the tip of the spiral wave described one loop of the cycloid.
In the case when the measurement point was relatively far from the center of the unperturbed trajectory, the tip of the spiral described a trajectory resembling the drift of a 4-leaf cycloid along a circle of large radius, the center of which was again at the “measurement point”. Both modes turned out to be stable with respect to small displacements of the measurement point, that is, they are attractions. A similar result is obtained if the light pulse is applied with some delay in relation to the moment of passage of the wave through the measurement point. The radius of the "great circle" along which the cycloid moves increases with increasing delay time.
Examples of self-organization in the simplest systems: Benard cells, Belousov-Zhabotinsky reaction. spiral waves.
According to modern ideas, the elementary process of evolution is self-organization. We can say that, in essence, evolution consists of an endless sequence of processes of self-organization. In a broad sense of the word, self-organization is understood as the tendency of the development of nature from less complex to more complex and ordered forms of organization of matter. Recently, the essence of self-organization in open systems has been studied in a new area of natural science - synergetics, which covers all the problems associated with the formation of ordered structures in complex systems as a result of the correlated behavior of subsystems.
In order to understand the essence of self-organizing systems considered by synergetics, let us consider a few simple examples of ordering (self-organization) in open systems.
