Absorption Log

Light meets biology in The Optics of Life by Sönke Johnsen. It’s a useful primer for anyone who wants to learn more about photons and the cells that detect them. Biology, chemistry, and physics are rolled into one served alongside just a few mathematical equations, and a sprinkling of wry humor. Yes, the book is science-nerdy. Yes, the second chapter is all about the importance of units and how not paying attention to wavelength versus frequency can really screw you up. But there are so many great nuggets, be they factoids or quotable jokes, that I’m quite willing to plow through the denser sections. Most important to me, reading it makes me think about all manner of interdisciplinary things!

 

I’ve just finished the fourth chapter, titled Absorption. Here’s the opening paragraph for a taste: “Absoprtion has been called the ‘death of photons’ (Bohren and Clothiaux, 2006). While the energy of a photon is never truly lost (reincarnation is a fact in physcis), most people find the conversion of photons into heat and chemical reactions less appealing than their original emission. I admit that I enjoy watching bioluminescent plankton more than contemplating the blackness of my T-shirt. Without absorption though, the earth would be a far less colorful place, with no paintings, flowers, leopard spots, or stained-glass windows.”

 

Johnsen will go on to cover paints, windows, the coloration in all manner of species. But first one has to learn about resonance, antennae, and how electromagnetic “signals” are propagated. Eventually he gets to the difference between absorptivity and absorbance. Our G-Chem students are introduced to this in their first semester of lab where they do some experiments to determine the concentration of an unknown dye with the help of a spectrometer. Absorbance is a funny thing, though. It is defined as the negative (natural) logarithm of the fraction of light that is transmitted. In equation form, this is A = –ln(f_T).

 

Natural logarithms show up in a variety of situations. Whenever you have a large enough sample of particles that can randomly do something or not do something, you observe macroscopic behavior that corresponds to an exponential decay curve. In the case of absorbance, this has to do with whether a photon hits a molecule and gets absorbed. In radioactive decay, it’s related to when an atomic nucleus might transform into another by emitting radiation. In chemical kinetics, a first-order reaction has a rate that is proportional to its concentration. We’re not used to thinking about exponential decays. We think linearly. It takes a bit to get my G-Chem 2 students to see that if rate is linearly proportional to concentration, then the concentration changes exponentially with time.

 

Johnsen explains why absorption and absorbance are often confused, pointing out that it’s partly because when the fraction of light absorbed is small, then absorbance takes approximately the same value. An equation that helps you see this: ln(1 + x) is approximately equal to x when x is small. Johnsen then explains what the absorption coefficient is and why it’s useful especially if you were a biologist trying to determine what the photoreceptors of marine creatures are detecting. Colors and light in the sea are an interesting business to the denizens of the deep especially since longer wavelength (redder) light is more easily absorbed by water, i.e., the bluer light has more penetrating power. All manner of adaptations arise, and Johnsen deftly explains the preponderance of different kinds of reds in many marine invertebrates.

 

I found the discussion on paints enlightening. Apparently “many oil paints look nearly black when they come out of the tube. It’s not until they are mixed with white paint that they look like the color on the label. White paint (and white in general) is more special than it looks. Rather than simply being paint without pigment, it is actually a mixture of a transparent latex or oil base and powdered titanium dioxide.” The key here is that TiO₂ has “a high refractive index in the visible range (~2.5), about the same as diamond… and scatters a lot light.” Artists have to know how much white to mix into their oils to get what they need. This same interplay of absorption and scattering is also true for colors of organisms. Johnsen goes through a series of examples and adaptations in cephalopods, birds, and more.

 

This is followed by another interesting discussion of Easter egg dyes, and he smoothly pivots into the odd case of green. Green dyes transmit in the green range, or more pertinently, they have pigments that strongly absorb the red and the blue. But yellow, orange or red dyes essentially just have a step function with low transmittance at short wavelength and high transmittance at longer wavelength. (For blue dyes, the step function is in the opposite direction.) We also observe these features in the molecules of color that living organisms use – the carotenoids. I find this odd and intriguing. Surely there are molecules that can provide the color peaks exactly where needed in the spectrum, but maybe there’s a limit to what can be biosynthesized that lead to the asymmetry. There’s something strange about all of this. It’s certainly opened my eyes to how much I don’t know about vision, color, and light, as it pertains to biology (and not just its simple physics). I’m tempted to pitch teaching a class about the “Chemistry of Living Color”, and add it to the list of courses I might want to do one day that will give me an excuse to delve deeper!