Time-Resolved Fluorescence Wiki

applications

Anonymous (anonymous@undisclosed.example.com) — 2026-01-12T10:25:53+00:00

2023/02/23 09:12		current
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	[[howto:antibunching_measurements\|Photon antibunching measurements]]		[[howto:antibunching_measurements\|Photon antibunching measurements]]
		+
		+	[[howto:burst_duration_and_fcs_diffusion_time:burst_duration_and_fcs_diffusion_time\|Burst Duration and FCS Diffusion Time]]


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	[[howto:calculate_ratiometric_single_pair_fret_distributions\|Calculate ratiometric single pair FRET distributions]]		[[howto:calculate_ratiometric_single_pair_fret_distributions\|Calculate ratiometric single pair FRET distributions]]
		+
		+	[[howto:burst_duration_and_fcs_diffusion_time:burst_duration_and_fcs_diffusion_time\|Burst Duration and FCS Diffusion Time]]

basics

Anonymous (anonymous@undisclosed.example.com) — 2024-10-11T08:23:47+00:00

2021/09/23 14:59		current
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	{{tag> basics introduction FCS fluorescence microscopy objective resolution NA tutorials}}		{{tag> basics introduction FCS fluorescence microscopy objective resolution NA tutorials}}
-	===== Basics =====	+	====== Basics ======

	* [[video_tutorials\|Fluorescence and Fluorescence Microscopy by Nico Stuurman]]		* [[video_tutorials\|Fluorescence and Fluorescence Microscopy by Nico Stuurman]]

beampath_of_the_zeiss_lsm880

Anonymous (anonymous@undisclosed.example.com) — 2024-10-11T08:39:05+00:00

2018/06/25 09:16		current
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		+	====== Beam Path of the Zeiss LSM880 ======
		+
	{{ youtube>QjKrLTHGnc8?large }}		{{ youtube>QjKrLTHGnc8?large }}

contributions

Anonymous (anonymous@undisclosed.example.com) — 2020-07-22T15:21:07+00:00

2020/07/22 17:20		current
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-	<AUTHORSTATS 12>	+	<AUTHORSTATS>

contributions12

Anonymous (anonymous@undisclosed.example.com) — 2020-07-31T11:54:14+00:00

2026/04/23 13:10	current
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	+	<AUTHORSTATS 12>

create_time_gated_image

Anonymous (anonymous@undisclosed.example.com) — 2020-10-14T12:10:44+00:00

2020/10/14 14:10		current
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-	//{{tag>howto analysis lifetime tutorial SymPhoTime}}//	+	{{tag>howto analysis lifetime tutorial SymPhoTime}}

	~~NOTOC~~		~~NOTOC~~

data_analysis

Anonymous (anonymous@undisclosed.example.com) — 2015-01-21T13:54:49+00:00

2026/04/23 13:10		current
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		+	This page is redirected to [[:software]].

drafts

Anonymous (anonymous@undisclosed.example.com) — 2025-03-14T08:51:44+00:00

2026/04/23 13:10	current
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	+	===== Drafts =====
	+	{{topic> faq +draft &nodate&nouser}}

faq

Anonymous (anonymous@undisclosed.example.com) — 2025-03-14T09:40:11+00:00

2025/03/14 10:34		current
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	{{topic> faq -draft &nodate&nouser}}		{{topic> faq -draft &nodate&nouser}}
-	[[FAQ:old dongles drivers for FluoFit SymPhoTime 32:old dongles drivers for FluoFit SymPhoTime 32\|Using old dongles for FluoFit and older versions of SymPhoTime (SymPhoTime 32) with Windows 10 or 11]]

flim_fcs_using_olympus_fluoview_fv3000_lsm_upgrade_kit

Anonymous (anonymous@undisclosed.example.com) — 2020-05-18T14:01:42+00:00

2020/05/18 16:01		current
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-	{{tag> video FLIM cquisition howto demo Olympus FV3000 LSM_upgrade}}	+	{{tag> video FLIM acquisition howto demo Olympus FV3000 LSM_upgrade}}

fluorescence_lifetime_measurements_using_the_fluotime_300

Anonymous (anonymous@undisclosed.example.com) — 2016-09-08T01:19:58+00:00

2016/09/08 03:18		current
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	{{ youtube>JLiDnlS5BS8?large }}		{{ youtube>JLiDnlS5BS8?large }}

-	This video demonstrates the special software application wizard of the FluoTime 300 system software for quantum yield measurements of Rhodamine 6G using an integrating sphere. The wizard guides the inexperienced user through all necessary steps to acquire high quality measurements.	+	This video demonstrates the special software application wizard of the FluoTime 300 system software for quantum yield measurements of Rhodamine 6G using an integrating sphere. The wizard guides the user through all necessary steps to acquire high quality measurements.

fluorophores_and_samples

Anonymous (anonymous@undisclosed.example.com) — 2014-02-21T13:55:21+00:00

2026/04/23 13:10	current
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	+	===== Fluorophores and Samples =====

	+	[[howto:diamond_nv_centers\|Nitrogen Vacancy (NV) centers in diamond]]

fullindex

Anonymous (anonymous@undisclosed.example.com) — 2018-09-19T09:02:01+00:00

2026/04/23 13:10		current
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		+	{{indexmenu>. \| notoc nojs}}

how_to_reinstall_symphotime

Anonymous (anonymous@undisclosed.example.com) — 2025-04-09T10:56:18+00:00

2025/04/09 12:55		current
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	Updating from Windows 10 to Windows 11 should work smoothly, and all software should stay as it is. However it is a good idea to back-up the files mentioned below.		Updating from Windows 10 to Windows 11 should work smoothly, and all software should stay as it is. However it is a good idea to back-up the files mentioned below.
		+
	Please note: The Framegrabber MOU camera is not compatible with Windows 11 Windows 11 works with the newer USB MOU camera.		Please note: The Framegrabber MOU camera is not compatible with Windows 11 Windows 11 works with the newer USB MOU camera.
	==== Getting everything from the old computer ====		==== Getting everything from the old computer ====

imprint

Anonymous (anonymous@undisclosed.example.com) — 2018-05-23T08:30:11+00:00

2018/05/23 10:29		current
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	https://www.picoquant.com\\		https://www.picoquant.com\\

-	Vertretungsberechtiger Geschäftsführer/General Manager: Rainer Erdmann	+	Vertretungsberechtiger Geschäftsführer/General Manager: Rainer Erdmann\\
-	HRB 60901 Berlin-Charlottenburg	+	HRB 60901 Berlin-Charlottenburg\\
-	VAT ID: DE 812140373	+	VAT ID: DE 812140373\\
-	WEEE-Reg.-Nr. DE 96457402	+	WEEE-Reg.-Nr. DE 96457402\\
-	Tax-ID.: 37/098/45817	+	Tax-ID.: 37/098/45817\\

interfacing_time_resolved_spectrometer_fluotime_300_microscope_microtime_100

Anonymous (anonymous@undisclosed.example.com) — 2020-05-18T14:19:46+00:00

2020/05/18 16:19		current
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-	{{tag> video FT300 easyTau MT100 FLIM microscopy howto tutorial draft}}	+	{{tag> video FT300 easyTau MT100 FLIM microscopy howto tutorial}}

	====== Interfacing a time-resolved spectrometer (FluoTime 300) with a microscope (MicroTime 100) ======		====== Interfacing a time-resolved spectrometer (FluoTime 300) with a microscope (MicroTime 100) ======

laser_safety_instructions

Anonymous (anonymous@undisclosed.example.com) — 2019-02-08T12:36:40+00:00

2026/04/23 13:10		current
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		+	This page is redirected to [[:fluotime250:laser_safety_instructions]].

legal_information

Anonymous (anonymous@undisclosed.example.com) — 2019-02-15T14:29:59+00:00

2026/04/23 13:10		current
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		+	This page is redirected to [[:fluotime250:legal_information]].

lifetime_component_decomposition_phasor_plot_analysis

Anonymous (anonymous@undisclosed.example.com) — 2025-06-16T07:17:47+00:00

2025/06/16 09:17		current
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	* Sample information:		* Sample information:
-	* Daisy Pollen	+	* Daisy pollen
		+
		+	---

	* Software information: NIS-Elements version 5.42.06 with PicoQuant FLIM-FCS full integration		* Software information: NIS-Elements version 5.42.06 with PicoQuant FLIM-FCS full integration
	{{:lifetime_component_decomposition_in_phasor_plot.mp4?1000\|}}		{{:lifetime_component_decomposition_in_phasor_plot.mp4?1000\|}}
-		+
	* Sample information:		* Sample information:
	* Glial Fibrillary Acidic Protein (GFAP) — labeled with BDP-TMR		* Glial Fibrillary Acidic Protein (GFAP) — labeled with BDP-TMR
	* Mitochondria (via TOM20) — labeled with CY3		* Mitochondria (via TOM20) — labeled with CY3

lsm710

Anonymous (anonymous@undisclosed.example.com) — 2016-07-21T13:31:38+00:00

2016/07/20 14:05		current
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-	====== FLIM Measurement Using a Zeiss LSM710 with a FLIM and FCS Upgrade ======	+	====== FLIM Measurement Using a Zeiss LSM710/LSM780/LSM880 with a FLIM and FCS Upgrade ======

	This tutorial shows the recording of FLIM images using an LSM upgrade kit, in this case a Zeiss LSM710.		This tutorial shows the recording of FLIM images using an LSM upgrade kit, in this case a Zeiss LSM710.
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	* to monitor concentration changes using a reporter dye		* to monitor concentration changes using a reporter dye

-	* To monitor interactions between two molecules via FRET.	+	* To monitor interactions between two molecules via FRET. \\
		+
		+
		+	\\
		+	{{ youtube>QXGqA2IsivM?large }} \\

	The data acquisition is analogous also for upgrades on an LSM780 or LSM880, and the general principles of the data acquisition are analogous in all LSM upgrade kits.		The data acquisition is analogous also for upgrades on an LSM780 or LSM880, and the general principles of the data acquisition are analogous in all LSM upgrade kits.
		+	\\ \\
		+	\\
		+	{{ youtube>vofLPLVmq-Q?large }} \\

-	{{ youtube>QXGqA2IsivM?large }}

measurement_hardware_instrumentation

Anonymous (anonymous@undisclosed.example.com) — 2018-06-25T07:18:07+00:00

2018/06/25 09:17		current
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	[[video_tutorials#Kurt Thorn: Optical Sectioning and Confocal Microscopy\|Confocal microscoy and optical sectioning by Kurt Thorn]]		[[video_tutorials#Kurt Thorn: Optical Sectioning and Confocal Microscopy\|Confocal microscoy and optical sectioning by Kurt Thorn]]

-	[[technical docs:Beampath of the Zeiss LSM880]]	+	[[Beampath of the Zeiss LSM880]]

	[[howto:check_overlap_of_different_color_confocal_volumes\|How to check the overlap of different color confocal volumes]]		[[howto:check_overlap_of_different_color_confocal_volumes\|How to check the overlap of different color confocal volumes]]

privacy_policy

Anonymous (anonymous@undisclosed.example.com) — 2019-12-03T15:49:17+00:00

2019/12/03 16:45		current
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	Grundsätzlich besteht für die betroffene Person die Möglichkeit, einer Erfassung der durch den Matomo erzeugten, auf eine Nutzung dieser Internetseite bezogenen Daten zu widersprechen und eine solche zu verhindern. Hierzu muss die betroffene Person in Ihrem Browser "Do Not Track" einstellen.		Grundsätzlich besteht für die betroffene Person die Möglichkeit, einer Erfassung der durch den Matomo erzeugten, auf eine Nutzung dieser Internetseite bezogenen Daten zu widersprechen und eine solche zu verhindern. Hierzu muss die betroffene Person in Ihrem Browser "Do Not Track" einstellen.
-
-	Ferner besteht für die betroffene Person die Möglichkeit der anonymisierten Datenerhebung durch das Programm Matomo jederzeit mit Wirkung für die Zukunft zu widersprechen, indem sie auf den untenstehenden Link klicken. In diesem Fall wird ein sog. Opt-Out-Cookie im Browser der betroffenen Person abgelegt, was zur Folge hat, dass Matomo keinerlei Sitzungsdaten mehr erhebt. Wenn betroffene Person ihre Cookies löschen, so hat dies jedoch zur Folge, dass auch das Opt-Out-Cookie gelöscht wird und daher von den betroffene Person erneut aktiviert werden muss.

	Die Logs mit den Daten der betroffene Person werden nach spätestens 6 Monaten gelöscht.		Die Logs mit den Daten der betroffene Person werden nach spätestens 6 Monaten gelöscht.
-	{{url>https://www.picoquant.com/piwik/index.php?module=CoreAdminHome&action=optOut&language=en&backgroundColor=&fontColor=&fontSize=&fontFamily=}}

	Weitere Informationen und die geltenden Datenschutzbestimmungen von Matomo können unter [[https://matomo.org/privacy/]] abgerufen werden.		Weitere Informationen und die geltenden Datenschutzbestimmungen von Matomo können unter [[https://matomo.org/privacy/]] abgerufen werden.

software

Anonymous (anonymous@undisclosed.example.com) — 2025-05-28T07:47:47+00:00

2025/05/28 09:18		current
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	{{tag> software acquisition analysis}}		{{tag> software acquisition analysis}}

-	~~TOC~~

	====== Software ======		====== Software ======

some_origins_of_multiexponetial_decays_for_single_dyes

Anonymous (anonymous@undisclosed.example.com) — 2019-03-19T12:31:43+00:00

start

Anonymous (anonymous@undisclosed.example.com) — 2021-06-17T14:47:30+00:00

2020/05/04 14:11		current
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-	<WRAP center round box 60%>
-	===== News from the community=====
-	* 29.04.20 [[https://www.fret.community/announcement-protein-folding-and-dynamics-webinar/\|Protein folding and dynamics Webinar-Series.]]
-	* 14.04.20 [[https://analyticalscience.wiley.com/do/10.1002/was.00050003/full/bioimagedataanalysis.pdf\|Bioimage Data Analysis.]] New Expanded version of a nice open-source introduction. \\ \\
-	* 14.04.20 [[https://science.sciencemag.org/content/368/6486/78\|De novo design of protein logic gates.]] Exciting fundamental enzymology work. Chen et al. describe the design of logic gates that can regulate protein association. \\ \\
-
-
-
-	[[general:community_news\|...see more...]]
-	</WRAP>

supported_th260_pc

Anonymous (anonymous@undisclosed.example.com) — 2017-09-20T15:42:57+00:00

2017/07/24 10:03		current
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		+	/*
	{{tag> PC TH260 Harps TCSPC}}		{{tag> PC TH260 Harps TCSPC}}
	~~TOC~~		~~TOC~~
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	\|HP ENVY 700-056 \|AMD A75 FCH\| \|		\|HP ENVY 700-056 \|AMD A75 FCH\| \|
	\|Dell Precision T3400 \|Intel X38 \| Installed in SLOT 3 , PCIe 8x(4,1)\|		\|Dell Precision T3400 \|Intel X38 \| Installed in SLOT 3 , PCIe 8x(4,1)\|
		+	\|Dell Optiplex 990 \|Intel X38 \| PCIe 8x \| /* See ticket 828080*\

	===== not-working mainboards / computer =====		===== not-working mainboards / computer =====
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	\|HP 200-G1 (Model L5L54US#ABA) \| \| \|		\|HP 200-G1 (Model L5L54US#ABA) \| \| \|
	\|Lenovo ThinkServer TS140 \| \| \|		\|Lenovo ThinkServer TS140 \| \| \|
		+
		+	*/

synchrotron_application

Anonymous (anonymous@undisclosed.example.com) — 2014-07-09T17:27:39+00:00

2026/04/23 13:10		current
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		+	This page is redirected to [[:synchrotron_applications]].

synchrotron_applications

Anonymous (anonymous@undisclosed.example.com) — 2017-05-17T08:31:53+00:00

2015/02/10 17:36		current
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	* A cython library to access the original's manufacturer library from python and in a pythonic way,		* A cython library to access the original's manufacturer library from python and in a pythonic way,
	* An agent in the [[https://www.tango-controls.org/\|Tango distributed control system]] that manage the instrument,		* An agent in the [[https://www.tango-controls.org/\|Tango distributed control system]] that manage the instrument,
-	* A [[http://taurus-scada.org/\|Taurus gui]] with access to the instrument from the control system	+	* A [[http://taurus-scada.org/\|Taurus GUI]] with access to the instrument from the control system

	There is a development now for another agent in the DCS to process the histogram given by the PicoHarp300 instrument to have the distribution mention before.		There is a development now for another agent in the DCS to process the histogram given by the PicoHarp300 instrument to have the distribution mention before.

	Please check [[http://www.picoquant.com/applications/category/metrology/bunch-purity-measurements]] for other Synchrotron-related applications.		Please check [[http://www.picoquant.com/applications/category/metrology/bunch-purity-measurements]] for other Synchrotron-related applications.

tutorials

Anonymous (anonymous@undisclosed.example.com) — 2015-02-05T13:08:57+00:00

2014/04/09 12:50		current
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-	{{tagpage> tutorial}}	+	{{topic>tutorial}}

video_tutorials

Anonymous (anonymous@undisclosed.example.com) — 2014-11-17T16:36:53+00:00

2014/06/18 12:02		current
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	[[http://www.ibiology.org/ibioseminars/techniques/kurt-thorn-part-1.html]]		[[http://www.ibiology.org/ibioseminars/techniques/kurt-thorn-part-1.html]]

-	=== Kurt Thorn: Two Photon Microscopy ===	+	==== Kurt Thorn: Two Photon Microscopy ====
	Kurt Thorn of UCSF talks about two-photon microscopy which uses intense pulsed lasers to image deep into biological samples. It can be used for imaging thick tissue specimens or even imaging inside of live animals.		Kurt Thorn of UCSF talks about two-photon microscopy which uses intense pulsed lasers to image deep into biological samples. It can be used for imaging thick tissue specimens or even imaging inside of live animals.

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-	=== Philippe Bastiaens: Fluorescence Lifetime Microscopy (FLIM) ===	+	==== Philippe Bastiaens: Fluorescence Lifetime Microscopy (FLIM) ====
	Fluorescence-lifetime imaging microscopy or [[glossary:flim\|FLIM]] is an imaging technique for producing an image based on the differences in the exponential decay rate of the fluorescence from a fluorescent sample. It can be used as an imaging technique in confocal microscopy, two-photon excitation microscopy, and multiphoton tomography.		Fluorescence-lifetime imaging microscopy or [[glossary:flim\|FLIM]] is an imaging technique for producing an image based on the differences in the exponential decay rate of the fluorescence from a fluorescent sample. It can be used as an imaging technique in confocal microscopy, two-photon excitation microscopy, and multiphoton tomography.
	The lifetime of the fluorophore signal, rather than its intensity, is used to create the image in FLIM. This has the advantage of minimizing the effect of photon scattering in thick layers of sample ([[wp>Fluorescence-lifetime_imaging_microscopy \| FLIM]]).		The lifetime of the fluorophore signal, rather than its intensity, is used to create the image in FLIM. This has the advantage of minimizing the effect of photon scattering in thick layers of sample ([[wp>Fluorescence-lifetime_imaging_microscopy \| FLIM]]).

2019/03/06 13:44		current
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-	The fluorescence lifetime of a dye measured with a TCSPC spectrometer can be multiexponential due to many reasons. The most obvious cases are due to scattering or presence of impurities. Although less obvious, it is also widely known that in an inhomogeneous media a pure dye will also exhibit a multiexponential decay. Advanced users know that if the decay is not measured with polarizers at magic angle, the rotation correlation time shows up as a second exponential in the decay (the second exponential is in fact the product of the rotation correlation time by the fluorescence lifetime, divided by their sum). And they also know that measuring without polarizers is not equivalent to measure at magic angle... But suspicion may arise when even a pure dye measured at magic angle in a homogeneous media exhibits a multiexponential decay. Is the spectrometer properly adjusted? Are the polarizers properly calibrated? A typical mistake is to measure the [[glossary:IRF]] at the nominal laser wavelength instead of measuring at the ideal wavelength for that specific laser head. Note that all diode lasers heads emit at slightly different wavelengths and each of them have an optimum at which the IRF should be measured. As little as 0.5 nm displacement from their optimum may induce a "non perfect" [[glossary:deconvolution]] fit.	+	The fluorescence lifetime of a dye measured with a TCSPC spectrometer can be multiexponential due to many reasons. The most obvious cases are due to scattering or presence of impurities. Although less obvious, it is also widely known that in an inhomogeneous medium a pure dye will also exhibit a multiexponential decay. Advanced users know that if the decay is not measured with polarizers at magic angle, the rotation correlation time shows up as a second exponential in the decay (the second exponential is in fact the product of the rotation correlation time and the fluorescence lifetime, divided by their sum). And they also know that measuring without polarizers is not equivalent to measuring at magic angle... But suspicion may arise when even a pure dye measured at magic angle in a homogeneous medium exhibits a multiexponential decay. Is the spectrometer properly adjusted? Are the polarizers properly calibrated? A typical mistake is to measure the [[glossary:IRF]] at the nominal laser wavelength instead of measuring at the ideal wavelength for that specific laser head. Note that all diode lasers heads emit at slightly different wavelengths and each of them have an optimum at which the IRF should be measured. As little as 0.5 nm displacement from their optimum may induce a "non perfect" [[glossary:deconvolution]] fit.

	But it is worth noting that even at magic angle in a perfectly aligned spectrometer pure dyes in homogeneous media may exhibit a multiexponential decay. The origin may be physical, like solvent relaxation, or chemical, when the fluorescent molecule undergoes a ground or excited state reaction. In this brief article a few examples are described.		But it is worth noting that even at magic angle in a perfectly aligned spectrometer pure dyes in homogeneous media may exhibit a multiexponential decay. The origin may be physical, like solvent relaxation, or chemical, when the fluorescent molecule undergoes a ground or excited state reaction. In this brief article a few examples are described.
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-	The electronic redistribution of electrons due to optical excitation leads in many cases to a different reactivity in the ground and excited states. In other words, a fluorescent molecule which is boring under the dark may become reactive upon excitation. Common excited state reactions are redox (electron transfer) and acid-base (proton transfer) reactions. Depending on the rate of the excited-state rection relative the the original fluorescence lifetime, the observed decay time measured with a TCSPC spectrometer may be single- or multiexponential.	+	The electronic redistribution of electrons due to optical excitation leads in many cases to a different reactivity in the ground and excited states. In other words, a fluorescent molecule which is mostly inert in the dark may become reactive upon excitation. Common excited state reactions are redox (electron transfer) and acid-base (proton transfer) reactions. Depending on the rate of the excited-state reaction relative the the original fluorescence lifetime, the observed decay time measured with a TCSPC spectrometer may be single- or multiexponential.

	Let us consider the reaction in Scheme 2 in different situations:		Let us consider the reaction in Scheme 2 in different situations:
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	Scheme 2		Scheme 2

-	//Starting point: The molecule A is promoted to the excited-state where it can react with a molecule X to form the compound B, through a rate constant $k_{AB}$. Once the compound B is formed the back-reaction can occur, with a rate constant $k_{BA}$. Compounds A and B are fluorescent with original fluorescence lifetimes $\tau_A$ and $\tau_B$. Once B decays to the ground state the back-reaction takes place. Hence the system is always in its starting position $(A + X)$ prior to any excitation pulse.//	+	//Starting point: The molecule A is promoted to the excited-state where it can react with a molecule X to form the compound B, through a rate constant $k_{AB}$. Once the compound B is formed, the back-reaction can occur with a rate constant $k_{BA}$. Compounds A and B are fluorescent with original fluorescence lifetimes $\tau_A$ and $\tau_B$. Once B decays to the ground state, the back-reaction takes place. Hence the system is always in its starting position $(A + X)$ prior to any excitation pulse.//

	//Case A) The constant kAB is too slow with respect to $\tau_A$ and $\tau_B$.// In this case the compound A would decay to the ground-sate before the excited-state reaction could take place. The decay measured would be single exponential and coincident with $\tau_A$.		//Case A) The constant kAB is too slow with respect to $\tau_A$ and $\tau_B$.// In this case the compound A would decay to the ground-sate before the excited-state reaction could take place. The decay measured would be single exponential and coincident with $\tau_A$.
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	being $Z = \sqrt{(M-Y)^2 + 4 k_{AB} k_{BA}[x]}$		being $Z = \sqrt{(M-Y)^2 + 4 k_{AB} k_{BA}[x]}$

-	$A_1= A_0 [M- (1/\tau_2)] / [(1/\tau_1 – 1/\tau_2]$	+	$A_1= A_0 [M- (1/\tau_2)] / [1/\tau_1 – 1/\tau_2]$

-	$A_2= A_0 [(1/\tau_1)- M] / [(1/\tau_1 – 1/\tau_2]$	+	$A_2= A_0 [(1/\tau_1)- M] / [1/\tau_1 – 1/\tau_2]$

-	$B_1= -A_0 k_{AB}[x] / [(1/\tau_1 – 1/\tau_2]$	+	$B_1= -A_0 k_{AB}[x] / [1/\tau_1 – 1/\tau_2]$

-	$B_2= A_0 k_{AB} [x] / [(1/\tau_1 – 1/\tau_2]$	+	$B_2= A_0 k_{AB} [x] / [1/\tau_1 – 1/\tau_2]$

	being $A_0$ the concentration of $A$ at $t=0$.		being $A_0$ the concentration of $A$ at $t=0$.
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	Note from $A(t)$ that, even if $B$ would not be fluorescent, the decay of $A$ will still be biexponential!		Note from $A(t)$ that, even if $B$ would not be fluorescent, the decay of $A$ will still be biexponential!

-	A situation like this may occur with molecules dissolved in an aprotic but hygroscopic media, like acetonirile. Water molecules may diffuse (diffusion happens in the nanosecond time scale) and react with fluorophores bearing proton-transfer groups like -OH or -NH2.	+	A situation like this may occur with molecules dissolved in an aprotic but hygroscopic medium, like acetonitrile. Water molecules may diffuse (diffusion happens in the nanosecond time scale) and react with fluorophores bearing proton-transfer groups like -OH or -NH2.

	//Case D) Interconversion rate constants $k_{AB}$ and $k_{BA}$ are very quick compared to the intrinsic lifetimes $\tau_A$ and $\tau_B$.// In this case the equations of case C would still apply. But in practice, a quick equilibrium between reactants and product would be established. This means that the concentrations of A and B with respect to each other would always be constant prior to their decay, and hence the whole system could be treated as a single dye. The decay would be single exponential, being an average of $\tau_A$ and $\tau_B$ weighted by their fraction in the equilibrium.		//Case D) Interconversion rate constants $k_{AB}$ and $k_{BA}$ are very quick compared to the intrinsic lifetimes $\tau_A$ and $\tau_B$.// In this case the equations of case C would still apply. But in practice, a quick equilibrium between reactants and product would be established. This means that the concentrations of A and B with respect to each other would always be constant prior to their decay, and hence the whole system could be treated as a single dye. The decay would be single exponential, being an average of $\tau_A$ and $\tau_B$ weighted by their fraction in the equilibrium.

-	This situation may happen if compounds A and X were directly in contact prior to excitation, for example throgh ground-state interactions.	+	This situation may happen if compounds A and X were directly in contact prior to excitation, for example through ground-state interactions.
	===== 3) Solvation dynamics =====		===== 3) Solvation dynamics =====


-	Even pure fluorophores in pure solvents may lead to multiexponential decays. This is the case of molecules with strong charge transfer character in polar solvents when undergoing solvation dynamics. In such cases the fluorescence spectra shifts to longer wavelengths in time. Measuring the decay in the blue edge of the steady-state spectrum will lead to a multiexponential decay. The ns lifetimes corresponds to the intrinsic fluorescence lifetime of the fluorophore, whereas the ultrafast components (ps) are related to the rate of the shift. Measuring in the red-flank of the steady-sate spectrum leads to multiexponential decays with positive (intrinsic lifetime, ns) an negative (rate of shift, ps) pre-exponential factors. This is depicted in Scheme 3.	+	Even pure fluorophores in pure solvents may lead to multiexponential decays. This is the case of molecules with strong charge transfer character in polar solvents when undergoing solvation dynamics. In such cases the fluorescence spectrum shifts to longer wavelengths on a picosecond time-scale. Measuring the decay in the blue edge of the steady-state spectrum will lead to a multiexponential decay. The ns lifetime corresponds to the intrinsic fluorescence lifetime of the fluorophore, whereas the ultrafast components (ps) are related to the rate of the shift. Measuring in the red-flank of the steady-sate spectrum leads to multiexponential decays with positive (intrinsic lifetime, ns) and negative (rate of shift, ps) pre-exponential factors. This is depicted in Scheme 3.


	{{:solvation_dynamics.png?800\|}}		{{:solvation_dynamics.png?800\|}}

-	Scheme 3. Left: energetic representation of solvation dynamics. The fluorophore is represented as a sphere with a pointing dipole. Solvent molecules are represented in gray around the fluorophore. Right up : Spectral consequence of solvation dynamics. The fluorescence spectrum shifts in time to lower energies. Right bottom: Decay traces measured in different spectral regions. Blue flanks are multiexponential with positive pre-exponentila factors, red flanks are multiexponential with rising components.	+	Scheme 3. Left : energetic representation of solvation dynamics. The fluorophore is represented as a sphere with a pointing dipole. Solvent molecules are represented in gray around the fluorophore. Right, top : Spectral consequence of solvation dynamics. The fluorescence spectrum shifts in time to lower energies. Right, bottom: Decay traces measured in different spectral regions. Blue curves are multiexponential with positive pre-exponentila factors, red curves are multiexponential with rising components.

-	Before the excitation, the fluorophore is in the ground state S0 , which has a characteristic dipole moment. Solvent molecules, which also have their characteristic dipole moment are oriented in such a way that the interactions dipole-dipole with the fluorophore are as favorable possible. When the fluorophore is prompted to the excited state, its electronic distribution switches almost instantly. At time zero after excitation the solvent molecules remain in their "original" orientation to solvate ground state . The resulting dipole -dipole interactions with the fluorophore are hence less favorable. As a result , the solvent begins to relax to solvate the S1 state and brings the system to a more favorable position. Spectroscopically, this is manifested by the time-shift of the emission spectrum to longer wavelengths. Consider that the Steady-State spectrum is the time integral of all those shifting spectra. Measuring in the blue flank (λ1) will lead to a multiexponential decay: the signal decreases because of the shift and the intrinsic decay. Measuring in the red flank (λ3) will lead to a multiexponential decay with a negative pre-exponential factor: the signal first rises due to the increase in signal due to the displacement, and then decays due to the fluorescence lifetime.	+	Before the excitation, the fluorophore is in the ground state S0 , which has a characteristic dipole moment. Solvent molecules, which also have their characteristic dipole moment are oriented in such a way that the dipole-dipole interactions with the fluorophore are as favorable as possible. When the fluorophore is prompted to the excited state, its electronic distribution switches almost instantly. At time zero after excitation the solvent molecules remain in their "original" orientation. The resulting dipole -dipole interactions with the fluorophore are hence less favorable. As a result, the solvent begins to relax to solvate the S1 state and brings the system to a more favorable position. Spectroscopically, this is manifested by the time-shift of the emission spectrum to longer wavelengths. Consider that the Steady-State spectrum is the time integral of all those shifting spectra. Measuring in the blue flank (λ1) will lead to a multiexponential decay: the signal decreases because of the shift and the intrinsic decay. Measuring in the red flank (λ3) will lead to a multiexponential decay with a negative pre-exponential factor: the signal first rises due to the increase in signal due to the displacement, and then decays due to the fluorescence lifetime.

	In fluid media, solvation dynamics can be described with a multiexponential function spanning from the femtosecond time-scale to tens of picoseconds. Hence, the tail of this process can be monitored with a TCSPC spectrometer equipped with fast detectors such as a [[glossary:MCP]] or a Hybrid-PMT. In viscous media or at low temperatures, the ps tail component slows down to ns, and the process can be monitored with slower detectors, such as standard [[glossary:PMT]].		In fluid media, solvation dynamics can be described with a multiexponential function spanning from the femtosecond time-scale to tens of picoseconds. Hence, the tail of this process can be monitored with a TCSPC spectrometer equipped with fast detectors such as a [[glossary:MCP]] or a Hybrid-PMT. In viscous media or at low temperatures, the ps tail component slows down to ns, and the process can be monitored with slower detectors, such as standard [[glossary:PMT]].