Principles of Fluorescence Spectroscopy

5
In the preceding chapter we described the theory and instrumentation
for measuring fluorescence intensity decays
using time-domain measurements. In the present chapter
we continue this discussion, but describe frequency-domain
fluorometry. In this method the sample is excited with light
that is intensity modulated at a high frequency comparable
to the reciprocal of the lifetime. When this is done, the
emission is intensity modulated at the same frequency.
However, the emission does not precisely follow the excitation,
but rather shows time delays and amplitude changes
that are determined by the intensity decay law of the sample.
The time delay is measured as a phase angle shift
between the excitation and emission, as was shown in Figure
4.2. The peak-to-peak height of the modulated emission
is decreased relative to the modulated excitation, and provides
another independent measure of the lifetime.
Time-resolved measurements, whether performed in
the time domain or in the frequency domain, provides information
about intensity decay of the sample. Samples with
multiple fluorophores typically display multi-exponential
decays. Even samples with a single fluorophore can display
complex intensity decays due to conformational heterogeneity,
resonance energy transfer, and transient effects in
diffusive quenching or fluorophore–solvent interactions, to
name just the most common origins. The goal of the timeresolved
measurement is to determine the form of the intensity
decay law, and to interpret the decay in terms of molecular
features of the sample.
Intensity decays can be single-exponential, multi-exponential,
or non-exponential. Irrespective of the complexity
of the decay, one can always define a mean or apparent
decay time. For a single exponential decay in the time
domain the actual lifetime is given by this the time when the
intensity decays to 1/e of its initial value. For a multi-exponential
decay, the 1/e time is typically not equal to any of
the decay times. In the frequency domain an apparent lifetime
(τ φ ) determined from the phase angle (φ ω ) or the appar-
Frequency-Domain
Lifetime
Measurements
ent lifetime (τ m ) determined from the modulation (m ω , eqs.
4.5 and 4.6). The apparent lifetimes are characteristic of the
sample, but do not provide a complete description of the
complex intensity decay. The values of τ φ and τ m need not
be equal, and each value represents a different weighted
average of the decay times displayed by the sample. In general,
the apparent lifetime depends on the method of measurement.
The earlier literature on time-resolved fluorescence
often describes apparent lifetimes. At present, there
are relatively few reports of only the mean decay times.
This is because the mean lifetimes represent complex
weighted averages of the multi-exponential decay. Quantitative
interpretation of mean decay times is usually difficult
and the results are often ambiguous.
Prior to 1983, frequency-domain fluorometry allowed
determination of mean lifetime, but was not able to resolve
complex intensity decays. This limitation was the result of
phase-modulation fluorometers, which only operated at
one, two, or three fixed light modulation frequencies. The
resolution of a complex decay requires measurements at a
number of modulation frequencies that span the frequency
response of the sample. While several variable-frequency
instruments were described prior to 1983, these were not
generally useful and were limited by systematic errors. The
first generally useful variable frequency instrument was
described in the mid 1980s. 1–2 These instruments allowed
phase and modulation measurements from 1 to 200 MHz.
These designs are the basis of currently available instruments.
Frequency-domain fluorometry is now in widespread
use, 3–9 and instruments are commercially available.
Frequency-domain fluorometers are now routinely used to
study multi-exponential intensity decays, and non-exponential
decays resulting from resonance energy transfer, timedependent
solvent relaxation, and collisional quenching.
In this chapter we describe the instrumentation for FD
measurements and the theory used to interpret the experimental
data. We will describe examples that illustrate the
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