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 @[email protected] (@[email protected], @[email protected]) @[email protected] resulting from @[email protected] Defined as: \[r = \frac{I_{\parallel} - I_{\perp }}{I_{\parallel} + 2I_{\perp }}\] where \(I_{\parallel}\) and \(I_{\perp }\) are the intensities measured with the @[email protected] for @[email protected] 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 @[email protected] intensity \(I\).
Notes:
  1. @[email protected] @[email protected] may also be characterized by the @[email protected] ratio, also called the degree of @[email protected] \(p\), \[p = \frac{I_{\parallel} - I_{\perp }}{I_{\parallel} + 2I_{\perp }}\] 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 @[email protected] because it is @[email protected]; the overall contribution of \(n\) components \(r_{i}\), each contributing to the total @[email protected] 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 @[email protected] is called steady-state emission @[email protected] (\(\bar{r}\)) 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 @[email protected] and \(I(t)\) is the @[email protected] of the emission, both at time \(d\) following a δ-pulse excitation.
  3. @[email protected] @[email protected] @[email protected], with linear polarizers placed in both beams, is usually performed on @[email protected] samples, but it may also be performed on oriented anisotropic samples. In the case of an anisotropic, @[email protected], five linearly independent @[email protected] spectra, instead of the two available for an @[email protected] sample, may be recorded by varying the two polarizer settings relative to each other and to the sample axis.
  4. The term fundamental emission @[email protected] describes a situation in which no depolarizing events occur subsequent to the initial formation of the emitting state, such as those caused by @[email protected] or @[email protected] It also assumes that there is no overlap between differently polarized transitions. The (theoretical) value of the fundamental emission @[email protected], \(r_{0}\), depends on the @[email protected] \(α\) 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 @[email protected] with δ-pulse excitation, the theoretical value at time zero is identified with the fundamental emission @[email protected]
Source:
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 332 [Terms] [Paper]