The Self-Made Tapestry Phần 3 pot

The idea that chemical reactions can develop travelling waves goes back a long waybefore, even, the

theory of oscillating reactions (which, as we saw, started with Lotka in 1910). At a meeting of German

chemists in Dresden in 1906, Robert Luther, director of the Physical Chemistry Laboratory in Leipzig,

presented a paper on the discovery and analysis of propagating chemical wavefronts in autocatalytic

reactions. Sceptics were apparently quelled by Luther's demonstration of the phenomenon before their

very eyeshe showed chemical waves in a reaction between oxalic acid and permanganate ions, projected

onto a screen in front of the audience.

Luther suggested that the waves arose from a competition between an autocatalytic reaction and the

process of diffusion that transports the chemical reagents through the reaction medium. Diffusion is a

random processmolecules of the reacting molecules are buffeted from all directions by collisions with

molecules of the surrounding solvent (generally water), and as a result they execute a convoluted,

meandering path often likened to a drunkard's walk. Despite this randomness, the molecules do actually

get somewhere rather than just meandering a little around their initial positionsbut the direction they

take is random, and the distance travelled from some initial location increases only rather slowly as time

progresses. (Whereas the distance covered by walking along a straight path at constant speed increases

in direct proportion to the time elapsed, the distance travelled by a random walker is proportional to the

square root of the elapsed time.) Random walks owing to diffusion were much studied at the beginning

of the century, notably by Albert Einstein.

When a chemical reaction is conducted under conditions where the concentrations are not maintained

uniformly throughout the medium by vigorous mixing, diffusion becomes important, since it limits the

rate at which a reagent that has become used up in one region can be replenished from elsewhere to

sustain further reaction. This is particularly important for autocatalytic reactions, since they can use up a

reagent locally at an extremely rapid rate. If diffusion cannot keep pace with this, the reaction runs into

problems. This is precisely the situation that I described earlieralthough not quite in these termsin the

vicinity of a wavefront in the BZ reaction. The inadequacies of diffusional transport create the

refractory period in the medium just behind an advancing wavefront, where the reaction has exhausted

itself but has not yet been replenished with fresh reagents. The poorly mixed BZ reaction is thus an

example of a so-called reaction-diffusion system, which is now clearly recognized as one of the most

fertile generic pattern-forming systems that we know of.

After Luther's pioneering studies, the theory of reaction-diffusion systems was placed on a firm

mathematical footing by the eminent population biologist Ronald Fisher and by the Russian

mathematician Andrei Kolmogoroff and co-workers, both of whom published seminal works in 1937.

Fisher was interested

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in reaction-diffusion processes for modelling the spread of an advantageous gene in a population, not

with their manifestation in chemistrya curious repetition of Volterra's assimilation of Lotka's ideas on

oscillating chemical reactions into mathematical biology earlier in the century. It is almost as if

chemists were for decades unwilling to face up to the existence of these complex and surprising

phenomena in their own field!

All the same, studies of waves in chemical media were conducted in parallel with, but independently

from, work on oscillatory reactions since the beginning of the century. In 1900 the German physical

chemist Wilhelm Ostwald described travelling pulses in an electro-chemical system. When he used a

zinc needle to prick the dark coating of oxidized iron on the surface of an iron wire immersed in acid,

Ostwald saw a colour change that propagated away from the point of contact at high speeds. From the

1920s onwards, many researchers studied this simple system as an analogue of nerve impulses (which

are also propagating electro-chemical waves), and in the early 1960s Jin-Ichi Nagumo and co-workers

in Tokyo observed spiral waves on the surface of a two-dimensional grid of iron wire subjected to this

treatment. But this work, published in Japanese, met the fate so common for studies that are not

reported in the English languageit was ignored in the West, until Zhabotinsky's efforts had established

the significance of this sort of wave activity.

The ripples spread

The BZ reaction is by no means unique: several other chemical mixtures share the same general

features of autocatalysis, feedback and competing reactions that lead to excitable and oscillatory

behaviour. It has been seen too in many biochemical processes, including, rather pleasingly, the

glycolytic cycle of metabolism that Belousov had first set out to emulate. Similar effects crop up in

some corrosion and combustion reactions. When these processes take place in poorly mixed conditions,

spatio-temporal patterns can arise whose forms are attractively diverse.

Fig. 3.7

Oscillations in the reaction of carbon

monoxide and oxygen on a platinum surface.

The reaction produces carbon dioxide.

Fig. 3.8

Target (a) and spiral (b) waves in the reaction of carbon monoxide and oxygen

on platinum. The images are all several tenths of a millimetre across.

(Photos: Gerhard Ertl, Fritz Haber Institute, Berlin.)

One of the functions of a catalytic converter in automobiles is to reduce emissions of carbon monoxide

(CO), a poisonous gas, in the exhaust fumes. This is done by combining CO with oxygen gas in the

converter to create carbon dioxide (CO2), a reaction that is

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speeded up by the use of a metal catalyst consisting of a mixture of rhodium and platinum. The reaction

takes place on the metal surface, where the chemical bonds in the reactant molecules are broken or

loosened up. So the reaction between CO and oxygen on a platinum surface is of considerable

technological interest. There is no obvious mechanism for autocatalysis here, howeverthe product is

simply CO2, which is not then involved in subsequent reactions.

So it was a surprise to Gerhard Ertl and colleagues at the Fritz Haber Institute in Berlin when they

found oscillatory behaviour in the rate of this reaction in 1985 (Fig. 3.7). And when in the early 1990s

the Berlin group developed a new kind of microscope to look at the way that the CO and oxygen were

distributed on the surface, they saw spiral and target patterns just like those of the BZ reaction, albeit

just a fraction of a millimetre across (Fig. 3.8). The bright regions in this figure correspond to parts of

the metal surface covered with CO molecules, and the dark regions are richer in oxygen atoms. Ertl's

team deduced that the molecules of CO that became stuck to the metal surface were altering its

structure, and thereby its catalytic behaviour, in a way that introduces feedback into this apparently

simple reaction.

Fig. 3.9

(a) The atomic structure of the 1 × 1 surface phase of platinum.

(b) In a vacuum, this surface will rearrange itself to the 1 × 2

reconstruction.

Platinum metal is a crystal: its atoms are packed together in a regular array like oranges on a fruit stall.

On a clean platinum surface exposed by cutting through the metal, the arrangement of atoms depends

on the angle at which the cut is made; for one particular cleavage plane, the surface looks like that in

Fig. 3.9a. This is called the {110} surface, and the arrangement of surface atoms is termed the (1 × 1)

phase. In a vacuum, the top-most atoms of a freshly exposed platinum (1 × 1) surface will

spontaneously shift their positions to create a different surface structure with a lower surface energy.

This is called the (1 × 2) phase, and has a 'missing' row of surface atoms (Fig. 3.9b). The rearrangement

process is called a surface reconstruction.

If CO molecules become attached to the reconstructed (1 × 2) surface of platinum, the balance of

energies gets shifted around, and the original (1 × 1) phase becomes more favourable. This means that,

as the reaction between CO and oxygen atoms on the platinum {110} surface proceeds, the surface does

not remain passive but shifts its structure between the (1 × 2) and (1 × 1) phases, depending on the

amount of CO on the surface.

Now the point is that these two surface phases have different catalytic abilities: the (1 × 1) phase is

considerably better at speeding up the reaction with oxygen than is the (1 × 2) phase. We can now see

the possibility of some subtle and complex interactions, which can give rise to feedback. The more the

bare (1 × 2) surface becomes covered in CO, the greater the extent of reconstruction to the (1 × 1) phase

and the more the catalytic potential of the metal is enhanced. But as the reaction proceeds, the CO gets

converted to CO2, which departs from the surface and leaves behind a bare (1 × 1) surface. On its own,

this prefers to revert to the reconstructed (1 × 2) phase.

Gerhard Ertl, David King at Cambridge University, and their co-workers have devised a six-step

reaction scheme that is akin to the Oregonator of the BZ reaction, which incorporates these various

processes for reactions on platinum surfaces. It includes an autocatalytic process in which the reaction

between CO and oxygen on the (1 × 1) surface creates new 'bare' catalytic sites. They have found that

this scheme produces oscillatory behaviour of the various reaction parameters, such as the rate of CO2

formation or the surface coverage of CO (Fig. 3.10). Like the Oregonator, the process jumps between

two branchesessentially a low-reactivity branch involving the (1 × 2) surface and a high-reactivity

branch involving the (1 × 1) surfacewith the autocatalytic steps providing a mechanism for rapid

switching between the branches. It is easy to see that sites of non-uniformity in these surface reactions

can act as the centres for the formation of travelling waves like those shown in Fig. 3.8.

Several other metal-catalysed surface reactions are now known to show oscillatory behaviour. One

difference between these essentially two-dimensional processes and those in flat dishes of the BZ

mixture is that for the latter the medium is isotropic: it looks the same in all directions. For surface

reactions taking place on metal crystals, on the other hand, all directions are not the same, because the

metal atoms are lined up in a regular checkerboard-like array. This means that the

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Fig. 3.10

The oscillations in the surface reaction

of CO and oxygen can be reproduced by

a theoretical model that includes the autocatalytic

processes. Oscillations are seen in both

the rate of reaction (a) and the amount of

carbon monoxide on the surface (b).

ability of the reacting molecules to move about can be similarly anisotropic (direction-dependent). It is

for this reason that the target and spiral patterns in Fig. 3.8 are elliptical rather than circularthe speed of

the chemical wave fronts differs in different directions. In extreme cases, this anisotropy means that the

symmetry of the underlying metal crystal surface can leave itself imprinted on the spatial patterns that

arise. For example, Ertl's colleague Ronald Imbihl has seen square travelling waves in the reaction of

nitric oxide and hydrogen on a rhodium surface, an echo of the square symmetry of the metal crystal

surface (Fig. 3.11).