Biomedical Engineering Reference
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a
c
b
Fig. 4.25
( a ) Critical molar ratio x c for various types of QDs as a function of the QD surface area
2 calculated from the radius R of the CdSe core and eventually the thickness D of the
ZnS shell. ( b ) The ratio
4
π (
R
+
D
)
K c ( dots ) as a function of QD surface area. ( c ) Geometrical
model of a CdSe quantum dot core (hexagonal wurtzite unit cell) including different crystal facets
with polar and non-polar orientation. Adapted from [ 64 ]
K c +
K c ) /
(
there is not a direct measure for this number. Again, according to the experiments
on PDI, this number may be a factor of up to 5 smaller than n max [ 74 , 94 ]. But even
if n can be estimated from the corresponding absorption coefficients for QD and
dye after precipitation and re-dissolution of the nanoassemblies [ 45 ], competitive
attachment-detachment processes may take place.
The important conclusion from Fig. 4.25 aisthat n is almost linearly related to
the QD surface area. Our interpretation is that only selected parts of the QD surface
area allow an immediate attachment of the dye molecules as it is inhomogeneous
with respect to its ligand dynamics. This argument is obvious from theoretical
investigations of the growth mechanisms of semiconductor nanocrystals leading
to facet structures [ 153 , 154 ] as well as experiments about a complex optical
transition moment attributed to strain within the crystal or an anisotropic growth
of QDs during synthesis [ 155 ] (see simplified sketch in Fig. 4.25 c). The relations
of specific surface facets and ligand binding dynamics have been discussed recently
in numerical simulations [ 48 ]. In the view of this picture, we see a relationship to
the fact that the particular crystal facets of the QD nanocrystals or even the edges
of these facets have a preferential chemical binding probability for an instantaneous
attachment of dye molecules: only sub-areas with a particular structure contribute
to the instanteneous attachment without significant competition with the original
ligands (e.g., TOPO). When these specific attachment sites become occupied (in
our picture, this happens around x
x c ), further PL quenching is controlled by more
complex processes that are based on a competition between the dye molecules and
the original ligands (TOPO) to attach on the QD surface.
=
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