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Absorption Spectroscopy

absorption_spectroscopy

Overview

As you learned in the quantum mechanics tutorial, light can interact with molecules. Here we will briefly examine this effect for the case of directing light (such as from a lamp) through a medium that can absorb the light (such as the gas in an engine).

Details

Imagine you are outside on a sunny day wearing sunglasses. The light reaching your eyes is dimmer than it would be without the sunglasses. This is because the sunglasses absorb some light. Imagine you stare straight at the sun through your sunglasses. This is not as painful as it would otherwise be, because the sunglasses are absorbing, we’ll say, half of the visible light (incidentally, they probably absorb much more than half in certain spectral regions outside the visible). Your eyes are thankful for not having to receive the full energy of the direct sunlight; where did the other energy go? Of course, it went into heating the sunglass eyepieces, in this example about ½ Watt per eyepiece, which of course doesn’t melt them but certainly raises their temperature a noticeable amount. The same thing happens when our lamp light is directed through the gas in an engine, the molecules absorb the light and the gas heats up; the temperature the gas reaches will depend on the brightness of the light and the opacity of the gas. Back to the sunglasses, imagine you still feel pain when you view the sun through the glasses. So you borrow your friend’s sunglasses (identical to your own) and put them on over the top of yours. What energy is absorbed by the second pair of glasses? The other half? In fact, no, just half of the remaining half, so the first sunglasses absorb ½ Watt (per eyepiece) and the second absorb ¼ Watt and the remaining ¼ Watt reaches your eye. Adding a third pair of sunglasses, the first absorb ½ Watt, the second ¼ Watt, and the third 1/8 Watt, so that only 1/8 Watt reaches your eye. Thus, you need an infinite number of sunglasses to completely shield your eyes from the sunlight. Accordingly, an exponential loss formula governs absorption spectroscopy, as deduced by August Beer in 1852:

Beer’s Law: I/Io = exp(-kλL)*,

where Io [Watts] is the intensity entering the absorber, I [Watts] is the intensity transmitted through the absorber, kλ [cm-1] is the spectral absorption coefficient at a specific wavelength (color), and L is the length of the absorber (the thickness of the sunglass eyepiece in our example).

absorption_spectroscopy

Plots of kλ versus wavelength λ are known as absorption spectra. The absorption spectrum for the sunglasses described here could be measured using a lamp, a prism and a linear camera as shown in the figure above. The absorption spectra of gases are much richer in information than the sunglasses in the example. Absorption spectra for some representative combustion gases are shown in the figure at the top. These are simulated using databases called HITRAN and HITEMP. There are several things to note, such as:

  1. H2O (water vapor, in black) is the dominant absorber in this infrared wavelength range (for reference 1 µm wavelength corresponds to twice a wavelength we would call bluish-green).
  2. H2O has ~ 5 features of similar shape in this wavelength range, getting generally stronger at longer wavelengths (these features are known as bands associated with both rotation and vibration of H2O, rather than rotation alone as described for OH in the quantum mechanics tutorial)
  3. The spectral width of these bands increases as temperature increases. This property forms a basis for gas thermometry by absorption spectroscopy.
  4. There are some spectral windows where species other than H2O have absorption stronger than H2O. Thus, with appropriate sources for measuring the spectra shown above, inside the engine cylinder, one can measure the gas composition as well as the temperature.
  5. A disclaimer accompanies these spectra: they are simulated from databases known to contain errors. Thus, actual spectra acquired in engines using wavelength-agile sources often reveal discrepancies.

Actual engine measurements demonstrate that absorption spectroscopy is a simple yet powerful technique for studying combustion. Note that gas temperature and/or composition measurements made by absorption spectroscopy generally represent line-of-sight-averaged quantities, unlike fluorescence spectroscopy.

* click here for details on this law and a nice illustration of light attenuation in a cuvette; note that several forms are used (sometimes base e, sometimes base 10, often kλ is replaced by something similar but defined, for example, on a molar concentration basis).