Biology Reference
In-Depth Information
In solution, PDI derivatives functionalized with poly(ethylene
glycol) form dynamic self-assemblies (Scheme 5.1). Although much of
current understanding of self-assembly comes from the examination
of static systems, the greatest challenges, and opportunities, lie
in studying dynamic systems. These dynamic self-assemblies are
driven by
interactions. The free PDI molecules in solution and
the self-assembled nanostructures of a group of PDI molecules
have dramatically different spectroscopic properties. Consequently,
molecular self-assemblies can be conveniently monitored using
spectroscopic techniques such as
π−π
1
H NMR, UV
−
vis spectroscopy, and
fluorescence emission.
•
Â
-
i
i
1
[]
[]
AK
A
obs
d
=
d
(5.1)
i
0
=
i
1
•
A
KA
[]
[]
Â
obs
i
i
0
0
d d
=+
[]
AK
(
dd
-
)
and
[]
A
ª
(5.2)
1
i
+
1
i
+
1
=
i
1
As the concentration of a perylene monomer increases, rapid
exchange of the free monomer and variously self-associated oligomers
can be observed on the NMR time scale. This concentration-driven
self-organization of PDI yields considerable upfield shift (Fig. 5.1)
of the aromatic protons (see Scheme 5.1 for assignment),
∆
d
(Ha) =
0.62 and
∆
d
(Hb) = 0.88 ppm when the initial concentration [
A
] is
0
−
5
−
1
changed from 10
to 10
M. To the first-order approximation, the
strength of
π−π
stacking is expected to be the same between the
i
th
oligomer and the (
i
+ 1)th oligomer; therefore, the equilibrium
K
i
is
approximately a constant
K
(i.e.,
K
=
K
=
K
=
…
=
K
j
=
K
). Since the
1
2
3
monomer (
1A
), self-assembled dimer (
1A:1A
), trimer (
1A:1A:1A
),
and other higher order oligomers (
) are in rapid
exchange, the observed chemical shift is the mole-fraction weighted
average of various oligomers given by Eq. 5.1, where [
1A:1A:1A
…
]
are the initial and equilibrium concentrations of free monomer,
respectively, and
A
] and [
A
0
th folded oligomer. The
power series in Eq. 5.1 must converge under our experimental
conditions (
d
i
is the chemical shift of
i
obs
is
finite and well defined. After some mathematical manipulations,
we obtained Eq. 5.2, from which the equilibrium constant
K
[
A
] < 1) because the observed chemical shift
d
K
for self-
−
1
association of PDI was determined to be
K
= 52
±
5 M
in CHCl
.
3
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