Principles of Fluorescence Spectroscopy

414 ADVANCED ANISOTROPY CONCEPTS
Figure 12.1. Model system for an associated anisotropy decay: a mixture of tryptophan in solution and in HSA.
Figure 12.2. Simulated associated anisotropy decay simulated for a
mixture of fluorophores, τ 1 = 3 ns, θ 1 = 50 ps, τ 2 = 8 ns, θ 2 = 40 ns,
r 01 = r 02 = 0.30. The individual intensity and anisotropy decays are
shown in Figure 12.3.
anisotropy of the tryptophan results in a transient decrease
in the measured value of r(t). At longer times, the emission
becomes dominated by HSA with its larger anisotropy,
resulting in an increase in r(t).
12.1.1. Theory for Associated Anisotropy Decay
It is useful to compare the equations describing associated
and non-associated anisotropy decays. For a single fluorophore
that displays a multi-exponential intensity and
anisotropy decay the parallel and perpendicular components
of the emission are given by
(12.2)
(12.3)
These expressions can be written in terms of the multiple
exponential components in I(t) and r(t):
I ||(t) 1
3 ∑ i
I (t) 1
3 ∑ i
I ||(t) 1
I(t)1 2r(t)
3
I(t) 1
I(t)1 r(t)
3
α i exp(t/τ i) [ 1 2 ∑ j
α i exp(t/τ i) [ 1 ∑ j
r 0j exp(t/θ j) ]
r 0j exp(t/θ j) ]
(12.4)
(12.5)