Employing Theories Far beyond Their Limits – Linear Dichroism Theory

Abstract

Using linear polarized light, it is possible in case of ordered structures, such as stretched polymers or single crystals, to determine the orientation of the transition moments of electronic and vibrational transitions. This not only helps to resolve overlapping bands, but also assigning the symmetry species of the transitions and to elucidate the structure. To perform spectral evaluation quantitatively, a sometimes "Linear Dichroism Theory" called approach is very often used. This approach links the relative orientation of the transition moment and polarization direction to the quantity absorbance. This linkage is highly questionable for several reasons. First of all, absorbance is a quantity that is by its definition not compatible with Maxwell's equations. Furthermore, absorbance seems not to be the quantity which is generally compatible with linear dichroism theory. In addition, linear dichroism theory disregards that it is not only the angle between transition moment and polarization direction, but also the angle between sample surface and transition moment, that influences band shape and intensity. Accordingly, the often invoked "magic angle" has never existed and the orientation distribution influences spectra to a much higher degree than if linear dichroism theory would hold strictly. A last point that is completely ignored by linear dichroism theory is the fact that partially oriented or randomly-oriented samples usually consist of ordered domains. It is their size relative to the wavelength of light that can also greatly influence a spectrum. All these findings can help to elucidate orientation to a much higher degree by optical methods than currently thought possible by the users of linear dichroism theory. Hence, it is the goal of this contribution to point out these shortcomings of linear dichroism theory to its users to stimulate efforts to overcome the long-lasting stagnation of this important field.

Beyond Beer's Law: Spectral Mixing Rules

“…S11 and S12), which adds another layer of complexity quantitative evaluation methods have to cope with. The situation is comparable to that of linear dichroism theory, which holds good for weak oscillators, shows noticeable deviations for medium strong oscillators, 24 and delivers poor and unacceptable results for strong oscillators like the n 3 mode of oxyanions. The reason is that a mixing similar to that for micro-heterogenous samples takes place, e.g., for the ordinary and the extraordinary rays in uniaxial materials.…”

“…The reason is that a mixing similar to that for micro-heterogenous samples takes place, e.g., for the ordinary and the extraordinary rays in uniaxial materials. 23–25…”

“…The reason is that a mixing similar to that for micro-heterogenous samples takes place, e.g., for the ordinary and the extraordinary rays in uniaxial materials. [23][24][25] It is far beyond the scope of this work to evaluate the performance of each chemometric method which assumes that absorbances from different components of a mixture are additive in light of above discussion. In particular, the band shifts, peak height and band shape changes displayed in Figs.…”

Beer's Law – Why Absorbance Depends (Almost) Linearly on Concentration

“…(8) and found that the differences are very small as long as the oscillators are comparably weak, like for organic and biological matter in the infrared spectral range. [10] Accordingly, we can predict that the approximation/ assumption of additivity, on which Beer's law and its standard derivation are based, is excellent in these cases.…”

The Bouguer‐Beer‐Lambert Law: Shining Light on the Obscure

“…For C=O vibrations deviations of up to % are possible. [102] In case of inorganic materials with their usually much stronger absorptions linear dichroism theory is generally inadequate. In fact, it was already obsolete long before it was founded.…”