k are energy donor decay rates in the absence, and presence, of
Singlet depletion. The singlet depletion technique is built on the assumption that the absorption resonances of the excited state are distinctly different from those of the ground state. It requires that one measure the differential absorbance in a region or regions where the ground state has absorption. Assuming that the absorbance is measured at a time after the excited singlet state is empty, that no photoproducts are formed, and that all excited electrons migrate to the lowest triplet state, the differential absorbance is written as
ΔA(λ) = (ε*T(λ)–εS(λ))L3M*J (15) where ε*T (λ), εs(λ), [3M*], and are the first excited triplet state molar extinction coefficient, the ground singlet state molar extinction coefficient, the first excited triplet state concentration, and the path length, respectively. Thus the ground state absorption features will give a negative contribution to the measured ΔA(λ), producing negative peaks where the ground state is more strongly absorbing than the excited triplet state. These negative peaks have the same shape as the ground state spectrum. Equation (15) can be recast as,
The technique is then used to form the ε s(λ) spectra by taking a well-measured ground state spectrum, εs(λ), and adding the ΔA(λ) adjusted by varying [3M*] as a parameter to remove the apparent negative peaks in the εT* (λ) spectra. Several methods have been developed to estimate [3M*] . One method not mentioned, which is just the embodiment of the original assumption in the method, is to minimize the correlation of ε s(λ) and εT* (λ) in a region around a ground state absorption feature. This is an objective and robust method. It must also be pointed
out that it is absolutely necessary that the ε s(λ) and ΔA(λ) spectra be measured under the exact same spectroscopic conditions, especially the spectral bandwidth. One limitation not often mentioned is that for those molecules that are excited to the S1 state and relax back to S0, a large amount of thermal energy must be dissipated. This, coupled with the fact that many molecules have a relatively strong thermochromic behavior, means that one cannot necessarily null out the ground state resonances in the triplet state construction due to thermal differences. Thus, it is necessary to minimize the laser pulse energy and photon energy, if possible.