Other investigators have since repeated the experiment using a number of salts and gels that produce rhythmic banding. Some of the reactions produce secondary logarithmic bands; others form bands that are periodic but not logarithmic. Collectively the patterns display all the colors of the rainbow.

Similar patterns are found in nature, some in minerals such as limonite, variscite and chalcedony and others in animals, including the wings of certain colorful butterflies. Not everyone agrees that any of these natural patterns are formed by the Liesegang reaction, nor has the reaction itself been explained to everyone's satisfaction. The puzzle continues to intrigue experimenters, including Roger Sassen of 80-21 231st Street, Jamaica, N.Y. 11427. Sassen, who is a graduate student in geology at Lehigh University, writes:

"The Liesegang experiment requires only a few pieces of fairly inexpensive apparatus: a balance that is capable of weighing chemicals to .1 gram, a graduated cylinder of 10-milliliter capacity, another one of 50-milliliter capacity, and a one-milliliter pipette graduated in divisions of .1 milliliter or, preferably, .01 milliliter. In addition you should have a few flat dishes and a dozen test tubes with a capacity of 30 to 50 milliliters for use as reaction vessels.

"The success of the experiments depends in part on preparing solutions of specified concentration. I shall specify concentration in terms of molarity. By convention a one-molar solution (1M) of any chemical contains 6.023 x 10²³ molecules of that chemical per liter of solution. This number of molecules, known as Avogadro's number, is exactly equal to the molecular weight of the chemical expressed in grams. For example, a molecule of acetic acid (CH₃COOH) contains two carbon atoms (each of atomic weight 12), two oxygen atoms (each of atomic weight 16) and four hydrogen atoms (each of atomic weight 1). Adding the atomic weights (24 + 32 + 4) gives 60 as the molecular weight of acetic acid. A quantity of 60 grams of the acid contains 6.023 x 10²³ molecules; diluted to a volume of 1,000 milliliters with water, it has a concentration of 1M. A .1M solution would be prepared by diluting with water six grams of the acid to a volume of 1,000 milliliters, and so on. The atomic weights of all chemical elements and the molecular weights of many compounds are listed in handbooks of chemistry.

"Liesegang made his experiment with gelatin gel, but a number of other gels can also be used. Among them are agar, gelled blood plasma, cellulose-derived thickeners and silica gel. Most of my experiments have been done with silica gel, prepared by adding acetic acid to a solution of sodium silicate that is commonly called water glass.

"Sodium silicate solution is available from druggists. It must be diluted to a density of 1.06 grams per milliliter. The density of the commercial material is usually unknown, but it can be determined by weighing a specimen of the solution. Weigh a clean, dry container. Transfer to the container exactly 100 milliliters of the solution and weigh again. Subtract the weight of the empty container from the weight of the filled container to determine the net weight of the solution. Typically the net weight of 100 milliliters of a commercial solution of sodium silicate will be about 130 grams.

"Assume that 130 grams is the weight in this example. The weight indicates that the solution contains 30 grams of sodium silicate, because 100 milliliters of water weighs approximately 100 grams. The solution to be used for making gel must contain only six grams of sodium silicate per 100 milliliters of solution. The necessary dilution is found by dividing 6 into 30, thereby obtaining a ratio of 5. Sodium silicate at a density of 1.06 can be made in this case by adding one part of the commercial solution to four parts of water.

"For convenience I usually make up several liters of the diluted stock solution at a time. Use distilled water for all solutions. Diluted sodium silicate solution is converted to gel immediately before use in each experiment. Gel is prepared by adding to the diluted solution an equal volume of acetic acid solution at concentrations ranging from .5M to 1M, depending on the requirements of the experiment. The gel forms in less than an hour.

"When the gel is examined under a microscope, it resembles a water-soaked sponge. The speed of chemical reactions in silica gel is governed by the slow pace at which fluids diffuse through the porous mass. For this reason crystals grow slowly in the gel, but they show a remarkable perfection of form.

"As an introduction to the gel technique I suggest that you grow crystals of silver acetate, which are long, color less and needle-like. Mix 10 milliliters of dilute sodium silicate of 1.06 density with 10 milliliters of 1M acetic acid and transfer it to a 30-milliliter test tube. After the gel has formed fill the space above it with a .5M solution of silver nitrate. The crystals appear within a matter of days as the silver nitrate diffuses into the gel.

"To reproduce a version of Liesegang's experiment dissolve three grams of plain unsweetened, unflavored gelatin in 96.6 grams of water heated to 140 degrees Fahrenheit. Stir .4 gram of potassium chromate into the mixture. Pour the mixture into a shallow dish and let it cool. While it is cooling dissolve 1/4 gram of silver nitrate in one milliliter of water. When the gel has formed, gently put a single drop of the silver nitrate solution on the gel near the center. Rings of silver chromate should begin to form within minutes.

"I prefer to let the reactions proceed in test tubes, so that bands rather than rings will appear. The tubes can be closed with stoppers to prevent evaporation so that the reactions can continue without attention. The test tube technique is particularly convenient for reactions that continue for several weeks, as in the case of copper acetate and potassium chromate, which combine to form interestingly spaced bands of brown copper chromate.

"Prepare the gel for this reaction by mixing 20 milliliters of sodium silicate with 20 milliliters of a solution consisting of two milliliters of 1M potassium chromate and .6 milliliter of concentrated acetic acid. Transfer the mixture to a 5O-milliliter test tube. After the gel has formed fill the remainder of the tube with .25M copper acetate solution, and thereafter replace it with fresh copper acetate solution weekly. When a number of bands have appeared, it is possible to verify the equation that relates the distances of successive Liesegang precipitations to a constant, Y_n/Y_n-1 = K, in which Y is the distance from the interface between the liquid and the gel to the center of a selected band, n is the number of that band, counting from the interface, and K is the constant.

"Liesegang bands can be grown within a week by using glass capillaries instead of test tubes. The capillaries should have uniform diameter, as do those used for determining the melting point of chemicals. The sealed ends of melting-point tubes must be broken off. To grow copper chromate bands by this technique I hold the capillary almost horizontally and dip one end in a freshly prepared solution of sodium silicate and an equal volume of .5M acetic acid that is also .025M in terms of potassium chromate. The tube fills by capillary attraction. When the gel has formed, the tube is placed for development in a stoppered test tube containing .25M copper acetate solution.

"The fully developed capillary is removed from the test tube for study. The distances between the bands can be recorded with a pencil by taping the capillary to a sheet of paper and measuring with a metric ruler and machinist's dividers. The bands form so rapidly in capillaries that in some cases it is possible to verify an equation stating that the distance of a band from the interface, divided by the square root of the time required for the growth of the band, is equal to a constant, Y_n/t_n^l/2 = K, in which Y is the band of interest and t is the time.

"A particularly attractive experiment involves the precipitation of metallic gold and the development of a banded pattern by exposing the gel to sunlight. To make this experiment prepare a sodium silicate solution that includes one milliliter of a 1 percent solution (by weight) of yellow gold chloride. Transfer the mixture to a test tube and make it gel by adding an equal volume of 1.5M sulfuric acid. Gelling takes a week or so. Fill the space above the gel with a solution made by dissolving as much oxalic acid as possible in water, creating a saturated solution. Within a matter of days thousands of minute, sparkling crystals of gold will form in the gel. If all has gone well, Liesegang bands will appear after the gel has been exposed to sunlight.

"The nature of the gel influences the form of the crystallized products, as can be demonstrated by growing crystals of lead iodide. In a test tube prepare a silica gel with 1M acetic acid solution that is .050M with respect to lead acetate. Place over the gel a saturated solution of potassium iodide. Translucent crystals of yellow lead iodide will appear in t the form of feathery dendrites and free growing hexagonal plates. When gelatin gel is substituted for silica gel, the same reaction yields Liesegang banding.

"Spiral patterns can also be grown. An example involves a green precipitate of cobalt hydroxide. Mix five milliliters of .1M cobaltous nitrate solution with 30 milliliters of hot, 10 percent gelatin solution in a 50-milliliter test tube. After the gel cools and sets fill the space above the gel with a .2M solution of ammonium hydroxide. A spiral or somewhat spiral pattern may form, but it does not always appear. If it does not, try again.

"Liesegang suggested that the rings and bands of agates arose when the Liesegang phenomenon operated in natural silica gels that were later altered to microcrystalline quartz, but geologists now generally agree that agate patterns can be attributed to the successive deposit of layers of silica gel and impurities. Banded patterns are also observed in some stalactites, oolites, a few sediments and, of course, tree rings. When the number of each band in the pattern of these materials is plotted against the logarithm of the distance of the band from its origin, the resulting graph is usually a curved line. On the other hand, comparable graphs of nearly all known Liesegang patterns are straight lines [Figure 1]. Structures of the mineral limonite that grow in the form of concentric rings during the weathering of sedimentary rocks yield graphs that approximate a straight line. The rings in most specimens, however, are distorted and incomplete.

"During the 1920's synthetic agates were prepared in the laboratory with the aim of discovering conditions that could have led to the formation of Liesegang rings in a geological environment. Silica gel containing potassium ferrocyanide was placed in collodion bags and immersed in copper sulfate solution. After a few weeks copper ions diffused into the balls of gel and reacted to form three-dimensional banded precipitates. The synthetic agates were then dried slowly under pressure until they acquired a hardness of about 5 on Mohs's scale, meaning that they were so hard they could barely be scratched with a knife. Although the experiment was suggestive, it failed to prove that agates are so formed.

"A two-dimensional version of this experiment is easy to do. Grow concentric rings of copper chromate in a thin layer of silica gel sandwiched between microscope slides. Pour a silica gel mixture made with .5M acetic acid, which is .025M with respect to potassium chromate, onto one plate and put the other plate on top, taking care not to trap air bubbles in the gel. A thicker layer, in which the rings are easier to see, can be made by spacing the glass plates apart with a few particles of crushed glass.

"Immerse the sandwich in a .25M solution of copper acetate. Within a week, as the copper ions diffuse inward, concentric rings will precipitate. They closely resemble the rings of limonite found occasionally in the cracks of rocks, suggesting that such formations may result from the penetration of ground water solutions into cracked rock [see Figure 4].

"One can demonstrate that the presence of gel in cracked rock is not essential to the growth of such patterns. Sandwich between a pair of glass plates a solution of .01M potassium iodide and let a solution of .5M silver nitrate diffuse into the thin film. Delicate but irregular rings will usually appear. The experiment does not always work, so that you may have to resort to trial and error.

"Other examples of periodic structures that form without gel can be observed by letting a drop of saturated potassium dichromate solution evaporate from a glass surface. Concentric rings of orange crystals usually develop. The phenomenon is called periodic crystallization. Fine spirals of potassium dichromate crystals can be grown by allowing a thin film of solution to evaporate from a warmed glass slide. Crystallization usually begins at the edge and spirals inward, but if a dust particle happens to lodge near the center of the film, crystal lization may start at the particle and spiral outward.

"Periodic crystal structures can also be prepared by cooling thin films of molten substances. An example is a thin film of molten sulfur that cools slowly on the sides of a Pyrex test tube. Molten organic substances, such as benzil and acetanilide, will also crystallize as concentric rings.

"Another interesting example of the Liesegang phenomenon, with air replacing gel as the medium, occurs when the fumes of hydrochloric acid and ammonium hydroxide diffuse into a long glass tube from opposite ends. Within an hour a finely banded precipitate of white ammonium chloride smoke will form near the middle of the tube. Construct the apparatus by cutting a piece of three-millimeter glass tubing to a length of 50 to 75 centimeters, fire-polish the ends, wash the tube with detergent solution, rinse it with distilled water and let it dry. (Do not use tubing larger than three millimeters in diameter.)

"Attach to the ends of the tube bulbs that have a capacity of about 100 milliliters and are filled with loosely packed glass wool. The bulbs can be improvised from straight drying tubes or any equivalent scheme such as a pair of 125-milliliter flasks closed with perforated stoppers [see Figure 3]. The apparatus must be airtight: a small leak can spoil the reaction. The diffusion tube should be level and protected from abrupt changes in temperature. Moisten the glass wool in one bulb with two milliliters of lOM hydrochloric acid and the wool in the other bulb with the same volume of 1.5M ammonium hydroxide. These solutions can be made from stock reagents; concentrated hydrochloric acid is usually 12M and concentrated ammonium hydroxide 15M.

"Most Liesegang patterns appear as rings or bands, but some of them are symmetrical figures. A straight line drawn through the axis of symmetry divides these patterns into mirror images that resemble the markings of certain living creatures. This resemblance, coupled with the fact that living body cells contain gel, has suggested to some biologists that Liesegang phenomena might be of biological significance.

"Charles Darwin described patterns of color in many organisms. Liesegang was tempted to explain the patterns as examples of periodic precipitation. 'As no ornaments are more beautiful,' he said, 'than the ocelli on the feathers of various birds, on the hairy coats of some mammals, on the scales of reptiles and fishes, on the skin of amphibians, on the wings of many Lepidoptera and other insects, they deserve to be specially noticed. An ocellus consists of a spot within a ring of another color, like the pupil within the iris, but the central spot is often surrounded by additional concentric zones.' Darwin described a South African moth 'in which a magnificent ocellus occupies nearly the whole surface of each hinder wing; it consists of a black center. . . surrounded by successive, ocher-yellow, black, ocher-yellow, pink, white, pink, brown and whitish zones. Although we do not know the steps by which these wonderfully beautiful and complex ornaments have been developed, the process has probably been a simple one.'

"Fascinating patterns of similar design and color can be grown in gel. For example, in one of my experiments the effect was demonstrated by letting a solution that contained both silver nitrate and mercurous nitrate diffuse into a layer of gel between glass plates. The gel, made with .5M acetic acid solution, was .025M with respect to potassium chromate. Incidentally, colonies of certain microorganisms grow in structures that consist of spirals or concentric bands, and Liesegang bands of growth-inhibiting substances have been used to grow cultures of bacteria in the form of concentric rings.

"Not many Liesegang patterns have been made with organic reactants, although several experimenters have induced the periodic precipitation of compounds by reacting inorganic substances with organic compounds. These reactions go quickest if the slowly diffusing organic compound is placed in the gel. I was able to grow bands by placing nickel nitrate solution over silica gel prepared with .5M acetic acid solution that contained a trace of dimethylglyoxime. The possibility that a vast number of organic reactions might proceed in gel media and that they may have biochemical significance suggests that the search for new organic examples of the Liesegang phenomenon could be an exciting and challenging hobby.

"Most of the chemicals used in these experiments are toxic. Some can cause severe burns. Handle them accordingly. Use a rubber squeeze bulb rather than your mouth for sucking solutions into the pipette. Work in a ventilated space and close to a source of running water so that in case of accident the chemicals can be washed quickly from the skin. Store the reacting chemicals out of the reach of children and pets."

Bibliography

CRYSTALLIZATION: THEORY AND PRACTICE. Andrew VanHook. Reinhold Publishing Corporation, 1961.

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