S. Hecht, A. F. Thꢀnemann et al.
Table 1. Structural parameters and dimensions derived from curve fits of
the SAXS measurements (see Figure 3) at 208C, below LCST, independ-
ently measured by different techniques (DLS, UV, CD).
nanorods are composed of flat dendrimer discs (see above)
spaced by a typical p,p-stacking distance of 3.5 ꢄ,[22] the ob-
served lengths correlate with increasing aggregation num-
bers for higher generation dendrimers, that is, 42, 48, and
165 for G-1g, G-2g, and G-3g, respectively. While the aggre-
gation numbers of the lower two generations are typical for
poly(ethylene oxide) based surfactants,[3,15,23,24] the third gen-
eration dendrimer forms rather large aggregates. The signifi-
cant increase in the aggregation number, when going from
the second to the third generation, is reflected in a much
higher aspect ratio, that is, length: radius ratio, for G-3a (22)
and G-3g (25). Assuming a simple isodesmic model for ag-
gregate growth,[3d,6] the association constant rises from K=
1.4·105 mꢀ1 (for G-2g) to K=1.7·107 mꢀ1 (for G-3g), approach-
ing the values of other heteroatom-containing extended p-
systems, such as perylene bisimides, in water.[6,25] This
strongly enhanced aggregation constant can be correlated to
the significant increase of the dendrimer coreꢃs hydrophobic
surface area from about 2ꢅ800 ꢄ2 (for G-2) to about 2ꢅ
1520 ꢄ2 (for G-3).[6]
To test our proposed structural model, a model-free data
evaluation procedure for the calculation of the radial densi-
ty profile developed by Glatter,[26] was used. In a first step,
we determined the cross-sectional pair distributions func-
tions with the established indirect Fourier transforma-
tion.[27,28] The radial electron density profiles of the cylindri-
cal micelles 1(r) were calculated in a second step using the
convolution square root method implemented in
DECON.[29–31] The resulting continuous density profiles, as
measured from the center of the cylinders (Figure 4), show
Dendrimer Shape
Length [nm] Radius [nm] LCST [8C]
DLS UV CD
[a]
[a]
[a]
G-1a
G-1g
G-2a
G-2g
G-3a
G-3g
disc
ca. 0.15
ca. 0.35
–
–
–
column 14.7ꢂ0.2
column 12.3ꢂ0.5
column 16.8ꢂ0.7
column 58.0ꢂ0.8
column 57.7ꢂ1.0
1.41ꢂ0.04
2.20ꢂ0.02
1.86ꢂ0.01
2.62ꢂ0.01
2.31ꢂ0.01
51
54
53
[a]
[a]
[a]
–
–
–
52
56
55
[a]
[a]
[a]
–
–
–
57
58
57.5
[a] No LCST Transition was detected for the carboxylate salt (pH 10).
In addition to determining the LCST transition, the
SAXS data provide valuable information about the structure
of the aggregates in solution. At 208C the form of the
curves of dendrimers G-ng are typical for a highly elongated
shape of the particles where the scattering intensity in the
q region from about 0.3 to 0.9 nmꢀ1 scales with qꢀ1 as indi-
cated by a straight line in Figure 3. At lower q values,
a Guinier region is visible, demonstrating that the total size
of the nanoparticles is attainable from the data. Finally, the
particle cross-section becomes visible in the high q range.
The obtained SAXS curves of dendrimers G-ng are most ap-
propriately described by assuming a nanorod structure
model. Reasonable curve fits for other simple shapes, such
as spherical or disk-like nanoparticles, could not be found.
By proper curve fitting(see the Supporting Information), the
dimensions of the nanorods, that is, lengths and radii, could
be determined (Table 1).
The radii of the nanorods increase with increasing genera-
tion number, nicely reflecting the larger size of the higher
generation dendrimers. The radii of the dendrimer cores of
1.0 nm, 1.6 nm, and 2.2 nm derived from molecular modeling
represent the lower limits of the radii, which upon addition
of the extended chiral oligo(ethylene glycol) chainsꢃ length
of ca. 0.8 nm give 1.8 nm, 2.4 nm, and 3.0 nm as upper limits
for G-1g, G-2g, and G-3g, respectively. Hence, the experimen-
tally determined radii are in agreement with a structural
model assuming that the cylinders are composed of stacks of
flat dendrimer discs. Note that at the first glance, it is sur-
prising that the radius of the carboxylate-terminated den-
drimers is larger than their corresponding oligo(ethylene
glycol)-terminated dendrimers in both the second and third
generations. The relatively large radii of G-2a and G-3a are
most likely a result of the sodium ions, which are condensed
to the surface of the nanorods and therefore contribute sig-
nificantly to electron density of the corona, rendering them
to appear bigger while the solvated ether side chains are
partially “invisible” due to their electron density matching
their surroundings.[21] This interpretation is supported by the
Figure 4. a) Cross-section density profiles of the nanorod as calculated
with DECON.[33] The arrow traverses the curves in the order of G-1g!
G-2g!G-2a!G-3g!G-3a (solid lines indicate oligo(ethylene glycol)
chain functionalized dendrimers, dashed lines indicate carboxylate-func-
tionalized dendrimers). b) Structural model of G-3g dendrimer aggregates
with dimensions as given in Table 1.
a clear decrease of electron density towards the periphery.[32]
The shift of the inflection points towards larger distances at
higher generations is in agreement with the increasing
radius of the dendrimer discs. Note that again the carboxyl-
ate-terminated dendrimers G-na appear to be more extend-
ed than the oligo(ethylene glycol) terminated dendrimers
G-ng due to the higher electron density of the sodium ions
fact that the differences of the radii, that is, r
2g)=0.34 nm and r (G-3g)=0.31 nm, are the same
(G-3a)ꢀr
within experimental error.
A
ACHTUNGERTN(NUNG G-
A
ACHTUNGTRENNUNG
The lengths of the nanorods reflect the aggregation
number, that is, how many dendrimer discs are stacked in
one cylindrical column. Based on the assumption that the
5840
ꢂ 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Chem. Eur. J. 2012, 18, 5837 – 5842