The Pixel Paradox and Transition-Metal ... - ACS Publications

Chemistry for Everyone edited by

Ed Vitz Kutztown University Kutztown, PA 19530

The Pixel Paradox and Transition-Metal Spectroscopy: One of Many Uses of the Handheld Digital Microscope in Chemical Demonstrations Ed Vitz Department of Physical Sciences, Kutztown University, Kutztown, Pennsylvania 19530 [email protected]

Many texts (1) present a color wheel and suggest that the color of a compound will be the complementary color of the absorbed light or the color opposite the absorbed color on the color wheel. This works surprisingly well in many cases, so we are tempted to ignore the fact that it may, by focusing our attention on absorbed light, impede understanding of the actual mechanism of color perception, which involves additive mixing of transmitted light. The color-wheel interpretation also presents difficulties when two or more colors are absorbed or transmitted, which is the general case. A more satisfying understanding of color is desirable not only for science majors, but for students in liberal arts chemistry courses. The “pixel paradox” demonstration provides insight into the additive mixing of colors. It is a demonstration of “metameric hues”, colors that appear identical but have widely different spectral compositions. For example, a solution that appears yellow may transmit yellow light, but it might also, paradoxically, absorb yellow while transmitting red and green light. The pixel paradox can be used to introduce chromaticity diagrams that improve on the simple color-wheel approach by quantifying additive mixing. Handheld Digital Microscopes There are many commercially available handheld digital microscopes (HDMs). We use one sold on the Web1 for about $90, but it is also possible to modify an ordinary “doc cam” (also called a “Web cam”) for use as a lower-powered HDM.2 Instructions for opening and modifying the Web Cam by reversing the lens are provided in the supporting material. Images of the pixels of a 12 in. screen on a Lenovo model 0764 laptop computer operating at 1024 768 resolution and 32 bit color quality are shown in Figures 1-3. The image in Figure 1 was recorded with the Logitech WebCam Communicator STX with the lens reversed and appears as a 3.5 2.5 in. image on the laptop screen. The same screen image photographed with Logitech WebCam with the lens screwed as far out as possible, allowing close focusing, is shown in Figure 2. Finally, the same screen image recorded with the Celestron 44300 HDM at 400, which gave a 4 6 in. image on the screen, is shown in Figure 3. Magnification will, of course, be proportionately increased when the laptop screen is projected. Demonstrations The Pixel Paradox Project a computer screen with any digital presentation projector and create patches of white, yellow, and other colors

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with the standard drawing tools of any convenient drawing or presentation program. Open the HDM software so that there is a live image on part of the same screen. Hold the HDM some distance (usually 1 cm is appropriate) from a patch of yellow on the computer screen, so a blurry yellow color is observed in the image, then move the HDM until it focuses on the pixels of the screen (the HDM may have a base that will be in contact with, or very close to, the screen). Paradoxically, only red and green pixels (no yellow!) are seen. This demonstrates that, when we see yellow, we may be seeing light of wavelength 565 nm or mixed wavelengths of (for example) 545 nm (green) and 610 nm (red). A freeware program, RGBtoHEX (2) can be used to show how varying quantities of red, green, and blue can be mixed to give a patch of any color rendered by the computer monitor. The color patch can then be viewed with the HDM to observe the individual pixels. This program shows how 256 levels of red, green, and blue may be combined to give “24 bit color” with 224 (= 2563 = 16,777,216) colors. The demonstration may be expanded to allow “inquiry” investigations by students if they are provided with small, inexpensive optical microscopes.3 With them, pixels on an LCD monitor may be observed in a laboratory setting, and students can explore additive mixing of colors of their choosing. Transition-Metal Spectroscopy The color of solutions of various complexes can be displayed by adding them to Petri dishes or beakers on an overhead projector or document camera. Copies of absorption and transmission spectra can also be projected (either before or after the solutions), and students can be challenged to predict colors from the spectra or vice versa. Absorbance spectra for several cobalt complexes, along with simplified methods of preparation for appropriate solutions, have been published (3). We display solutions of the hexaaquacobalt(III) ion and tris(oxalate)cobalt(III) ion (see the supporting material for the procedures). Absorbance and transmission spectra were obtained on a Varian Cary 50 Bio UV-vis spectrophotometer with Cary WinUV software version 2.00(182). To illustrate how transmitted colors combine to give the perceived color for the complex, we demonstrate “Chromaticity Diagram and Color Gamut” (CDCG) applets that have been added to the DigiDemos site as a Supplement.4 The applets show how a chromaticity diagram (vide infra), may be used to synthesize a color on the computer screen to match the color of the projected cobalt solution.

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r 2010 American Chemical Society and Division of Chemical Education, Inc. pubs.acs.org/jchemeduc Vol. 87 No. 3 March 2010 10.1021/ed8000792 Published on Web 02/09/2010

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Chemistry for Everyone

Figure 1. Image recorded with Logitech WebCam with lens reversed. Figure 4. Crystals of sodium acetate before recrystallization.

Figure 2. Image recorded with Logitech WebCam with lens at outermost threads. Figure 5. Crystals of sodium acetate after recrystallization.

Figure 3. Image recorded with Celestron Model 44300 HDM at 400.

Other Demonstrations with the HDM The HDM is a valuable addition to a demonstrator's toolbox. With most HDMs, either still images or videos can be recorded. Devices with various magnifications are useful for displaying crystals, bubble or color formation at microelectrodes, fibers and other forensic samples, Brownian motion, and a virtually unlimited number of other microscopic objects or phenomena. In many cases, magnified images are more beautiful than what might be observed macroscopically, but even where large-scale demonstrations are effective, supplementation with microscopic images can improve the presentation. As examples, movies of crystallization from supersaturated solutions have been mounted at the DigiDemos site as supporting material.5 These were produced by placing crystals of sodium acetate on a clean microscope slide resting on an inverted Celestron HDM. Then, while recording the image, a few drops of supersaturated sodium acetate solution were added. This procedure obviously reduces consumption of chemicals, but also adds a new perspective to a demonstration done on a large scale by one of the previously published methods (4). Still images of crystals of sodium acetate before recrystallization are shown in Figure 4 and after recrystallization in Figure 5, both taken with the Celestron HDM at 400. Hazards If cobalt complexes are synthesized from cobalt(II) compounds, the procedure should be carried out in a hood, because 276


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these compounds are suspected carcinogens by inhalation. Rubber gloves should be worn because the cobalt complexes are skin irritants. Cobalt complexes should be disposed of as hazardous waste. Cobalt is a micronutrient (essential in vitamin B12), but ingestion of excessive quantities has led to a variety of health problems, discovered when cobalt was added to beer as a foam stabilizer in the 1960s (5). Sodium acetate has low toxicity, but it is a skin, lung, eye, and digestive track irritant, so it should be handled in the hood with gloves. Discussion Chromaticity Diagrams It is possible to improve significantly on the color-wheel approach by introducing chromaticity diagrams, because they potentially explain the color perceived when light of more than one wavelength falls on the eye. Chromaticity diagrams (unlike color wheels) explain why yellow is observed when violet is absorbed, because they focus on additive mixing of the red and green that remain. Since perception of color is complex, it is unrealistic to expect to be able to infallibly predict the perceived color from a spectrum. This is doubly true because most transmission bands are broad (monochromatic light is of theoretical significance only, although lasers produce a very narrow band). The Commission Internationale d'Eclairage (International Commission on Illumination) in 1931 created “Standard Valency System” known as the CIE 1931 chromaticity diagram (6, 7), one of which is reproduced in Figure 6 (8). The curved horseshoe-shaped boundary is defined by the monochromatic spectral colors (hues) in full saturation. A straight line connects the red and blue ends of the curved spectrum and includes points representing different shades of magenta (which does not exist in the visible spectrum, but is created by additive mixing of red and violet). The diagram might be considered a distorted color wheel with a lot of quantitative spectral detail. The center of the

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r 2010 American Chemical Society and Division of Chemical Education, Inc.


Figure 6. A chromaticity diagram: letters are discussed in the text (8).

diagram is white, and a straight line drawn through the center of the white region will intersect the boundary at complementary colors. By definition, complementary colors combine additively to give white (more precisely, achromatic light or light devoid of hue). For example, line ABC connects the boundary at 487 nm to that at 584 nm, and mixing a beam of 487 nm light of intensity proportional to the length of BC with a beam of 584 nm light with intensity proportional to the length of AB will give white light. All the other hues and saturation levels along any line like ABC can be created by mixing appropriate intensities of the wavelengths indicated at the intersection of the line with the boundary. The CDCG applets can be used to show the color that results by additive mixing of two or three colors chosen by their locations on a chromaticity diagram. Specifically for the pixel paradox demonstration above, line DEF connecting 545 (green) with 610 nm (red) points shows that approximately equal intensities (DE = EF) of these two wavelengths will produce yellow, although there are obviously many combinations of wavelengths that will produce yellow. This can be modeled with the CDCG applet by clicking on the border of the chromaticity diagram at 545 nm, then clicking twice on the border at 610 nm (the applet is designed to mix 3 colors, but two can be mixed by selecting the same point twice). The slider can be moved to mix the colors in different percentages until yellow appears. The yellow so produced appears identical to light of a single wavelength of about 570 nm, and these two yellows are metameric hues. Colors may vary somewhat depending on the monitor used to view them. Green light of wavelength 500-560 nm does not have a complement in the spectrum. The chromaticity diagram shows that these wavelengths are complemented by the magenta hues, which cannot be assigned wavelengths because they are additive mixes of red and violet. Some color wheels represent magenta in exactly the same way as colors that are in the spectrum, and may actually mistakenly show the “wavelength” of the magenta light. If three nonlinear points, such as GHI, are chosen (Figure 6), any color within the triangle they describe may be created, and in one CIE system, 700.0, 546.1, and 435.8 nm wavelengths of light are used to create all the hues. Since our eye contains cone cell receptors sensitive to short, medium, and long wavelengths, a three-color system should be capable of producing all perceived colors. Other systems, such as the familiar RGB, create wide ranges of colors, but they must display a limited chromaticity diagram for three reasons: First, their saturation is not as great as the maximum represented by the borders of some


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chromaticity diagrams. Second, their emission maxima cannot (such as GHI) “triangulate” all the colors that a high quality reproduction of a chromaticity diagram includes. And finally, they are far from monochromatic, so their emission “tails” may combine to overemphasize certain spectral regions. Chromaticity diagrams generated by different RGB monitors will not reproduce exactly the same perceived colors. Two recent articles in the Journal have dealt more quantitatively with chromaticity diagrams (9, 10). Color wheels are based on the assumption that the spectrum can be broken into thirds, so if the “violet” third is absorbed, the green and red spectral regions remain, which add to give yellow (the complement of violet). This seems reasonable because it roughly conforms to the mechanism of color perception by the eye. The boundaries of the regions and intensities are assumed to be such that all three regions add to give white light. But spectral distributions of perceived colors of solutions are seldom the “perfect thirds” of the spectrum that color wheels ideally represent. The spectral ranges of perceived colors are so ill defined that it is impossible to imagine how they could possibly match those of wheel colors. If perceived colors do not match wheel colors spectroscopically, it makes no sense to say that absorption of that color leads to perception of its complement. Rarely would colors perceived to be complementary combine, as colors on the wheel and those opposite them do, to give white. Relating Solution Colors to Spectra For all the faults of color wheels, they do surprisingly well at predicting colors, if one is not concerned with accurate explanations. The “observed color results when the complementary color is absorbed” approach works with varying success for many species. For example, KMnO4 appears purple with a single broad absorption band centered at λmax = 528 nm (green, which might predict a redder appearance), and CrO42- with a single broad absorption band at λmax = 373 nm (blue) appears orange. But how would a color wheel explain a green complex, since no single wavelength is the complement of green? What if more than one color is absorbed? Several relatively narrow absorption (and transmission) bands are frequently observed in transition-metal spectra. Yellow [Co(en)3]3þ has absorption bands centered at 339 nm (UV region) and 467 nm (teal). A color wheel might predict that absorption of 467 nm light should lead to a red-orange complex. Some species, such as pink Mn(II) solutions, have so many absorbances (and transmission bands) (11) that it is hard to imagine how a prediction would be made with a color wheel. Unfortunately, the situation may not be much better when chromaticity diagrams are used, because the perceived color that results from additive mixing of many ill-defined transmission bands (let alone monochromatic wavelengths) are virtually impossible to predict. But chromaticity diagrams are more accurate, consistent with the close-to-colorless “light pink” of Mn(II) solutions, for example, that result from transmission of many wavelengths, with only slightly enhanced intensities in the red region compared to white light. Co(III) complexes are interesting because they generally have two absorbances in the visible region because the most common t62g low-spin configuration gives rise to just one ground state (1A1g), but there are two t52ge1g triply degenerate excited states (1T1g and 1T2g). If there are two absorbances, the


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Figure 7. Absorption (solid) and transmission spectra (dashed) of [Co(H2O)6]3þ.

The tris(oxalate)cobalt(III) ion, [Co(C2O4)3]3-, is teal blue and has absorptions (Figure 8) centered at 425 nm (deep blue) and 602 nm (orange), with broad visible transmission bands at 480-550 nm (deep blue, green) and >680 nm. If three wavelengths (480, 550, and 680 nm) are combined with the CDCG applet in proportions of 53%, 31%, and 16%, teal hues are obtained. With an absorption centered around 425 nm, a color wheel would predict that the sample would appear red-orange, and there is no way to predict the effect of the second absorption. It is interesting to see the results of reduced hue saturation by selecting points within the chromaticity diagram rather than on its boundary. Conclusion

Figure 8. Absorption (solid) and transmission spectra (dashed) of [Co(C2O4)3]3-.

color-wheel approach seems in principle to be inapplicable. There must be more than one transmission band, and they must combine to give the perceived color, predicted by a chromaticity diagram. Color perception is so complex, however, that it is optimistic to think that chromaticity diagrams can be used to make reliable predictions. There may be no cobalt complex that appears yellow because it transmits red and green, but the hues of complexes may be reproduced by combining colors of two or three transmission bands, using a chromaticity diagram as illustrated below. The hexaaquacobalt(III) ion, [Co(H2O)6]3þ, is blue and has absorptions centered at 409 nm (violet) and 607 nm (orange) as shown in Figure 7. It is hard to imagine how the color wheel would predict the color of this complex. If we focus on the transmitted light, with a broadband centered around 490 nm (green) and >690 nm (red), the CDCG applets can be used to generate a color close to what we perceive. This is done by opening the applet and clicking on the border of the diagram at three wavelengths that might represent the transmitted light, for example, 460, 500, and 700 nm. If these are added (by moving the sliders) in the proportions 46%, 34%, 20%, a good simulation of the color of hexaaquacobalt(III) is obtained. Some guidance for moving the sliders is provided by the movement of the marker for the resultant hue within the chromaticity diagram. Additive mixing of two colors can be simulated by, for example, clicking twice on 490 nm and once on 700 nm, then adjusting the mixture to see the entire gamut of hues that can be generated. For reasons already mentioned, this illustrates the principle of color mixing of three (or two) broad bands; it does not correctly represent the infinite number of wavelengths impingent on our eye. The wavelengths were represented on an RGB monitor that cannot create the actual chromaticity diagram faithfully. It is interesting that the transmission bands that result in what we might call “green” and “red” in the hexaaquacobalt(III) spectrum are quite different from the spectral bands of the RGB system, which combine additively to give yellow, not blue! 278


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A comparison of perceived colors on a computer screen with magnified images of the pixels that create the colors can be used to demonstrate the principles of additive mixing. Chromaticity diagrams provide a better way of modeling and explaining color mixing than color wheels do, but it is probably fair to say that no simple means of interpreting spectra can really predict color in any reliable way. For spectra with a single absorption, color wheels can often be used to predict the perceived color, but explanations based on them are misleadingly oversimplified and fail for complex spectra with several absorptions. Notes 1. Celestron 44300 Handheld Digital Microscope, USB cable, 20 or 400, with white illumination by 4 LEDs powered through the USB connector, purchased through Optics Planet, Inc., http://www.opticsplanet.net/. (accessed Nov 2009). 2. Several Web sites describe this procedure, but poorly. For example, see: http://hackedgadgets.com/2008/04/03/webcam-microscope/ (accessed Nov 2009). 3. We use Radio Shack 30 illuminated microscopes, model 10084. 4. The applets were developed by Eugene Vishnevsky, under the direction of N. C. Schaller at the Rochester Institute of Technology. The applets are available at the DigiDemos site: http://jchemed.chem.wisc.edu/JCEDLib/DigiDemos/index.html. 5. The movies are available at the DigiDemos site: http:// jchemed.chem.wisc.edu/JCEDLib/DigiDemos/index.html.

Literature Cited 1. For example, see: (a) Housecroft, C. E.; Sharpe, A. G. Inorganic Chemistry, 3rd ed.; Prentice Hall: New York, 2008; p 615. (b) Harris, D. C. Quantitative Chemical Analysis, 4th ed.; W. H. Freeman and Company: New York, 1995; p 128. (c) Chang, R. Chemistry, 9th ed.; McGraw Hill: Boston, MA, 2007; p 950. (d) Shakhashiri, B. Z. Chemical Demonstrations, A Handbook for Teachers of Chemistry; The University of Wisconsin Press: Madison, WI, 1983; Vol. 1, p 262. 2. No Nonsense Software Home Page. http://www.no-nonsensesoftware.com/freeware/ (accessed Nov 2009). 3. Riordan, A. R.; Jansma, A.; Fleischman, S.; Green, D. B.; Mulford, D. R. Chem. Educ. 2005, 10, 115-119. DOI 10.1333/ s00897040867a, http://chemeducator.org/sbibs/s0010002/ 1020115dm.htm (accessed Nov 2009). 4. Shakhashiri, B. Z. Chemical Demonstrations, A Handbook for Teachers of Chemistry; The University of Wisconsin Press: Madison, WI, 1983; Vol. 1, p 27.


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5. Public Health Statement for Cobalt, Agency for Toxic Substances and Disease Registry, U.S. Department of Health and Human Services, http://www.atsdr.cdc.gov/toxprofiles/phs33.html (accessed Nov 2009) 6. Nassau, K. The Physics and Chemistry of Color. The Fifteen Causes of Color, 2nd ed.; John Wiley and Sons: New York, 2001; pp 9-26. 7. Kuppers, H. Color: Origin, Systems, Uses; Van Nostrand Reinhold Ltd.: London, 1972; p 106; translated by F. Bradley. 8. Glynn, E. F. Chromaticity Diagrams, http://www.efg2.com/ Lab/Graphics/Colors/Chromaticity.htm (accessed 12/30/2009). Used with permission (http://www.efg2.com/Lab/Copyright.htm, accessed 1/23/2009).


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9. Williams, D. L.; Flaherty, T. J.; Jupe, C. L.; Coleman, S. A.; Marquez, K. A.; Stanton, J. J. J. Chem. Educ. 2007, 84, 1873. 10. Williams, D. L.; Flaherty, T. J.; Alnasleh, B. K. J. Chem. Educ. 2009, 86, 333. 11. Lee, J. D. Concise Inorganic Chemistry; Chapman and Hall: London, 1996; p 966.

Supporting Information Available Instructions for opening and modifying the Web Cam by reversing the lens; synthetic procedures for hexaaquacobalt(III) ion and tris(oxalate)cobalt(III) ion. This material is available via the Internet at http://pubs.acs.org.


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The Pixel Paradox and Transition-Metal ... - ACS Publications

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