Biomedical Engineering Reference
In-Depth Information
perpendicular to the metallic surface. The most remarkable effect is
observed when a luorophore is perpendicular to the surface of a
spheroid with
a
/
b
= 1.75 with an enhancement factor of 1000-fold
or greater. The dominant effect of the perpendicular orientation is
likely due to an enhancement of the local ield along the long axis
along the particle; the luorophore's dipole and the dipole in the
metal are synergistic. The effect is smaller for a sphere (
a
/
b
= 1.0) or
a more elongated spheroid (
a
/
b
= 3.0) when the optical transition is
not in resonance with the particle.
10.2.1 Fluorescence Quenching
Fluorescence quenching of a luorophore by a quencher (
Q
u
) is
related to its biomolecular rate constant
k
q
that decreases the
quantum yield (
Q
) according to:
(
)
⎡
⎣⎦
(10.6)
Q
=
ΓΓ
+ +
k
k
Q
nr q u
In the presence of a quencher,
τ
of the quenched luorophore
decreases due to an additional nonradiative path to the ground state
with a rate
k
q
[
Q
u
]:
(
)
-1
⎡⎤
τ
Γ
⎣⎦
(10.7)
=+
kkQ
nr q u
To understand how a metal causes luorescence quenching of a
luorophore, we irst provide the basic concept of Förster resonance
energy transfer (FRET) that physically originates from the weak
electromagnetic coupling of two dipoles. One can imagine that
the FRET limit can be circumvented by introducing additional
dipoles, providing more coupling interactions. To understand the
consequences of this physical interaction, we must invoke the Fermi
Golden Rule in the dipole approximation of energy transfer.
34
The
Golden Rule approximation relates the energy transfer rate (
k
FRET
) to
a product of the interaction elements of the donor (
F
D
) and acceptor
(
F
A
):
k
FRET
≈
F
D
F
A
. These interaction elements can be simpliied such
that their separation distance (
r
) dependencies are sole functions of
their geometric arrangement. Because FRET consists of two single
dipoles (
F
≈ 1/
r
3
), its energy transfer rate (
k
FRET
) is easily derived
from this rule:
k
FRET
≈
F
D
F
A
≈ (1/
r
3
)(1/
r
3
) ≈ 1/
r
6
. More commonly,
the relationship between
k
FRET
and
r
in FRET is written as:
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