The Self-Made Tapestry Phần 10 ppt

Page 270 Appendix 2 Oscillating Chemical Reactions There is a variety of reliable oscillatory chemical reactions described in the chemistry literature, including many accessible recipes in books intended for teaching or for a general readership. One of the most striking in terms of the colour change is the iodate/iodine/peroxide oscillator . The recipe that I have tested for myself is as follows: Solution A: 200 ml of potassium iodate (KIO 3 ) solutionmade by adding 42.8 g KIO 3 and 80 ml of 2M sulphuric acid to distilled water to make a total volume of 1 litre. Solution B: 200 ml of malonic acid/manganese sulphate (MnSO 4 ) solutionmade by adding 15.6 g malonic acid and 4.45 g MnSO4 to distilled water to a total of 1 litre. Solution C: 40 ml of 1% starch solutionmade by adding a slurry of 'soluble' starch to boiling water. Solution D: 200 ml of 100 vol. (about 30%) hydrogen peroxide (H 2 O 2 ) solution. Mix solutions A, B and C together in a conical flask and then initiate the reaction by adding solution D. Mix well using a magnetic stirrer. After a minute or two the solution, which is initially blue (owing to the formation of iodine, which reacts with starch to form a blue compound), turns a pale yellow (as the iodine intermediate disappears), and then abruptly blue again to begin another cycle. The colour changes persist for about 15–20 min, but finally run out of steam because some of the initial reagents are consumed in each cycle and not replenished. After a few minutes the mixture begins to bubble, as carbon dioxide gas is generated from the oxidation of malonic acid. If the mixture is not stirred, the colour changes still take place but grow from filamentary patches throughout the solution. It is important that the malonic acid solution is not prepared too far in advanceit begins to decompose over the course of several weeks. The most famous oscillatory reaction is the Belousov-Zhabotinsky reaction, for which various recipes are available in the literature. Here's one that I have seen work: Solution A: 400 ml of 0.5M malonic acid (52.1 g malonic acid in a litre of water). Solution B: 200 ml of 0.01M cerium(IV) sulphate (Ce(SO 4 ) 2 ) in 6M sulphuric acid. Solution C: 0.25M potassium bromate (KBrO 3 ) (41.8 g KBrO 3 in 1 litre of water). Mix solutions A and B in a magnetically stirred conical flask, and then add solution C to initiate the reaction. After about 3 min, the solution starts to alternate between colourless and yellow. The oscillations last for 10–15 min. This is the colour change that Belousov first saw; but it can be made more dramatic by adding 1 ml of an indicator called ferroin (iron tris(phenanthroline)), which makes the solution change between blue and a purplish red. The chemistry behind these oscillations is described in Chapter 3. I have taken these recipes from the chemical demonstrations leaflet of the chemistry department of University College, London, and am extremely grateful to Graeme Hogarth and Andrea Sella for help in performing these experiments and those in the following two appendices. There are many other oscillating reactions, and variants of these two recipes, to be found in: B.Z. Shakhashiri (1985). Chemical Demonstrations: A Handbook for Teachers of Chemistry. University of Wisconsin Press, Madison. H.W. Roesky & K. Möckel (1996). Chemical Curiosities. VCH, Weinheim. L.A. Ford (1993). Chemical Magic. Dover, New York. Page 271 Appendix 3 Chemical Waves in the BZ Reaction The target patterns of the inhomogeneous Belousov-Zhabotinsky (BZ) reaction always looked to me so extraordinary that I found it hard to believe they would be easy to reproduce. I was thrilled to find, when I tried the reaction first-hand, that this was not the case. This is a recipe that seems very reliable: Solution A: 2 ml sulphuric acid + 5 g sodium bromate (NaBrO 3 ) in 67 ml water. Solution B: 1 g sodium bromide (NaBr) in 10 ml water. Solution C: 1 g malonic acid in 10 ml water. Solution D: 1 ml of ferroin (25 mM phenanthroline ferrous sulphate). Solution E: 1 g Triton X-100 (a kind of soap) in 1 litre of water. Put 6 ml of solution A into a Petri disk about 3 inches in diameter, add 1–2 ml of solution B and 1 ml of solution C. The solution turns a brownish colour as bromine is produced. Make sure you do not inhale deeply over the dishbromine is noxious! After a minute or so the brown colour will disappear. Once the solution has become clear, add 1 ml of solution D (which will turn the liquid red) and a drop of solution E. Swirl the Petri dish gently to mix the solutions (it will turn blue as you do so, but then quickly back to red), then leave to stand. Gradually, blue spots will appear in the quiescent red liquid, and these will slowly expand as circular wave fronts. New wave fronts will be initiated behind the expanding waves. Typically there will be one to a dozen or so separate target-wave centres, and the blue fronts annihilate one another as they collide. This reaction is most impressively seen when the dish is placed on an overhead projector (see above). The heat of the projector will warm the solution and accelerate the wave fronts somewhat. After some time, bubbles (of carbon dioxide) will start to appear. These can begin to obscure or disrupt the pattern, but you can get rid of them and restart the process by swirling the solution around a little. This recipe is taken from the chemical demonstrations leaflet of the chemistry department of University College, London. Page 272 Appendix 4 Liesegang Bands This is a wonderful experiment, but takes several days. The bands are zones of precipitation of an insoluble compound, which occur at intervals down a column filled with a gel, through which one of the reagents of the precipitation reaction diffuses from above. You can use a burette as the column (about 1-cm diameter), although ideally a glass tube without gradation markings is best. The recipe I have used involves the reaction between cobalt chloride and ammonium hydroxide, which precipitates bluish bands of cobalt hydroxide. The cobalt chloride is dispersed in a gelatin gel:mix 1.5 g of fine-grained gelatin and 1 g of hydrous cobalt chloride (CoCl 2 .6H 2 O) with 25 ml of distilled water and heat to boiling point for five minutes. Then transfer this mixture immediately to the glass column, cover the top of the column with plastic film, and allow to stand for 24h to set at room temperature (22°C). Then add 1.5 ml of concentrated ammonia solution to the top of the solidified gel using a pipette. Cover the tube again and leave it to stand. After several days, the bands begin to appear down the column. They are closely spacedabout a millimetre apart, although the spacing is not constant (see p. 62). You have to get on eye level with the bands to see them clearly, but they should be sharp and well defined (see figure). This recipe is taken from: R. Sultan and S. Sadek (1996). Patterning trends and chaotic behaviour in Co 2+ /NH 4 OH Liesegang systems. Journal of Physical Chemistry 100, 16912. References to other systems are given in Henisch (1988) (see Bibliography: Waves). Page 273 Appendix 5 The Hele-Shaw Cell The cell is basically two clear, rigid plates separated by a small gap. The plates are in fact trays, having raised edges to contain the liquid. Glass is recommended, but clear plastic (Perspex) works fine and is easier to work with. I have taken my design from: Tamás Vicsek (1988). Construction of a radial Hele-Shaw cell. In Random Fluctuations and Pattern Growth, (ed. H.E. Stanley and N. Ostrowsky), p. 82. Kluwer Academic Publishers, Dordrecht. The top tray measures 27 × 27 cm, and the bottom one 34 × 34 cm; the Perspex is 4 mm thick. The pieces are glued with epoxy resin. The top plate is separated from the lower one by flat spacers at each cornerBritish pennies give about the right separation. The viscous liquid is glycerine, purchased from a pharmacist; the viscous fingering patterns are clearer if the glycerine is coloured with food colouring. (Using glycerine rather than oil makes the assembly easier to clean in water.) Air is injected through a small hole in the top plate. A 3- mm hole is recommended, but I simply used the empty ink tube from a ball-point pen, which is closer to 2 mm in internal diameter. This was glued in place in the central hole. The air can be injected through a large plastic syringe if you can get one; but it is just as good to blow. Remember that the viscous fingering pattern is a non-equilibrium shape, so that you should blow quite sharply rather than slowly to ensure that the bubble grows out of equilibrium. Page 274 Appendix 6 Bénard Convection Polygonal convection cells will appear in a thin layer of a viscous liquid heated gently from below. This is a classic 'kitchen' experiment, since it really does not involve much more than heating oil in a saucepan on a cooker. The base of the pan must be flat and smooth, however, and preferably also thick to distribute the heat evenly. A skillet works well. The oil layer need be only about 1 or 2 mm deep. The flow pattern can be revealed by sprinkling a powdered spice such as cinnamon onto the surface of the oil. For a more controlled experiment, silicone oil can be used: this is available commercially in a range of viscosities, and a viscosity of 0.5 cm 2 /s is generally about right. The convection cells can be seen more clearly if metal powder is suspended in the fluid (see Plate 1). Bronze powder can be obtained from hardware shops or arts suppliers. Aluminium flakes can be extracted from the pigment of 'silver' model paints, by decanting the liquid and then washing the residual flakes in acetone (nail-varnish remover). These powders will settle in silicone oil if left to stand. These procedures are based on: S.J. VanHook and Michael Schatz (1997). Simple demonstrations of pattern formation. In Physics Teacher, October 1997. This paper provides the names and addresses of some US suppliers of the substances involved. Page 275 Appendix 7 Grain Stratification in the Makse Cell My Makse cell is not a masterpiece of engineering, because I was impatient to put it together and see if the experiment worked. No doubt far more elegant varieties could be devised. The main feature I wanted to include was that the Perspex plates be detachable, so that they might be cleaned. Ideally they should also be treated with an anti-static agent, like those used on vinyl records, to prevent grains from sticking to the surface, but I haven't found this essential. The plates are 20 × 30 cm, with a gap of 5 mm between them (see figure). (I am told that the Boston team have made a cell 2-ft high for lecture demonstrations, but I haven't seen this in action.) The cells described in the original paper by Makse et al. are left open at one end, but I have preferred to secure the plates to an endpiece at both ends. Partly this helps to ensure that they remain parallel (which is otherwise trickier to ensure if the plates are not glued to the base), but it also means that the striped layers can be deposited to fill the cell completely, which I think makes for a more attractive effect. The prettiest results are achieved with coloured grains, but granulated sugar and sand (purchased from a pet shop) work well. The important factor is that the grains be both of different sizes and of different shapesthe sugar grains are larger and more square. (Table salt, which is more similar to the sand in both size and shape, didn't work at all.) And the best results are obtained by pouring the 50 : 50 mixture of grains at a slow and steady rate into one corner of the cell. To ensure this, I used an A5 envelope as a funnel, with the tip of one corner cut off. This is one of the most satisfying experimentsa dramatic result for rather little effort. [...]... Experimental and theoretical study of toroidal vesicles Physical Review Letters 68, 2551 P Harting (1872) On the artificial production of some of the principal organic calcareous formations Quarterly Journal of the Microscopy Society 12, 118 S Hildebrandt and A Tromba (1996) The Parsimonious Universe Springer-Verlag, New York S Hyde, S Andersson, K Larsson, Z Blum, T Landh, S Lidin and B Ninham (1997) The Language... bicoid protein 101 bicontinuous phase 35, 47 bifurcation 67, 102 -3, 203, 226, 255, 257-60, 264 biological form and pattern 6-9 biomineralization 38-43 Blackman, V.H 40 block co-polymer 45-8, 261 blood flow 128, 130-3 Bodenschatz, Eberhard 172 bone 38 boundary effects 171, 263-4 Boveri, Theodor 100 Brady, Robert 113-15 braided rivers 157-8 branching patterns 110- 39, 143-58, 161 Bravais, L and A 107 Bray,... University Press P.S Stevens (1974) Patterns in Nature Penguin, London I Stewart (1998) Life's Other Secret The New Mathematics of the Living World Wiley, New York I Stewart and M Golubitsky (1993) Fearful Symmetry Penguin, London D'A Thompson (1961) On Growth and Form Cambridge University Press See also the Complete Revised Edition: Dover, New York, 1992 M.M Waldrop (1992) Complexity Penguin, London... 154-5,246-9, 251 diffusion 58, 79, 80, 100 -1, 113 diffusion-limited aggregation 113-20, 123,126-7,130-4,136,146, 148, 154-6,160, 192, 243-4, 246-51, 260,264,266 dinoflagellate 39 dipolar vortex 195 dislocation 142-3, 172-3, 263 dissipative structure 210, 255-6 Distal-less gene 99 DLA, see diffusion-limited aggregation DNA 8 ,100 -1,135 dorsal protein 101 -2 Douady, Stephane 107 -8 Dresher, Melvin 234 Drosophila... Nature 352, 610 Q Ouyang and H.L Swinney (1995) Onset and beyond Turing pattern formation In Chemical Waves and Patterns (ed R Kapral and K Showalter) Kluwer Academic Publishers, Dordrecht S Kondo and R Asai (1995) A reaction-diffusion wave on the skin of the marine angelfish Pomacanthus Nature 376, 765 I Stewart (1995) Nature's Numbers Weidenfeld and Nicolson, London A Turing (1952) The chemical basis... (1995) The Artful Universe Penguin, London S.B Forrest and P.K Haff (1992) Mechanics of wind ripple stratigraphy Science 255, 1240 V Frette, K Christensen, A Malthe-S/orenssen, J Feder, T J/ossang and P Meakin (1996) Avalanche dynamics in a pile of rice Nature 379,49 H.M Jaeger and S.R Nagel (1992) Physics of the granular state Science 255,1523 H.M Jaeger, S.R Nagel and R.P Behringer (1996) The physics... Stanley (1995) Modelling urban growth patterns Nature 377,608 R May (1991) The chaotic rhythms of life In Exploring chaos A Guide to the New Science of Disorder, (ed.N Hall) W.W Norton, New York R.M May (1976) Simple mathematical models with very complicated dynamics Nature261, 459 M Milinski (1987) TIT FOR TAT in sticklebacks and the evolution of cooperation Nature 325,433 M.A Nowak and R.M May (1992)... Biological Superstructures Princeton University Press J Cohen and I Stewart (1994) The Collapse of Chaos Penguin, London P Coveney and R Highfield (1995) Frontiers of Complexity Faber and Faber, London R Dawkins (1990) The Selfish Gene Oxford University Press R Dawkins (1996) The Blind Watchmaker W.W Norton, New York M Ghyka (1977) The Geometry of Art and Life Dover, New York S.J Gould (1991) Wonderful Life... Elsevier, Amsterdam R Lipowsky (1991) The conformation of membranes Nature 349, 475 S Mann and G.A Ozin (1996) Synthesis of inorganic materials with complex form Nature 382, 313 X Michalet and D Bensimon (1995) Vesicles of toroidal topology: observed morphology and shape transformations J Phys II France 5, 263 G.A Ozin and S Oliver (1995) Skeletons in the beaker: synthetic hierarchical inorganic materials... patterns with continuoulsy tunable morphology: the fractal properties of some real snowflakes Journal of Physics A 20, L1185 B Perrin and P Tabeling (1991) Les dendrites La Recherche May 1991, 656 P Prusinkiewicz and A Lindenmayer (1990) The Algorithmic Beauty of Plants Springer, New York L.M Sander (1987) Fractal growth Scientific American 256(1), 94 100 H.E Stanley and N Ostrowsky (eds) (1986) On . flask, and then add solution C to initiate the reaction. After about 3 min, the solution starts to alternate between colourless and yellow. The oscillations last for 10 15 min. This is the colour. centres, and the blue fronts annihilate one another as they collide. This reaction is most impressively seen when the dish is placed on an overhead projector (see above). The heat of the projector. ammonia solution to the top of the solidified gel using a pipette. Cover the tube again and leave it to stand. After several days, the bands begin to appear down the column. They are closely spacedabout