probability density functions of the occurrence of the nth nearest molecule is shown
below [10]:
f r, σ N
ð
Þ¼3
4
3
πσ N
n
r
3nÀ1 e
À
4
3 σ N πr
3
ð13Þ
Figure 2 shows a PDF of the occurrence of EA molecules near EDs over short
distances (<40 nm) for EA concentrations of 1.0, 0.1, and 0.01 mmol L
À1 . At the
highest concentration, a fraction of the intermolecular distances is also within the
range 0–10 nm, which are intermolecular distances which might be efficient for
FRET. Much broader functions are observed if the concentration was reduced
tenfold (0.1 mmol L
À1 ), and only the nearest neighboring molecule can be found
within the efficient range of distances. The second-, third-, and fourth-nearest
molecule would mainly occur at distances over 10 nm from the ED molecule. The
concentration 10
À2 mmol L
À1 represents more or less the upper concentration limit,
0.00
0.05
0.10
0.15
0.20
0.00
0.05
0.10
0.15
0.20
0
1 0
2 0
3 0
4 0
0.00
0.05
0.10
0.15
0.20
1st
2nd
3rd
4th
1 mM
0.1 mM
F
D
P
1st
2nd
3rd
4th
0.01 mM
r / nm
1st
2nd
3rd
4th
Fig. 2 Probability density
functions (PDFs) of
intermolecular distances
between ED and EA
molecules in homogeneous
solutions. The functions are
calculated using Eq. (13)
Resonance Energy Transfer in Hybrid Systems of Photoactive Dye Molecules and. . .
213