Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 901
ation is occurring at a rate comparable to the intensity
decay rate.
A7.3. The lifetime of the R state (τ OR ) can be calculated
from the phase angle difference ∆φ = φ R – φ F . At 100
MHz this difference is 58E, which corresponds to a
lifetime of 16 ns.
A7.4. A. Acridine and acridinium may be reasonably
expected to display distinct absorption spectra.
The emission spectrum in 0.2 M NH 4 NO 3 (Figure
7.49) shows evidence for emission from both
acridine and acridinium. Hence if both species
were present in ground state, the absorption
spectrum should be a composite of the absorption
spectra of acridine and acridinium. In contrast,
if the acridinium is formed only in the
excited state, then the absorption spectrum in 0.2
M NH 4 NO 3 should be almost identical to that of
neutral acridine.
B. Examination of the data (Table 7.6) reveals two
decay times that are independent of emission
wavelength. This indicates that there are two
emitting species and that their decay rates are
independent of emission wavelength. On the
short-wavelength side of the emission the decay
is a single exponential. This result indicates the
reaction is irreversible and that the measured
decay times at other wavelengths contain contributions
from both acridine and acridinium.
Proof of an excited-state reaction is provided by
observation of negative pre-exponential factors.
As the observation wavelength is increased this
term becomes more predominant. At the longest
observation wavelengths one finds that the preexponential
factors are nearly equal in magnitude
and opposite in sign. This near equality of
the pre-exponential factors indicates that at 560
nm the emission is predominantly from the
relaxed species. The fact that α 2 is slightly larger
than α 1 indicates that there is still some emission
from neutral acridine at 560 nm.
A7.5. Red-edge excitation selects for fluorophores that are
most strongly interacting with the solvent. The solvent
configuration around these selected fluorophores is
similar to that in a solvent-relaxed state. The TRES
with 416-nm excitation do not show a time-dependent
CHAPTER 8
shift because the fluorophore is already in the relaxed
state.
A8.1. The apparent bimolecular quenching of 2-AP by Cu 2+
can be found by noting that F 0 /F = 1.10 at 2 x 10 –6 M
Cu 2+. Hence K = 50,000 M –1 and k q = 5 x 10 12 M –1 s –1.
Similarly, F 0/F = 1.7 at 0.001 M DMA, yielding K =
700 M –1 and k q = 7 x 10 10 M –1 s –1 . Both values are
larger than the maximum value possible for diffusive
quenching in water, near 1 x 10 10 M –1 s –1. This implies
some binding or localization of the quenchers near the
fluorophores.
A8.2. The data in Figure 8.72 can be used to calculate the
lifetimes of pyrene, which are 200, 119, and 56 ns in
the presence of N 2, air or O 2, respectively. Assuming
the oxygen solubility in DMPC vesicles is fivefold
larger than in water (0.001275 M/atm in water), the
oxygen bimolecular quenching constant is k q = 2 x 10 9
M –1 s –1 . This value is about 20% of the value expected
for a fluorophore dissolved in water.
A8.3. The data in the absence of benzyl alcohol (Figure
8.73) can be used to calculate a bimolecular quenching
constant of 6 x 10 9 M –1 s –1 . This indicates that the
naphthalene is mostly accessible to iodide and probably
not bound to the cyclodextrin. This conclusion is
supported by the data in the presence of benzyl alcohol.
In the presence of benzyl alcohol the Stern-
Volmer plots curve downward in the presence of β-CD
(Figure 8.74). This suggests the presence of two naphthalene
populations, one of which is less accessible to
iodide quenching. In the presence of benzyl alcohol
and 5.1 mM β-CD the Stern-Volmer plot is still
curved, and the apparent value of k q decreases, which
indicates shielding from iodide quenching. Under
these conditions it seems that naphthalene binds to β-
CD only in the presence of benzyl alcohol.
A8.4. Figure 8.77 shows a plot of F 0 /F versus [I –]. From the
upward curvature of this plot it is apparent that both
static and dynamic quenching occur for the same population
of fluorophores. The dynamic (K D ) and static
(K S ) quenching constants can be calculated by a plot
of the apparent quenching constant (K app ) versus the