Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 239
Figure 7.3. Energy schematic for continuous spectral relaxation.
Figure 7.4. Energy schematic for an excited-state reaction.
constant k 1 describes the rate at which the F state is transformed
into the R state.
7.1.1. Time-Resolved Emission Spectra
Excited-state processes result in complex time-dependent
decays. The intensity decays depend on the observation
wavelength because of the time needed for the F state to
Figure 7.5. Schematic of time-resolved emission spectra. I T (t) represents
the decay of the total emission. I F (t) and I R (t) are the intensity
decays on blue and red sides of the emission spectrum, respectively.
The upper insert shows the emission spectra at t = 1, 2, or 3 ns.
become an R state or some intermediate state. This situation
is illustrated in Figure 7.5. In this figure the solid line shows
the intensity decay of the total emission, or the decay that
would be observed in the absence of excited-state processes.
Now suppose the intensity decay is measured on the
short-wavelength side of the total emission. This decay,
I F (t), is more rapid than the decay of the total emission,
I T (t), because the short-wavelength emission is decaying by
both emission and relaxation, which is removing excited
fluorophores from the observation wavelength. On the
long-wavelength side of the emission the emitting fluorophores
are those that have relaxed.
Time is needed for the F-state molecules to reach the R
state. Even if the F and R states have the same intrinsic
decay time, the long-wavelength decay will appear to be
slower. Also, at the moment of excitation all the molecules
are assumed to be in the F state. No molecules are in the R
state until some relaxation has occurred. For this reason one
typically observes a rise in the intensity at long wavelengths
representing formation of the relaxed state. The rise time is
frequently associated with a negative pre-exponential factor
that is recovered from the multi-exponential analysis. Following
the rise in intensity, the decay I R (t) typically follows
the total emission. Another way of understanding the wavelength-dependent
decays is to recall that emission is a random
event. Some fluorophores emit at earlier times, and