Shapes of dendrimers from rotational-echo double-resonance NMR

Article abstract of DOI:10.1021/ja962285e

The solid-state shape, size, and intermolecular packing of a fifth-generation dendritic macromolecule were determined by a combination of site-specific stable-isotope-labeling, rotational-echo double-resonance (REDOR) NMR and distance-constrained molecula

Full text of DOI:10.1021/ja962285e

J. Am. Chem. Soc. 1997, 119, 53-58
53
Shapes of Dendrimers from Rotational-Echo Double-Resonance
NMR
Karen L. Wooley,* Christopher A. Klug,† Kenzabu Tasaki,‡ and Jacob Schaefer
Contribution from the Department of Chemistry, Washington UniVersity,
St. Louis, Missouri 63130
ReceiVed July 5, 1996X
Abstract: The solid-state shape, size, and intermolecular packing of a fifth-generation dendritic macromolecule were
determined by a combination of site-specific stable-isotope-labeling, rotational-echo double-resonance (REDOR)
NMR and distance-constrained molecular dynamics simulations. REDOR experiments measured dipolar couplings
between 13C atoms located near the chain ends and an 19F label placed at the core of benzyl ether dendrimers
(generations 1-5) based on 3,5-dihydroxybenzyl alcohol as the monomeric repeat unit. Intramolecular 13C-19F
coupling was distinguished from intermolecular coupling by dilution with nonlabeled dendrimer. The average
intramolecular 13C-19F distances for generations 3-5 were each approximately 12 Å, which indicates inward-
folding of chain ends with increasing generation number. The average intermolecular 13C-19F dipolar coupling
decreased with increasing generation number, consistent with decreased interpenetration for larger dendrimers. The
measured intra- and intermolecular distances for the fifth-generation dendrimer were used as constraints on energy
minimizations and molecular dynamics simulations, which resulted in visualizations of the dendrimer packing and
an estimate of density in the solid state.
Introduction
of porphyrins by dendrimers to generate synthetic mimics of
electron transfer proteins. The recent demonstration of efficient
coupling between chain ends and the core for layered electrolu-
minescent dendrimers is consistent with the encapsulation of
the core.12 Meijer’s dendritic box13 has illustrated the feasibility
of temporary and selective encapsulation of small molecules
within the core of dendrimers. Poly(amidoamine) dendrimers
are being explored for various biological applications, including
their ability to act as agents that complex and transport DNA
into eukaryotic cells.14 Applications for dendritic structures as
catalysts, conducting polymers, lubricants, and coatings attempt
to take advantage of the large number of chain ends or the lack
of chain entanglements.15,16
The composition of a dendrimer is the same as that of a linear
polymer with a repeating side chain that is equivalent to the
functional group of the dendrimer chain end. Therefore, the
extraordinary properties that dendrimers exhibit must result from
structural constraints imposed by the branching and not from
the number of chain end functional groups. The conformation,
shape, and packing of dendrimers are issues that have been
debated for several years. A number of theoretical approaches
have been proposed to describe the dendritic structure, in
particular, the location of the chain ends. A self-consistent
mean-field analysis by de Gennes and Hervet17 placed chain
ends at the periphery of the dendrimer and found a density
maximum on the surface. In contrast, the computer simulation
Polymers whose main chains branch at each repeat unit have
been given the name dendritic macromolecules1-4 because the
chain backbone has many ends and resembles the branches of
a tree. This structural architecture of dendritic macromolecules
imparts highly interesting material properties. Light-scattering
measurements5 have shown that dendritic poly(benzyl ether)s
are more compact than linear random-coil polymers of equiva-
lent molecular weight. In solution, dendrimers have unusually
low intrinsic viscosities6 that decrease with increasing molecular
weight. These observations lead to the conclusions that dendritic
macromolecules possess globular shapes and lack intermolecular
entanglements. In addition, solvatochromic studies of poly-
(benzyl ether) dendrimers,7 involving the placement of a solvent-
sensitive chromophoric probe at the focal point, have revealed
that a unique microenvironment exists near the core. This result
suggests that the center of the dendrimer is engulfed by the
branching repeat units and chain ends.
The employment of this interior site for catalysis8 or transport
has been suggested in the design of protein-like structures.
Several reports have appeared,9-11 detailing the encapsulation
* Corresponding author.
† Present Address: Department of Chemical Engineering, Stanford
University, Stanford, CA 94305.
‡ Present Address: Mitsubishi Chemical America, Inc., San Jose, CA
95134.
X Abstract published in AdVance ACS Abstracts, December 1, 1996.
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A.; Sanford, E. M. Angew. Chem. 1994, 106, 1821; Angew. Chem., Int.
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1990, 102, 119; Angew. Chem., Int. Ed. Engl. 1990, 29, 138.
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S0002-7863(96)02285-8 CCC: $14.00 © 1997 American Chemical Society

54 J. Am. Chem. Soc., Vol. 119, No. 1, 1997
Wooley et al.
of kinetic starburst growth by Lescanec and Muthukumar18
allowed for inward-folding of the chain ends, which resulted
in a density maximum between the assumed dense core and
the periphery. Monte Carlo calculations performed by Mans-
field and Klushin19 found the chain ends to be distributed
throughout the structure and revealed a density maximum
midway between the center of mass and the periphery. Mo-
lecular dynamics simulations by Naylor et al.20 predicted open
structures and a decreasing aspect ratio (more spherical shape)
with increasing generation number. Molecular dynamics simu-
lations which allowed varying solvent quality recently reported
by Murat and Grest21 found significant inward-folding of chain
end groups, a high-density region near the central core for all
of the solvents, and increasing overall dendrimer density with
decreasing solvent quality.
Solution-state characterizations of dendrimers5-7 generally
support the presence of a globular shape with the chain ends
accessible to the surface. However, details of the precise shape
and chain end locations remain uncertain. Melt-viscosity
measurements of dendrimers22 have shown that the increase in
viscosity with increasing molecular weight is less for dendrimers
than for the corresponding linear polymers. Much less solid-
state characterization has been performed. Liquid crystalline
dendrimers23 reorient faster and at lower electric and magnetic
fields than their linear counterparts. Atomic force microscopy24
has shown that thin films of dendritic materials are easily
machined at lower tip forces than are films of linear polymers.
Although these results suggest a general lack of dendrimer
entanglement, quantitative data describing the size, shape, and
packing of dendrimers are still needed to understand fully their
structure and to aid in the design of dendrimers for specific
applications.
In this study, rotational-echo double-resonance (REDOR)
solid-state nuclear magnetic resonance (NMR) spectroscopy25
was used as a direct-measurement technique to characterize a
series of stable-isotope-labeled poly(benzyl ether) dendrimers.
REDOR provides a direct measure of heteronuclear dipolar
coupling between isolated pairs of labeled nuclei. The dipolar
interaction between two spins depends on the inverse cube of
the internuclear distance, on the orientation of the internuclear
vector with respect to the applied static magnetic field, and on
the magnetic moments of the two nuclei. That is, the dipolar
coupling depends both on space and spin coordinates. Magic
angle sample spinning suppresses the dipolar interaction by
averaging over the space coordinates. This averaging process
can be defeated and the dipolar coupling partially restored by
a competing averaging using rotor-synchronized radio-frequency
pulses, which operate exclusively on the spin coordinates. The
space- and spin-averaging processes are both coherent and are
of comparable frequency; therefore, their combination produces
destructive interference of averaging leading to recoupling. The
extent of the interference is a measure of the dipolar coupling
and hence the distance between nuclei. Measurement of
carbon-fluorine internuclear distances of 12 Å are possible.26,27
The dephasing of magnetization in REDOR arises from a local
dipolar field gradient and involves no polarization transfer.
The location of the chain ends and the extent of interpenetra-
tion of the dendrimers were determined by REDOR NMR
experiments, by the measurement of dipolar couplings between
13C labels near the chain ends of poly(benzyl ether) dendrimers
and an 19F label placed at the focal point (core). The location
and mobility of the chain ends are expected to be affected by
the nature of the chain ends, the nature of the monomeric repeat
units, the rigidity of the structure, the multiplicity of the branch
sites, and the environment surrounding the dendrimer. There-
fore, to evaluate a dendritic structure in a homogeneous
environment, with compatibility between the chain ends and
monomeric repeat units, benzyl-terminated poly(benzyl ether)
dendrimers (generations 1-5, molecular weights 416-6814
amu) were examined as pure solids. For the fifth-generation
dendrimer, which is large enough to possess the unique
properties that are typical for dendrimers after adoption of a
globular shape,6,7 the REDOR NMR data were combined with
molecular modeling to generate illustrations and measurements
of the overall size, shape, density profile, and packing in the
solid state. This is the first report of the use of experimental
constraints on molecular modeling for the prediction of dendritic
structure.
Experimental Section
Synthesis. The labeled dendrimers were prepared by literature
procedure5 with the 13C label incorporated near the chain ends in the
first step of dendrimer growth using 13C-methylene-carbon-labeled
benzyl bromide. This label was prepared by reduction of [13C]-benzoic
acid (Isotec, Inc., Miamisburg, Ohio) with lithium aluminum hydride,
followed by reaction of the resulting 13C-labeled benzyl alcohol with
carbon tetrabromide and triphenylphosphine. The 19F label was
incorporated in the last step of the synthesis by reaction of 4-fluo-
rophenol with the dendritic benzylic bromide, in the presence of
potassium carbonate and 18-crown-6. Purifications were achieved by
flash chromatography with elution initially by methylene chloride and
finally by 10% diethyl ether in methylene chloride. The composition
and purity of the products were confirmed by IR, 1H NMR, 13C NMR,
19F NMR, and gel permeation chromatography.
REDOR Instrumentation and Experiments. Powdered dendrimer
(100 mg) was packed into high-performance 7.5 mm outside-diameter
zirconia rotors fitted with Kel-F spacers and drive cap. Cross-
polarization, magic angle spinning spectra were obtained at 4.7 T and
room temperature using a four-channel probe28 with a single 9 mm
diameter solenoidal coil which permits 1H, 19F, 13C, and 15N detection
or dephasing at 200, 188, 50, and 20 MHz, respectively. Fluorine
incorporation into dendrimers was measured by direct 19F NMR
detection and calibrated by comparisons to spectra of materials of
known fluorine content.29 REDOR experiments began after a 2.0 ms
matched spin-lock cross-polarization transfer from protons to carbons
at 50 kHz, followed by proton decoupling at 100 kHz. The sequence
repetition time for most experiments was 4 s. The magic angle stators
were obtained from Chemagnetics (Fort Collins, CO). A controlled
spinning speed of 5000 Hz was used for all REDOR experiments.
The 13C rotational echoes that form each rotor period following a
proton to carbon cross-polarization transfer were prevented from
reaching full intensity by insertion of two 19F pulses per rotor cycle,
one in the middle of the rotor period and the other at the completion
of the rotor period. The 19F pulses were applied using an XY8 phase-
cycling scheme to suppress offset effects and compensate for pulse
imperfections.30 A single 13C pulse replaced the 19F pulse in the middle
(18) Lescanec, R. L.; Muthukumar, M. Macromolecules 1990, 23, 2280.
(19) Mansfield, M. L.; Klushin, L. I. Macromolecules 1993, 26, 4262.
(20) Naylor, A. M.; Goddard, W. A., III; Kiefer, G. E.; Tomalia, D. A.
J. Am. Chem. Soc. 1989, 111, 2339.
(21) Murat, M.; Grest, G. S. Macromolecules 1996, 29, 1278.
(22) Hawker, C. J.; Farrington, P. J.; Mackay, M. E.; Wooley, K. L.;
Fre´chet, J. M. J. J. Am. Chem. Soc. 1995, 117, 4409.
(23) Percec, V.; Chu, P.; Ungar, G.; Zhou, J. J. Am. Chem. Soc. 1995,
117, 11441.
(27) McDowell, L. M.; Lee, M.; McKay, R. A.; Anderson, K. S.;
Schaefer, J. Biochemistry 1996, 35, 3328.
(24) Kowalewski, T.; Fields, H. R.; Wooley, K. L. Unpublished results.
(25) Gullion, T.; Schaefer, J. AdV. Magn. Reson. 1989, 13, 57.
(26) Holl, S. M.; Marshall, G. R.; Beusen, D. D.; Kociolek, K.; Redlinski,
A. S.; Leplawy, M. T.; McKay, R. A.; Vega, S.; Schaefer, J. J. Am. Chem.
Soc. 1992, 114, 4830.
(28) Holl, S. M.; McKay, R. A.; Gullion, T.; Schaefer, J. J. Magn. Reson.
1990, 89, 620.
(29) Pan, Y. Solid State Nucl Magn. Reson. 1995, 5, 263.
(30) Gullion, T. G.; Baker, D. B.; Conradi, M. S. J. Magn. Reson. 1990,
89, 479.

REDOR NMR of Dendrimers
J. Am. Chem. Soc., Vol. 119, No. 1, 1997 55
Figure 1. REDOR dephasing by 19F of the methylene-carbon line of undiluted, crystalline, 13C-labeled G1 (left) and a homogeneous mixture of
one part of 13C-labeled G1 and nine parts of polystyrene (right). The calculated dephasings for a single 13C-19F pair (next-nearest neighbor effects
not included) with internuclear separations of either 3.2 or 5.0 Å are shown on the left and those for a Gaussian distribution (5-15 Å) centered at
8.5 Å are on the right. The chemical shifts for the two labeled methylene carbons of crystalline G1 are resolved (insert, left). Magic angle spinning
was at 5 kHz.
of the evolution period to refocus 13C chemical shifts. When many
cocrystallize G1 with nonfluorinated versions of the molecule
13C spins are present, the use of only one 13C pulse minimizes effects
were unsuccessful. However, dilution of G1 in polystyrene
of homonuclear coupling.31 The REDOR difference (the difference
(freeze dried from a benzene solution) eliminates the fast
dephasing associated with G1 aggregates and therefore proves
between a 13C NMR spectrum, S, obtained under these conditions and
one obtained with no 19F pulses, S0) has a strong dependence on the
that the mixing is microscopically homogeneous (Figure 1,
dipolar coupling and hence the inverse cube of the internuclear distance.
right). On the basis of observed distribution of isotropic
Modeling. For molecular dynamics simulations, Newton’s equations
of motion were integrated numerically using the Verlet algorithm32 with
a time step of 1 fs and constant NVE. The united-atom model together
chemical shifts and 13C-19F dipolar couplings (Figure 1, right),
G1 adopts a wide range of local conformations in polystyrene.
The broad 70 ppm methylene-carbon line for undiluted,
amorphous 13C-labeled G3 (Figure 2) indicates a distribution
of local conformations for this higher-generation dendrimer as
well. The increased size of G3 means that at least some of the
labeled methylene carbons should be farther removed from the
fluorine label than the corresponding methylene carbons of
labeled G1. Nevertheless, the S/So for G3 is 0.75 after 32 rotor
cycles (Figure 2, top and middle; Figure 3, bottom), which
represents more dephasing than that observed for diluted G1
(Figure 1, right). This result suggests the occurrence of either
inward-folding of the chain ends or intermolecular 13C-19F
dipolar coupling.
Self-dilution of 13C- and 19F-labeled dendrimers by an excess
of unlabeled dendrimers is practical for noncrystalline G3, G4,
and G5. Dephasing for the diluted labeled dendrimers arises
exclusively from intramolecular dipolar coupling, while dephas-
ing for the undiluted samples is due to a combination of
intramolecular and intermolecular dipolar couplings. Evaluation
of the REDOR data of only the self-diluted samples, shows that
the intramolecular dephasings by 19F for 13C-labeled G3, G4,
and G5 are comparable and are slightly less than 20% after 32
ms (160 rotor cycles, Figure 3). Some insights into the nature
of the distribution are possible from the dependence of S/So on
the number of rotor cycles. For example, a structure for G4
that has a distribution of the 16 13C-19F distances given by
two at 4.4 Å, two less than 10 Å, and the rest over 20 Å, would
result in 13% dephasing by 19F in less than 40 rotor cycles,
25% dephasing in 120 rotor cycles, and little further dephasing
between 120 and 160 rotor cycles.34 The observed values are
5% in 40 rotor cycles, 10% in 120 rotor cycles, and no indication
with the CHARMM potential of Quanta 4.0 (Biosym Molecular
Simulation, San Diego, CA) were employed for all calculations.
Electrostatic energies were treated with a distance-dependent dielectric
constant of 4 and truncated at a cutoff distance of 8 Å. The harmonic
potential k(r - ro)2 was used in the constraint minimizations and
molecular dynamics simulations; k is the force constant, r is the
instantaneous distance as a function of time, and ro is the constrained
distance. Computations were performed using a Silicon Graphics Power
Challenge. A 20 ps simulation for a seven-molecule G5 cluster with
3577 atoms required 5 h of CPU time on an R8000 processor.
Results and Discussion
Rotational-Echo Double-Resonance Applied to Dendrim-
ers. Packing in the crystal for the first-generation structure G1
results in much shorter inter- than intramolecular distances
between 19F and the two labeled methylene carbons as deter-
mined by X-ray crystallography.33 The shortest intermolecular
distances are 3.2 and 5.0 Å, and the shortest intramolecular
distances are 10.0 and 12.1 Å. Thus, essentially full dephasing
by 19F is observed in less than about 10 ms for both kinds of
chemically distinct carbons in labeled G1 (Figure 1, left). The
72 ppm line is completely dephased after 8 rotor cycles,
corresponding to a 13C-19F distance of about 3 Å. The
dephasing of the 69 ppm line is slower, and the initial rate
suggests an average distance of the order of 5 Å. Attempts to
(31) Gullion, T.; Vega, S. Chem. Phys. Lett. 1992, 194, 423.
(32) Allen, N. P.; Tildesley, D. J. Computer Simulation of Liquids;
Clarendon Press: Oxford, 1989.
(33) The crystal structure was determined by Alicia Beatty of the X-ray
Crystallography Facility, Department of Chemistry, Washington University,
St. Louis, MO.

56 J. Am. Chem. Soc., Vol. 119, No. 1, 1997
Wooley et al.
Figure 4. REDOR dephasing by 19F of the 13C-labeled, methylene-
carbon line of a homogeneous mixture of one part each of 13C-labeled
G3 (closed circles), G4 (open circles), and G5 (closed squares) and
nine parts of either the corresponding 13C- and 19F-unlabeled dendrimer
(top) or polystyrene (bottom). Solid and dotted lines show the calculated
dephasings for single 13C-19F pairs.
Figure 2. REDOR full-echo (So) and dephased (S) 13C NMR spectra
of undiluted, amorphous 13C-labeled G3 with magic angle spinning at
5 kHz. The spectra are dominated by the signal at 70 ppm from the
eight 13C-labeled methylene carbons per molecule. Aromatic-carbon
signals from natural-abundance 13C appear between 110 and 160 ppm.
Spinning sidebands are designated “ssb.”
average is only consistent with increasing inward-folding of the
chain ends with increasing generation number.
The decrease of the intermolecular contributions to dephasing
with increasing generation number (comparison of open and
closed circles, Figure 3) supports a transition from an open
structure with significant intermolecular interpenetration of
dendrimer chain ends (contributing to the measurements of more
rapid dephasing through shorter intermolecular 13C-19F dipolar
couplings) for G3 and G4 to a more closed structure with the
intradendrimer chain ends filling more of the space around the
core for G5.
The more rapid dephasing observed for the polystyrene
diluted materials, in comparison to that of the self-diluted
samples (Figure 4), suggests a more collapsed structure for the
dendrimers in polystyrene. About a 10% decrease in the average
13C-19F distance is observed for G3, G4 and G5. This
shrinkage is most likely due to incompatibility between the
benzyl ether dendrimers and polystyrene. The theoretical
model21 of dendrimers in solution predicts an increase in density
with decreasing solvent quality.
The homogeneous T2 for the full-echo signal of the labeled
methylene carbons of G3 is 8.3 ms, increasing to 14.2 ms for
G5 (data not shown). Echo-train lifetimes of the order of 10
ms for methylene carbons indicate the absence of large-
amplitude motions in the low-kHz regime.35 Neither slow cross-
polarization transfer rates nor unusually fast spin-lattice relax-
ation rates were observed, indicating the absence of large-
amplitude molecular motions even though the room temperature
NMR measurements were close to the glass-transition temper-
atures for G3, G4, and G5 of 32, 39 and 42 °C, respectively.
Molecular Modeling Constrained by REDOR Distances.
A computer-generated G5 structure was relaxed by a 20 ps
molecular dynamics simulation at 1000 K, followed by 100 and
200 steps of steepest-descent and conjugate-gradient energy
minimizations for quenching, respectively. The energy mini-
mizations were performed such that all 13C-19F distances that
were initially greater than 20 Å were constrained to distances
of less than 18 Å using a force constant of 50 kcal/mol. The
Figure 3. REDOR dephasing by 19F of the methylene-carbon line of
undiluted, 13C-labeled G3, G4, and G5 (open circles) and of a
homogeneous mixture of one part each of 13C-labeled G3, G4, and G5
and nine parts of the corresponding 13C- and 19F-unlabeled dendrimer
(closed circles). Magic angle spinning was at 5 kHz; 160 rotor cycles
of dipolar evolution correspond to 32 ms of dephasing.
of a plateau (Figure 3, middle panel). This kind of structure is
therefore not a likely candidate to describe G4. Instead, the
uniform, monotonic decrease of S/So as a function of the number
of rotor cycles of dephasing suggests a modest distribution of
13C-19F distances with an average of about 12 Å (Figure 4,
top). The fact that G3, G4, and G5 all have the same 12 Å
(34) Tong, G.; Pan, Y.; Afeworki, M.; Poliks, M. D.; Schaefer, J.
Macromolecules 1995, 28, 1719.
(35) Lee, P. L.; Kowalewski, T.; Poliks, M. D.; Schaefer, J. Macromol-
ecules 1995, 28, 2476.

REDOR NMR of Dendrimers
J. Am. Chem. Soc., Vol. 119, No. 1, 1997 57
Figure 5. Space-filling rendition of a structure for an isolated G5
dendrimer obtained by a distance-constrained energy minimization.
Color code: black, carbon; yellow, 13C-labeled carbon; red, oxygen;
blue, hydrogen; cerise, fluorine.
Figure 6. Space-filling rendition of a structure for a seven-molecule
G5 cluster obtained by a 20 ps, distance-constrained, molecular
dynamics simulation. The central G5 is shown in red and its neighbors
are shown in yellow. A slice through the approximate center of the
cluster has been made to reveal the fluorine (in blue green) of the central
G5. Most of the atoms of the central G5 are either internal with no
contact with a neighboring molecule or are on an interface with only
surface contact, but a few are mixed with the atoms of a partially
interpenetrating neighboring molecule.
distances to the 32 labeled methylene carbons in the resulting
structure (Figure 5) range from 8 to 18 Å, consistent with the
observed intramolecular contributions to REDOR dephasing.
The fluorine is encapsulated in this simulated quenched
structure, which has an ellipsoidal shape and overall dimensions
of 31 × 37 × 41 Å.
Intermolecular packing was explored by surrounding the G5
structure of Figure 5 by six neighboring, identical G5 structures
in a face-centered cubic (fcc) array to make a seven-molecule
cluster. A 500-step energy minimization for the entire cluster
preceded a 20-ps molecular dynamics simulation performed in
the gas phase at 300 K. Intra- and intermolecular constraints
were imposed based on the REDOR distance results of Figures
3 and 4. These 13C-19F distances were imposed both during
the energy minimization and the molecular dynamics simulation.
The intramolecular constraints were unchanged from the isolated
molecule calculation. For the intermolecular constraints, each
labeled carbon of the central G5 was required to be within 13
Å of at least one of the surrounding six fluorines using a force
constant of 50 kcal/mol. This requirement was designed to
produce intermolecular contributions to REDOR dephasing that
would be about equal to intramolecular contributions. Because
the fluorine of G5 is not in the center of the molecule (see insert,
Figure 2), requiring intermolecular 13C dephasing by the
neighbor with the most distant fluorine was not practical. For
this fluorine, five of the labeled methylene carbons of the central
G5 were required to be within 12 Å, which guaranteed
significant intermolecular REDOR dephasing by the most
remote fluorine even though the majority of 13C labels of the
central G5 might be too distant to be affected. The intermo-
lecular constraints ensured that the seven-member G5 cluster
would stay together throughout the 20 ps molecular dynamics
simulation. Other reasonable starting conditions and REDOR-
consistent constraints can be imagined.
Figure 7. Radial number densities (atoms Å-3) for the isolated G5
dendrimer of Figure 5 (open circles) and for the seven-molecule G5
cluster of Figure 6 (closed circles). The radial number densities were
obtained by counting the number of C(Hn) and O atoms of the dendrimer
repeat unit in the volume between spherical shells separated by 1.5 Å
in radius as a function of increasing radius. Spheres were centered at
the center of mass of the total structure. Equivalent density distributions
for the G5 cluster were obtained from single snapshots at 10, 17.5,
and 20.0 ps of the distance-constrained molecular dynamics simulation,
as well as from 2.5 ps, 50-point averages between 10 and 20 ps. The
dashed line indicates a density of 1 g/cc, assuming an effective atomic
mass of 13.4 atomic mass units.
are 13 Å or less from fluorines on other molecules. The central
molecule of the G5 cluster therefore is qualitatively consistent
with all the intra- and intermolecular constraints derived from
the G5 REDOR dephasing results of Figure 3.
The results of the simulation are shown in Figure 6. Twenty-
six of the thirty-two 13C labels of the central G5 are between 7
and 17 Å from the fluorine of the central molecule; three are
more distant and three are less distant. The shape of the central
G5 is the same as that resulting from the isolated-molecule
energy minimization, with the 19F label at the core totally
encapsulated. All 32 13C labels of the central G5 are within 17
Å of at least one fluorine on another molecule; most have two
or three fluorines within this range, and fifteen of the 13C labels
Density Profiles for Dendrimers in the Solid State. The
radial density profiles for the G5 dendrimer and the seven-
molecule dendrimer cluster are plotted in Figure 7. The radial
number densities (number of atoms/Å3) were obtained by
counting the number of C(Hn) and O atoms of the dendrimer
repeat unit in the volume between spherical shells differing in
radius by 1.5 Å as a function of increasing radius. The origin
of each shell was the center of mass of the total structure.
Ignoring statistical scatter for a radius of less than 5 Å, we see

58 J. Am. Chem. Soc., Vol. 119, No. 1, 1997
Wooley et al.
that the radial density for the single G5 dendrimer decreases
monotonically with increasing distance from the center of mass,
consistent with all of the theoretical predictions cited earlier,18-21
except that of de Gennes and Hervet.17 However, a comparison
of the radial density of a single G5 molecule and the G5 cluster
emphasizes that this decrease in density for a single G5 is largely
the result of the sampling for a molecule of finite size. The
radial density for the G5 cluster, which is everywhere greater
than that of the isolated G5 (Figure 7), is approximately constant
and close to 1 g/cc throughout the center of the packed structure
(radius between 8 and 18 Å). The density decreases near the
periphery because the population of chain ends has been reduced
by inward-folding. In solution, this peripheral void space is
filled with solvent and, in the solid, by chain ends of other
dendrimers.
A density of 1.2 g/cc was measured for an annealed sample
of G5. We attribute the approximately 20% difference in
density between experiment and simulation mostly to the fact
that the simulations were limited to only seven molecules. In
addition, the REDOR distances were determined for powdered
samples which generally have 5% lower densities than the
corresponding annealed glasses. REDOR measurements on
annealed dendrimers are in progress. It is also possible that
the fcc packing model for the G5 cluster and the limited duration
of the simulations underestimated the true packing density.
size, shape, and packing results generated from the REDOR
NMR data combined with molecular modeling for the G5 benzyl
ether dendrimer are valid for a flexible and compositionally-
compatible structure. Other types of dendrimers, particularly
those displaying phase separation or containing rigid monomeric
repeat units, could behave differently. We believe that the
details of the long-range potentials used in the calculations are
not crucial because of the realistic constraints imposed by the
long-range experimental distances. The modeling provides
estimates of the fraction of atoms in internal, surface, and
entangled branches (see Figure 6), and we anticipate that these
insights will be important for guiding experiments in drug
delivery, DNA binding, and other practical applications of
dendrimers. Work in progress in our laboratory includes
correlating the microscopic structure of dendrimers obtained
from distance-constrained modeling with macroscopic measure-
ments of size, density, and mechanical properties by atomic force
microscopy. Future work will involve 13C labeling at specific
internal, monomer sites within the dendrimer to obtain additional
distances for more closely defined conformational constraints.
Acknowledgment. Financial support for this work by
National Science Foundation grants DMR-9458025 (K.L.W.),
DMR-9015864 (J.S.), and MCB-9316161 (J.S.) is gratefully
acknowledged. The authors thank Professor Robert Yaris
(Washington University) for helpful discussions and Christopher
G. Clark, Jr., (Washington University) for assistance with density
measurements and analysis.
Conclusions
The proposed molecular model that is based on these REDOR
results is representative of a large number of possible conforma-
tions, which leads to the definition of an average structure. The
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