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some_origins_of_multiexponetial_decays_for_single_dyes [2015/11/03 14:09] adminsome_origins_of_multiexponetial_decays_for_single_dyes [2019/03/06 12:44] admin
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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 $Adecreases 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 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.//+//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 $\tau_A$.
  
-//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, $\tau_B$.+//Case B) The forward reaction constant $k_{AB}$ is fast, but the back-reaction constant $k_{BA}$ 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 $(\tau_1 = 1/ (kr_A+knr_A k_{AB}[x])$, where [x] denotes the concentration of X and $krand $knrthe 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.
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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/$\tau_2$}+$A(t) = A_1 e^{-t/\tau_1} + A_2 e^{-t/\tau_2}$
  
-B(t) = B1 e^{-t/$\tau_1$} + B2 e^{-t/$\tau_2$}+$B(t) = B_1 e^{-t/\tau_1} + B_2 e^{-t/\tau_2}$
  
 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 $A$$k_A=1/\tau_A$ )
  
-being Y = kBA kB (summation of disappearance constant of compound B; kB=1/$\tau_B$)+being $Y = k_{BA} k_B$ (summation of disappearance constant of compound $B$$k_B=1/\tau_B$)
  
-being Z = (M-Y)^2 + 4 kAB kBA[x]]^(1/2)+being $Z = \sqrt{(M-Y)^2 + 4 k_{AB} k_{BA}[x]}$
  
-A1A0 [M- (1/$\tau_2$)] / [(1/$\tau_1– 1/$\tau_2$]+$A_1A_0 [M- (1/\tau_2)] / [(1/\tau_1 – 1/\tau_2]$
  
-A2A0 [(1/$\tau_1$)- M] / [(1/$\tau_1– 1/$\tau_2$]+$A_2A_0 [(1/\tau_1)- M] / [(1/\tau_1 – 1/\tau_2]$
  
-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_2A_0 k_{AB} [x] / [(1/\tau_1 – 1/\tau_2]$
  
-being A0 the concentration of A at t=0.+being $A_0$ the concentration of $Aat $t=0$.
  
-**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 $Bwould not be fluorescent, the decay of $Awill 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 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_Aand $\tau_B$.// 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 throgh ground-state interactions.
- 
 ===== 3) Solvation dynamics ===== ===== 3) Solvation dynamics =====
  
some_origins_of_multiexponetial_decays_for_single_dyes.txt · Last modified: 2019/03/19 12:31 by oschulz