Since about 40 years, the quantity absorbance, defined by the negative decadic logarithm of the transmittance or the relative reflectance, builds the fundament of infrared spectroscopy. Absorbance is intimately connected to the Bouguer-Beer-Lambert-law which states that the absorbance increases linearly with the thickness of a sample and the concentration if the sample consists of a solution, be it solid, liquid or gaseous.
Unfortunately, absorbance is, in general, a quantity that is not consistent with Maxwell’s equations, an insight that somehow got lost over the last 40 years. Indeed, only in spectrophotometric applications, where absorbance is, deviating from its definition, actually calculated as a negative decadic logarithm of the transmittance of the solution normalized by the transmittance of the pure solvent, the quantity becomes to a good approximation compatible with Maxwell’s equations. If neat substances are investigated, as it is often the case in infrared spectroscopy, such a normalization is not possible.
In addition, if films are studied, either in free-standing form or deposited on dielectric or metallic substrates, electric field standing waves exist within the films. Often, but not necessarily, these standing waves manifest itself as interference fringes in the spectra and are seen as a major nuisance that needs to be removed before spectra can be interpreted. These fringes, however, are just one side of the coin.
More importantly, the electric field standing wave effects lead to a variation of the electric field strengths, periodic in both, the distance from the interface and the frequency or wavenumber of the incoming radiation. As a result of the latter, absorbance can become highly non-linear and even decrease with increasing thickness of the layers. Furthermore, the peak positions can be strongly altered by up to 25 cm-1 and more if the film is placed on a metallic substrate. Since usually (and, actually, erroneously) alterations of peak positions are interpreted of structural changes, these alterations in concert with the non-linear intensity changes strongly impair the interpretation of spectra.
Since these effects are not well-known in the related scientific community, it is also not well-known, that absorbance (which should better be called “apparent absorbance”) spectra need to be treated either by dispersion or Kramers-Kronig analyses, in general, to be quantitatively interpretable (the usual baseline correction after conversion to absorbance by more or less advanced chemometric methods is highly unphysical and cannot remove electric field standing wave effects).
Unfortunately, dispersion analysis, which is based on using oscillator models to describe the dielectric function (or dielectric function tensor for anisotropic materials), needs some experience to be applied, since, e.g., meaningful starting values for the oscillators have to be chosen. A Kramers-Kronig analysis, on the other hand, requires in principle a spectrum measured over the whole spectral range where the material posses absorption. This is usually not possible or requires too high an effort. Accordingly, different schemes are used to extrapolate the spectral properties in spectral ranges that have not been measured. Therefore, also experience is required and ambiguity is introduced.
Since in particular for biomedical applications infrared imaging is a very promising technology, neither conventional dispersion analysis nor Kramers-Kronig analysis-based evaluation methods are qualified to take on the challenge. Therefore it is of urgent necessity to develop a third method that is reliable, user-friendly (i.e. fully automatic) and, in particular, fast. At the moment we focus on developing such a method and first results promise an evaluation technique that allows calculating true absorbance and is, in addition to all of the above, highly parallelizable, fully compatible with Maxwell’s equations and takes less than a minute on a conventional office PC.
Helpful References
- Employing Theories far beyond Their Limits—The Case of the (Boguer-) Beer-Lambert Law, ChemPhysChem 2016
- The electric field standing wave effect in infrared transflection spectroscopy, Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 2018
This study, The Electric Field Standing Wave Effect in Infrared Transmission Spectroscopy was recently published in the journal ChemPhysChem.