Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 427
Figure 12.19. Anisotropy decay of perylene in glycerol at 30°C. Excitation
at 254 nm where r 0 = –0.14. The data were fit as r(t) = 0.1
exp(–t/17 ns) – 0.24 exp(–t/2.7 ns). Revised and reprinted with permission
from [49]. Copyright © 1981, American Institute of Physics.
Figure 12.20. Effect of faster in-plane rotations on the anisotropy
decay of perylene with r 0 = –0.2. Revised and reprinted with permission
from [37], Academic Press Inc.
An intuitive description of the unusual perylene
anisotropy decay is shown in Figure 12.20. When excited at
a wavelength with r 0 = –0.2 the emission moments are symmetrically
distributed in the laboratory x–y plane, and the
horizontal intensity is greater than the vertical intensity (r 0
< 0). Because the in-plane rotation is more rapid than the
out of plane rotation, the effect at short times is to rotate the
emission dipoles out of the x–y plane toward the vertical
axis. This results in transient anisotropy values above zero
(Figure 12.19). At longer times the slower out-of-plane
motions contribute to depolarization, and the anisotropy
decays to zero (Figure 12.20).
12.6.2. Frequency-Domain Studies of Anisotropic
Rotational Diffusion
Anisotropic rotational diffusion can be studied using frequency-domain
methods. In fact, the earliest reports on the
anisotropic rotation of fluorophores were performed using
fixed-frequency phase-modulation fluorometers. 54–56 At
that time the phase-modulation instruments operated at only
one or two fixed frequencies. Hence it was not possible to
recover the anisotropy decay law. The experiments were
performed by measuring the differential polarized phase
angles (∆ ω ) as the temperature was varied. It is relatively
simple to predict the maximum value of ∆ ω for known values
of the lifetime and fundamental anisotropy. For an
isotropic rotator the predicted value of ∆ ω is given by
tan ∆ ω
(12.39)
where m 0 = (1 + 2r 0 ) (1 – r 0 ). The value of tan ∆ ω is a function
of the rotational rate (D), r 0, τ, and ω. The maximum
value of tan ∆ ω is given by
tan ∆ max
ω
(2Dτ) ωτr0
1
9 m0(1 ω 2 τ 2 ) (2Dτ)/3(2 r0) (2Dτ) 2
3ωτr 0
(2 r 0) 2m 0(1 ω 2 τ 2 ) 1/2
(12.40)
and is independent of the rotational rate. We note that these
expressions are only valid for an isotropic rotor with a single
fluorescence lifetime. The maximum differential tangent
depends only on τ, r 0 , and ω. If there is more than one
rotational rate the maximum value of tan ∆ is decreased. 54
Anisotropic rotation of perylene was detected by measurements
of the temperature-dependent values of tan ∆,
measured at a single modulator-frequency. 55 The values of
tan ∆ are only nonzero in the temperature range where rotational
diffusion is on a timescale comparable to the lifetime.