Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 285
Figure 8.6. Acrylamide quenching of NATA in water (!). The open
circles show the values of F 0 /(F e V[Q] ) where V = 2.0 M –1 . Revised
from [20].
Figure 8.7. Acrylamide quenching of dihydroequilenin (DHE) in
buffer containing 10% sucrose at 11°C. The value of V was 2.4 M –1 .
Revised and reprinted with permission from [21]. Copyright © 1990,
American Chemical Society.
8.7). The upward-curving Stern-Volmer plots could be analyzed
in terms of the static and dynamic quenching constants
(eq. 8.19). This analysis yields K S values near 2.8 and
5.2 M –1 for acrylamide quenching of NATA and DHE,
respectively. These values imply that quencher concentrations
near 0.3 M are required to quench half of the fluorophores
by a static process. Such a weak association suggests
that the fluorophores and quenchers do not actually
form a ground-state complex. Instead it seems that the
apparent static component is due to the quencher being
adjacent to the fluorophore at the moment of excitation.
These closely spaced fluorophore–quencher pairs are
immediately quenched, and thus appear to be dark complexes.
This type of apparent static quenching is usually interpreted
in terms of a "sphere of action" within which the
probability of quenching is unity. The modified form of the
Stern-Volmer equation that describes this situation is
F 0
F (1 K DQ) exp(QVN/1000)
(8.24)
where V is the volume of the sphere. 22 The data in Figures
8.6 and 8.7 are consistent with a sphere radius near 10 Å,
which is only slightly larger than the sum of the radii of the
fluorophore and quencher. When the fluorophore and
quencher are this close, there exists a high probability that
quenching will occur before these molecules diffuse apart.
As the quencher concentration increases, the probability
increases that a quencher is within the first solvent shell of
the fluorophore at the moment of excitation.
8.6.1. Derivation of the Quenching Sphere
of Action
Assume the existence of a sphere of volume V within which
the probability of immediate quenching is unity. Intuitively,
if a fluorophore is excited when a quencher is immediately
adjacent, then this fluorophore is quenched and is therefore
unobservable. The only observable fluorophores are those
for which there are no adjacent quenchers. The modified
form of Stern-Volmer eq. 8.24 is derived by calculating the
fraction of fluorophores that does not contain a quencher
within its surrounding sphere of action. 22
The probability of finding a number (n) of quenchers
molecules in a given volume can be calculated from the
Poisson distribution:
P(n) λn
n! eλ
(8.25)
where λ is the mean number of quenchers per volume V.
The average concentration in molecules/cm 3 is given by
[Q]N/1000, so the average number of molecules in the
sphere is λ = V[Q]N/1000. Only those fluorophores without
nearby quenchers are fluorescent. The probability that no
quenchers are nearby is
P(0) e λ
(8.26)
Thus, the existence of the sphere of action reduces the proportion
of observable fluorophores by the factor
exp(–V[Q]N/1000), which in turn yields eq. 8.24. Division