## 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]