Biomedical Engineering Reference
In-Depth Information
Fig. 4.12
Scheme of surface attachment of DPP and DTPP molecules to a CdSe/ZnS QD surface
(
a
) and calculated FRET QD
(
b
). The
inset
represents a scheme of the geometrical model being used in calculations. From geometrical
constraints the orientation for DTPP molecule with respect to QD surface corresponds to
→
Dye efficiency for DPP and DTPP as a function of angle
φ
0
◦
φ
≈
90
◦
, respectively. Simple calculations of FRET efficiency (
E
FRET
)
have been carried out using the standard Foerster model [
128
]
E
FRET
and for DPP molecule to
φ
≈
(
R
DA
/
R
0
)
6
]
−
1
,where
R
0
corresponds to the Foerster transfer radius and
R
DA
is the center-to-center donor-acceptor
distance. While almost all relevant parameters are nearly the same with respect to DPP and DTPP,
they differ considerably in
R
DA
=
[1
+
r
QD
, the (vectorial) distance between the centers of the
QD and the dye (
R
PDI
/2 corresponds to the distance of the coordinating point to the center of PDI
chromophore while
r
QD
is the radius of CdSe/ZnS QD). Adapted from [
162
]
=
R
PDI
/2
+
which allows to determine the dependence of dynamic QD-Dye interactions upon
variation of the spatial arrangement of the dye molecule with respect to QD surface
(e.g., distance and orientation) [
74
,
94
]. Indeed, it is seen from Fig.
4.11
that at
the same molar ratio
x
QD-AM PL quenching is stronger for DTPP molecules
with respect to that found for the DPP dye. In order to analyze this difference
one should look at Fig.
4.12
a, which shows different attachment angles for DPP
and DTPP molecules coordinating via pyridyl and terpyridyl substituents to the
ZnS shell of the QD. The parallel orientation of DTPP on the QD surface is
reasonable, since the attachment of the terpyridyl unit to the QD surface needs the
coordination of the two ortho-pyridyl groups, which can only be achieved in a flat
and slightly drilled configuration of the terpyridyl unit. A direct consequence of
this coordination to the surface is a spectral red shift observed for DTPP in case of
the reduction of excess of TOPO from the solution [
94
]. It follows from geometrical
considerations that for a hypothetical perpendicular position of both DPP and DTPP
molecules with respect to QD surface the distances become
R
DA
(DPP)
=
3.6 nm and
R
DA
(DTPP)
4.75 nm. This implies that FRET should be stronger for DPP than for
DTPP, which is quite opposite to what is observed experimentally (see Fig.
4.11
).
However, taking into account the steric restrictions discussed above we calculated
the FRET efficiency as a function of the orientation
=
of the long molecular axis
with respect to the QD surface as is shown in the inset of Fig.
4.12
a. Now
E
FRET
becomes 0.85 for DTPP at
φ
90
o
which is in rough
agreement with the experimental result with respect to relative FRET efficiencies.
0
o
φ
=
and0.68forDPPat
φ
=
