Biodetection Based on Fluorescence Quenching and Surface-Enhanced Fluorescence Using Noble Metal Nanoparticles - From Bioimaging to Biosensors: Noble Metal Nanoparticles in Biodetection - page 219

6

⎛⎞
⎜⎟

1 R

0

k =

τ ⎝⎠

(10.8)

FRET

r

0

In which R 0 is the Förster radius that is a function of the oscillator
strengths of the donor and acceptor molecules and their mutual
energetic resonance. Typically a detectable distance is limited to
<50 Å in FRET.
Using a similar formalism of FRET, we can describe the rate
of energy transfer from a dipole to a metallic surface interband
transition. 35-37 Instead of k FRET , a surface energy transfer (SET) rate
( k SET ) is used for a luorophore near a metal surface: k SET ≈ F D F A ≈
(1/ d 3 )(1/ d ) ≈ 1/ d 4 . Herein, d is the distance between a luorophore
and the metal surface. Thus, energy transfer to a surface follows a
very different distance trend and magnitude of interaction from that
in FRET. The exact form of the dipole-surface energy transfer is:

4

⎛⎞
⎜⎟

d

1

0

k =

τ ⎝⎠

(10.9)

SET

d

0

The characteristic distance length is

1/4

⎛ ⎞ 3

cQ

⎜ ⎟

D

d = 0.525

(10.10)

⎜ ⎟

0

2

ωω

k

⎝ ⎠ ff

In which Q D is a function of the donor quantum eficiency, ω is the
frequency of the donor electronic transition, ω f is the Fermi frequency,
and k f is the Fermi wave vector of the metal. The interaction of
luorophores with metal surfaces is different, depending on the
distance regime. At very close distances (<10 Å), radiative rate
enhancement is observed; at intermediate distances (20-300 Å),
energy transfer is the dominant process; and at very large distances
(>500 Å), luorescence oscillations due to dipole-mirror effects
occur. The quantum eficiency (Φ SET ) of the energy transfer between
a luorophore and a metal can be expressed as:

1

(10.11)

Φ

=

SET

n

⎛⎞
⎜⎟
⎝⎠

d
d

1+

0

In which n is 4. Recall that n is 6 in FRET. Thus, interrogation of the
slope of a plot of the energy transfer eficiency versus the separation