some_origins_of_multiexponetial_decays_for_single_dyes
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some_origins_of_multiexponetial_decays_for_single_dyes [2015/11/03 14:08] – admin | some_origins_of_multiexponetial_decays_for_single_dyes [2019/03/06 12:44] – admin | ||
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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... | + | 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 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 | 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 | ||
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- | Note that this situation corresponds to the typical case of Static-Quenching in which the intensity of A decreases with the concentration of X, but where the lifetime $\tau_A$ remains constant. | + | Note that this situation corresponds to the typical case of Static-Quenching in which the intensity of $A$ decreases with the concentration of $X$, but where the lifetime $\tau_A$ remains constant. |
===== 2) Excited-state reactions ===== | ===== 2) Excited-state reactions ===== | ||
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Scheme 2 | Scheme 2 | ||
- | //Starting point: The molecule A is prompted | + | //Starting point: The molecule A is promoted |
//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 $\tau_A$. | ||
- | //Case B) The forward reaction constant | + | //Case B) The forward reaction constant |
Note that this situation is the typical case of dynamic quenching with the particular case that the product being formed is fluorescent. | Note that this situation is the typical case of dynamic quenching with the particular case that the product being formed is fluorescent. | ||
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//Case C) The interconversion rate constants kAB and kBA are in the same order of $\tau_A$ and $\tau_B$.// In this case, the decay curves measured for species A and B would be biexponential for both, with common lifetimes $\tau_1$ and $\tau_2$. However, $\tau_1$ and $\tau_2$ would not correspond to $\tau_A$ or $\tau_B$ , but would be a function of both and of their interconversion rate constants kAB and kBA, as well as of the concentration of X. The system would have to be solved mathematically. For a system like in Scheme 2 the time evolution of species A and B would be: | //Case C) The interconversion rate constants kAB and kBA are in the same order of $\tau_A$ and $\tau_B$.// In this case, the decay curves measured for species A and B would be biexponential for both, with common lifetimes $\tau_1$ and $\tau_2$. However, $\tau_1$ and $\tau_2$ would not correspond to $\tau_A$ or $\tau_B$ , but would be a function of both and of their interconversion rate constants kAB and kBA, as well as of the concentration of X. The system would have to be solved mathematically. For a system like in Scheme 2 the time evolution of species A and B would be: | ||
- | A(t) = A1 e^{-t/$\tau_1$} + A2 e^{-t/$\tau_2$} | + | $A(t) = A_1 e^{-t/ |
- | B(t) = B1 e^{-t/$\tau_1$} + B2 e^{-t/$\tau_2$} | + | $B(t) = B_1 e^{-t/ |
where: | where: | ||
- | $\tau_1$= 2/(M+Y-Z) | + | $\tau_1= 2/(M+Y-Z)$ |
- | $\tau_2$ = 2/(M+Y+Z) | + | $\tau_2 = 2/(M+Y+Z)$ |
- | being M = kAB[x] + kA (summation of disappearance constant of compound A; kA=1/$\tau_A$ ) | + | being $M = k_{AB}[x] + k_A$ (summation of disappearance constant of compound |
- | being Y = kBA + kB (summation of disappearance constant of compound B; kB=1/$\tau_B$) | + | being $Y = k_{BA} |
- | being Z = [ (M-Y)^2 + 4 kAB kBA[x]]^(1/2) | + | being $Z = \sqrt{(M-Y)^2 + 4 k_{AB} k_{BA}[x]}$ |
- | A1= A0 [M- (1/$\tau_2$)] / [(1/$\tau_1$ – 1/$\tau_2$] | + | $A_1= A_0 [M- (1/\tau_2)] / [(1/\tau_1 – 1/\tau_2]$ |
- | A2= A0 [(1/$\tau_1$)- M] / [(1/$\tau_1$ – 1/$\tau_2$] | + | $A_2= A_0 [(1/ |
- | B1= A0 kAB [x] / [(1/$\tau_1$ – 1/$\tau_2$] | + | $B_1= -A_0 k_{AB}[x] / [(1/\tau_1 – 1/\tau_2]$ |
- | B2= -A0 kAB [x] / [(1/$\tau_1$ – 1/$\tau_2$] | + | $B_2= A_0 k_{AB} |
- | being A0 the concentration of A at t=0. | + | being $A_0$ the concentration of $A$ at $t=0$. |
- | **Note from A(t) that, even if B would not be fluorescent, | + | **Note from $A(t)$ that, even if $B$ would not be fluorescent, |
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 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. | ||
- | //Case D) Interconversion rate constants | + | //Case D) Interconversion rate constants |
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 throgh ground-state interactions. | ||
- | |||
===== 3) Solvation dynamics ===== | ===== 3) Solvation dynamics ===== | ||
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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 " | 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 " | ||
- | 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 MCP or a Hybrid-PMT. In viscous media or at low temperatures, | + | 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, |
some_origins_of_multiexponetial_decays_for_single_dyes.txt · Last modified: 2019/03/19 12:31 by oschulz