Elucidating the structure of the pm3n cubic phase of supramolecular dendrimers through the modification of their aliphatic to aromatic volume ratio

Article abstract of DOI:10.1002/chem.200901324

The synthesis, and structural and retrostructural analysis of a library of second-generation conical dendrons that self-assemble into spherical supramolecular dendrimers is reported. This library consists of amphiphilic dendrons with n-alkyl groups contai

Full text of DOI:10.1002/chem.200901324

DOI: 10.1002/chem.200901324
¯
Elucidating the Structure of the Pm3n Cubic Phase of Supramolecular
Dendrimers through the Modification of their Aliphatic to Aromatic Volume
Ratio
Virgil Percec,*[a] Mihai Peterca,[a, b] Yusuke Tsuda,[a] Brad M. Rosen,[a] Satoshi Uchida,[a]
Mohammad R. Imam,[a] Goran Ungar,[c] and Paul A. Heiney[b]
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Chem. Eur. J. 2009, 15, 8994 – 9004

FULL PAPER
Abstract: The synthesis, and structural
and retrostructural analysis of a library
of second-generation conical dendrons
that self-assemble into spherical supra-
molecular dendrimers is reported. This
library consists of amphiphilic den-
drons with n-alkyl groups containing
from 4 to 16 carbon atoms. The den-
drons containing 6 to 16 carbon atoms
in their n-alkyl groups self-assemble
into spherical supramolecular dendri-
generated from the supramolecular
dendrimers demonstrated that the
of the spherical supramolecular den-
drimers. The relative intensity of the
higher order diffraction peaks of the
AHCTUNGTRENNUNG
volume of the aromatic core of the
spherical dendrimers is not dependent
on the number of carbon atoms from
their alkyl groups. This result facilitat-
ed the calculation of the average
values of the absolute electron density
of the aliphatic and aromatic domains
¯
Pm3n lattice increases as the volume
of the aliphatic part of the sphere
mediated by the number of carbon
atoms in the n-alkyl groups decreases.
This study demonstrates the maximum
increase of the relative intensity of the
higher order diffraction peaks of the
¯
Pm3n lattice generated from non-
Keywords: cubic phase · dendrim-
ers · liquid crystals · self-assembly ·
X-ray diffraction
¯
A
a
Pm3n
hollow supramolecular dendrimers.
cubic lattice. The structural and retro-
¯
structural analysis of the Pm3n lattices
Introduction
delivery of molecular species.[11] Amplification of chirality
by supramolecular spheres is also an unprecedented
event.[11,12]
Further expansion of the role of spherical self-assembling
dendrons as functional nanomaterials[13] requires greater
elaboration of their assembled structure and their relation-
ship to lattice properties. While an impressive diversity of
periodic cubic lattices have been documented for benzyl
ether, phenylpropyl ether, and other aryl alkyl ether den-
drons, including tetragonal P42/mnm,[2n] body-centered cubic
Amphiphilic benzyl ether dendrons prepared through con-
ventional convergent iterative approaches[1] with aliphatic
groups on their periphery self-assemble and self-organize in
a diversity of periodic[2–4] and quasi-periodic[2q,5] arrays. The
primary structure of the dendron induces a preferred molec-
ular conformation that controls the solid angle of the den-
dron.[2g] As the solid angle increases, the self-assembly and
self-organization process is gradually shifted from lamellar/
smectic to columnar to spherical supramolecular struc-
[3]
[4]
[2s,14]
¯
¯
¯
Im3m, bicontinous cubic Ia3d, cubic Pm3n,
and 12-
¯
tures.[2k,q,r] Detailed structural and retrostructural analysis,
fold liquid quasicrystal quasi-periodic arrays,[2q,5] the Pm3n
lattice is by far the most ubiquitous and was coincidentally
first observed in soft-condensed matter in these systems.[2d]
Many aryl alkyl ether dendrons possess thermally reversible
phase transitions between columnar and spherical assem-
blies. As temperature increases the molecular taper angle in-
creases, resulting in a series of lattices. In such cases, the
order of phases is typically hexagonal columnar p6mm!
including the application of helical diffraction theory,[6] have
guided the design of new functions based on dendrons pre-
disposed to columnar self-assembly, such as: controlled reac-
tivity,[7] aquaporin mimics,[8] self-repairing electronic materi-
als,[9] and nanomechanical actuators.[10] The development of
functional materials based upon spherical self-assembling
dendrons is in an earlier stage. It has recently been observed
that certain spherical self-assembling dendrons exhibit re-
duced electron density in their center,[2s] thereby enabling
the design of chiral and achiral spherical architectures con-
taining a hollow center with potential for encapsulation and
¯
cubic Pm3n!tetragonal P42/mnm!body-centered cubic
[3a]
¯
¯
Im3m. Thus, the cubic Pm3n lattice exists at the border
between columnar and spherical assemblies. Extensive work
through transmission electron microscopy,[2e] scanning force
microscopy,[7b] atomic force microscopy,[2h] and isomorphous
replacement[2l] was required to definitively establish a spher-
ical model as opposed to an interlocked columnar model for
[a] Prof. V. Percec, Dr. M. Peterca, Prof. Y. Tsuda, B. M. Rosen,
Prof. S. Uchida, Dr. M. R. Imam
¯
Roy & Diana Vagelos Laboratories
the Pm3n lattice.
Department of Chemistry, University of Pennsylvania
Philadelphia, Pennsylvania, 19104-6323 (USA)
Fax : (+1)215-573-7888
While many aspects of the relationship between the struc-
ture of self-assembling aryl alkyl ether dendrons and the
Pm3n lattices they form have been elaborated, critical ques-
¯
E-mail: percec@sas.upenn.edu
tions remain. Of particular interest is the nature of the aro-
matic core structure and the minimum number of carbon
atoms in the alkyl groups that are needed to form a supra-
molecular sphere. For example, in the pioneering publica-
[b] Dr. M. Peterca, Prof. P. A. Heiney
Department of Physics and Astronomy
University of Pennsylvania, Philadelphia
Pennsylvania, 19104-6396 (USA)
[c] Prof. G. Ungar
¯
tion on the cubic Pm3n lattice it was considered that a mini-
Department of Engineering Materials
University of Sheffield, Mappin Street
Sheffield S1 3JD (UK)
mum of 12 carbon atoms in the alkyl group is needed to
generate the spherical assemblies.[2d] Further, one signature
¯
used to distinguish hollow from filled spheres in the Pm3n
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/chem.200901324.
cubic phase is the relative enhancement of the higher order
Chem. Eur. J. 2009, 15, 8994 – 9004
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8995

V. Percec et al.
X-ray powder diffraction peaks. One cause of such enhance-
ment is the variation of the electron-density at the hollow
center boundary. However, the ratio between the aliphatic
and aromatic domains could also affect the higher order
peak intensities.[11] As hollow spheres and filled spheres
would be targeted for dramatically different functions, it is
essential to be able to definitively distinguish between these
two structures. Both of these questions relating to the funda-
mental structure of the aromatic core are addressed in this
study through the synthesis and structural analysis of seven
dendritic acids, in which the number of methylenic units in
the aliphatic periphery was varied, (Scheme 1). Structural
and retrostructural analysis demonstrated that the aromatic
core contains a constant number of dendrons regardless of
tail length, suggesting that the packing of the aromatic
region is preserved. From this, we were able to calculate a
specific molecular and supramolecular conformation of the
aromatic core. These results can be used to evaluate the
structure of other spherical self-assembling dendrons. As the
dendritic acids chosen in this study self-assemble into filled
supramolecular spherical structures that self-organize into
X-ray powder diffraction peaks. This investigation demon-
strates that spherical supramolecular dendrimers self-assem-
ble with an unexpectedly large range of the number of
carbon atoms in the alkyl groups (six to sixteen), in contrast
to the previous estimate.[2d] In addition, powder diffraction
simulations were used to demonstrate that the enhancement
of higher order XRD amplitudes, (Table 1), is caused by the
faster spatial variation of the electron density in the supra-
molecular dendrimers with a thinner aliphatic shell. The ob-
served increase of the relative intensity of the higher order
X-ray powder diffraction peaks is at least three times small-
er than the increase observed for hollow supramolecular
spheres self-assembled from other benzyl ether den-
drons.[2s,11] This result definitively demonstrates that for the
previously reported hollow supramolecular spheres only a
fraction of the observed enhancement was generated by the
reduction of the number of carbon atoms from the alkyl
groups. Finally, a model for the aromatic core of the supra-
molecular sphere was calculated for the first time.
¯
the Pm3n cubic phase, it is possible to single out the role
Results and Discussion
played by the aliphatic region in the amplification of higher
order X-ray diffraction peaks. In this work we perform a
systematic variation of the aliphatic groups from six to six-
teen carbon atoms to establish the effect of a change in aro-
matic to aliphatic volume ratio on the formation of this
cubic phase and on the relative intensity of the higher order
Synthesis: The seven dendritic acids investigated in this
study were synthesized according to iterative procedures de-
scribed previously (Scheme 1).[2e] Methyl 3,4,5-trihydroxy-
benzoate (1) was etherified with either n-bromobutane (2a),
n-bromohexane (2b), n-bromooctane (2c), n-bromodecane
Scheme 1. Synthesis of the second-generation (3,4,5)2nG2-COOH (7a–7g) series of dendritic acids. Reagents and conditions: a) K2CO3, DMF, 658C; b)
LiAlH4, Et2O; c) SOCl2, CH2Cl2; d) KOH, EtOH, reflux.
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Dendrimers
FULL PAPER
2
¯
Table 1. Structural and retro-structural analysis for the (3,4,5) nG2-COOH (7a–7g) library of dendritic acids self-assembled into Pm3n cubic phase.
[b]
[b]
[b]
[b]
[b]
[b]
[b]
[c]
[d]
[d]
[f]
[f]
[g]
[h]
n[a] A200
A210
A211
A220
A320
A321
A400
Mwt
a908C
[ꢁ]
a1108C
[ꢁ]
1[e]
[gcmꢀ3
m908C m1108C Valiph
Varom
[%]
[a.u.]
[a.u.]
[a.u.]
[a.u.]
[a.u.]
[a.u.]
[a.u.]
]
[%]
6
8
111.4
109.0
100.0
100.0
100.0
100.0
100.0
100.0
89.1
87.7
85.6
84.2
83.4
83.4
11.4
8.3
9.9
21.2
17.7
7.9
26.3
21.4
14.8
7.8
45.0
32.5
23.8
21.7
1341.9 58.1
1594.4 62.2
1846.8 66.1
2099.3 70.5
2351.8 72.7
2604.3 75.5
57.7
61.4
65.2
68.5
71.6
74.6
1.03
1.02
1.00
1.00
0.99
0.99
11.3
11.6
11.8
12.5
12.2
12.3
11.1
11.1
11.3
11.5
11.6
11.9
57.12
42.88
36.09
31.15
27.41
24.47
22.09
63.91
68.85
72.59
75.53
77.91
10 106.9
12 110.1
14 106.7
16 107.2
[i]
9.2
–
[i]
–
–
[i]
[a] Number of C atoms in the alkyl periphery. [b] Ahk: (hkl) relative scaled diffraction peak amplitude, calculated after applying the multiplicity and Lor-
¯
entz corrections. [c] Dendron molecular weight. [d] Experimental lattice parameter of the Pm3n cubic phase calculated at the indicated temperatures.
[e] Experimental density measured at 208C. [f] Number of dendrons per supramolecular cluster at two representative temperatures calculated using m=
A A
9Mtail/Mwt, in which Mtail =molecular weight of one (C2nH2n+1) n-alkyl chain. [h] Aromatic volume fraction calculated from the molecular structure using
arom =1ꢀValiph. [i] X-ray diffraction peak with weak intensity, (i.e. intensity comparable with the background level).
V
(2d), n-bromododecane (2e), n-bromotetradecane (2 f), or
n-bromohexadecane (2g) in DMF at 658C. The resulting
methyl trisalkoxybenzoates (3,4,5)nG1-COOMe (3a–3g)
were reduced with LiAlH4 to form the corresponding benzyl
alcohols (3,4,5)nG1-CH2OH (4a–4g). Chlorination with
SOCl2 furnished benzyl chlorides (3,4,5)nG1-CH2Cl (5a–
5g). Second-generation benzyl ether dendrons (3,4,5)2nG2-
COOMe (6a–6g) were prepared by alkylation of the precur-
sor benzyl chloride with methyl 3,4,5-trihydroxybenzoate in
DMF at 658C. Basic hydrolysis with KOH in EtOH provid-
ed the dendritic acids (3,4,5)2nG2-COOH (7a–7g).
Structural and retrostructural analysis: The structural and
retrostructural analysis of the library of dendritic acids in-
volves solution NMR spectroscopy, differential scanning cal-
orimetry, small- and wide-angle powder X-ray diffraction,
molecular modeling, and reconstruction and simulation[11] of
the three-dimensional electron density distribution.
The differential scanning calorimetric experiments re-
vealed that the dendritic acid with n=4 is the only one from
¯
the series that does not exhibit a thermotropic Pm3n cubic
¯
phase. From n=6 to 16 the Pm3n cubic mesophase is ob-
Figure 1. Second heating and cooling differential scanning calorimetric
(DSC) traces of 7a–7g series of dendritic acids. Transition temperatures
in 8C and phases are indicated; k: unidentified crystal phases, Cub: Pm3n
cubic phase; i: isotropic phase.
served in all supramolecular structures assembled at high
temperature. We note that, upon the increase of n from 6 to
8 and to 10, the isotropization transition temperature shifts
to slightly higher values. As n is further increased, from 10
to 12, 14, and to 16 (Figure 1), the isotropization transition
temperature shifts to slightly lower values. Overall, these
shifts are small, demonstrating that the increase of n has a
relative small impact on the thermodynamics of the self-as-
sembly process. Therefore, the interactions within the aro-
matic region are dominant, even though their volume frac-
¯
tion with temperature. This suggests that the number of den-
drons in the spherical aggregates does not change with the
temperature. In fact for supramolecular spherical dendri-
AHCTUNGTREGmNNNU ers such a change would be highly energetically unfavora-
ble, as it would require a disruption of the dendrimer core
aromatic to aromatic interactions. As the temperature is in-
creased, the diameter of the supramolecular dendrimers de-
creases slightly (Table 1), most probably due to the “melt-
ing” of paraffinic chains that contributes to a better packing
of the aliphatic region. This thermal process changes the
density of the system and therefore can account for the
small variations of m listed in Table 1.
Table 1 also shows that the calculated value of m is also
quite insensitive to the length of the alkyl chain. For exam-
ple, upon the increase of n from 6 to 16, m varies from 11.1
to 11.9 (Table 1), a negligible increase that is well within the
tion is reduced from Varom =42.88% for n=6 to Varom
22.09% for n=16 (Table 1).
=
¯
The temperature dependence of the Pm3n cubic phase
lattice parameter, a, is summarized in Figure 2. For all the
dendritic acids investigated the temperature variation of a is
small. For example, in the case of n=8 the lattice parameter
a decreased with less than 3% in between 20 and 1108C. As
a consequence, the calculated number of dendrons, m listed
in Table 1, that self-assemble to form the supramolecular
¯
dendrimers in the Pm3n cubic phase, exhibits a small varia-
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V. Percec et al.
3
¯
Figure 3. Third power of the Pm3n phase lattice dimension a of 7a–7g
as a function of n at two representative temperatures. The fitted parame-
ters and estimated lattice dimension of the an=0 dendron are shown.
role of the aromatic region due to the presence of a larger
or smaller region of low electron density at the center of the
supramolecular columns or spheres. In the present case,
such low electron density regions are not present, simplify-
ing the task of elucidating the influence of the aliphatic to
aromatic region volume fraction on the X-ray powder dif-
fraction intensity profile.
Figure 2. Temperature dependence of the lattice parameter a of the
Pm3n phase generated from 7a–7g (a) and detailed plots for 7c n=8 (b)
and 7e n=12 (c).
¯
experimental error. Furthermore, the linear dependence of
the third power of the lattice dimension as a function of the
number of methylenic units in the paraffinic chains
(Figure 3) demonstrates that the number of dendrons that
self-assemble into the supramolecular dendrimers of the
¯
In Figure 4 the relative intensities of the Pm3n cubic
phase powder diffraction peaks are indicated for the n=8
and n=12 dendritic acids. The data are scaled to the ampli-
tude of the (210) diffraction peak. Table 1 lists the scaled
diffraction peak amplitudes for the complete library. The
amplitudes listed are calculated from the X-ray powder dif-
fraction peaks area, after applying the appropriate Lorentz
and multiplicity corrections. In general, upon decreasing the
length of the alkyl chains, the relative intensity of the higher
order X-ray diffraction peaks increases.
¯
Pm3n cubic phase must be the same for this library. This
linear dependence allows us to extrapolate the value of the
¯
Pm3n lattice parameter to the case of a dendritic acid with
no alkyl periphery. This value is approximately 37.9 ꢁ
(Figure 3) and it will be used later in the calculation of the
average absolute electron density.
Influence of the aliphatic to aromatic volume ratio: Recent
studies on amphiphilic dendritic architectures have suggest-
ed a correlation between the relative intensity of the higher
order diffraction peaks and the size of the aliphatic region
for both columnar and cubic phases.[11] In these cases, the in-
fluence of the alkyl region thickness on the X-ray powder
diffraction intensity profile could not be separated from the
The reconstructed relative electron density distributions,
calculated by Fourier series reconstruction from the ampli-
tudes listed in Table 1, are presented in volumetric represen-
tation in Figure 4a for n=8 and in Figure 4b for n=12. The
electron density reconstruction highlights the aromatic–ali-
phatic phase segregation,[2d,5,11] as indicated by the electron
¯
density histograms calculated for the Pm3n unit cell and
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Dendrimers
FULL PAPER
upon the decrease of n. There are three possibilities: 1) the
enhancement may be due to a higher degree of positional
order that follows from the reduction of the conformational
freedom in the structures with lower n; 2) the reduction of
the aliphatic region thickness may change the actual value
of the aliphatic region electron density, enhancing the ali-
phatic to aromatic electron density contrast; or 3) the short-
er alkyl chains may cause a faster spatial change of the elec-
tron density triggering the enhancement. The first possibility
is difficult to address. In a later section, it will be demon-
strated that the powder XRD data can be simulated without
the need of introducing the extra parameters required to
take into account such sphere-sphere disorder. Therefore
this possibility cannot be completely excluded, but the XRD
simulations demonstrate that the role played by long-range
correlations is not dominant.
To evaluate the second option, we extrapolate the lattice
parameter to a putative n=0 dendritic acid (Table 2) to cal-
culate the absolute average electron density of the aromatic
and of the aliphatic regions for this library of dendritic
acids. Table 1 demonstrates that, within the experimental
error, the number of dendrons that self-assemble into the
¯
supramolecular dendrimers of the Pm3n cubic phase is inde-
pendent of the temperature or the alkyl chain length. This
indicates that the electron density in the aromatic region of
the n=6 to 16 dendritic acids is the same (Figure 3 and 5,
Table 2). This result is then used to calculate the absolute
electron density of the aliphatic region for all the dendritic
acids listed in Table 2. The calculated average values of the
absolute electron densities of 0.5 eꢁꢀ3 for the aromatic
region and of 0.3ꢁ0.02 eꢁꢀ3 for the aliphatic region are in
the range observed for similar structures already reported.[14]
Similar average electron densities were calculated indepen-
Figure 4. Powder diffraction intensity versus q plots collected at 1108C
for 7c n=8 (a) and 7e n=12 (b). Diffraction peak positions, scaled am-
plitudes (with assigned phases + or ꢀ) and corresponding three-dimen-
sional relative electron density reconstruction shown for one unit cell in
volumetric representation are indicated. For clarity, only the highest elec-
tron density regions are shown.
shown in Figure 5d, e, and f. There is a distinct difference in
the shapes of the high electron density regions for the two
dendritic acids compared in Figure 4: the n=8 self-assem-
bled dendrimers are more distorted from spherical symme-
try than those self-assembled from n=12, 14, or 16 dendritic
acids. These differences, together with the unit cell distribu-
tion of the relative electron density, are illustrated in
Figure 5. Note that the electron density scales, although nor-
malized separately between the minimum and maximum
density for each individual compound, are nevertheless ap-
proximately comparable as the minima and maxima corre-
spond roughly to the aliphatic and aromatic electron density,
respectively. These values are similar for all the dendritic
acids (Table 2). As expected, the fractional volume occupied
by the high electron density regions decreases as the length
of the alkyl chain is increased, (Figure 5d, e, f). This is also
apparent from the blunt density maxima in 7c, that is, the
large white areas in Figure 5a and the sharp cutoff at the
high-density end of the histogram in Figure 5d. The volume
fraction values from Figure 5d, e and f reflect these archi-
tectural changes, and they are calculated based on the chem-
ical structure, as shown in Table 2.
ACHTUNGTRENdNUGN ent of the shape or size of the supramolecular clusters, for
example, 1arom =0.49 eꢁꢀ3 and 1aliph =0.28 eꢁꢀ3 for the n=6
compound, (caption Table 2). Thus, the changes in aliphatic
region electron density are negligible, and we can exclude
the second option.
We are thus lead to the third explanation for the enhance-
ment of the higher order diffraction peak amplitudes. The
calculated dimensions and electron densities for the aromat-
ic and aliphatic regions of the self-assembled supramolecular
dendrimers are presented in Figure 6a. We use the pub-
lished[11] ideal spherical or distorted spherical model to cal-
culate the X-ray powder diffraction patterns. We considered
a two-level model illustrated in Figure 6b, consisting of
spherical or distorted spherical shells of constant electron
densities for the aromatic regions embedded in an aliphatic
continuum. Using the calculated values of average absolute
electron densities and diameters of the aliphatic and aro-
matic region, the powder diffraction simulations in Fig-
ure 6c, d, and e show that, indeed, the faster spatial varia-
tion of the electron density is the primary factor in the en-
hancement of the higher order diffraction peaks amplitudes.
In other words, the decrease of n generates faster spatial
changes that trigger more non-zero Fourier components and
a gradual increase of their weight in the XRD patterns. In a
We now discuss the origin of the enhancement of the
higher order X-ray diffraction peak amplitudes observed
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8999

V. Percec et al.
Figure 5. Reconstructed relative electron density two-dimensional maps of the plane z=0 (a, b, c) and the corresponding histograms calculated from the
¯
three-dimensional volumetric electron density distribution of the Pm3n unit cell (d, e, f) of 7a–7g. In a), b), and c) for clarity the maps are shown for a
2ꢂ2 unit cell; in d), e), and f) the rectangles approximate the volume fraction occupied by the aliphatic (dashed rectangles) and aromatic (dotted rectan-
gles) regions as calculated in Table 2.
simplified way the distribution presented in Figure 6a can
be envisioned as being similar to a series of slits forming a
diffraction grating in optical experiments. In this case it is
easy to understand the correlation between the slit separa-
tion or width and the optical diffraction intensity profile.
The fitted aromatic radii, 11.6–12.7 ꢁ as indicated in Fig-
ure 6b for n=6, 8, and 12, are close to the calculated value
of Rarom =11.65 ꢁ, Table 2. The fitted distortion from the
spherical symmetry of the dendrimers on the faces of the
unit cell varies from 0.89 for n=12 to 0.86 for n=6 and 8,
(a value of 1.00 corresponds to a sphere and a value smaller
than 1.00 corresponds to an oblate spheroid[11]). These
values are in agreement with the reconstructed electron den-
sity maps shown in Figure 5 that highlight an increased devi-
ation from spherical symmetry to an oblate spheroid shape
of the dendrimers on the faces of the unit cell as n is re-
duced.
Table 2. Average electron densities in the aromatic and aliphatic region
of the (3,4,5)2nG2-COOH (7a–7g) library of dendritic acids self-assem-
¯
bled into Pm3n cubic phase.
[b]
[c]
[d]
[e]
[f]
[g]
n[a]
Narom
Rarom
[ꢁ]
1arom
[eꢀꢁꢀ3
Naliph
Raliph
[ꢁ]
1aliph
[eꢀꢁꢀ3
]
[eꢀ]
G
]
[eꢀ]
E
6
8
10
12
14
16
295
295
295
295
295
295
11.65
11.65
11.65
11.65
11.65
11.65
0.51
0.51
0.51
0.51
0.51
0.51
441
585
729
873
1017
1161
18.01
19.26
20.21
21.22
22.19
23.12
0.28
0.29
0.30
0.30
0.29
0.29
[a] Number of methylenic units in the alkyl chain. [b] Narom =number of
electrons in the aromatic region of the dendron calculated using Narom
=
6C ꢂ28+8O ꢂ14+1H ꢂ15=295 eꢀ. [c] Rarom =calculated aromatic region
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Structure of the supramolecular dendrimers: In the previous
sections it was demonstrated that the number of dendrons
that self-assemble into the supramolecular dendrimers of
3
radii using Rarom ¼ 37:9 ꢂ 3=ð32pÞ ¼ 11:65ꢁ, in which 37.9 ꢁ is the es-
timated lattice dimension for the n=0 dendron (Figure 3). [d] 1arom =cal-
culated average electron density of the supramolecular cluster aromatic
region using 1=mNarom(4pR3arom/3), in which m is the average number of
dendrons per supramolecular cluster (Table 1). [e] Naliph =number of elec-
¯
the presented Pm3n cubic phase is independent both of tem-
perature changes and of the size of the aliphatic region. The
reconstructed electron density distributions in Figures 4 and
5 demonstrate that powder X-ray diffraction can yield de-
tailed information about the size and shape of the aromatic
region. Moving the level of the isoelectron surface from low
to high density in the three-dimensional maps in Figure 4
can be thought of as peeling away layer after layer of atoms
from the aliphatic region. The results presented imply that
the aromatic core of the dendrimers on the faces of the unit
trons in the aliphatic region of the dendron calculated using Naliph
=
9[6Cn+1H(2n+1)] [f] Raliph =calculated aliphatic region radii using
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
3
Raliph ¼ a ꢂ 3=ð32pÞ, in which a is the experimental lattice parameter
(Table 1). [g] 1aliph =calculated average electron density of the supra-
molecular cluster aliphatic region using 1=mNaliph(4pR3aliph/3). Remark:
similar average electron densities values were calculated from the unit
cell volume without any spherical shaped approximation; for example for
n=6 the calculated values are 1arom =mcellNaromaꢀ3 =8ꢂ11.09ꢂ295ꢂ
37.9ꢀ3 =0.49 eꢀ ꢁꢀ3
and
1aliph =mcellNarom(a3ꢀaa3rom
)
ꢀ1 =8ꢂ11.1ꢂ441ꢂ
(57.73ꢀ37.93)ꢀ1 =0.28 eꢀ ꢁꢀ3
.
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Dendrimers
FULL PAPER
Figure 6. a) Average electron density (1) for the aromatic and aliphatic region (Table 2) plotted along the face clusters close contact direction, for clarity
the plots are y axis shifted. b) The two-level model of constant electron densities used to simulate the powder XRD intensities. c), d), and e) Measured
and two-level fitted X-ray diffraction plots for 7b, 7c, and 7e, respectively; no background was subtracted from the measured plots.
cell, as indicated in Figure 7b, is slightly larger and more
distorted than the aromatic core of the supramolecular den-
drimers at the corners and the center. Furthermore, the Vor-
¯
onoi polyhedral space filling representation of the Pm3n
unit cell shown in Figure 7b illustrates the slightly larger
volume occupied by the “face” dendrimers in comparison
with the “corner/center” ones.[11]
It is clear that the number of dendrons in a spherical
supramolecular dendrimer must be an integer. The average
¯
number of dendrons in the Pm3n unit cell of the investigat-
ed dendritic acid library is approximately 92 (Table 1,
Figure 7). We combine these observations to conclude that
the “face” supramolecular dendrimer is self-assembled from
twelve dendrons and the “corner/center” one from ten, as
shown in Figure 7b. Density functional theory, together with
1H NMR experiments,[2d] demonstrated the most probable
conformation of the dendron in the supramolecular den-
¯
drimers of the Pm3n cubic phase. In Figure 7a the proposed
molecular model illustrates that the 4-aromatic substitution
is in an orthogonal conformation with respect with the core
phenyl. The two outer 3- and 5-aromatic substituted phenyls
adopt a symmetric tilted conformation with respect with the
core aromatic phenyl. The aromatic core region of the
supramolecular dendrimer self-assembled from twleve den-
drons is shown in Figure 7c in stick-view and in Figure 7d in
Figure 7. Molecular model of the supramolecular sphere self-assembled
from 7a–7g: a) DFT conformation; b) number of dendrons per supra-
molecular dendrimer and per unit cell; c) and e) detail of the aromatic
core region; d) and f) supramolecular dendrimer in space-filling view.
Chem. Eur. J. 2009, 15, 8994 – 9004
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www.chemeurj.org
9001

V. Percec et al.
General methods: 1H NMR (360 MHz) and 13C NMR (90 MHz) spectra
were recorded on a Bruker AC-360 instrument. Thin-layer chromatogra-
phy (TLC) was performed by using precoated TLC plates (silica gel with
F254 indicator; layer thickness, 200 mm; particle size 5–25 mm; pore size
60 ꢁ, SIGMA-Aldrich). MALDI-TOF-MS was performed on the Voyag-
er-DE PRO Biospectrometry Workstation with 2,5-dihydroxybenzoic
acid as a matrix. A Perkin–Elmer Series 10 HPLC equipped with an LC-
100 column oven, Nelson Analytical 900 Series integrator data station,
and two Perkin–Elmer PL gel columns of 5ꢂ102 and 1ꢂ104 ꢁ was used
in both HPLC and GPC mode. THF was used as solvent at the oven tem-
perature of 408C unless otherwise noted. Detection was by UV absorb-
ance at 254 nm. Polystyrene standards (1.02ꢃMw/Mn ꢃ1.13) were used to
construct the calibration curve. Thermal transitions were measured on a
Perkin–Elmer DSC-7. Zn and In were used as calibration standards. In
all cases, the heating and cooling rates were 108C minꢀ1 unless otherwise
noted. First-order transition temperatures were reported as the maxima
and minima of their endothermic and exothermic peaks. Glass transition
temperatures (Tg) were read at the middle of the change in heat capacity.
X-ray diffraction (XRD) measurements were performed using CuKa1 ra-
diation (l=1.54178 ꢁ) from a Bruker-Nonius FR-591 rotating anode X-
ray source equipped with a 0.2ꢂ0.2 mm2 filament operated at 3.4 kW.
The Cu radiation beam was collimated and focused by a single bent
mirror and sagitally focused through a Si (111) monochromator, generat-
ing in a 0.3ꢂ0.4 mm2 spot on a Bruker-AXS Hi-Star multiwire area de-
tector. To minimize attenuation and background scattering, an integral
vacuum was maintained along the length of the flight tube and within the
sample chamber. Samples were held in thin-wall glass capillaries (0.7–
1.0 mm in diameter), mounted in a temperature-controlled oven (temper-
ature precision: ꢁ0.18C, temperature range from ꢀ120 to 2708C). The
distance between the sample and the detector was 12.0 cm for wide
angles diffraction experiments and 54.0 cm for intermediate angles dif-
fraction experiments respectively. XRD peaks position and intensity
analysis was performed using Datasqueeze Software (version 2.01) that
allows background elimination and Gaussian, Lorentzian, Lorentzian
squared, or Voigt peak-shape fitting.
space filling view, while that of the supramolecular dendri-
ACHTUNGTRENNUNGmers self-assembled from ten dendrons in Figure 7e and f.
Conclusions
The systematic investigation of a library of dendritic acids as
a function of the number of methylenic units in the paraffin-
ic groups revealed the structure of the spherical supramolec-
¯
ular dendrimers that self-organize into the Pm3n cubic
phase. This is the cubic phase most often encountered
during the self-assembly of amphiphilic dendrons or den-
drimers. The combination of electron density reconstruction,
experimental density and molecular modeling demonstrated
that there are two types of supramolecular dendrimers in
this phase, as already reported for other libraries.[2s,11] For
¯
the presented library it was shown that for the Pm3n cubic
phases the corner spherical supramolecular dendrimers self-
assembled from ten dendrons and the face distorted spheri-
cal dendrimers are self-assembled from twelve dendrons.
The preferred structure of the dendron of the supramolec-
ular dendrimer was predicted by DFT methods and provides
insight into the molecular arrangement of the aromatic-core
of spherical dendrimers. Moreover, the present study re-
vealed the extent to which the change in spatial variation in
electron density, generated by the variation of the aromatic
to aliphatic volume fraction, can increase the relative inten-
¯
sity of the higher order X-ray diffraction peaks of the Pm3n
cubic phase. In relative scaled amplitudes the (400) peak in-
tensity was shown here to increase to at most 45% of the
(210) peak. For hollow supramolecular dendrimers the value
was reported to range from 100% to 170%, for dendrons
with similar aliphatic to aromatic volume ratios.[11] A com-
parison of these numbers demonstrates that, without a
hollow center, the relative amplitudes of the high order dif-
fraction peaks are at least three times less intense, suggest-
ing that a definitive assignment to hollow phases can be
made in cases of such large amplifications. Finally, for the
first time, this study provides the average absolute electron
densities of the aliphatic and aromatic regions of amphiphil-
ic dendrons, namely, 0.5 eꢁꢀ3 and 0.3ꢁ0.02 eꢁꢀ3 respec-
tively. These values are critical for the accurate modeling of
dendrimer lattices, a key step in the retrostructural analysis
of self-assembling dendrons.
Computational techniques: All calculations were performed using the
Spartanꢃ06 Quantum Mechanics Program (PC/X86).[16] To obtain the pre-
dicted self-assembled conformation of 7a–7g, a molecular mechanics
conformation distribution for a test compound bearing shortened alkyl
tails, (3,4,5)22G2-COOH, was generated at the MMFF level. Of the 1728
benzyl linkage conformers examined the 100 hundred unique conforma-
tions generated were inspected for relative energy and symmetry. Full ge-
ometry optimizations of the lowest energy structures and those bearing
appropriate symmetry for spherical self-assembly were performed at the
B3LYP/6-31G* level. The optimized geometries were subjected to single-
point energy and frequency calculations at the B3LYP/6-31G* level, to
confirm that there were no imaginary modes and that the structures were
true local minima and not merely saddle points.
Synthesis: The detailed synthesis and characterization of the second-gen-
eration 7a–7g series of dendritic acids can be found in the Supporting In-
formation.
Acknowledgements
Experimental Section
Financial support by the National Science Foundation (DMR-0548559
and DMR-0520020) and the P. Roy Vagelos Chair at University of Penn-
sylvania is gratefully acknowledged. B.M.R. gratefully acknowledge the
financial support from American Chemical Society—Division of Organic
Chemistry Graduate Research Fellowship, sponsored by Roche, Inc.
Materials: Al2O3 (activated, basic, Brockmann I, standard grade, ~150
mesh, 58 ꢁ) and silica gel (ICN EcoChrom Silitech 23–63 D 60 ꢁ) was
used as received. Et2O (Fisher, A.C.S. reagent grade) was refluxed over
sodium benzophenone ketyl and distilled freshly before use. LiAlH4
(95+ %), SOCl2 (99+ %), methyl 3,4,5-trihydroxybenzoate (98%), n-
bromobutane, n-bromohexane, n-bromooctane, n-bromodecane, n-bro-
mododecane, n-bromotetradecane, and n-bromohexadecane (all from Al-
drich) were used as received. Anhydrous K2CO3, KOH, EtOH, DMF,
and CH2Cl2 (all A.C.S. reagent grade, from Fisher) were used as re-
ceived.
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Received: May 18, 2009
Published online: August 26, 2009
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