Editing Fluorescence (section)

== Physical principles ==
=== Mechanism ===
[[File:Ruby ball fluorescence @ 520nm laser illumination.jpg|thumb|A ruby [[ball lens]] atop a green laser-pointer. The green beam [[Vergence (optics)|converges]] into a cone within the crystal and is focused to a point on top. The green light is absorbed and spontaneously remitted as red light. Not all of the light is absorbed, and a small portion of the 520&nbsp;nm laser light transmits through the top, unaltered by the ruby's red color.]]
Fluorescence occurs when an excited molecule, atom, or [[nanostructure]], relaxes to a lower energy state (usually the [[ground state]]) through emission of a [[photon]] without a change in [[electron spin]]. When the initial and final states have different multiplicity (spin), the phenomenon is termed [[phosphorescence]].<ref>{{Cite journal |last=Verhoeven |first=J. W. |date=1996-01-01 |title=Glossary of terms used in photochemistry (IUPAC Recommendations 1996) |url=https://www.degruyter.com/document/doi/10.1351/pac199668122223/html |journal=Pure and Applied Chemistry |language=de |volume=68 |issue=12 |pages=2223–2286 |doi=10.1351/pac199668122223 |issn=1365-3075}}</ref>

When a molecule in its ground state (called S<sub>0</sub>) is photoexcited it may end up in any one of a number of excited states (S<sub>1</sub>, S<sub>2</sub>, S<sub>3</sub>,...). These higher excited states are different vibrational levels, populated in proportion to their overlap with the ground state according to the [[Franck-Condon principle]].<ref name="Berberan-Santos, Mario-2012"/>{{rp|31}} These vibrational excited states typically decay rapidly by to S<sub>1</sub>, followed by radiative transition to the ground state or to vibrational states close to the ground state. This transition is called fluorescence. All of these states are [[singlet state]]s.<ref name="Mallick-2023">{{Cite book |last=Mallick |first=Prabal Kumar |url=https://link.springer.com/10.1007/978-981-99-0791-5 |title=Fundamentals of Molecular Spectroscopy |date=2023 |publisher=Springer Nature Singapore |isbn=978-981-99-0790-8 |location=Singapore |language=en |doi=10.1007/978-981-99-0791-5}}</ref>{{rp|225}}

A different pathway for deexcitation is intersystem crossing from the S<sub>1</sub> to a [[triplet state]]   T<sub>1</sub>. Decay from T<sub>1</sub> to S<sub>0</sub> is typically slower and less intense and is called phosphorescence.<ref name="Mallick-2023"/>{{rp|225}}

Absorption of a photon of energy <math>h \nu_{ex} </math> results in an excited state of the same multiplicity (spin) of the ground state, usually a singlet (S<sub>n</sub> with n > 0). In solution, states with n > 1 relax rapidly to the lowest vibrational level of the first excited state (S<sub>1</sub>) by transferring energy to the solvent molecules through non-radiative processes, including  internal conversion followed by vibrational relaxation, in which the energy is dissipated as [[heat]]. Thus the fluorescence energy is typically less than the photoexcitation energy.<ref name="Berberan-Santos, Mario-2012" />{{rp|38}}

The excited state S<sub>1</sub> can relax by other mechanisms that do not involve the emission of light. These processes, called non-radiative processes, compete with fluorescence emission and decrease its efficiency.<ref name="Berberan-Santos, Mario-2012" /> Examples include [[Internal conversion (chemistry)|internal conversion]], [[intersystem crossing]] to the triplet state, and energy transfer to another molecule. An example of energy transfer is [[Förster resonance energy transfer]]. Relaxation from an excited state can also occur through collisional [[Quenching (fluorescence)|quenching]], a process where a molecule (the quencher) collides with the fluorescent molecule during its excited state lifetime. Molecular [[oxygen]] (O<sub>2</sub>) is an extremely efficient quencher of fluorescence because of its unusual triplet ground state.

=== Quantum yield ===
The fluorescence [[quantum yield]] gives the efficiency of the fluorescence process. It is defined as the ratio of the number of photons emitted to the number of photons absorbed.<ref name=Lakowicz-1999/>{{rp|style=ama|p= 10}}<ref name="Berberan-Santos, Mario-2012">
{{cite book
 |author1=Valeur, Bernard
 |author2=Berberan-Santos, Mario
 |year=2012
 |title=Molecular Fluorescence: Principles and applications
 |publisher=Wiley-VCH
 |isbn=978-3-527-32837-6
 |page=64
}}
</ref>
: <math> \Phi = \frac {\text{Number of photons emitted}} {\text{Number of photons absorbed}} </math>

The maximum possible fluorescence quantum yield is 1.0 (100%); each [[photon]] absorbed results in a photon emitted. Compounds with quantum yields of 0.10 are still considered quite fluorescent. Another way to define the quantum yield of fluorescence is by the rate of excited state decay:
: <math> \Phi = \frac{ { k}_{ f} }{ \sum_{i}{ k}_{i } } </math>
where <math>{ k}_{ f}</math> is the rate constant of [[spontaneous emission]] of radiation and
: <math> \sum_{i}{ k}_{i } </math>
is the sum of all rates of excited state decay. Other rates of excited state decay are caused by mechanisms other than photon emission and are, therefore, often called "non-radiative rates", which can include:
* dynamic collisional quenching
* near-field dipole–dipole interaction (or [[resonance energy transfer]])
* internal conversion
* [[intersystem crossing]]

Thus, if the rate of any pathway changes, both the excited state lifetime and the fluorescence quantum yield will be affected.

Fluorescence quantum yields are measured by comparison to a standard.<ref>{{Cite journal |last=Levitus |first=Marcia |date=2020-04-22 |title=Tutorial: measurement of fluorescence spectra and determination of relative fluorescence quantum yields of transparent samples |url=https://doi.org/10.1088/2050-6120/ab7e10|journal=Methods and Applications in Fluorescence |volume=8 |issue=3 |pages=033001 |doi=10.1088/2050-6120/ab7e10 |pmid=32150732 |bibcode=2020MApFl...8c3001L |s2cid=212653274 |issn=2050-6120 |access-date=9 June 2021 |archive-date=4 May 2022|archive-url=https://web.archive.org/web/20220504144923/https://iopscience.iop.org/article/10.1088/2050-6120/ab7e10 |url-status=live}}</ref> The [[quinine]] salt ''quinine sulfate'' in a [[sulfuric acid]] solution was regarded as the most common fluorescence standard,<ref>
{{cite journal
 |last=Brouwer |first=Albert M.
 |date=2011-08-31
 |title=Standards for photoluminescence quantum yield measurements in solution
 |series=IUPAC Technical Report
 |journal=Pure and Applied Chemistry
 |volume=83 |issue=12 |pages=2213–2228
 |doi=10.1351/PAC-REP-10-09-31
 |s2cid=98138291 |issn=1365-3075
 |doi-access=free
}}
</ref>
however, a recent study revealed that the fluorescence quantum yield of this solution is strongly affected by the temperature, and should no longer be used as the standard solution. The quinine in 0.1&nbsp;[[mole (unit)|M]] perchloric acid ({{nowrap|1=Φ = 0.60}}) shows no temperature dependence up to 45&nbsp;°C, therefore it can be considered as a reliable standard solution.<ref>
{{cite journal
 |last1=Nawara |first1=Krzysztof
 |last2=Waluk  |first2=Jacek
 |date=2019-04-16
 |title=Goodbye to quinine in sulfuric acid solutions as a fluorescence quantum yield standard
 |journal=Analytical Chemistry |language=en
 |volume=91 |issue=8 |pages=5389–5394
 |doi=10.1021/acs.analchem.9b00583
 |pmid=30907575 |s2cid=85501014 |issn=0003-2700
 |url=https://pubs.acs.org/doi/10.1021/acs.analchem.9b00583
 |url-status=live
 |archive-url=https://web.archive.org/web/20210207194942/https://pubs.acs.org/doi/10.1021/acs.analchem.9b00583
 |archive-date=7 February 2021
}}
</ref>

=== Lifetime ===
[[File:Jablonski Diagram of Fluorescence Only-en.svg|thumb|[[Jablonski diagram]]. After an electron absorbs a high-energy photon the system is excited electronically and vibrationally. The system relaxes vibrationally, and eventually fluoresces at a longer wavelength than the original high-energy photon had.]]

The fluorescence lifetime refers to the average time the molecule stays in its excited state before emitting a photon. Fluorescence typically follows [[first-order kinetics]]:
: <math> \left[S_1 \right] = \left[S_1 \right]_0 e^{-\Gamma t} </math>
where <math>\left[S_1 \right]</math> is the concentration of excited state molecules at time <math>t</math>, <math>\left[S_1 \right]_0</math> is the initial concentration and [[Gamma|<math>\Gamma</math>]] is the decay rate or the inverse of the fluorescence lifetime. This is an instance of [[exponential decay]]. Various radiative and non-radiative processes can de-populate the excited state. In such case the total decay rate is the sum over all rates:
: <math> \Gamma_{tot}=\Gamma_{rad} + \Gamma_{nrad} </math>
where <math>\Gamma_{tot}</math> is the total decay rate, <math>\Gamma_{rad}</math> the radiative decay rate and <math>\Gamma_{nrad}</math> the non-radiative decay rate. It is similar to a first-order chemical reaction in which the first-order rate constant is the sum of all of the rates (a parallel kinetic model). If the rate of spontaneous emission, or any of the other rates are fast, the lifetime is short. For commonly used fluorescent compounds, typical excited state decay times for photon emissions with energies from the [[Ultraviolet|UV]] to [[near infrared]] are within the range of 0.5 to 20 [[nanoseconds]]. The fluorescence lifetime is an important parameter for practical applications of fluorescence such as [[fluorescence resonance energy transfer]] and [[fluorescence-lifetime imaging microscopy]].

=== Jablonski diagram ===
The [[Jablonski diagram]] describes most of the relaxation mechanisms for excited state molecules. The diagram alongside shows how fluorescence occurs due to the relaxation of certain excited electrons of a molecule.<ref name="mehta">[http://pharmaxchange.info/press/2013/03/animation-for-the-principle-of-fluorescence-and-uv-visible-absorbance/ "Animation for the Principle of Fluorescence and UV-Visible Absorbance"] {{webarchive|url=https://web.archive.org/web/20130609034835/http://pharmaxchange.info/press/2013/03/animation-for-the-principle-of-fluorescence-and-uv-visible-absorbance/ |date=9 June 2013 }}. ''PharmaXChange.info''.</ref>

=== Fluorescence anisotropy ===
Fluorophores are more likely to be excited by photons if the transition moment of the fluorophore is parallel to the electric vector of the photon.<ref name=Lakowicz-1999/>{{rp|style=ama|pp= 12–13}} The polarization of the emitted light will also depend on the transition moment. The transition moment is dependent on the physical orientation of the fluorophore molecule. For fluorophores in solution, the intensity and polarization of the emitted light is dependent on rotational diffusion. Therefore, anisotropy measurements can be used to investigate how freely a fluorescent molecule moves in a particular environment.

Fluorescence anisotropy can be defined quantitatively as
: <math>r = {I_\parallel - I_\perp \over I_\parallel + 2I_\perp}</math>
where <math>I_\parallel</math> is the emitted intensity parallel to the polarization of the excitation light and <math>I_\perp</math> is the emitted intensity perpendicular to the polarization of the excitation light.<ref name="Berberan-Santos, Mario-2012"/>

Anisotropy is independent of the intensity of the absorbed or emitted light, it is the property of the light, so photobleaching of the dye will not affect the anisotropy value as long as the signal is detectable.

=== Fluorescence ===
[[File:US $20 under blacklight.jpg|thumb|Fluorescent security strip in a US twenty dollar bill under UV light]]
Strongly fluorescent pigments often have an unusual appearance which is often described colloquially as a "neon color" (originally "day-glo" in the late 1960s, early 1970s). This phenomenon was termed "Farbenglut" by [[Hermann von Helmholtz]] and "fluorence" by Ralph M. Evans. It is generally thought to be related to the high brightness of the color relative to what it would be as a component of white. Fluorescence shifts energy in the incident illumination from shorter wavelengths to longer (such as blue to yellow) and thus can make the fluorescent color appear brighter (more saturated) than it could possibly be by reflection alone.<ref>{{cite journal|last1=Schieber|first1=Frank|s2cid=2439728|title=Modeling the Appearance of Fluorescent Colors|journal=Proceedings of the Human Factors and Ergonomics Society Annual Meeting|date=October 2001|volume=45|issue=18|pages=1324–1327|doi=10.1177/154193120104501802}}</ref>