Release caged compounds
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Publicado: 30 de noviembre de 2011
Theoretical evaluation of the release
The evaluation of the uncaging is as follows: The absorbance A is a measurement of the ratio of incoming light versus the outgoing light,which by the Beer Lambert equation is:
[pic]Where epsilon is the extinction coefficient, E0 is the energy of the flash, c the concentration of caged compound and l the lengthof the path of the light through the sample. The typical values for this are ε = 106 M-1m-1, l = 10-3m and c = 10-6 M and thereby, the exponent is typically on the order of 10-3.This allows us to perform a Taylor expansion for the absorbed energy:
It is important to observe that this result is wavelength dependent as E0 as well as ε depend on thewavelength.
[pic]
Now, for a given wavelength distribution of energy, as in the spectrum on figure 8, the amount of energy that we have for a given lambda is:
From thisenergy, only the fraction given by the Beer-Lambert equation is absorbed. It is possible to calculate the total amount of photons that are then absorbed using the equation:
Where clis the speed of the light and h is the constant of Planck. From here we can write the number of effective photolytic reactions for an infinitesimal width of the spectrum as:Now, only the fraction φ of these photons that are absorbed will lead to a successful photolytic reaction. Finally, if we use this expression we can derive the uncaging efficiencyor the percentual fraction released by one flash as:
Where NA is the number of Avogadro and A is the area irradiated by the flash.
[pic]
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Figure 8:Extinction coefficient from several caged compounds
[pic]
Δλ
S(λ)
Figure 9: Calculation of the number of photons per wavelength
[pic]
[pic]
[pic]
[pic]
The evaluation of the uncaging is as follows: The absorbance A is a measurement of the ratio of incoming light versus the outgoing light,which by the Beer Lambert equation is:
[pic]Where epsilon is the extinction coefficient, E0 is the energy of the flash, c the concentration of caged compound and l the lengthof the path of the light through the sample. The typical values for this are ε = 106 M-1m-1, l = 10-3m and c = 10-6 M and thereby, the exponent is typically on the order of 10-3.This allows us to perform a Taylor expansion for the absorbed energy:
It is important to observe that this result is wavelength dependent as E0 as well as ε depend on thewavelength.
[pic]
Now, for a given wavelength distribution of energy, as in the spectrum on figure 8, the amount of energy that we have for a given lambda is:
From thisenergy, only the fraction given by the Beer-Lambert equation is absorbed. It is possible to calculate the total amount of photons that are then absorbed using the equation:
Where clis the speed of the light and h is the constant of Planck. From here we can write the number of effective photolytic reactions for an infinitesimal width of the spectrum as:Now, only the fraction φ of these photons that are absorbed will lead to a successful photolytic reaction. Finally, if we use this expression we can derive the uncaging efficiencyor the percentual fraction released by one flash as:
Where NA is the number of Avogadro and A is the area irradiated by the flash.
[pic]
-----------------------
Figure 8:Extinction coefficient from several caged compounds
[pic]
Δλ
S(λ)
Figure 9: Calculation of the number of photons per wavelength
[pic]
[pic]
[pic]
[pic]
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