Principles of Fluorescence Spectroscopy

256 DYNAMICS OF SOLVENT AND SPECTRAL RELAXATION
sion spectra. In some circumstances it is possible to obtain
information about the rate of relaxation using only steadystate
measurements. The basic idea is to use collisional
quenching to decrease the lifetime of the excited state (τ) to
a value comparable to the relaxation time (τS ). As described
in Section 7.5, the center of gravity of the emission can be
expected to decay exponentially from ν 0 at t = 0 to ν∞ at t
= 4 according to
ν cg(t) ν ∞ (ν 0 ν ∞) exp(t/τ S)
(7.13)
Suppose the total intensity decays with a single decay time
τ. The center of gravity observed in a steady-state emission
spectra is given by the integral average of ν cg (t) over the
intensity decay:
ν cg
∞
0 ν cg(t) exp (t/τ) dt
∞
0 ν cg (t)dt
Substitution of eq. 7.13 into 7.15 yields
νcg ν∞ (ν0 ν∞) τS τ
(7.14)
(7.15)
This expression connects the center-of-gravity observed in
a steady-state experiment, with the relative values of the
decay time τ and the spectral relaxation time τ S . From this
expression one can also understand the spectral shifts
observed at low and high temperatures. At low temperature,
τ S >> τ, and the center of gravity is ν 0 . At high temperature,
τ S