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| some_origins_of_multiexponetial_decays_for_single_dyes [2019/03/06 12:40] – admin | some_origins_of_multiexponetial_decays_for_single_dyes [2019/03/06 12:43] – 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 $A$ decreases with the concentration of $X$, but where the lifetime $\tau_A$ remains constant. |
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| ===== 2) Excited-state reactions ===== | ===== 2) Excited-state reactions ===== |
| Scheme 2 | Scheme 2 |
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| //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.// |
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| //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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| //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 $kr$ 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, $\tau_B$. |
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| 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. |
