Biomedical Engineering Reference
In-Depth Information
(
)
ΓΓ
(10.1)
Q
s
is the fraction of the excited luorophores which decay through
emission (Γ) relative to the total decay (Γ +
k
nr
). A luorophore with
a higher radiative rate has a higher quantum yield and a shorter
lifetime. Γ is determined by the oscillator strength (extinction
coeficient) of the electronic transition. The extinction coeficient of
a luorophore is only slightly dependent on its environment, and thus
Γ is essentially constant for any given luorophore. In other words,
Q
s
is only controlled by varying
k
nr
;
Q
s
increases upon decreasing
k
nr
. In
the absence of other quenching interactions,
τ
0
is given by
Q
=
+
k
s
nr
)
-1
(
(10.2)
τ
=+
k
Γ
0
nr
The sum of the rates that depopulate the excited state determines
τ
0
. When
k
nr
= 0,
τ
0
= Γ
−1
. In this case, we often use
τ
N
(the natural
lifetime of a luorophore) to represent
τ
0
. Like
Q
s
,
τ
0
is dependent
on
k
nr
;
τ
0
decreases as
k
nr
increases. Almost invariably,
Q
s
and
τ
0
increase or decrease together.
When a luorophore is placed on a metal surface, its luorescence
properties are also dependent on the metal species. Nearby metal can
increase the intrinsic radiative decay rate of the luorophore, which
is not similar to luorescence spectroscopy.
28
Assume the presence
of a nearby metal surface increases the radiative rate by addition of
a new rate Γ
m
(see Fig. 10.1, bottom). For the present discussion, we
will not consider the quenching effect of the metal (
k
m
). In this case,
the quantum yield (
Q
m
) and lifetime (
τ
m
) of the luorophore near the
metal surface are given by
+
=
++
ΓΓ
ΓΓ
(10.3)
m
Q
m
k
m r
(
)
-1
τ
ΓΓ
(10.4)
=++
k
m r
As the value of Γ
m
increases,
Q
m
increases while
τ
m
decreases. It is
informative to compare the effects of increasing values of Γ
m
with
increased quenching of the luorescence intensity of a luorophore.
Figure 10.2 shows this comparison in terms of the Stern-Volmer
plots. The Stern-Volmer equation is
0
F
, in which
F
0
and
F
are the luorescence intensities in the absence and presence of the
quencher, respectively. The effects of the rate Γ
m
are dramatically
=1+ [ ]
kQ
qu
F
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