IF YOU MIXED several chemicals thoroughly, you would expect the mixture to have a single uniform color. Certain chemical reactions, however, yield a surprising oscillation of color. About once a minute for an hour or so they change from one color to another and back again.

One of the most famous oscillators of this kind was discovered in 1958 by the Russian chemist B. P. Belousov and was subsequently investigated by A. M. Zhabotinsky and others. The original reaction involved a mixture of potassium bromate, ceric sulfate and citric acid in dilute sulfuric acid. The oscillation was from colorless to yellow. Other mixtures that have been found since then oscillate between red and blue, violet and blue, red and green and even from colorless to gold to blue. Here I shall describe how you can make several of these oscillators and how you might look into the events that determine their periodicity.

In this work you will be dealing with questions that have not been fully answered. Oscillations might be expected in nonuniform mixtures, because they can be attributed to the diffusion of the ingredients. Oscillations in a closed system consisting of a homogeneous mixture, however, were thought to be impossible on the ground that they would violate a basic law of physics and chemistry to the effect that any spontaneous reaction must steadily lower the Gibbs free energy of the system. (I shall return to the matter of Gibbs free energy.)

In 1970 Zhabotinsky and A. N. Zaikin reported finding periodic structures (circular waves) running through a solution that was a slightly altered version of the original mixture. Later Arthur T. Winfree, who is now at Purdue University, improved the formula for the solution and extensively examined the periodic structures of the rotating spiral waves that appeared in it [see "Rotating Chemical Reactions," by Arthur T. Winfree; SCIENTIFIC AMERICAN, June, 1974]. Winfree has devised for me a do-it-yourself kit that I shall describe.

He suggests the following procedure for mixing the reagents for a red-to-blue oscillator. Add two milliliters of concentrated sulfuric acid and five grams of sodium bromate to 67 milliliters of pure water (distilled or deionized) to get 70 milliliters of solution. As a rule of safety always add the acid slowly to the water, not the water to the acid, because of the danger of explosion.

Pour six milliliters of this solution into a glass container and add .5 milliliter of a sodium bromide solution made by adding one gram of sodium bromide to 10 milliliters of water. Next add one milliliter of a malonic acid solution (malonate) made by putting one gram of malonic acid in 10 milliliters of water. After the bromine color disappears mix in one milliliter of .025-molar phenanthroline ferrous sulfate (a dye sometimes called ferroin). Add the tiniest trace (about one gram per liter) of either Triton X-100 surfactant or "photoflo" (a substance employed in photographic darkrooms) to reduce the surface tension and thereby aid the spreading of the fluid in a thin layer.

Pour out such a layer in a clean vessel such as a culture dish. Stir the solution well and then wait five minutes or so for the color oscillations to begin. From time to time thereafter gently swirl the solution around in the dish or gently stir it. The colors will pulse with a period of about one minute, although the blue will persist for only about five or 10 seconds at a time. Small bubbles of carbon dioxide will also form in the solution. They result from one of the reactions involved in the oscillation and can be removed by stirring the fluid occasionally.

The concentrations are not crucial. You must take care, however, to use only clean containers and to keep your fingers out of the solution and off of surfaces that the solution will touch. The chloride in the salt on your skin can prevent the oscillation reactions.

Before Winfree puts the sodium bromate into his mixture he usually recrystallizes it to remove impurities that can prevent oscillations. You can do this by dissolving as much sodium bromate as possible in a clean container of warm distilled water, taking care not to bring anything soaked with the sodium bromate near an open flame because of the danger of rapid oxidation. Wrap the closed container in an insulating material such as Styrofoam and leave it undisturbed for a week or two. Then pour off the remaining liquid, since you might want it for the next recrystallization, and scrape the sodium bromate off the walls with a clean instrument.

Before I go into variations on the basic mixture I should explain why color oscillations arise. The reactions that appear to be responsible for the oscillations are somewhat complicated. In the solution both the bromide and the bromate react with the malonate to form bromomalonate. If it were not for an inhibitory effect of the bromide, the bromate would also react with the phenanthroline dye by oxidizing the iron in it (adding one electron to the outer shell of electrons of each iron atom). The reduced (ferrous) state of the dye is red, whereas the oxidized (ferric) state is blue, so that if the bromide were to stop inhibiting the oxidation, the solution would switch from red to blue.

Eventually that is exactly what happens, because the bromide is almost totally consumed in the reaction with the malonate. Then the oxidation can proceed, the phenanthroline dye is oxidized and the solution turns from red to blue.

Why does it subsequently change back to red? The bromomalonate that has been and is still being produced reduces the ferric form back to the ferrous form. (Reduction is the opposite of oxidation.) The solution therefore becomes red again. Moreover, bromide is released from the bromomalonate as a product of the reaction, so that the inhibition of the oxidation of the dye by bromate is reinstated. Soon the bromide has been consumed again, and the cycle is renewed. The oscillations continue for an hour or so until the solution becomes permanently blue or red, depending on the initial concentrations.

Winfree has described several variations that you can make on his basic mixture. In order to try them you will need to be familiar with the terms molar and normal as they apply to concentrations. The term molar is based on the atomic weight of the molecule or complex being put into a solution. In a one-molar solution the number of grams of the solute put into one liter of the solvent is equal in number to the atomic mass of the solute (expressed in atomic mass units). The number is usually printed on the container of the chemical. The phenanthroline as sold is already in the concentration required. A normal solution is similar to a molar solution but is also proportional to the charge number of one of the ionic species released in dissociation. For example, a one-normal solution of sulfuric acid is also a two-molar solution, two because once the acid is in solution the two hydrogen atoms from a dissociated molecule have a net charge of plus two.

Now for Winfree's variations. One is to leave out bromide (which will, of course, still be produced when the bromomalonate reduces the ferrous phenanthroline). The color oscillations are then more frequent, since less of the bromide must be consumed in each color cycle before the bromide's inhibiting effect on the oxidation of the iron is eliminated and the color of the solution can change to blue.

You can enhance the oscillations and obtain a deeper view into the solution by replacing some of the ferroin with ceric sulfate having an initial concentration of .1 molar. If you want to avoid acid stains that result from spilling the reagent in the experiment, substitute sodium bisulfate for the sulfuric acid. You might want to vary either the temperature of the solution or the concentration of the basic ingredients to see how the period of oscillation is altered. (Teachers interested in setting up a laboratory so that students can try these variations will find helpful an arrangement worked out by John F. Lefelhocz of Virginia Commonwealth University; his paper describing the setup is cited in the bibliography of this issue.)

Mixtures other than Winfree's can produce color oscillations. The original Belousov reactions involved ceric-cerium rather than feric-ferrous solutions; the transitions were from colorless to yellow and back. Richard J. Field of the University of Montana suggests adding ferroin to produce the more striking variation from red to blue. The concentrations he recommends for a lecture demonstration are shown in the top illustration on page 156. The colors you see in such mixtures depend on the relative amounts of the cerium-ceric ions (which oscillate between colorless and yellow) and the iron ions (which oscillate between red and blue). With appropriate amounts of yellow the colors may oscillate between blue and violet or green and red.

Oscillations between brownish-yellow and pink can be obtained from solutions of manganese II and III, which replace the cerium III and IV and the iron II and III couples of the Belousov and Winfree reactions. (The Roman numeral describes the ionization state; iron II is the doubly ionized iron atom, or the ferric state.) The malonic acid can be replaced by other acids: citric, maleic, malic, bromomalonic and dibromomalonic. In many of the solutions the oscillations arise only if the solution is gently stirred. For some solutions one must wait as long as 40 minutes until the oscillations begin.

A system that changes from colorless to gold to blue and back again can be achieved at relatively low expense with an iodine clock that has been described by Thomas S. Briggs and Warren C. Rauscher of Galileo High School in San Francisco. I have tripled their published concentrations (in distilled water) in order to be clear about the amounts of chemicals to be put into each of three containers. The containers hold equal amounts, so that the final mixing (in which the contents of the three containers are put into one container) will yield the published concentrations.

Pour into the first container 3.6-molar hydrogen peroxide, made by adding 40 milliliters of 30 percent hydrogen peroxide to 60 milliliters of water. Handle the hydrogen peroxide with extreme care. In the second container mix .201-molar potassium iodate (4.3 grams per 100 milliliters of solution with water) and .159-molar perchloric acid, made by adding 2.3 milliliters of 70 percent perchloric acid to enough water to make 100 milliliters of solution. You will probably have to warm the potassium iodate solution to dissolve the chemical completely. In the third container mix .150-molar malonic acid (1.5 grams per 100 milliliters of solution with water), .0201-molar manganese (II) sulfate (.3 gram per 100 milliliters of solution with water) and .03 percent starch. (Percentage refers to the constituent's percentage of the weight of the solution. Here .3 gram of starch in one liter of distilled water is a .03 percent starch solution.)

When you are ready for the oscillations, mix together equal amounts of the three solutions. The blue comes from the blue starch complex that develops periodically when the iodide concentration is near its maximum value. Briggs and Rauscher obtained brief oscillations when they replaced malonic acid with 2,4-pentanedione. The oscillations are faster if you replace manganese with cerium.

In order to get bulk oscillations of color in many of these mixtures the solution must be continuously stirred (with a magnetic stirrer if you have access to one) or swirled. Otherwise another phenomenon occurs, although it is one of much interest in itself. Winfree has studied it in detail. Waves of color appear on and in the solution, propagate through it at a few millimeters per minute, rotate around points of origin, destroy each other as they meet and describe a variety of shapes: rings, ellipses and spirals.

To enhance these color waves (by diminishing the bulk oscillations) Winfree suggests using more bromide and less sulfuric acid in the basic mixture. For example, in the sodium bromate solution use one milliliter of concentrated sulfuric acid and 67 milliliters of distilled water.

To enhance the visibility of the waves pour some of the final solution to a depth of about a millimeter in a container such as a plastic tissue-culture dish. The container must be very clean; any small grains of dirt or scratches will promote the formation of bubbles of carbon dioxide during the experiment and may generate too many simultaneous waves. Visual contrast is improved if you place the dish over another dish containing blue copper sulfate and a few drops of sulfuric acid and then place a light below the two dishes. The solution in the bottom dish will also protect the chemical waves from disruption by absorbing heat from the light. Cover the tissue-culture dish with its top to protect the waves from air currents and to eliminate evaporation. Leave the dish undisturbed. If the waves do not begin within a few minutes, touch the solution with a hot needle, which will set off waves. Usually, however, there will be enough bubbles, scratches or dust motes in the solution to give you a few waves.

Presumably the waves result from the same chemistry that gives rise to bulk oscillations. The solution stays in the red state with some equilibrium concentration of bromide. Once the mixture is disturbed by a bubble, a scratch, a dust mote or a hot needle a portion of the solution consumes its bromide. The bromate can then switch the color of solution to blue by oxidizing the iron in the phenanthroline. This conversion propagates outward as a wave because as diffusion brings bromide from the red area just outside the blue ring into the blue area the additional bromide is also consumed and the formerly red area turns blue. Once the blue ring has passed a particular area the solution regains its redness as the bromomalonate reduces the iron in the phenanthroline and releases more bromide.

The waves are truly chemical waves rather than hydrodynamic waves because the fluid is motionless. Moreover, they will not reflect from barriers placed in their way, and waves traveling in opposite directions will not pass through each other.

You will find that the waves, which have a length of a few millimeters, assume several shapes. Among them are concentric closed rings forming a bull's-eye, with new rings appearing in the center at regular intervals. These patterns do not rotate. Other waves form spirals, all of which have the same period, a shorter one than any of the variety of periods of the closed-ring patterns. These spiral patterns rotate. If the axis of rotation lies perpendicular to the surface of the solution, scroll waves (as Winfree has named them) propagate from the axis, producing a spiral structure around a central region surrounding the top of the axis as you look from above the solution. The structure is technically an involute spiral, which could be drawn mechanically by having a pencil tied to a string that is slowly unwound from a central cylinder instead of a single point. In the chemical involute spiral the central core is less than a millimeter in diameter.

If the solution is deep enough (deeper than the width of the spiral's core), the axis may lie tilted to one side. From above you then see elongated spirals f~ surrounding the central area of the pattern. Also in an appropriately deep solution the scroll axis may bend over to form a U with its top on one surface of the solution and its bottom on the other. From one orientation you see a nest of rings surrounding a central point. If the U shape shrinks away from the surface having the rings, the rings disappear on that surface just before becoming complete circles. When the axis of rotation lies parallel to a surface and in a closed ring, the surface has concentric circles with the inner one propagating inward as the outer one propagates outward.

If you would like to place barriers in the way of the wave, a more viscous solution is desirable. It can be made by adding two milliliters of colloidal silicon dioxide to each milliliter of solution. Winfree describes the resulting solution as having a consistency similar to that of peanut butter.

You can preserve the patterns and lift them out of the solution by putting filters in the solution. The formation and propagation of waves are unaltered by the filters which can be obtained from the Millipore Corporation (Ashby Road, Bedford, Mass. 01730) at $16.20 for a package of 10 type GSWP 142 00 filters. You must guard against contamination of the solution when you put the filters in it. Use nylon forceps and do not touch the filters with your fingers. If you first warm up the filters (even with body heat), the patterns are more lively.

Once the solution has been absorbed into a filter Winfree removes the filter and puts it between sheets of plastic (such as a food wrap), places it in oil to reduce evaporation and exclude oxygen, or sticks it to the inside of the lid of a plastic dish. A filter can be used again if you rinse it out well with water.

When Winfree puts a filter in oil, he can play a game with the chemical waves by touching the filter briefly through the film of oil with a piece of iron such as the edge of a razor blade. The resulting red layer, which he calls the "iron curtain," blocks waves in that area for several seconds. The redness apparently results from the fact that the acid in the solution pulls ferrous-state iron out of the razor blade.

You may want to photograph the waves as they develop. You can also stop them in place on a filter by following a procedure that Winfree devised. (It will not work with a filter that has been put in oil.) At a time when waves are propagating through the filter remove the filter and put it in ice-cold saturated salt water to stop the reaction. Leave the filter there for about five minutes (until all the chemicals have diffused out of it except for the red ferrous phenanthroline) and then blot it dry, dip it in a solution of sodium iodide (one gram per 40 milliliters of solution with water) and blot it dry again. Then leave it for 10 minutes in the iodine vapor emanating from a bottle containing iodine crystals. This procedure permanently fixes the ferroin.

Rinse the filter in distilled water, dry it in air and clear it by floating it on paraffin oil. Blot it again. Finally, sandwich it between two sheets of clear sticky plastic such as Contact paper. Winfree says that such preserved specimens of chemical waves have lasted for years with full sharpness. Preservation for about a day can be achieved more easily by dipping the filters in an ice-cold solution of 3 percent perchloric acid, but the sharpness is diminished somewhat, and the pattern vanishes when the filter dries fully.

If you develop waves in a stack of filters (you need at least three per stack to get the elongated structures), you can peel them apart (as Winfree did) to see the vertical structures of the waves. In this way you can follow the scroll axis downward or unfold a U-shaped structure. Bubbles of carbon dioxide can be a bother if they separate the filters, which happens within about five minutes.

A stack of Millipore filters leads to a better understanding of the horizontal scroll ring. In such a ring the scroll axis is horizontal and closes back on itself to form a circle. Place a stack of five filters in the solution and touch the center of the top filter with a hot needle to initiate a cylindrical wave. After the wave has propagated outward through the top filter lower another stack of five filters onto the first stack, with the new stack in the initial red state of the solution. Soon a cylindrical wave will appear on the top of the new stack and the circle will split into two parts, one moving inward and one outward. When the new stack of filters is put into place, the scroll wave in the initial stack moves into the new stack and eventually emerges on the new top.

Winfree has another technique that he employs to prepare filters for a demonstration. Mix one-molar ammonium bromomalonate with an equal volume of .025-molar ferrous phenanthroline. Combine the mixture with an equal volume of four-molar ammonium bisulfate (46 grams per 100 milliliters of solution with water). Place a Millipore filter on the solution, lift it up to drain the surface liquid and then put it on a plastic surface to dry. Meanwhile, put a Whatman No. 1 paper filter in .33-molar sodium bromate (five grams per 100 milliliters of solution with water) and then dry it. When you want to demonstrate the scroll waves, wet the filter with pure water, put it on a clean surface (such as a plastic dish) and cover it with the Millipore filter. After waiting a few minutes you will find blue dots on the top filter; eventually you will see blue waves propagating through the filter at a rate of a few millimeters per minute.

A 12-square-inch sample of a Millipore filter already impregnated with chemicals for generating waves can be bought for $4 from Winfree (Arthur T. Winfree, Institute for Natural Philosophy, 51 Knoll Crest Court, West Lafayette, Ind. 47906). Send a self-addressed label with your order. The filter need only be wetted to give a 30-minute display. The filter can be warmed, cooled, cut with scissors, touched with an iron object to block the waves, stimulated with a hot needle and stacked to make three-dimensional waves.

How can a uniformly mixed solution at constant temperature and pressure oscillate in color, in concentration of molecular species, in conductivity or in anything else? The question has puzzled chemists since the 19th century. The oscillations are still debated, and a few chemists continue to argue that oscillations in such circumstances are impossible. In scientific terms the question is: Can oscillations occur in a homogeneous closed system at constant temperature and pressure? It is well accepted that oscillations can occur in mediums having inhomogeneous constituents and gradients of density in the molecular species undergoing diffusion. It is also well accepted that oscillations can arise if the system is open to the addition of more materials. In the bulk oscillators, however, oscillations are apparently turning up in a system that is homogeneous and closed.

In unraveling the puzzle some investigators concentrate on the Gibbs free energy of the system because any spontaneous reaction in a closed homogeneous system at constant temperature and pressure must decrease the Gibbs free energy of the system. The Gibbs free energy is an indicator of the spontaneity of a reaction (the tendency of the reaction to proceed on its own with no external activation). In any spontaneous reaction the system tends to reduce its energy (measured by enthalpy) and to increase its disorder (measured by entropy). It is not inevitable that both of these ends will be reached. For example, some reactions may be able to proceed spontaneously even though their energy (enthalpy) increases; the reason is that the disorder (entropy) increases more. Other reactions may be spontaneous for the converse reason. Hence neither ethalpy nor entropy alone is a good indicator of spontaneity. What one employs is a combination of the two called the Gibbs free energy. Any reaction that will reduce the Gibbs free energy is one that can proceed spontaneously.

At first the oscillating reactions I have described appear to violate the universally accepted rule that any spontaneous reaction must move steadily toward its final equilibrium state while steadily losing its Gibbs free energy. Actually oscillations seem to violate the second law of thermodynamics, which prohibits oscillations around the equilibrium point. The paradox is resolved rather easily, however, by noting that no thermodynamical rule prevents oscillations -when the reactants are far from equilibrium and as the net reactions decrease the Gibbs free energy. For example, in Winfree's mixture the net chemical reactions consume very little of the bromate and malonic acid in each cycle of oscillation, and the cycles began with the reactants far from their final equilibrium values. In the steady drive of the net reactions toward equilibrium, the concentrations of the minor constituents bromide and phenanthroline can vary considerably, although they remain small with respect to the concentrations of bromate and malonic acid. Eventually the bromate and the malonic acid are sufficiently consumed in the net reactions so that the entire process stops and all the concentrations are in equilibrium. Thus the solution can oscillate in the concentration of its species (with a color change in the present case) as long as the principal reactants are plentiful and far from the final equilibrium concentrations. Once the equilibrium state is reached the oscillations cease. The second law of thermodynamics is not violated.

There must be other requirements for a solution to be able to oscillate or a chemistry class would be far more colorful. Indeed, the reactions taking place must be complex, and at least one reaction must catalyze itself (be autocatalytic) and be coupled to the other reactions in some way such as a dependence on the concentrations in the other reactions or by an inhibition or activation of the reactions. This coupling to other reactions is commonly called feedback, and most oscillating systems are characterized by it.

In the Winfree mixture the coupling is by way of the bromide ion and the phenanthroline. The bromide reacts with the malonic acid, inhibits the bromate reaction with the ferrous phenanthroline and is a product of the reaction of bromomalonate and ferric phenanthroline. One autocatalytic reaction is a bromate reaction with malonic acid. In other examples of bulk oscillators, such as the iodine clock, I am not certain that the complex mechanisms responsible for the oscillations have yet been sorted out and understood in thermodynamical terms.

Many of the chemicals you will need are available from Fisher Scientific Company (1600 West Glenlake Avenue, P.O. Box 171, Itasca, III. 60143), including the sodium bromate at,$15.75 per pound, the sodium bromide at $5.95 per pound, the phenanthroline ferrous sulfate at $3.35 per fluid ounce, the sodium bisulfate at $5.75 per pound, the cerium ammonium nitrate at $10.95 per pound, the potassium bromate at $ 11.40 per pound, the sodium iodide at $7.30 per quarter pound, the iodine crystals at $7.50 per quarter pound and the ammonium bisulfate at $ 10.65 per pound. (The prices are from the 1977 chemical list.) Fisher also sells Whatman filters at about 55 cents for 100. The malonic acid is sold by the J. T. Baker Chemical Company (222 Red School Lane, Phillipsburg, N.J. 08865) at $21.65 per 100 grams; the same company sells Triton X-100 at $9.75 per pint and ceric sulfate at $35.60 for 500 grams. Colloidal silicon dioxide is available from the Apache Chemical Co. (P.O. Box 126, Seward, Ill. 61077) at about $20 for 25 grams.

Bibliography

THE COLOR BLIND TRAFFIC LIGHT. John F. Lefelhocz in Journal of Chemical Education, Vol.49. No.5, pages 312314; May, 1972.

OSCILLATING CHEMICAL REACTIONS IN HOMOGENEOUS PHASE. Hans Degn in Journal of Chemical Education. Vol. 49, No.5, pages 302-307; May, 1972.

A REACTION PERIODIC IN TIME AND SPACE. Richard J. Field in Journal of Chemical Education. Vol. 49, No. 5. pages 308-311; May, 1972.

AN OSCILLATING IODINE CLOCK. Thomas S. Briggs and Warren C. Rauscher in Journal of Chemical Education, Vol. 50, No.7 pages 496; July, 1973.

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