emission anisotropy

Also contains definitions of: degree of (polarization) anisotropy, luminescence anisotropy, time-resolved anisotropy, \(r(t)\)
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.
  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 = 2 5 1 2; when the transition moments are perpendicular, the values are r p =- 1 5- 1 3. 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 fi = Ii/I, is given by:
    r = ∑ i = 1 n f i r i with i=1∑n fi = 1
  2. On continuous illumination, the measured emission @AT06776@ is called steady-state emission @AT06776@ (r(bar)) 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 t 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@, r0, 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. r0 can take on values ranging from -1/5 for α = 90° (perpendicular transition moments) to 2/5 for α = 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@.
PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 332 (https://doi.org/10.1351/pac200779030293)