emission anisotropy

Also contains definitions of: degree of (polarization) anisotropy, luminescence anisotropy, time-resolved anisotropy, \(r(t)\)
https://doi.org/10.1351/goldbook.ET07370
Used to characterize @L03641@ (@F02453@, @P04569@) @P04712@ resulting from @PT07461@. Defined as: \[r = \frac{I_{\parallel} - I_{\perp }}{I_{\parallel} + 2I_{\perp }}\] where \(I_{\parallel}\) and \(I_{\perp }\) are the intensities measured with the @L03555@ for @E02056@ parallel and perpendicular, respectively, to the electric vector of linearly polarized incident electromagnetic radiation (which is often vertical). The quantity \(I_{\parallel} + 2I_{\perp }\) is proportional to the total @F02453@ intensity \(I\).
Notes:
  1. @F02453-1@ @P04712@ may also be characterized by the @P04712@ ratio, also called the degree of @P04712@ \(p\), \[p = \frac{I_{\parallel} - I_{\perp }}{I_{\parallel} + 2I_{\perp }}\] For parallel absorbing and emitting transition moments the (theoretical) values are \((r,p) = \left (^2/_5,^1/_2 \right)\); when the transition moments are perpendicular, the values are \((r,p) = \left ( -^1/_5,-^1/_3 \right )\). In many cases, it is preferable to use emission @AT06776@ because it is @A00134@; the overall contribution of \(n\) components \(r_{i}\), each contributing to the total @F02453-2@ intensity with a fraction \(f_{i} = I_{i}/I\), is given by:
    \(r = \sum_{i=1}^{n} f_{i}\, r_{i}\) with \(\sum_{i=1}^{n} f_{i} = 1\)
  2. On continuous illumination, the measured emission @AT06776@ is called steady-state emission @AT06776@ (\(\bar{r}\)) and is related to the time-resolved anisotropy by: \[\bar{r} = \frac{\int_{0}^{\infty} r(t)\, I(t)\, \text{d}t}{\int_{0}^{\infty} I(t)\, \text{d}t}\] where \(r(t)\) is the @AT06776@ and \(I(t)\) is the @R05045@ of the emission, both at time \(d\) following a δ-pulse excitation.
  3. @L03641@ @P04712@ @S05848@, with linear polarizers placed in both beams, is usually performed on @I03353@ samples, but it may also be performed on oriented anisotropic samples. In the case of an anisotropic, @UT07493@, five linearly independent @L03641@ spectra, instead of the two available for an @I03353@ sample, may be recorded by varying the two polarizer settings relative to each other and to the sample axis.
  4. The term fundamental emission @AT06776@ describes a situation in which no depolarizing events occur subsequent to the initial formation of the emitting state, such as those caused by @R05410@ or @E02116@. It also assumes that there is no overlap between differently polarized transitions. The (theoretical) value of the fundamental emission @AT06776@, \(r_{0}\), depends on the @A00346@ \(α\) between the absorption and emission transition moments in the following way: \[r_{0} =\, <3\, cos^{2}\, \alpha -1>\! /5\] where \(<>\) denotes an average over the orientations of the photoselected molecules. \(r_{0}\) can take on values ranging from \(-1/5\) for \(\alpha = 90\, °\) (perpendicular transition moments) to \(2/5\) for \(\alpha = 0\, °\) (parallel transition moments). In spite of the severe assumptions, the expression is frequently used to determine relative transition-moment angles.
  5. In time-resolved @F02453-2@ with δ-pulse excitation, the theoretical value at time zero is identified with the fundamental emission @AT06776@.
Source:
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 332 [Terms] [Paper]