In Fourier-transform infrared spectroscopy results, I am trying to understand why either [a.u.] or no units are often reported for the area under the curve. Should it not be [cm^-1 * a.u.] if it is an area? Why are the [cm^-1] ignored?
It's somewhat pointless. Usually, you measure the area and compare it to the area of another peak. Since both peak areas have the same units, you end up with a dimensionless ratio.
John Francis Miller there is a little bit more behind. According to the Kramers-Kronig sum rules, the integral of absorption index times the wavenumber (i.e. ln(10)*absorbance/(4 pi d) is the oscillator strengths times pi/4. The oscillator strengths is given by q2N/(με0), where q is the charge, N the number of dipole moments per unit volume, μ is the reduced mass and the ε0 the vacuum permittivity. See section 5.8.3 of this book: Book Wave Optics in Infrared Spectroscopy - Theory, Simulation, a...
Coming back to the original question, the unit of the intregral of absorbance should be accordingly cm-1. If this is ignored then probably because people are not aware of the underlying theory?!
It's not relevant to the practical application of FTIR. It's an analytical technique and most commonly the peak area is compared to another peak area from the spectrum from the same sample. Some instruments use cm-1, others use wavelength.
The same is true in chromatography. The y-axis is some detector response that no-one needs to know. It's about relative peak areas.
John Francis Miller It is generally a bad idea to compare the area of one band to that of another "from the spectrum from the same sample" (or the peak heights) except for gases. As an example, just think of a film of a polymer on CaF2. If you compare the same ratio for different film thicknesses you see that the ratios change with thickness.
Instead of the areas of -log10(I/I0) (which is actually -log10(T/T0) or -log10(R/R0)) you can use the area of absorption index times the wavenumber to avoid the problem, but this works only for neat substances.
It's done all the time in analytical chemistry esp in the pharma industry. OP has not explained their application. I appreciate the pureness of your comments but the real world often doesn't worry about the semantics. As long as it's being used as part of a validated method all is good.
Yes - "we have always done it this way" is certainly a convincing argument... certainly more convincing than mine... ;-)
Anyway, on a personal note, this seems to be a good way to show someone who questions practices like the OP how things should be done in science...
The application is in wood material science. I am trying to determine the hydroxyl group accessibility of wood, for example. This determination involves deuterating the material. A colleague reported the band area underneath the deuteroxyl groups (hydrogen in the hydroxyl group exchanged for deuterium) with [a.u.], which got me thinking since I do not understand why the unit is as it is.
Mikko Juhani Valkonen You are absolutely right to question things. In fact, Infrared Spectroscopy is an extrem fragmented field with different communities ranging from solid state physicists to biologists with very different levels of theory. Absorbance is, e.g., something that was rarely used 40 years ago. Integrating it means frequently that you have to remove baselines, which is a highly questionable practice from a theoretical point of view...