Biomedical Engineering Reference
In-Depth Information
Tabl e 4. 1
Complexation constants
K
c
for “QD-porphyrin” nanoassemblies based
on CdSe/ZnS QD (
d
CdSe
=
2.5 nm,
n
ZnS
=
2) and (Pyr)
n
-H
2
P ligands with
n
=
1, 2,
3and4
Ligand
(
m
-Pyr)
1
H
2
P(
m
ˆPyr)
2
H
2
P(
m
-Pyr)
3
H
2
P(
m
-Pyr)
4
H
2
P
K
c
(
×
10
7
M
−
1
)
<
0.015
0.34
0.78
2.6
C
QD
=
5
×
10
−
8
M in toluene at 295 K
e
−
x
∑
x
n
I
(
x
)
/
I
0
=
/
n
!
(
1
+
nk
Q
/
k
D
)[
122
]
(4.2)
or
I
(
)
I
0
=
∑
x
k
D
nk
Q
x
n
exp
(
−
x
)
n
[
62
,
101
]
,
(4.3)
=
o
k
D
+
n
!
where
k
D
is the total QD PL intrinsic decay rate and
k
Q
the QD PL quenching rate.
The experimental PL quenching data
I
(
x
)/
I
(0) of Fig.
4.6
b presented as function
of the rescaled molar ratio
x
demonstrate that
nk
Q
is approximately the same
for most of the arrays based on QD. This implies that all variants of (Pyr)
n
H
2
P
molecules exhibit the same quenching mechanism upon assembling on QD. In
addition, the dynamic equilibrium in the “QD-H
2
P” nanoassemblies does not favor
a strong complexation of (Pyr)
n
-H
2
P on the QD surface or that there are only a
limited number of accessible sites on the QD surface. In fact, the maximum number
of anchored H
2
P molecules depends on several factors, such as the number and
kinds of “empty places” on the QD surface which are not occupied by TOPO
ligands, the competitive dynamic equilibrium between TOPO and H
2
P molecules
depending on both complexation constants
K
c
for TOPO and porphyrin molecules
and their relative concentrations. It follows from detailed spectral observations
[
101
,
127
] that at low molar ratios
x
all (Pyr)
n
-H
2
P molecules especially those
with four pyridyl rings are attached to the CdSe/ZnS surface. In addition, since
the well-defined QD PL quenching effects are even observed at molar ratios
x
1 (see curves 7 and 8 in Fig.
4.6
a), one can neglect (following statistical
arguments) nanoassemblies with more than one (Pyr)
n
H
2
P molecules per QD. Thus,
the experimental titration data can be discussed on the basis of a bi-molecular
reaction scheme valid for a dynamic equilibrium between self-assembled and free
constituents as has been usually applied in numerous experiments on the formation
of multipophyrin assemblies [
107
,
108
]. Following this idea and using the values of
the complexation constant (see Table
4.1
)
K
c
may be estimated for solutions of QD
as a function of various (Pyr)
n
H
2
P ligands [
101
] according to
<
1
=(
−
β
)
×
)
,
K
c
1
(4.4)
C
D0
·
β
(
x
+
β
−
1
where
C
D0
is the initial concentration of QD;
β
=
I
/
I
0
corresponds to the QD PL
ratio as a function of the molar ratios at
x
=
[H
2
P]/[QD] and
x
=
0, respectively.
