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some_origins_of_multiexponetial_decays_for_single_dyes [2014/05/19 16:00] – veigasome_origins_of_multiexponetial_decays_for_single_dyes [2014/05/21 14:52] – veiga
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-The fluorescence lifetime of a fluorophore 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 in a  homogeneous media exhibits multiexponential decays. Is the spectrometer properly adjusted? Are the polarizers properly calibrated? A typical mistake is to measure the 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" reconvolution 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 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 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" reconvolution 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.
  
-===== 1) Ground state reaction with the medium =====+===== 1) Ground-state reactions =====
  
  
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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 tA 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 =====
  
  
-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 fluorescent 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 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. 
  
 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
  
-The molecule A is prompted to te excited-state where it can react with a molecule X to form the compound B, through a rate constant kAB. Once the compound B is formed the back-reaction can occur, with a rate constant kBA. Compounds A and B are fluorescent with intrinsic 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 prompted to te excited-state where it can react with a molecule X to form the compound B, through a rate constant kAB. Once the compound B is formed the back-reaction can occur, with a rate constant kBA. 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 decays before the excited-state reaction can take place. The decay measured is 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 kAB is fast, but the back-reaction constant kBA is too slow in comparison to $\tau_A$ and $\tau_B$. In this case the decay time measured in the spectral region of A will be single exponential, with decay time $\tau_1$. However $\tau_1$ is shorter than $\tau_A$, and it depends on the concentration of X ($\tau_1$ = 1/ (krA+knrA + kAB[x]), where [x] denotes the concentration of X and kr and knr the intrinsic radiative and non-radiative rate constants) . The lifetime measured in the spectral region of B is biexponential with times $\tau_1$ and $\tau_2$. $\tau_1$ has a negative pre-exponential factor (rising component) and it is coincident with the decay time measured in the spectral region of A. The decaying component $\tau_2$ is coincident with the original lifetime of compound B, $\tau_B$.+//Case B) The forward reaction constant kAB is fast, but the back-reaction constant kBA is too slow in comparison to $\tau_A$ and $\tau_B$.// In this case the decay time measured in the spectral region of A would be single exponential, with decay time $\tau_1$. However $\tau_1$ would be shorter than $\tau_A$, and it would be dependent on the concentration of X ($\tau_1$ = 1/ (krA+knrA + kAB[x]), where [x] denotes the concentration of X and kr and knr the intrinsic radiative and non-radiative rate constants of A, respectively) . The lifetime measured in the spectral region of B would be biexponential with times $\tau_1$ and $\tau_2$. $\tau_1$ would have a negative pre-exponential factor (rising component) and it would be coincident with the decay time measured in the spectral region of A. The decaying component $\tau_2$ would be coincident with the original lifetime of compound B, $\tau_B$.
  
 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.
  
-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 is biexponential for both, with common lifetimes $\tau_1$ and $\tau_2$. However, $\tau_1$ and $\tau_2$ do not correspond to $\tau_A$ or $\tau_B$ , but are a function of both and their interconversion rate constant kAB and kBA, as well as the concentration of X. The system has to be solved mathematically. For Scheme 2 the equations are:+//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) = A1 e^{-t/$\tau_1$} + A2 e^{-t/$\tau_2$}
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 being A0 the concentration of A at t=0. being A0 the concentration of A at t=0.
  
-**Note from the equations that even if B is not 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 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 kAB and kBA 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 will be established. This means that the concentrations of A and B with respect to each other is always constant prior to their decay, and hence the whole system can be treated as a single dye. The decay would be single exponential: an average of $\tau_A$ and $\tau_B$ weighted by their fraction in the equilibrium.+//Case D) Interconversion rate constants kAB and kBA 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 nd B are directly in contact prior to excitation (i.e. excited state reaction with the solvent).+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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 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 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.
  
-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, which raises the total energy of the system , displacing the coordinate solvation from its equilibrium position . As a result , the solvent begins to relax to solvate the S1 state and brings the system to a new equilibrium position. Spectroscopically this manifests 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 intrinsic 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 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.
  
-In fluid media, solvation dynamics can be described with a multiexponential function spanning from the fs 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, the ps tail component slows down to ns, and the process can be monitored with slower detectors, such as standard 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 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 PMT.
  
some_origins_of_multiexponetial_decays_for_single_dyes.txt · Last modified: 2019/03/19 12:31 by oschulz