## 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 luminescence (fluorescence, phosphorescence) polarization resulting from photoselection. Defined as: $r = \frac{I_{\parallel} - I_{\perp }}{I_{\parallel} + 2I_{\perp }}$ where I∥ and I⊥ are the intensities measured with the linear polarizer for emission parallel and perpendicular, respectively, to the electric vector of linearly polarized incident electromagnetic radiation (which is often vertical). The quantity I∥ + 2I⊥ is proportional to the total fluorescence 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. @L03641-1@ @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 @L03641-2@ 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 (https://doi.org/10.1351/pac200779030293)