I might hazard a guess. Absorbance can be used directly for analysis of concentration through Beer's law. The simplicity and proven utility of the expression for an analytical chemist far outweigh the fundamental concerns that you mention.

In summary, this is a case where physicists see a process and want to describe it at the deepest fundamental level whereas chemists see the same process and want to describe it for the best possible further use.

I might hazard a guess. Absorbance can be used directly for analysis of concentration through Beer's law. The simplicity and proven utility of the expression for an analytical chemist far outweigh the fundamental concerns that you mention.

In summary, this is a case where physicists see a process and want to describe it at the deepest fundamental level whereas chemists see the same process and want to describe it for the best possible further use.

I absolutely see the utitliy of absorbance in UV-Vis spectrophotometry. In infrared spectrophotometry, however, the big difference is the small thickness of the cuvettes which leads to interference effects. This renders absorbance completely useless... See e.g.

Article Some Problems in Infrared Spectrophotometry

This will not be an issue for RAIRS or ATR or transmission through a solid (polymer) film or DRIFTS. This range of techniques covers a significant set of useful samples for an analytical chemist.

I wish you were right.

It is definitely a major issue for RAIRS (IRRAS) and transmission through a polymer film. For RAIRS it has not been noticed for a long time, probably because the metal substrate suppresses interference fringes in regions where there is no absorption. The more these fringes come forth around bands. Interference also leads to strong changes of band intensity ratios. Furthermore strong band shifts can occur (refs. 1 and 2).

The same effect is also present in transmittance measurements of polymer films and any other films. It can only be suppressed by a clever choice of the substrate in some cases (refs. 3 and 4).

Interference might not be a general problem in ATR, but the corresponding definition of absorbance ("reflectance absorbance") is at least strongly tainted if there are not only very weak bands present (ref. 5)!

In the three cases above there are remedies, which cost a little bit more effort and time like e.g. applying a procedure called "dispersion analysis". Not so in case of DRIFTS. There does not even exist an analytical solution which conforms with Maxwell's equations. DRIFTS can only be a last resort...

Article The inherent problem of transflection-mode infrared spectros...

Article Thickness-Dependent Optical Effects in Infrared Reflection-A...

Article The Measurement of the Optical Constants of Thin Solid Films...

Article Employing Theories Far beyond Their Limits-The Case of the (...

Article Expended Formulas for Attenuated Total Reflection and the De...

I stand corrected. Thank you for the references.

I must add some additional notes to follow up on my quick post immediately above.

I've done an undergraduate lab demo using ATR that proves Beer's law can be used to calibrate for concentration ratio in mixtures of palm oil and pump oil . By comparison, I've also done ATR on diamond/graphite films where changes in film thickness caused significant changes in background shape, thereby making quantitative analysis of film composition a complicated if not impossible task.

For free-standing films in transmission mode, I would expect that, when film thickness is kept constant, interference effects in a standing polymer film would be normalized or remain unchanged so that changes in the absorbance of a given peak can be mapped to a composition change in the film.

The RAIRS that I reference is from sub-monolayer to monolayer films on metals. There, analysis is done using s and p polarization for reference (s) and signal (p), ostensibly to normal path length effects and presumably therefore also to normalize so that absorbance is proportional to coverage (concentration).

In summary, the references provided are all relatively new and/or relatively specialized. I will say, they do not dismiss the idea that absorbance is useful even in IR spectroscopy. My experiences and the references do however suggest that, when IR is to be used for quantitative analysis (i.e. using Beer's law via absorbance), care must be taken to confirm the validity of the equation being used. That being said, a good analytical chemist knows this rule. The utility of absorbance for chemistry remains (one might say ... even despite the reservations of the physicists in the room).

First of all I have a confession to make - I am a chemist... ;-)

I do not doubt that by careful design of the experiment and critical evaluation of the results information about the concentration can be extracted. Indeed, taking your example from above if the thickness is kept constant in case of a polymer film I agree that concentrations can be extracted after a proper calibration. Without calibration however, there is no chance since the molar extinction coefficient would be different for different thicknesses.

My point is that the use of absorbance suggests to the average user a simplicity of interdependencies that is often not present in infrared spectroscopy. And determining concentrations is certainly just one of the many uses of vibrational spectroscopy. Just think of e.g. the dichroic ratio to determine the orientation in polymers which does not only suffer from the absorbance problem, but is additionally flawed by the shortcomings of linear dichroism theory, another skeleton in the closet. Or something more fundamental: how meaningful is to provide an absorbance spectrum of a material when band positions and relative intensitites depend on the thickness of the sample? There are good reasons why a certain prominent spectral database does not provide a single absorbance spectrum...

My feeling is that we urgently require an extensive evaluation in infrared spectroscopy to determine what works under which conditions and what does not work. If I read through the textbooks of vibrational spectroscopy I miss such a critical evaluation, or is there something around?

> First of all I have a confession to make - I am a chemist... ;-)

Ah! Then I must apologize. I am more aware of having discussions of the fundamental nature that you raise within physics ... chemical physics if you will. I should set my presumptions aside, lest I also fall in to the trap of some chemists who might claim that, unless you are studying chemical reactions of some kind or another, you are not really doing chemistry.

> My feeling is that we urgently require an extensive evaluation in infrared spectroscopy to determine what works under which conditions and what does not work. If I read through the textbooks of vibrational spectroscopy I miss such a critical evaluation, or is there something around?

The audience is certainly rather broad. Is this a good or bad thing? On the one hand, analytical chemists or "benchtop" chemists (the perspective that I have somewhat taken) want a method that works easily either for quantitative analysis (the former) or "fingerprinting" (the latter). They could likely care less about having an extensive evaluation. Give them a Beer's law plot or a library lookup and they are happy. On the other hand, the chemical physicists / phyiscal chemists / spectroscopists are focused on the tool as applied to a small subset of the variations in sample sets and/or methods. Give them a well-defined formulation specific to their method, their instrument, and their samples and they are happy. Why do they need an extensive evaluation?

I applaud your significant insights and thoughts on this. It sounds however to be more than any one person could handle alone. Would a conference type book do the job? Invite the top-known researchers in specific applications of IR. Ask them to prepare a contribution on the good, bad, and ugly about the use of IR for quantitative analysis for the given application. Perhaps focus on themes: Freestanding Films; Coatings; Gas Monolayers; Powders ...

I would love to have a conference of the type you suggest. Unfortunately it is also something I could not handle and not even initiate on my own. What does not help either is that it is not some type of skyrocket science and involves some digging up the dirt...

I have still no answer to my original question, but I found a couple of things:

- Neither Bouguer, nor Lambert, nor Beer used absorbance in their publications

- Georges Urbain did not introduce it in his famous book "Introduction à l'étude de la spectrochimie" (at least not in the German version; many thanks to Jean-Rene (Jean Rene Grezes ) for providing me a copy of the pages in question!)

- Absorbance cannot be found in the publications of Voigt, Czerny, Schaefer, Matossi or Mecke (see https://www.researchgate.net/post/Who_of_the_infrared_spectroscopists_knows_the_following_pioneers_of_infrared_spectroscopy), but also Coblentz did not use it.

The earliest use I found is the one by Kortüm 1936, who used "Extinktion" instead of absorbance: https://www.degruyter.com/view/j/zpch.1936.33.issue-1/zpch-1936-3321/zpch-1936-3321.xml

Thanks to Jean Rene Grezes we are much closer to the solution than before. I had expected to find a paper where absorbance or extinction had been introduced. It seems that such a singularity has never occured. Instead it seems that the near final form of the Bouguer-Beer-Lambert law was introduced by Bunsen and Roscoe in 1857: https://onlinelibrary.wiley.com/doi/10.1002/andp.18571770605

Probably it was peu à peu introduced, e.g. by J. Precht, who suggest to call the product of attenuation constant, thickness and concentration "extinction" in a lecture of a conference about photochemistry in 1900... from the same field comes the "optical density" (originally: density), which already appears much earlier, see e.g. “The Photographic Researches of Ferdinand Hurter & Vero C. Driffield” (https://ia800300.us.archive.org/28/items/memorialvolumeco00hurtiala/memorialvolumeco00hurtiala.pdf )