some_origins_of_multiexponetial_decays_for_single_dyes
Differences
This shows you the differences between two versions of the page.
Both sides previous revisionPrevious revision | |||
some_origins_of_multiexponetial_decays_for_single_dyes [2019/03/06 12:44] – admin | some_origins_of_multiexponetial_decays_for_single_dyes [2019/03/19 12:31] (current) – correct some typos etc. oschulz | ||
---|---|---|---|
Line 6: | Line 6: | ||
- | 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 | + | 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 |
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 | ||
Line 25: | Line 25: | ||
- | 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 | + | 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 |
Let us consider the reaction in Scheme 2 in different situations: | Let us consider the reaction in Scheme 2 in different situations: | ||
Line 34: | Line 34: | ||
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 $\tau_A$. | ||
Line 60: | Line 60: | ||
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/ | + | $A_2= A_0 [(1/ |
- | $B_1= -A_0 k_{AB}[x] / [(1/\tau_1 – 1/\tau_2]$ | + | $B_1= -A_0 k_{AB}[x] / [1/\tau_1 – 1/\tau_2]$ |
- | $B_2= A_0 k_{AB} [x] / [(1/\tau_1 – 1/\tau_2]$ | + | $B_2= A_0 k_{AB} [x] / [1/\tau_1 – 1/\tau_2]$ |
being $A_0$ the concentration of $A$ at $t=0$. | being $A_0$ the concentration of $A$ at $t=0$. | ||
Line 72: | Line 72: | ||
**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 | + | A situation like this may occur with molecules dissolved in an aprotic but hygroscopic |
//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, | //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, | ||
- | This situation may happen if compounds A and X were directly in contact prior to excitation, for example | + | This situation may happen if compounds A and X were directly in contact prior to excitation, for example |
===== 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 | + | 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 |
{{: | {{: | ||
- | 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 | + | 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. |
- | 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 | + | 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 |
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: | 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: |
some_origins_of_multiexponetial_decays_for_single_dyes.txt · Last modified: 2019/03/19 12:31 by oschulz