Geoscience Reference
In-Depth Information
a molecule in the lowest vibrational energy level of an excited electronic state returns to
a lower energy electronic state by emitting a photon. Because molecules usually return to
their ground state by the fastest mechanism, fluorescence is observed only if it is a more
efficient means of relaxation than the combination of internal conversion and vibrational
relaxation. These nonradiative processes compete with those that lead to radiative decay.
Contrary to Planck's frequency equation (
Eq. [1.1]
) fluorescence emission occurs over a
range of wavelengths that correspond to several vibrational transitions, within a single
electronic transition, that take place in the ground state. In
Figure 1.3
the straight verti-
cal arrows pointing downward represent fluorescence and phosphorescence, processes that
involve the release of a photon of energy. The other deactivation steps, as indicated by
wavy arrows, represent the radiationless processes, which compete with fluorescence.
1.3.4.1 Stokes Shift
The change in energy during a fluorescence transition is less than that for the absorp-
tion process. As a result, the fluorescence emission spectrum is almost always shifted
to a longer wavelength than the respective absorption spectrum (
Figure 1.9
). This is due
mostly to the high efficiency of vibrational relaxation of excited electron to the lowest
vibrational level in an excited state. This observed shift between the absorption and spec-
trum spectra is called the
Stokes shift
. The Stokes shift is defined as the difference between
the maximum of the first absorption band and the maximum of the fluorescence spectrum
(
Figure 1.9
). Fluorescence may return the molecule to any of the vibrational energy levels
in the ground electronic state, and therefore fluorescence emission occurs over a range of
wavelengths.
1.3.4.2 Fluorescence Decay Kinetics
The decay of the excited state obeys first-order kinetic; therefore an excited population of
fluorophores, [M*], decays according to
−
[ ]
=
dM
dt
*
kM
F
[
*
]
(1.7)
where the rate constant,
k
F
, is the sum of the rate constants for all radiative and nonradiative
decay processes (
k
F
=
k
R
+
Σ
k
NR
). Following integration of
Eq. (1.7)
, the concentration of
the excited state as a function of time can be represented as
[ ]
( )
=
Mt
[
M
]
exp
(
−
k t
F
)
(1.8)
*
*
0
where [M*]
0
is the initial concentration of M* at
t
= 0. The parameter monitored during
fluorescence lifetime experiments is the fluorescence intensity,
I
, which is the rate of the
emission of photons and is related to the excited state concentration by
( )
=
[ ]
( )
It kM t
F
*
(1.9)
R
