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I am looking for a good explanation explaining why infrared absorption technique is essentially nonlinear (eg. for carbon monoxide quantification).

When using UV/visible/near-IR absorption technique, Beer-Lambert Law often is valid and then you have quite straight way to convert transmittance into absorbance which linearly respond to concentration (provided BLL limitations are not met).

Above technique relies on electronic transitions, when IR absorption technique relies on vibrational and rotational transitions for molecules which has permanent or transient dipole moments. I would like to figure out why such technique is essentially nonlinear.

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  • $\begingroup$ Could you please clarify what you mean by "essentially nonlinear". There is no intrinsic reason why IR absorption is different from absorption if visible light. $\endgroup$
    – gigacyan
    Jul 26, 2014 at 13:28
  • $\begingroup$ I use different models of IR absorption analysers (not FFT) for quantification of CO and CO2. Constructor (Thermo Scientific) claims the method is nonlinear and they does not use BBL as final transduction formula. But for UV absorption for O3 quantification constructor does make use of BBL. I read some book chapters about IR absorption and they does not use BLL for quantification, they only do when using near-IR. I am wondering why? $\endgroup$
    – jlandercy
    Jul 26, 2014 at 14:16

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Edit: putting the summary of discussion in comments into my answer.

Beer-Lambert law assumes that every photon has equal probability to be absorbed by every molecule. It is only valid for sufficiently monochromatic light – that is, the bandwidth of light source should be smaller than the width of the absorption line. When absorption is measured with a laser tuned to a particular rovibrational line of a molecule, the Beer-Lambert law works well.

The method discussed here uses a broadband light source that covers a spectral range containing many rovibrational lines of $CO$, but also regions between those lines, where light is not absorbed at all. There is no simple model that could describe such behavior. In theory, one can calculate the absorption spectrum of a molecule, including temperature- and pressure-dependent line broadening, and then calculate it's convolution with the spectrum of the light source. In practice, using gas samples of known composition one can build a calibration curve Absorption vs gas concentration and use it to convert absorption to gas concentration.

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My old answer described another case where Beer-Lambert law may be not valid:

The only nonlinear effect that comes to my mind is saturation. Beer-Lambert Law is valid if the population of the ground state is not depleted. However, vibrational bands in mid-IR have very strong absorption, and with intense light source (like laser) one could deplete the ground state - see answer to this question.

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  • $\begingroup$ Are you sure that infrared absorption can be safely modelled by Beer-Lambert as this? It looks like to me that it is not that easy to measure infrared absorption, because it is in a spectrum region where everything around us emit light in this wavelength range. What if I am not using a LASER, but instead a resistor as source? I know that it invalidate monochromatic source hypothesis. But are you saying that with LASER it works like a charm? $\endgroup$
    – jlandercy
    Jun 7, 2016 at 21:54
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    $\begingroup$ @jlandercy Beer-Lambert law is only valid for sufficiently monochromatic light, i.e. narrower than the absorption line, and it also works in mid-infrared if you use laser light to probe a single absorption line. With broadband source, as you have, part of emitted radiation will not be resonant with any rovibrational line, so it will not be absorbed and B-L law is not applicable. $\endgroup$
    – gigacyan
    Jun 9, 2016 at 7:59
  • $\begingroup$ Yes that does make sense. Is there another theory/model to assess IR absorption when using broad source and non selective detector. (I am using Thermo 41/48i Series to measure CO/CO2. Source is a resistor, hashing and sampling is performed by a correlation wheel, that contains pure N2 in a cell and pure analyte in another.) $\endgroup$
    – jlandercy
    Jun 9, 2016 at 9:58
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    $\begingroup$ @jlandercy I don't think there would be a simple model. Theoretically, one could simulate spectrum of CO and then calculate its convolution with the emission spectrum. However it would be very difficult to make it precise. The easiest would be to measure absorption of samples with known concentrations to build a calibration curve. $\endgroup$
    – gigacyan
    Jun 9, 2016 at 20:07
  • $\begingroup$ Yes I think it is the way those analyser work. Do you mind summarize your comments in your answer then I can accept it. Thank you. $\endgroup$
    – jlandercy
    Jun 9, 2016 at 20:34

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