The oscillatory reaction of Belousov-Zhabotinsky is called. Self-oscillatory reaction of Belousov-Zhabotinsky

Change in color of the reaction mixture in the Belousov-Zhabotinsky reaction with ferroin

Belousov-Zhabotinsky reaction- a class of chemical reactions occurring in an oscillatory mode, in which some reaction parameters (color, concentration of components, temperature, etc.) change periodically, forming a complex spatiotemporal structure of the reaction medium.

Under certain conditions, these systems can demonstrate very complex forms of behavior from regular periodic to chaotic oscillations and are an important object of study of universal patterns nonlinear systems. In particular, it was in the Belousov-Zhabotinsky reaction that the first experimental strange attractor was observed in chemical systems and an experimental verification of its theoretically predicted properties was carried out.

The history of the discovery of the oscillatory reaction by B. P. Belousov, experimental study its and numerous analogues, study of the mechanism, mathematical modeling, historical meaning are given in the collective monograph.

History of discovery

Reaction mechanism

Jabotinsky-Korzukhin model

The first model of the Belousov-Zhabotinsky reaction was obtained in 1967 by Zhabotinsky and Korzukhin based on the selection of empirical relations that correctly describe oscillations in the system. It was based on the famous conservative Lotka-Volterra model.

d X 1 d t = k 1 X 1 (C − X 2) − k 0 X 1 X 3 (\displaystyle (\frac (dX_(1))(dt))=k_(1)X_(1)(C- X_(2))-k_(0)X_(1)X_(3)) d X 2 d t = k 1 X 1 (C − X 2) − k 2 X 2 (\displaystyle (\frac (dX_(2))(dt))=k_(1)X_(1)(C-X_( 2))-k_(2)X_(2)) d X 3 d t = k 2 X 2 − k 3 X 4 (\displaystyle (\frac (dX_(3))(dt))=k_(2)X_(2)-k_(3)X_(4))

Here X 2 (\displaystyle X_(2))= , C= 0 + 0 , X 1 (\displaystyle X_(1))- autocatalyst concentration, X 3 (\displaystyle X_(3)) = .

Brusselator

The simplest model proposed by Prigogine, which has oscillatory dynamics.

Oregonator

The mechanism proposed by Field and Noyes is one of the simplest and at the same time the most popular in works studying the behavior of the Belousov-Zhabotinsky reaction:

I	A+Y		X
II	X+Y	⟶ (\displaystyle \longrightarrow )	P
III	B+X	⟶ (\displaystyle \longrightarrow )	2X+Z
IV	2 X	⟶ (\displaystyle \longrightarrow )	Q
V	Z	⟶ (\displaystyle \longrightarrow )	f Y

The corresponding system of ordinary differential equations:

d [ X ] d t = k I [ A ] [ Y ] − k I I [ X ] [ Y ] + k I I I [ B ] [ X ] − k I V [ X ] 2 (\displaystyle (\frac (d[X] )(dt))=k_(I)[A][Y]-k_(II)[X][Y]+k_(III)[B][X]-k_(IV)[X]^(2) ) d [ Y ] d t = − k I [ A ] [ Y ] − k I I [ X ] [ Y ] + f k V [ Z ] (\displaystyle (\frac (d[Y])(dt))=-k_( I)[A][Y]-k_(II)[X][Y]+fk_(V)[Z]) d [ Z ] d t = k I I I [ B ] [ X ] − k V [ Z ] (\displaystyle (\frac (d[Z])(dt))=k_(III)[B][X]-k_( V)[Z])

This model demonstrates the simplest oscillations, similar to those observed experimentally, but it is not capable of showing more complex types of oscillations, such as complex periodic and chaotic ones.

Advanced Oregonator

The Showalter, Noyes and Bar-Eli model was developed to model complex periodic and chaotic reaction behavior. However, it was not possible to obtain chaos in this model.

1	A+Y		X+P
2	X+Y	↔ (\displaystyle \leftrightarrow )	2P
3	A+X	↔ (\displaystyle \leftrightarrow )	2 W
4	C+W	↔ (\displaystyle \leftrightarrow )	X+Z"
5	2 X	↔ (\displaystyle \leftrightarrow )	A+P
6	Z"	→ (\displaystyle \rightarrow )	g Y + C

Where A (\displaystyle A)- BrO 3 − ; X (\displaystyle X)- HBrO 2; Y (\displaystyle Y)- Br − ; C (\displaystyle C)- Ce 3+; Z (\displaystyle Z)" - Ce 4+; W (\displaystyle W)- BrO 2; P (\displaystyle P)- HOBr.

Under certain conditions, these systems can demonstrate very complex forms of behavior from regular periodic to chaotic oscillations and are an important object of study of the universal laws of nonlinear systems. In particular, it was in the Belousov-Zhabotinsky reaction that the first experimental strange attractor in chemical systems was observed and its theoretically predicted properties were experimentally verified.

The history of the discovery of the oscillatory reaction by B.P. Belousov, the experimental study of it and numerous analogues, the study of the mechanism, mathematical modeling, and historical significance are given in the collective monograph.

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Subtitles

Hello everyone, Alexander Ivanov is with you, and the project "Chemistry - Simply" Today we are starting a series of videos in which we will look at oscillatory reactions. In 1937, the German chemist Hans Krebs discovered the oxidation cycle of citric acid, an important discovery for which Krebs received the Nobel Prize in Chemistry. Cycle The Krebs reaction is a key reaction underlying oxygen respiration, energy supply, and cell growth. In the Soviet Union, there was a scientist who wondered if it was possible to obtain a simpler - ideally - inorganic analogue of the complex Krebs cycle? This would make it possible to simulate complex processes occurring in a living cell, a simple chemical reaction that is easier to study and understand. In 1951, Belousov wrote an article about such a chemical reaction in the journal of the USSR Academy of Sciences. But it was turned down - the reviewer turned down the article, categorically asserting that such a chemical reaction was impossible. However, our chemist did not give up and continued his research. And at this time, science did not stand still. English mathematician- Alan Turing, suggested that the combination chemical reactions with diffusion processes can explain a whole class biological phenomena For example, this can explain the periodic stripes on the skin of a tiger. Soviet physicist and chemist Ilya Romanovich Prigogine, in 1955, came to the conclusion that in nonequilibrium thermodynamic systems, which include all biological systems, chemical vibrations are possible. Neither Turing nor Prigogine even suspected that the phenomenon under discussion had already been discovered. It’s just that an article on this topic has not been published. Finally, Belousov sends a new version of his work to another Science Magazine , however, the article is returned again with a refusal to publish. The reviewer suggested that the author reduce it to a couple of pages. Such impudence, Belousov could not stand it and threw the article into the trash bin and forever stopped communicating with academic journals. And only 8 years later, a note about the oscillatory reaction was published in the collection of works of radiation medicine. There were rumors in Moscow that somewhere there is a glass in which a chemical heart beats. This interested the chemist Simon Shnoll. He found Boris Pavlovich and took the recipe for a wonderful reaction. And when he performed it, he was extremely surprised. He instructed his graduate student, Anatoly Markovich Zhabotinsky, to study the vibrational chemical phenomenon in detail. Soon , dozens of people have already participated in the study of this reaction - they published hundreds of articles, received candidate and doctoral degrees. Belousov did not participate in this activity; he was well over 70, and he continued to work at his institute, and then the bureaucrats got to him and sent him away on retire. Left without work, Boris Pavlovich soon died. The famous chemical reaction he discovered, now named after Belousov-Zhabotinsky, became a turning point in the modern worldview. Now, the oscillatory reaction is included in the golden fund of science of the 20th century. Soon, many different oscillatory reactions were discovered, so let's do some chemistry and carry out the Belousov-Zhabotinsky reaction ourselves. To carry it out, we will prepare 3 solutions. Their compositions are shown on the screen. Instead of double cerium and ammonium nitrate, in principle, an equivalent amount of any other cerium (IV) salt will do. Mix solutions A and B, and stir constantly after a minute, add solution C. As we see, the solution changes its color. But we won’t stop there. , and improve this reaction by adding a ferroin solution. You can see its composition on the screen. The most complete mechanism of what is happening can be described by a set of 80 elementary reactions. These transformations look like this. Even if you are a chemist, it is not worth remembering in detail. We are simply showing the scale of the tragedy, or rather how such beauty occurs. This is how the color changes if the solution is constantly stirred, and if we stop stirring or fill a tall, narrow vessel with this solution, then it looks completely cosmic. And for those who haven’t bothered, We will analyze what is happening in general terms. After we have mixed solutions A and B, several processes take place in the glass. You see their reactions on the screen. These reactions compete with each other. The yellow color of the solution is due to the release of bromine. What color is bromine - you can see in the video about bromine. Next, bromine reacts with malonic acid and the yellow color disappears. Then, the oxidation reaction of Cerium occurs, which is initiated by the following reactions. Moreover, bromous acid is unstable and decomposes to form bromate ions, which accelerate the previous reactions. By the way, cerium is a catalyst in this process. A catalyst is a substance that accelerates a reaction, but does not participate in the reaction itself. And if in this reaction cerium was oxidized, then in this one it returns to its original state. It can be seen that the concentration of cerium 3+ and cerium 4+ ions constantly fluctuates. Here, we must remember that we last added a solution of feroin to the glass, which can change color depending on the value of the redox potential, which, in turn, is determined by the ratio of the concentrations of cerium 4+ and cerium 3+ ions in the solution. What is oxidation-reduction potential? restorative potential, we will look at it some other time. If the concentration of cerium 4+ ions increases, then it increasingly oxidizes iron in feroin, from 2-valent to 3-valent. The complex of 2-valent iron is red, and the complex of 3-valent iron is blue. Thus, when the ratios of concentrations of various cerium ions change, the color of the solution changes. Fluctuations occur due to the fact that the processes occurring in the glass constantly compete with each other. At some point, there is more bromine, at some point there are bromate ions, and into some bromide ions The color of the solution depends on the concentration of which of the substances is greater at the moment. The released bromine gives a yellow color. When there is little bromine and a lot of bromate ions, the solution has a blue color. Also, we modified this reaction by adding pheroin to the solution which also changes its color, depending on the concentration of cerium 4+ ions between blue and red. One should not, of course, forget about the color of cerium ions. If cerium 3+ ions are colorless, then cerium 4+ ions color the solution yellow. And when all these colors are superimposed, the solution can have all the other colors that you see. Naturally, you have a question - “What practical application does this reaction have?” The answer is simple - none! The maximum for which this particular chemical reaction can be used is purely for demonstrative purposes. A little later, in other videos, we will look at other similar oscillatory reactions, including one that has practical use And that’s all - subscribe, give a thumbs up, don’t forget to support the project and be sure to tell your friends Bye bye!

History of discovery

Reaction mechanism

Jabotinsky-Korzukhin model

Here X 2 (\displaystyle X_(2))= , C= 0 + 0 , X 1 (\displaystyle X_(1))- autocatalyst concentration, X 3 (\displaystyle X_(3)) = .

Brusselator

The simplest model proposed by Prigogine, which has oscillatory dynamics.

Oregonator

The mechanism proposed by Field and Noyes is one of the simplest and at the same time the most popular in works studying the behavior of the Belousov-Zhabotinsky reaction:

I	A+Y		X
II	X+Y	⟶ (\displaystyle \longrightarrow )	P
III	B+X	⟶ (\displaystyle \longrightarrow )	2X+Z
IV	2 X	⟶ (\displaystyle \longrightarrow )	Q
V	Z	⟶ (\displaystyle \longrightarrow )	f Y

The corresponding system of ordinary differential equations:

Advanced Oregonator

The Showalter, Noyes and Bar-Eli model was developed to model complex periodic and chaotic reaction behavior. However, it was not possible to obtain chaos in this model.

1	A+Y		X+P
2	X+Y	↔ (\displaystyle \leftrightarrow )	2P
3	A+X	↔ (\displaystyle \leftrightarrow )	2 W
4	C+W	↔ (\displaystyle \leftrightarrow )	X+Z"
5	2 X	↔ (\displaystyle \leftrightarrow )	A+P
6	Z"	→ (\displaystyle \rightarrow )	g Y + C

Among the numerous oscillatory chemical and biochemical reactions, the most famous is the class of reactions first discovered by the Russian scientist B.P. Belousov (1958).

A.M. also made a great contribution to the study of these reactions. Zhabotinsky, and therefore in the world literature they are known as “BZ-reactions” (Belousov-Zhabotinskii reaction). The Belousov-Zhabotinsky reaction has become the basic model for studying self-organization processes, including the formation of spatially inhomogeneous distributions of concentrations of reacting substances, the propagation of patches, spiral waves and other autowave processes. It has been studied in hundreds of laboratories around the world in vessels of various shapes, in a duct, on porous media, under various influences - temperature changes, light and radiation exposure.

In the reaction studied by B.P. Belousov, the main stage is the oxidation of malonic acid in an acidic environment with bromate ions BrO - 3. The process takes place in the presence of a cerium catalyst, which has two forms Ce 3+ and Ce 4+. Full text The article “Periodically acting reaction and its mechanism”, published in a collection of abstracts on radiation medicine for 1958 (Belousov 1958), is given in the book (Field and Burger 1988). B.P. himself Belousov describes the reaction he discovered as follows:

“The reaction below is remarkable in that when it is carried out in the reaction mixture, a number of hidden redox processes occur, ordered in a certain sequence, one of which is periodically revealed by a distinct temporary change in the color of the entire reaction mixture taken. Such an alternating change in color from colorless to yellow and vice versa is observed indefinitely (an hour or more) if the constituent parts of the reaction solution were taken in a certain quantity and in the appropriate general dilution. For example, a periodic change in color can be observed in 10 ml of an aqueous solution of the following composition: citric acid 2.00 g, cerium sulfate 0.16 g, potassium bromate 0.20 g, sulfuric acid(1:3) 2.00 ml. Water to a total volume of 10 ml.”

Oscillations and autowave processes can also be observed in analogues of this reaction, constructed by replacing bromate with iodate, citric acid with malonic or bromomalonic acid. Many other transition metals can be used as catalysts instead of cerium. Ferroin-ferriin systems containing the Fe ion complexed with phenanthroline are often used for demonstrations, since the transition Fe(II) → Fe(III) is accompanied by a color change from red to blue. As organic compound the most commonly used malonic acid is HOOCCH 2 COOH.

Experiment

In a closed vessel with intense stirring, after a short induction period, fluctuations in the concentrations and . Typical experimental curves are presented in Fig. 1 .

Rice. 1. Experimentally observed readings taken from a platinum electrode, (a) and an electrode recording the current of bromide ions (b). Initial concentrations of reagents: = 6.25·10 -2 M; [malonic acid] = 0.275 M; = 2·10 -3 M. The maximum amplitude of oscillations at the electrode is 100 mV, which corresponds to a change in concentration by a factor of 100, the oscillation period is about 1 min (Gray and Scott, 1994)

The onset of oscillations has the character of “hard excitation.” The system passes through a subcritical Andronov-Hopf bifurcation. Fluctuations in ion concentration recorded on a platinum electrode have a constant amplitude. The bromide electrode records an increase in amplitude, its maximum value corresponds to a difference in ion concentrations of two orders of magnitude, the shape of the oscillations changes slightly over time, the period lengthens to 2 minutes after 1.5 hours. After this, the amplitude of the oscillations gradually decreases, they become irregular, and very slowly disappear.

The first model of the observed processes was proposed by A.M. Zhabotinsky. The reaction cycle he considered consists of two stages. The first stage (I) is the oxidation of trivalent cerium with bromate:

The second stage (II) is the reduction of tetravalent cerium with malonic acid:

The bromate reduction products formed at stage I bromide MC. The resulting bromo derivatives of MK are destroyed with the release of . Bromide is a strong reaction inhibitor. The scheme of a self-oscillatory reaction can be qualitatively described as follows. Let there be ions in the system. They catalyze the formation (stage II), which interacts with the Y species 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 drops, thereby removing the blockage of reaction I. The rate of reaction I increases, and the concentration increases. When the upper threshold value is reached, the concentration also reaches large values, and this again leads to blocking reaction I. And so on (Fig. 2).

Rice. 2. Scheme of the autocatalytic reaction of malonic acid (MA) oxidation.

Local models. Behavior of reagent concentrations over time. Jabotinsky model

The model proposed by V.M. Zhabotinsky to describe the process (Zhabotinsky, 1974) includes three variables: ion concentration ( x), the concentration of stage I autocatalyst is an intermediate product of the reduction of bromate to hypobromite ( y) and the concentration of stage I inhibitor bromide ( z).

The process diagram is presented as:

The model takes into account that the total concentration of cerium ions is constant value: + = With. It is assumed that the rate of an autocatalytic reaction is proportional to the concentration. The model for dimensionless concentrations has the form:

Where k 1 = k 1 - k 3 and member k 6 (k 7 y - k 8) 2 x selected empirically in such a way that the threshold values x in the model corresponded to the experimental values.

Taking into account the hierarchy of reaction rate constants allows us to replace differential equation for variable z algebraic and after introducing dimensionless variables to arrive at a system of two equations:

In equations (2) ε is a small parameter, so the vibration shape is relaxation. The phase portrait of the system is shown in Fig. 3a. In Fig. Figure 3b shows the oscillations of the variable x corresponding to the dimensionless concentration of Ce 4+ ions.

Rice. 3. a - phase portrait of system (2). The dotted line indicates null isoclines, the thick line indicates the limit cycle. x- dimensionless concentration of Ce 4+ ions. y- dimensionless autocatalyst concentration is a fast variable. b - kinetics of concentration of Ce 4+ ions - relaxation vibrations. N, M- the smallest and highest value variable, T 1 , T 2 - time of increase and decrease in the concentration of Ce 4+ ions. T- period of oscillation (Zhabotinsky, 1974)

Spatiotemporal regimes in the Belousov-Zhabotinsky system

The disadvantage of the Jabotinsky model is the presence of a variable y- an “autocatalyst” that does not correspond to any real chemical compound. Subsequently, several models were proposed to describe the mechanism of the BZ reaction. The most popular of these is the reaction scheme proposed by Field, Koros et al. 1972, consisting of 10 reactions with seven intermediates. Later, Field and Noyes (Field. and Noyes 1974) proposed a simpler scheme, called the “oregonator” after the University of Oregon (USA), where it was developed. The reaction scheme looks like:

Here A, B are the initial reagents, P, Q are the products, X, Y, Z are intermediate compounds: HBrO 2 - bromide, Br - bromide ion, and Ce 4+.

The concentrations of the initial reagents are assumed to be constant in the model. Let us denote by small letters the variables corresponding to the concentrations of the reagents and write down the equations for their changes over time in accordance with the law of mass action:

The numerical values of the rate constants of direct reactions were estimated by the authors from experimental data. Their meanings:

[A] = [B] = 0.06 M; k 1 = 1.34 M/s, k 2 = 1.6·10 9 M/s, k 3 = 8·10 3 M/s, k 4 = 4·10 7 M/s (5) Stoichiometric factor f and a constant k 5, parameters associated with reagent consumption varied.

The dimensionless form of writing the Oregonator model has the form:

Here are the dimensionless concentrations: x - , y - , z- metal ion concentration, parameter f considered in the range 0< f< 2 (Field and Noyes, 1974).

System (6) may have a zero stationary state:

which is always unstable, and one positive stationary state:

Analysis of the stability of this stationary state (Field and Noyes, 1974) allowed us to find the region in which solution (8) loses stability. Bifurcation diagram of the system for the parameter plane f,k 5 is shown in Fig. 4 a, in Fig. Figure 4 b shows the oscillation shape of the variable. The parameter values are given in the caption to the figure.

Rice. 4. a is the region of stability (A) and instability (B) of the positive stationary solution (17.8) of the Oregonator model (17.4, 17.6). b - high-amplitude oscillations of the variable x. Parameter values: s= 77.27, q= 8.375·10 -6, w= 0.161 k 5 (Field and Noyes 1974).

The relationship of parameters in the system is such that there is a hierarchy of characteristic times of change of variables. From Fig. 4b also shows that x- a fast variable for which the differential equation can be replaced by an algebraic one. Equating the right side of the first equation of system (6) to zero, we obtain:

From equation (9) we get x as a function y:

Substituting expression (10) into the second and third equations of system (6), we obtain a reduced “oregonator” model from two equations:

System (11) has a stable, large-amplitude limit cycle, and within it an unstable, small-amplitude limit cycle (Rinzel and Troy, 1982).

It is in this (or similar) form that the Field-Noyes system of equations was studied by many authors as a local element of a distributed system of the reaction-diffusion type. Due to the possibility of observing the BZ reaction in experiment different kinds autowave modes, models simulated various types of influences on system parameters (for example, periodic), modes were considered in two-dimensional and three-dimensional systems in the presence of various types of boundaries.

In Fig. Figure 5 (a, b, c, d) shows the sequence of development over time of various types of regimes on the surface of a Petri dish during the Belousov-Zhabotinsky reaction. It is known that if a local element of the system has oscillatory properties, distributed system can demonstrate leading centers (a), spiral waves (c), complex spatiotemporal distributions (b, d).

Rice. 5. Various spatial regimes in the Belousov-Zhabotinsky reaction. Each series of figures (a-d) shows the sequential development of processes over time (Zhabotinsky, 1975)

The question arises whether it is possible to influence the development of these complex structures in time and space with the help of external influences. The effects consist of changing the rate of influx of final and intermediate substances into the reaction sphere, various modes of constant and periodic lighting, and radioactive irradiation with high-energy particles. Such studies have great practical meaning. They make it possible to find ways to control autowave activity and help to search for modes of influence on spiral waves in the active tissue of the heart, the decay of which leads to fibrillation. Indeed, already in the first axiomatic models of active media (see lecture 18) it was discovered that if there is a spiral wave in the medium, the exit of its “tip” to the boundary of the active region will lead to the attenuation of such a wave (Ivanitsky, Krinsky et al. 1978). The Belousov-Zhabotinsky reaction provides a good experimental model for studying the control of wave dynamics.

When studying effects of different natures, different modifications of the BZ reaction are used. The effect of high-energy α-particles from a cyclotron is studied on a system in which ferroin, a complex of divalent iron Fe(II) with phenanthroline (phen), is used instead of Ce 4+ compounds. When a solution is irradiated in a capillary, two flat waves, which diverge into opposite directions from the irradiation center. When a solution is irradiated in a Petri dish, a concentration wave appears with its center on the irradiated portion of the solution. Under the influence of total irradiation of the entire reaction volume, complete extinction of autowave processes is observed (Lebedev, Priselkova et al. 2005).

From the point of view of experimental possibilities, it is especially convenient to use different protocols of light exposure, constant illumination of the entire reaction system or part of it, constant illumination of different intensities, periodic illumination, etc. Control using light exposure becomes possible when using light-sensitive Ru ions as a reaction catalyst. bpy) 3 2+ . Typically, the reaction is carried out in a Petri dish filled with a thin layer of silicone gel, to which the reagents necessary for the BZ reaction to occur have been added. In such a system, divergent spiral waves are observed, but the action of a thin laser beam leads to a break in the front and the appearance of two spiral waves (Fig. 6) (Muller, Plesser et al. 1986; Muller, Markus et al. 1988).

Rice. 6. Spiral waves in a thin layer of an excitable Belousov-Zhabotinsky reaction medium, cell size 9 square meters. mm. (Muller, Plesser et al. 1986)

Spiral wave tip trajectory control

In the laboratory of Prof. Stefan Müller (University of Magdeburg, Germany) developed a technique that allows one to “extend” the tip of one of the waves beyond the boundary of a Petri dish, and subsequently observe the evolution of a single spiral wave, the “tip” ( tip) which makes complex spatial movements, the trajectory depends on the lighting regime (Grill, Zykov et al., 1995).

Rice. 7. Two types of spiral wave tip trajectories obtained in an experiment for the photosensitive BZ reaction. Distance from the center of the unperturbed trajectory (dashed line) to the measurement point (cross) a - 0.49 mm, b - 0.57 mm (Grill et al., 1995)

Under constant illumination, the tip describes a cycloid with four “petals” (Fig. 7, dotted line). The effect of light pulses on the trajectory of the tip of a spiral wave was studied. Pulses were supplied at the moment when the wave front reached a certain point (marked with a cross in Fig. 7), or with a certain specified delay.

Two types of regimes 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. 7a ). 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 shaped like the drift of a 4-lobed cycloid along a circle of large radius, the center of which is again located at the “measurement point.” Both modes turned out to be stable with respect to small displacements of the measurement point, that is, they are attractors. A similar result is obtained if the light pulse is supplied with some delay relative to the moment the wave passes through the measurement point. The radius of the “great circle” along which the cycloid moves increases with increasing delay time.

With periodic modulation of constant illumination, synchronization of the movement of the tip and drift of the “tip” of the wave are observed (Fig. 7a). A model was used to describe the process mathematically (Zykov, Steinbock et al., 1994):

Here are the variables u, v And w correspond to the concentrations of HBrO 2 , catalyst and bromide concentrations, respectively. Member ø in the third equation reflects the light-induced flow of Br - ions, f, q- dimensionless parameters. An assessment of the rate constants of individual reactions shows the presence of a time hierarchy of processes in the system:

έ <<ε<<1. (13)

The fulfillment of this inequality allows us to calculate the bromide concentration w“a very fast variable”, equate the right side of the equation for this variable to zero, and find an expression for its quasi-stationary value in terms of the concentrations of slower variables:

Substituting this expression into the first and second equations of system (12), and taking into account the diffusion of reagents, we obtain for such a modified “oregonator” model a reaction-diffusion type system:

Here are the variables u And v correspond to the concentrations of HBrO 2 and catalyst.

In the works of the group of S. Muller and V. Zykov (Zykov, Steinbock et al. 1994; Grill, Zykov et al. 1995), using system (15), the system parameters were studied on the model, at which the regimes observed in the experiment are reproduced (Fig. 8 ).

Rice. 8. The trajectories of the tip of the spiral wave calculated using model (15) for the impact amplitude A = 0.01 and different values of the delay time τ in the “control loop” of light pulses. a - τ = 0.8; b - τ = 1.5 (Grill, Zykov et al., 1995).

Rice. 9. Types of trajectories of the tip of a spiral wave obtained during computational experiments on model (15) at different periods of harmonic modulation of the parameter ø sensitive to light. The abscissa axis shows the modulation period, and the ordinate axis shows the modulation amplitude. The dotted lines indicate the boundaries of the regions in which the resonant “capture” of the system’s natural oscillation frequency by the impact frequency occurs. l/m- the ratio of the number of loops that the tip of the spiral wave describes to the number of periods of modulation of light exposure. T 0 is the intrinsic period of rotation of the tip of the spiral in the absence of external influence (Zykov, Steinbock et al., 1994).

The model also makes it possible to study possible modes of behavior of the tip of a spiral wave at different amplitudes and frequencies of modulation of periodic light exposure. The general picture of the types of trajectories is summarized in Fig. 9, the general theory of this type of system was developed by V.I. Arnold, and the graphs of areas in which this type of behavior is observed are called “Arnold's languages.”

Model studies of autowave processes in the Belousov-Zhabotinsky reaction have made an important contribution to the study of the possibilities of controlling autowave processes in such vital organs as the brain and heart. In subsequent studies, it was shown that using this reaction it is possible to simulate a wide variety of processes, including the formation of spiral waves - in the terminology of cardiologists - reentry, the appearance of which in the myocardium is associated with fibrillations and various arrhythmias - dangerous heart diseases (Fig. 10)

Rice. 10. Three-dimensional rotating vortex (reentry) in the ventricles of a dog (a, b), model (Aliev and Panfilov 1996) and in the Belousov-Zhabotinsky reaction, experiment (c, d) (Aliev, 1994). The complex shape of the vortex in the three-dimensional model arises from the complex geometry and anisotropy of the ventricular environment.

Experimental and theoretical research into the BZ reaction has been ongoing for more than half a century. Dissipative structures of various kinds, oscillatory standing clusters, standing waves, localized structures and many others are studied experimentally. The current state of science in this area is reflected in the monograph by Vladimir Karlovich Vanag (Published by IKI-RKhD, 2008), which is accompanied by a CD with software and examples of the implementation of remarkable space-time structures observed in the Belousov-Zhabotinsky reaction and similar systems.

Literature

Aliev R.R. and Panfilov A.V. A simple two-variable model of cardiac excitation, Chaos. Solutions and Fractals, 7(3), 293-301, 1996

Field R., J., E. Koros, et al. Oscillations in chemical systems. Part 2. Thorough analysis of temporal oscillations in the bromat-cerium-malonic acid system. J. Am. Che. Soc. 94, 8649-8664, 1972

Field R.J. and Noyes R.M. Oscillations in chemical systems. Part 4. Limit cycle behavior in a model of a real chemical reaction. J. Chem. Phys. 60, 1877-1944, 1974

Gray P., Scott S. Chemical oscillations and instabilities. Non-linear chemocal kinetics/International series of monographs on chemistry. v. 21. Clarendon Press, Oxford, 1994

Grill S., Zykov V.S., et al. Feedback controlled dynamics of meandring spiral waves. Physical Review Letters 75(18), 3368-3371, 1995

Muller S.C., T. Plesser, et al.. "Two-dimensional spectrophotometry and pseud-color representation of chemical patterns." Naturwiss. 73>, 165-179, 1986

Muller, S., M. Markus, et al.. Dynamic Pattern Formation in Chemistry and Mathematics. Dortmund, max-Plank Institute. 1988

Zykov V.S., O. Steinbock, et al. "External forcing of spiral waves." Chaos 4(3), 509-516, 1994

Aliev R.R. Simulation of the electrical activity of the heart on a computer. On Sat. Medicine in the mirror of computer science. P. 81-100, M., Nauka, 2008

Belousov B.P. Periodically acting reaction and its mechanisms. Collection of abstracts on radiation medicine for 1958. M., p. 145, 1958

Vanag V.K. Dissipative structures in reaction-dissipative systems. Ed. IKI-RHD. M.-Izhevsk, 2008

Zhabotinsky A. M. “Concentration self-oscillations.” M., Nauka, 1974

Zhabotinsky A. M., Otmer H., Field R. Oscillations and traveling waves in chemical systems. M., Mir, 1988

Ivanitsky G.R., Krinsky V.I., Selkov E.E.. Mathematical biophysics of the cell. M., Nauka, 1978

Lebedev V.M., Priselkova A.B., et al.. "Initiation of leading centers in the Belousov-Zhabotinsky reaction under the influence of a beam of alpha particles with an energy of 30 MeV." Preprint SINP MSU 31.797: 1-14. 2005)

Field, R., & Burger, M. (Eds.). Oscillations and traveling waves in chemical systems. M., Mir, 1988

Topic 2

MN-12: Marina Makarova, Yuri Likhachev, Ivan Korotkevich, Natalia Kutsan, Ekaterina Kostyuchenkova, Ermovsky Velor.

Give the concept

Entropy

Information

Basics of systems analysis

System, rules for allocating systems

Types of systems:

Homogeneous – heterogeneous

Open – closed

Equilibrium - nonequilibrium.

The second law of thermodynamics, its interpretation from the positions of thermodynamics, cosmology, philosophy.

Entropy as a measure of molecular disorder

Statistical nature of the second law of thermodynamics

The second law of thermodynamics as the principle of increasing disorder and destruction of structures

The main paradox of the evolutionary picture of the world: the pattern of evolution against the background of a general increase in entropy

Entropy of an open system: entropy production in the system, entropy flows in and out

Thermodynamics of life: extracting order from the environment

Thermodynamics of the Earth as an open system

Justify why living organisms are nonequilibrium open systems.

Give the concept

Nonlinearity

Bifurcation

Give the concept

Fluctuation

Self-organization

What are chaotic systems

Give the concept of an attractor

Examples of self-organization in the simplest systems: laser radiation, Benard cells, Belousov-Zhabotinsky reaction, spiral waves

Why is the phenomenon of self-organization possible only in open, nonequilibrium systems? The essence of self-organization. Identify the phases and construct a diagram of the process of development of open nonequilibrium systems with the emergence of a new order.

Why is the theory of self-organization applicable in different disciplines (physics, chemistry, biology, economics, politics, psychology.....)

Principles of organization of modern natural science.

1. Matter is a set of quantized fields, the quantum of which is elementary particles (Babanazarova O.V. Concepts of modern natural science. Part 1: tutorial/ Yaroslavl State. univ. Yaroslavl, 2000)

Matter- this is everything weighty, everything that occupies space or everything earthly (stone, wood, air, etc.); the general abstract concept of materiality, corporeality, everything that is subject to feelings: the opposite of the spiritual (mental and moral) (Explanatory Dictionary of the Living Great Russian Language by Vladimir Dahl).

Matter- this is that imperishable, unchanging, constantly abiding thing that underlies the changing, sensually perceived physical phenomena (Small Encyclopedic Dictionary of Brockhaus and Efron).

Energy- (from the Greek energyeia - activity) - a measure of various types of movement and interaction in the forms: mechanical, thermal, electromagnetic, chemical, gravitational, nuclear (Gorelov A.A. Concepts of modern natural science. - M.: Center, 2002. p. 76 ).

Energy- a scalar physical quantity, which is a unified measure of various forms of motion of matter and a measure of the transition of the motion of matter from one form to another (Dictionary of Natural Sciences. Glossary.ru).

Energy- a general quantitative measure of the movement and interaction of all types of matter (Great Soviet Encyclopedia).

2. Entropy- this is a measure of disorder, disorganization of the system (Gorelov A.A. Concepts of modern natural science. - M.: Center, 2002. p. 75).

Information– (from Latin informatio – familiarization, explanation) is a measure of the organization of the system (Gorelov A.A. Concepts of modern natural science. – M.: Center, 2002. p. 75).

3. System- a whole made up of parts; it is a collection of interconnected elements that form some kind of integral unity.

System allocation rules:

Set a goal;

Identify elements that are considered indivisible at a given level of analysis;

Identify connections between elements;

Understand the laws of composition by which elements interact and form integrity.

4. Types of systems:

I 1) Homogeneous– systems in which the same elements are present;

2) Heterogeneous - systems whose constituent elements are of different natures.

II 1) Open– systems that exchange energy, information, matter;

2) Closed– systems that do not receive energy from the outside.

III1 ) Equilibrium– systems that, when transitioning from one state to another, require an influx of energy; when making this transition, the system can maintain its state for quite a long time without an additional influx of energy, matter, or information;

2) Nonequilibrium– systems that require a constant influx of energy, matter, information to maintain their complexity, since part of the energy is constantly dissipated.

(Gorelov A.A. Concepts of modern natural science. - M.: Center, 2002. pp. 72-83).

5. Natural processes are always directed towards the system achieving an equilibrium state (mechanical, thermal or any other). This phenomenon is reflected second law of thermodynamics, which is also of great importance for analyzing the operation of thermal power machines. In accordance with this law, for example, heat can spontaneously transfer only from a body with a higher temperature to a body with a lower temperature. To carry out the reverse process, some work must be expended. There are severalequivalentformulations of the second law of thermodynamics:

Clausius's postulate:“A process is impossible, the only result of which would be the transfer of heat from a colder body to a hotter one”(this process is called Clausius process).

Thomson's postulate:“A circular process is impossible, the only result of which would be the production of work by cooling the thermal reservoir”(this process is called Thomson process).

From the perspective of thermodynamics, this law can be interpreted as follows: 1) transfer of heat from a cold source to a hot one is impossible without the cost of work;

2) it is impossible to build a periodically operating machine that performs work and, accordingly, cools the thermal reservoir;

3) nature strives for a transition from less probable states to more probable ones.

In other words, the second law of thermodynamics prohibits the so-called perpetual motion machines of the second kind, showing that it is impossible to convert all the internal energy of a body into useful work.

From the perspective of cosmology, this law can be interpreted as follows:

If our Universe is an isolated (closed) system, then energy exchange with other systems is impossible. None of the scientists doubted that our world is an isolated system, but then, according to the second law of thermodynamics, all types of energy must eventually turn into heat, which will be evenly distributed throughout the system, that is, the Universe will come to a state of thermal equilibrium and all macroscopic the movements in it will stop. The so-called heat death of the universe. Many have tried to resolve this contradiction. In order to reconcile this conclusion with the infinite existence of the Universe, Boltzmann argued that, due to the statistical nature of the second law, it does not hold accurately. In some fairly large region of the Universe, a fluctuation occurred, and the entropy in it decreased. Although this phenomenon is extremely rare, due to the infinity of the Universe, we have an infinite amount of time to wait for it. As we will see in the conversation about the evolution of the Universe, negative gravitational energy was not taken into account in these considerations, since the expansion of the Universe was not yet known. Taking into account the negative energy of gravity, without violating the law of conservation of energy, leads to the fact that the positive part of the energy can increase, and the increase in entropy that necessarily occurs does not necessarily lead to the fading of processes in the Universe.

From a philosophical perspective, this law can be interpreted as follows:

Order can never, under any circumstances, emerge from chaos by itself. In other words, spontaneous complication of any system is impossible.

Kirillin V.A. Technical thermodynamics: Textbook for universities. - 4th ed., revised. - M.: Energoatomizdat, 1983.

6. The discrepancy between the transformation of heat into work and work into heat leads to a one-sided direction of real processes in nature, which reflects the physical meaning of the second law of thermodynamics in the law on the existence and increase in real processes of a certain function called entropy, determined as a measure of molecular disorder.

Entropy – it is a measure of the disorder of a system, a measure of the dissipation of energy, a form of expressing the amount of bound energy that a substance has.

According to the second law of thermodynamics, all real processes in the Universe must occur with increase in entropy. Entropy, as Boltzmann showed, characterizes the degree of disorder in a system: the greater it is, the greater the disorder.

The physical meaning of the increase in entropy comes down to the fact that the

from a certain set of particles isolated (with constant energy)

the system tends to move to a state with the least order

particle movements. This is the simplest state of the system, or

thermodynamic equilibrium in which the movement of particles is chaotic.

Maximum entropy means complete thermodynamic equilibrium, which

equivalent to chaos.

However, based on Prigogine's theory of change, entropy is not just

non-stop sliding of the system to a state devoid of any

there was no organization. Under certain conditions, entropy becomes

the progenitor of order.

(Gorelov A.A. Concepts of modern natural science. – M.: Center, 2002. pp. 86-87;

Kirillin V.A. Technical thermodynamics: Textbook for universities. - 4th ed., revised. - M.: Energoatomizdat, 1983)

7 . The second law of thermodynamics is statistical in nature (has a statistical nature) that is

applicable only to systems containing a large number of particles. Really,

Let's consider an example: a gas located in one half of the vessel tends to be evenly distributed throughout its entire volume if the partition is removed. This happens because the first state is more ordered; it can be achieved in only two ways, when the gas is in either one or the other half of the vessel. The second state, when the gas is uniformly distributed throughout the entire volume, is the most random, since it can be achieved in a huge number of ways due to the mutual rearrangement of all gas molecules while maintaining their total energy. And if in our example the gas contained a dozen particles, then due to fluctuations they would sometimes collect in one half of the vessel or the other. However, with an increase in the number of particles, these states would occur less and less often, and with a number of particles of the order of 10 22 such an event would be simply incredible. Although in principle it can occur, since the probability of its occurrence, although infinitely small, is not exactly zero.

(

8. The second law of thermodynamics states that all real processes in the Universe must occur with increasing disorder and destruction of structures– with an increase in entropy.

A more precise formulation of the second law of thermodynamics then takes

view: During spontaneous processes in systems with constant energy, entropy always increases.

In a state of equilibrium it is maximum. Entropy, as Boltzmann showed, characterizes the degree of disorder in a system: the greater it is, the greater the disorder. It is now clear that equilibrium thermal energy is useless for doing work because it is the most disordered. It becomes clear why all natural processes in nature involve energy dissipation. Because it increases clutter.

(Kirillin V.A. Technical thermodynamics: Textbook for universities. - 4th ed., revised. - M.: Energoatomizdat, 1983)

9.Evolution- an objective change occurring over time, manifested as rigorous, continuous improvement, leading to an increase in the quality level and degree of organization of objects, and on the basis of this - their successful adaptation and effective functioning within certain conditions.

Evolution- this is a way for the living to resist entropy, growing chaos and disorder. It creates various innovations, but natural selection preserves only those that give organisms resistance to further changes, those that allow them to reproduce their copies in a long series of generations, practically without changing. Strange as it may seem, it turns out that evolution works against itself.

We are accustomed to the fact that evolution is the creation of something new, more complex and perfect. But in fact, evolution is the creation of not just new things, but new things that resist further change. The surprising thing is that, while resisting entropy, evolution is actually driven by this very entropy. Thus, organisms cannot escape mutations - failures in the mechanism of transmission of hereditary information from parents to descendants. Mutations ultimately lead to the death of organisms and the extinction of species. But what is surprising is that during this inherently destructive process (a particular manifestation of entropy), innovations are accidentally created, which, again, by chance may turn out to be resistant to further degradation. It is they who are preserved by selection. This is how the genetic code once arose (no wonder it is universal for all organisms!) and the mechanism for organisms to recreate their copies from environmental material, this is how a diploid set of chromosomes and sexual reproduction arose, this is how care for offspring and various other complex forms of animal behavior arose (and in after all, our culture). In short, this is how everything was formed that allows organisms to reproduce themselves in descendants without disappearing from the face of the Earth.

10 . In open systems there are three streams of entropy.

The first flow is its own entropy, which, as in closed systems, always grows.

The second flow is the exported entropy (outgoing flow) removed from the system to the external environment. This flow is briefly called entropy export.

The third flow is imported entropy (incoming flow) entering the system from the external environment.

The resulting entropy of an open system depends on the relationship between these three flows and can behave in any way: increase, decrease, or be constant. If entropy is constant, then the system is said to be in stationary mode.

(A.P. Sadokhin Concepts of modern natural science. M., 2005)

11 . For terrestrial organisms, general energy exchange can be simplified as the formation of complex carbohydrate molecules from CO2 and H2O in photosynthesis, followed by the degradation of photosynthesis products in respiration processes. It is this energy exchange that ensures the existence and development of individual organisms - links in the energy cycle. So is life on Earth in general. From this point of view, the decrease in the entropy of living systems in the process of their life activity is ultimately due to the absorption of light quanta by photosynthetic organisms, which, however, is more than compensated by the formation of positive entropy in the depths of the Sun. In other words, living organisms extract orderliness from the environment.

This principle also applies to individual organisms, for which the supply of nutrients from the outside, carrying an influx of “negative” entropy, is always associated with the production of positive entropy during their formation in other parts of the external environment, so that the total change in entropy in the system organism + external environment is always positive .

Under constant external conditions in a partially equilibrium open system in a stationary state close to thermodynamic equilibrium, the rate of entropy increase due to internal irreversible processes reaches a non-zero constant minimum positive value.

diS/dt => Amin > 0

This principle of minimum entropy gain, or Prigogine's theorem, is a quantitative criterion for determining the general direction of spontaneous changes in an open system near equilibrium.

This condition can be represented differently:

d/dt (diS/dt)< 0

This inequality indicates the stability of the stationary state. Indeed, if a system is in a stationary state, then it cannot spontaneously exit it due to internal irreversible changes. When deviating from a stationary state, internal processes must occur in the system, returning it to a stationary state, which corresponds to Le Chatelier’s principle - the stability of equilibrium states. In other words, any deviation from the steady state will cause an increase in the rate of entropy production.

In general, a decrease in the entropy of living systems occurs due to free energy released during the breakdown of nutrients absorbed from the outside or due to the energy of the sun. At the same time, this leads to an increase in their free energy. Thus, the flow of negative entropy is necessary to compensate for internal destructive processes and loss of free energy due to spontaneous metabolic reactions. In essence, we are talking about the circulation and transformation of free energy, due to which the functioning of living systems is supported.

12. The thermodynamics of the Earth as an open system arises under the influence of two factors:

Under the influence of the external environment

Change within the system itself

Knowing these factors, we can calculate the rate of change of entropy

dS/dt = d e S/dt + d i S/dt.

The resulting expression means that the rate of change in the entropy of the system dS/dt is equal to the rate of entropy exchange between the system and the environment plus the rate of entropy generation within the system.

The term d e S/dt , which takes into account the processes of energy exchange with the environment, can be both positive and negative, so that when d i S > 0, the total entropy of the system can either increase or decrease.

Negative value d e S/dt< 0 соответствует тому, что отток положительной энтропии от системы во внешнюю среду превышает приток положительной энтропии извне, так что в результате общая величина баланса обмена энтропией между системой и средой является отрицательной. Очевидно, что скорость изменения общей энтропии системы может быть отрицательной при условии:

dS/dt< 0 if d e S/dt < 0 and |d e S/dt| >d i S/dt.

Thus, the entropy of an open system decreases due to the fact that conjugate processes occur in other parts of the external environment with the formation of positive entropy.

(S.H. Karpenkov Concepts of modern natural science.-M.: 2002)

13. Open systems are characterized by the exchange of matter and energy with the environment, including with other systems, while for closed systems such exchange is excluded. Closed systems practically do not exist in reality; this is a certain idealization technique for solving research problems. A non-equilibrium system is characterized by the need for a constant supply of energy to achieve a new state, since energy is constantly dissipated; this situation is far from equilibrium. A plant, animal or person is an amazing example of a heterogeneous, open, nonequilibrium chemical system. In an unstable balance. They are an extremely low-probability structure with very low entropy. This instability is especially pronounced when death occurs.

(Babanazarova O.V. Concepts of modern natural science. Part 1: textbook / Yaroslavl State University Yaroslavl, 2000. c 19-20).

14. Nonlinearity– differential equations that describe phenomena have several solutions (Babanazarova O.V. Concepts of modern natural science. Part 1: textbook / Yaroslavl State University Yaroslavl, 2000. p. 43).

Bifurcation– branching, bifurcation in the trajectory of the system at a certain point (Grushevitskaya T.G., Sadokhin A.P. Concepts of modern natural science: textbook - M.: higher school, 1998. p. 366)

Bifurcation– (from Latin Bifurcus - bifurcated) - the acquisition of a new quality by the movements of a dynamic system with a small change in its parameters, the point of an abrupt change in the state of the system

(Babanazarova O.V. Concepts of modern natural science. Part 1: textbook / Yaroslavl State University Yaroslavl, 2000. p. 42)

15. Fluctuation– random deviation of the system from the equilibrium position (Grushevitskaya T.G., Sadokhin A.P. Concepts of modern natural science: textbook - M.: Higher School, 1998. p. 380)

Self-organization– a natural jump-like process that transfers a nonequilibrium system, which has reached a critical state in its development, into a new stable state with a higher level of complexity and order compared to the original one. (Grushevitskaya T.G., Sadokhin A.P. Concepts of modern natural science: a textbook – M.: Higher School, 1998. p. 378)

16 .Chaotic systems- these are systems that are hypersensitive to the weakest fluctuations; these are unpredictable systems.

17 .Attractor– close to the concept of goal. A relatively stable state of the system, which seems to attract the entire set of trajectories of the system’s movement. If a system falls into an attractor cone, then it inevitably evolves to this relatively stable state

(Babanazarova O.V. Concepts of modern natural science. Part 1: textbook / Yaroslavl State University Yaroslavl, 2000. p. 25).

18. Examples of self-organization in the simplest systems: laser radiation, Benard cells, Belousov-Zhabotinsky reaction, spiral waves.

The generation of laser radiation is considered example of temporaryself-organization A continuous laser is a highly nonequilibrium open system formed by excited particles (atoms, molecules) and electromagnetic modes. fields in the resonator. The disequilibrium of this system is maintained by a continuous influx of energy from the outside. incoherent source (pumped). At low pump intensities, the radiation of the system consists of wave trains that are not phased with each other. With increasing pump intensity up to a certain threshold value, the radiation of the system becomes coherent, i.e. represents a continuous wave train, in which the phases of the waves are strictly correlated macroscopically. distances from the emitter. This transition to the generation of coherent oscillations can be interpreted as self-organization

H. Benard cells. A classic example of the emergence of a structure is the Bénard convective cell. If you pour mineral oil into a frying pan with a smooth bottom, add small aluminum filings for clarity and start heating, we will get a fairly clear model of a self-organizing open system. With a small temperature difference, heat transfer from the lower layer of oil to the upper occurs only due to thermal conductivity, and the oil is a typical open chaotic system. But at a certain critical temperature difference between the lower and upper layers of oil, ordered structures appear in it in the form of hexagonal prisms (convective cells), as shown in Figure 1.

Picture 1.

In the center of the cell, the oil rises up, and at the edges it goes down. In the upper layer of a hexagonal prism it moves from the center of the prism to its edges, in the lower layer - from the edges to the center. It is important to note that for the stability of fluid flows, heating adjustment is necessary, and this occurs self-consistently. A structure emerges that supports the maximum speed of heat flows. Since the system exchanges only heat with the environment and in a stationary state (at T1) it receives as much heat as it gives off (at T2< Т1), то

S=(Q/T1)-(Q/T2)< 0, т.е. внутренняя структура (или самоорганизация) поддерживается за счет поглощения отрицательной энтропии, или негэнтропии из окружающей среды. Подобные конвективные ячейки образуются в атмосфере, если отсутствует горизонтальный перепад давления.

Belousov-Zhabotinsky reaction. Chemical clock. Self-organization in chemical systems is associated with the entry of new substances from outside, which ensure the continuation of the reaction, and the release of waste substances into the environment.

Figure 2

Such reactions were obtained in the 50s of the 20th century by Soviet scientists B. Belousov and A. Zhabotinsky. However, the results they obtained were so unusual that scientists could not publish them for a long time. Only in the 80s did they gain recognition. The essence of the Belousov-Zhabotinsky reaction is the oxidation of an organic acid with potassium bromide. By adding an indicator of redox reactions (ferroin), you can monitor the progress of the reaction by periodically changing the color of the solution. Externally, self-organization is manifested by the appearance of concentric waves in a liquid medium or by a periodic change in the color of the solution from blue to red and vice versa (Figure 2). This oscillatory process occurs without any external intervention over several tens of minutes and is called a “chemical clock.”

It should be noted that the oscillations occur around an unstable stationary state far from equilibrium states. (Near stable stationary states such periodic oscillations are impossible.)

Spiral waves. In synergetics (the theory of dissipative systems), the most fundamental factor is the self-organization of spiral autowave structures in active media with energy dissipation. Spiral waves represent the main type of elementary self-sustaining structures in homogeneous excitable media. Such a medium is precisely the physical vacuum. Therefore, the elementary particles of matter inevitably had to self-organize in it and, precisely, only in the form of spiral autowaves. This is also indicated by the basic patterns common to elementary particles and spiral waves:

corpuscular-wave nature of elementary particles (they, like the nuclei of spiral waves, have spatial coordinates);

cooperative behavior of both particles and spiral waves;

the presence of inertia of motion (both in elementary particles and in spiral autowave structural elements);

the presence of annihilation upon collision (both in elementary particles and antiparticles, and in converging and diverging spiral waves);

the presence of uncertainty in the time and space of the fulfillment of the quantum of action (it is fundamentally impossible to determine the beginning and end of any spiral turn that carries the quantum of action and, therefore, to accurately determine the coordinates of the world points of the fulfillment of the action);

the possibility of interpreting the terminal local sinks of spiral waves as negative electrical elementary charges, and their primary local sources as positive elementary charges;

the electron has its own angular momentum, not associated with its rotation (the radial movement of the turns of a spiral wave is similar to the effect of the rotation of a rigid logarithmic spiral);

the presence of positive and negative spin values in elementary particles (similar to right and left twisted spirals);

the formation of an orbital wave by an electron in an atom (similar to the formation of simple vortex rings by spiral waves);

the impossibility of the existence of both a lone quark and a lone twisted vortex ring;

the presence of asymptotic freedom, both in quarks and in twisted vortex rings meshed with each other (interaction forces arise only when an attempt is made to separate them);

a similarity of topological prohibitions that limit the number of permissible elementary particles and three-dimensional spiral structures;

a very short lifespan of both elementary particles and three-dimensional spiral structures, unable to self-organize into structures of a higher hierarchical level.

M. Eigen. Self-organization of matter and evolution of biological macromolecules. M. "Mir", 1973.

Dubnischeva T.Ya. Concepts of modern natural science. - Novosibirsk: UKEA, 1997.

19. Why is the phenomenon of self-organization possible only in open, nonequilibrium systems? The essence of self-organization. Identify the phases and construct a diagram of the process of development of open nonequilibrium systems with the emergence of a new order.

SELF-ORGANIZATION- spontaneous (not requiring external organizing influences) formation of ordered spatial or temporal structures in highly nonequilibrium open systems (physical, chemical, biological, etc.).

Continuous flows of energy or substances entering a system maintain it in a state far from equilibrium. Under such conditions, the system develops its own (internal) instabilities (areas of unstable behavior), the development of which is self-organization.

Self-organization represents the possibility of changing the state of the system, and the impact can only be exerted on open system and only a nonequilibrium system is capable of change and development. Such systems are sensitive to the influences of internal system elements. Therefore, the phenomenon of self-organization is possible only in open, nonequilibrium systems.

Phases in the evolution of open nonequilibrium systems:

development according to linear laws (maintaining homeostasis, predictability, the ability to experience influences as random as a result of external and internal interactions. Consequently, disequilibrium increases. Connections between elements are broken. In this state, a transition to phase 2 is possible)

bifurcation point (bifurcation) The system behaves unpredictably, nonlinearly. At the bifurcation point, the system does not remember its past. A development path is chosen and a new structure is formed.

With self-organization, new structures arise, order increases, the free energy of the system increases, and entropy decreases.

(Nikolis G., Prigozhin I., Self-organization in nonequilibrium structures, trans. from English, M., 1979)

Belousov-Zhabotinsky reaction

Change in color of the reaction mixture in the Belousov-Zhabotinsky reaction with ferroin

Currently, this name unites a whole class of related chemical systems, similar in mechanism, but differing in the catalysts used (Ce 3+, Mn 2+ and Fe 2+, Ru 2+ complexes), organic reducing agents (malonic acid, bromomalonic acid, citric acid, malic acid, etc.) and oxidizing agents (bromates, iodates, etc.). Under certain conditions, these systems can demonstrate very complex forms of behavior from regular periodic to chaotic oscillations and are an important object of study of the universal laws of nonlinear systems. In particular, it was in the Belousov-Zhabotinsky reaction that the first experimental strange attractor in chemical systems was observed and its theoretically predicted properties were experimentally verified.

History of discovery

Some configurations arising during the Belousov-Zhabotinsky reaction in a thin layer in a Petri dish

Reaction mechanism

Jabotinsky proposed the first reaction mechanism and a simple mathematical model that was capable of demonstrating oscillatory behavior. Subsequently, the mechanism was expanded and refined, the experimentally observed dynamic modes, including chaotic ones, were theoretically calculated and their correspondence to experiment was shown. Full list The elementary stages of the reaction are very complex and amount to almost a hundred reactions with dozens of substances and intermediates. Until now, the detailed mechanism is unknown, especially the reaction rate constants.

Reaction opening value

The Belousov-Zhabotinsky reaction has become one of the most famous chemical reactions in science; many scientists and groups of various people are studying it. scientific disciplines and directions all over the world: mathematics, chemistry, physics, biology. Its numerous analogues have been discovered in various chemical systems (see, for example, the solid-phase analogue - self-propagating high-temperature synthesis). Thousands of articles and books have been published, many candidate and doctoral dissertations have been defended. The discovery of the reaction actually gave impetus to the development of such branches of modern science as synergetics, the theory of dynamic systems and deterministic chaos.

Notes

Links

From the history of the discovery and study of self-oscillatory processes in chemical systems: on the 50th anniversary of the discovery of the Belousov-Zhabotinsky reaction
B. P. Belousov and his oscillatory reaction, magazine “Knowledge is power”
Belousov Jabotinsky and Briggs Rauscher reaction schemes, differential equations
V. A. Vavilin. Self-oscillations in liquid-phase chemical systems
A. A. Pechenkin. Worldview significance of oscillatory chemical reactions
Oscillations and traveling waves in chemical systems. Ed. R. Field and M. Burger. M., “Mir”, 1988 / Oscillations and traveling waves in chemical systems. Ed. by R.J.Field and M.Burger. 1985 by John Wiley and Sons, Inc. (Engl)/

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Belousov's reaction- Change in the color of the reaction mixture in the Belousov-Zhabotinsky reaction with ferroin. The Belousov-Zhabotinsky reaction is a class of chemical reactions occurring in an oscillatory mode, in which some reaction parameters (color, concentration ... Wikipedia

Belousov-Zhabotinsky reaction

Briggs-Rauscher reaction- (“iodine clock”) self-oscillating chemical reaction. When hydrogen peroxide, iodic acid, manganese (II) sulfate, sulfuric and malonic acids and starch interact, an oscillatory reaction occurs with colorless golden blue transitions.... ... Wikipedia

Oscillatory reactions- Change in the color of the reaction mixture in the Belousov-Zhabotinsky reaction with ferroin. The Belousov-Zhabotinsky reaction is a class of chemical reactions occurring in an oscillatory mode, in which some reaction parameters (color, concentration of components ... Wikipedia

Belousov, Boris Pavlovich- Boris Pavlovich Belousov Photo from 1930 Date of birth: February 7 (19), 1893 (1893 02 19) Place of birth: Moscow Date from ... Wikipedia

The oscillatory reaction of Belousov-Zhabotinsky is called. Self-oscillatory reaction of Belousov-Zhabotinsky

History of discovery

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Jabotinsky-Korzukhin model

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Brusselator

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Experiment

Local models. Behavior of reagent concentrations over time. Jabotinsky model

Spatiotemporal regimes in the Belousov-Zhabotinsky system

Spiral wave tip trajectory control

Literature

18. Examples of self-organization in the simplest systems: laser radiation, Benard cells, Belousov-Zhabotinsky reaction, spiral waves.

Belousov-Zhabotinsky reaction

History of discovery

Reaction mechanism

Reaction opening value

see also

Notes

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