Analysis of Excited-State Reactions by Phase-Modulation Fluorometry

Several aspects of these equations ate woithy of mention. Since we have initially assumed that F and R are separately observable, and the reveise reaction does not occur, the decay of F is a single exponential. Hence, for the F state 

The phase and modulation of the R state, when measured relative to the excitation, are complex functions of the various Idiietic constants. These values are given by 

In contrast to the values for the Fstate, the measured values for the R state cannot be directly used to calculate the fluorescence lifstime of the R state. The complexity of the measured values and mx) illustrates why use of the apparent phase (t and modulation (I ) lifebmes of the relaxed state is not advisable. 

Closer examination of Etjs. [18.17]-[18.20] reveals important relationships between the phase and modulation values of the F and R states. For an excited-state process, the phase angles of the F and R states are additive, and the modulations multiply. Once this is understood, the complex expressions (Eqs. [18.19] and[18.20]) become easier to understand. Let be the phase angle of the R state that would be observed if this state could be excited directly. Of course, this is related to the lifetime of the directly excited R state by tan = cmOx. Using Eq. [18.19], die law for the tangent of a sum, and tan (9x f- = tani g, one finds 

The demodulatioo factois of the two states diqilay similar propesties. I om Eq. [18.20], one finds that the demodulatioo of the relaxed stale (nix) is the product of the demodulation of the unrelaxed state (ntf,) and that demodulation doe to the intrinsic decay of the R state done (mm). That is. 

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