r = ∑ i = 1 n f i r i with i=1∑n fi = 1","2":"On continuous illumination, the measured emission anisotropy is called steady-state emission anisotropy (r(bar)) and is related to the time-resolved anisotropy by: r(bar) = ∫0∞r(t).It.dt∫0∞ where r(t) is the anisotropy and I(t) is the radiant intensity of the emission, both at time t following a δ-pulse excitation.","3":"Luminescence polarization spectroscopy, with linear polarizers placed in both beams, is usually performed on isotropic samples, but it may also be performed on oriented anisotropic samples. In the case of an anisotropic, uniaxial sample, five linearly independent luminescence spectra, instead of the two available for an isotropic sample, may be recorded by varying the two polarizer settings relative to each other and to the sample axis.","4":"The term fundamental emission anisotropy describes a situation in which no depolarizing events occur subsequent to the initial formation of the emitting state, such as those caused by rotational diffusion or energy transfer (in photochemistry). It also assumes that there is no overlap between differently polarized transitions. The (theoretical) value of the fundamental emission anisotropy, r0, depends on the angle α between the absorption and emission transition moments in the following way: r 0 = 3 cos 2 α- 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 fluorescence with δ-pulse excitation, the theoretical value at time zero is identified with the fundamental emission anisotropy."},"links":[{"title":"Fluorescence","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/F02453"},{"title":"polarization","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/P04712"},{"title":"anisotropy","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/AT06776"},{"title":"additive","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/A00134"},{"title":"spectroscopy","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/S05848"},{"title":"isotropic","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/I03353"},{"title":"uniaxial sample","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/UT07493"},{"title":"rotational diffusion","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/R05410"},{"title":"angle","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/A00346"},{"title":"luminescence","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/L03641"},{"title":"photoselection","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/PT07461"},{"title":"linear polarizer","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/L03555"},{"title":"energy transfer (in photochemistry)","type":"internal","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/E02116"},{"title":"phosphorescence","type":"internal","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/P04569"},{"title":"emission","type":"internal","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/E02056"},{"title":"radiant intensity","type":"internal","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/R05045"}],"math":[{"alttext":"r = I ∥- I ⊥ I ∥ + 2 I ⊥","latex":"r = \\frac{I_{\\parallel} - I_{\\perp }}{I_{\\parallel} + 2I_{\\perp }}"},{"meaning":"Parallel emission","type":"symbol","alttext":"I∥","latex":"I_{\\parallel}"},{"meaning":"Perpendicular emission","type":"symbol","alttext":"I⊥","latex":"I_{\\perp }"},{"type":"math","alttext":"I∥ + 2I⊥","latex":"I_{\\parallel} + 2I_{\\perp }"},{"alttext":"I","latex":"I"},{"alttext":"p","latex":"p"},{"alttext":"p = I ∥- I ⊥ I ∥ + I ⊥","latex":"p = \\frac{I_{\\parallel} - I_{\\perp }}{I_{\\parallel} + 2I_{\\perp }}"},{"alttext":"r p = 2 5 1 2","latex":"(r,p) = \\left (^2\/_5,^1\/_2 \\right)"},{"alttext":"r p =- 1 5- 1 3","latex":"(r,p) = \\left ( -^1\/_5,-^1\/_3 \\right )"},{"alttext":"n","latex":"n"},{"alttext":"r i","latex":"r_{i}"},{"alttext":"fi = Ii\/I","latex":"f_{i} = I_{i}\/I"},{"alttext":"r = ∑ i = 1 n f i r i","latex":"r = \\sum_{i=1}^{n} f_{i}\\, r_{i}"},{"type":"equation","alttext":"i=1∑n fi = 1","latex":"\\sum_{i=1}^{n} f_{i} = 1"},{"alttext":"r(bar)","latex":"\\bar{r}"},{"alttext":"r(bar) = ∫0∞r(t).It.dt∫0∞ ","latex":"\\bar{r} = \\frac{\\int_{0}^{\\infty} r(t)\\, I(t)\\, \\text{d}t}{\\int_{0}^{\\infty} I(t)\\, \\text{d}t}"},{"alttext":"r(t)","latex":"r(t)"},{"meaning":"Radiant intensity of emission at time t","type":"quantity","alttext":"I(t)","latex":"I(t)"},{"alttext":"t","latex":"d"},{"alttext":"r0","latex":"r_{0}"},{"type":"symbol","alttext":"α","latex":"α"},{"alttext":"r 0 = 3 cos 2 α- 1 5","latex":"r_{0} =\\, <3\\, cos^{2}\\, \\alpha -1>\\! \/5"},{"alttext":"< >","latex":"<>"},{"alttext":"r 0","latex":"r_{0}"},{"type":"numeric value","alttext":"-1\/5","latex":"-1\/5"},{"type":"equation","alttext":"α = 90°","latex":"\\alpha = 90\\, °"},{"alttext":"2\/5","latex":"2\/5"},{"type":"equation","alttext":"α = 0°","latex":"\\alpha = 0\\, °"}],"sources":["PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 332 (https:\/\/doi.org\/10.1351\/pac200779030293)"]}],"links":{"html":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/ET07370\/html","json":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/ET07370\/json","xml":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/ET07370\/xml","plain":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/ET07370\/plain","pdf":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/ET07370\/pdf"},"citation":"Citation: 'emission anisotropy' in IUPAC Compendium of Chemical Terminology, 3rd ed. International Union of Pure and Applied Chemistry; 2006. Online version 3.0.1, 2019. 10.1351\/goldbook.ET07370","license":"The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/) for individual terms.","collection":"If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org .","disclaimer":"The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.","accessed":"2023-12-10T00:12:22+00:00"}}