Supramolecular assemblies with symmetrical octahedral structures - Synthesis, characterization, and electrochemical properties

Article abstract of DOI:10.1002/ejic.201200923

Functional nanosized cage complexes with an octahedral framework have been synthesized by the facile self-assembly reactions of six 90° Pd ^II-containing compounds {[Pd(dppf)(OTf)₂] or [Pd(PPh ₃)(OTf)₂], dppf = 1

Full text of DOI:10.1002/ejic.201200923

FULL PAPER
DOI:10.1002/ejic.201200923
Supramolecular Assemblies with Symmetrical Octahedral
Structures – Synthesis, Characterization, and
Electrochemical Properties
Fei Jiang,[a,b] Jun Wang,[a] Jianzhong Li,[a] Ning Wang,[a]
Xichang Bao,[a] Ting Wang,[a] Ying Yang,[a] Zhenggang Lan,*[a] and
Renqiang Yang*[a]
Keywords: Self-assembly / Nanostructures / Cage compounds / Electrochemistry / Palladium / N ligands
Functional nanosized cage complexes with an octahedral
framework have been synthesized by the facile self-assembly
reactions of six 90° PdII-containing compounds {[Pd(dppf)-
(OTf)2] or [Pd(PPh3)(OTf)2], dppf = 1,1Ј-bis(diphenylphos-
phanyl)ferrocene, OTf = trifluoromethylsulfonate} and four
120° functional tritopic ligands [2,4,6-tri(4-pyridyl)-1,3,5-tri-
azine] in acetone. Diffusion-ordered NMR spectroscopy
(DOSY) and AFM images clarify the formation of 3–4 nm
nanoparticles. These highly symmetrical cage complexes are
discrete, face-directed, functional nanoparticles with sym-
metrical octahedral structures. The self-assembled functional
cage complexes exhibit interesting electrochemical activi-
ties, and thus will potentially be useful in the catalysis of re-
dox reactions, the encapsulation of sizeable guest molecules
and the control of organic synthetic reactions.
teins. We have presented an instantaneous synthetic route
for the preparation of thiophene-coated functional
nanospheres that show interesting electrochemical proper-
ties.[5] These initial studies have demonstrated that the intro-
duction of functional groups to individual building blocks
results in new multifunctionality and controllable structures
on the basis of the original topology of the assembling poly-
hedral molecules. These thermodynamically and kinetically
stable transition metal complexes can exhibit thermo-,
chemo- and mechanoresponses, as well as light-emitting
properties.[6–8]
Introduction
Multifunctional polymers[1] and dendrimers[2] have re-
ceived wide research interest, because they can potentially
be employed in the design of functionalized nanomaterials
and devices. Traditionally, these functional materials are
synthesized by using covalent synthetic protocols, which
often suffer from rather time-consuming procedures, very
low yields and largely uncertain final structures. Recently,
a new coordination-driven self-assembly method has been
proposed as a powerful alternative technique for the ef-
ficient synthesis of such multifunctional polyhedral mole-
cules, because it allows for the incorporation of multiple
functional centres of various geometries and properties. To
obtain a deeper understanding of the nature of such coordi-
nation-driven self-assembly processes, a great deal of effort
has been made to investigate artificial functional supra-
molecular systems. For example, Stang et al.[3] have re-
ported an interesting route to snowflake-shaped metallod-
endrimers with hexagonal cavities as their cores. Fujita[4]
and coworkers have prepared saccharide-coated molecular
spheres that form aggregates after interactions with pro-
In particular, cavity-cored polyhedral molecules have re-
ceived considerable attention because of their elaborate
structures and potential applications in molecular recogni-
tion and sensors. For example, supramolecular octahedral
nanocages have unique hollow structures that allow them to
play essential roles in the fields of encapsulation of sizeable
guests,[9] control of organic synthetic reactions[10] and catal-
ysis of redox reactions.[11] A highly symmetric octahedral
M6L4 structure can be synthesized when six 90° ditopic
metal units (M) combine with four 120° planar tritopic li-
gand units (L).[12] Generally, these octahedral molecules
have been prepared in water, and the resulting octahedra
are water soluble mainly because of the properties of the
[a] Qingdao Institute of Bioenergy and Bioprocess Technology,
Chinese Academy of Sciences,
–
189 Songling Rd., Qingdao 266101, China
Fax: +86-532-8066-2778
corresponding cation (NO3 ). These octahedral molecules
can have a large hydrophobic cavity that can encapsulate
sizeable guest molecules in water. However, highly symmet-
ric octahedral complexes that have a nanoscopic hollow
cavity have been scarcely reported in organic phase systems.
Thus, stimulated by the power and versatility of coordina-
E-mail: lanzg@qibebt.ac.cn; yangrq@qibebt.ac.cn
Homepage: http://english.qibebt.cas.cn/rh/rs/bic/aomd/
[b] University of the Chinese Academy of Sciences,
Beijing 100049, China
Supporting information for this article is available on the
WWW under http://dx.doi.org/10.1002/ejic.201200923.
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tion-driven self-assembly, we present a new type of symmet- the triphenylphosphanyl-substituted complex 5 is soluble
ric octahedral molecule that is soluble in common organic only in more polar solvents such as acetone and DMSO.
solvents instead of an aqueous solvent system. Moreover, The synthetic route is a simple and quick method to pre-
functional moieties can be attached at different positions pare the self-assembled complexes and facilitates isolation
around the periphery of the octahedral structures. Thus, the and purification. In principle, the self-assembled complex 4
supramolecular self-assembly allows us to precisely control should exhibit novel electrochemical properties, as six ferro-
the shape and size of the resulting molecules as well as the cenyl-substituted groups occupy different positions at the
distribution and total number of incorporated functional vertexes of the octahedral cage molecule. Moreover, the li-
moieties.[13]
gand 3 is extremely electron-deficient owing to the triazine
Here, we report the preparation of functionalized M6L4 groups.[14] Therefore, the cage complexes provide a nano-
cage complexes through the facile self-assembly reactions of scopic hollow environment that can preferentially bind elec-
six 90° ditopic PdII-containing [Pd(dppf)(OTf)2] [1, dppf = tron-rich guests. This may cause electron transfer from
1,1Ј-bis(diphenylphosphanyl)ferrocene, OTf = trifluorome- guest molecules to the four triazine ligands.
thylsulfonate] or [Pd(PPh3)(OTf)2] (2) subunits and four
120° tritopic 2,4,6-tri(4-pyridyl)-1,3,5-triazine (3) ligand
subunits in acetone solution (Scheme 1). The cage structure
has a very large conjugated range owing to the triazine
Results and Discussion
groups linked with three pyridine rings in every ligand sub-
Based on the design strategy, complexes with an octahe-
unit. Two functional PdII building blocks (1 and 2) were dral framework can be synthesized by directed self-as-
considered that include bis(diphenylphosphanyl)ferrocene sembly reactions of four 120° planar tritopic subunits 3
or bis(triphenylphosphanyl) moieties, respectively, at the with six 90° ditopic PdII subunits 1 or 2 in acetone solution.
vertex of the 90° PdII metal subunit. The generated com- Cage complexes 4 and 5 with roughly octahedral cavity
plexes (4 and 5) were insoluble in water, but soluble in or- structures are spontaneously formed by simply mixing the
ganic solvents, mainly owing to the presence of six cationic six metal precursors (M) and the four organic ligands (L)
PdII centres (containing trifluoromethylsulfonate, OTf–). in a 3:2 ratio. The cage structure can be readily understood
The 90° ferrocenyl-substituted precursor 1 [Pd(dppf)- by considering a hypothetical octahedron. Six metal precur-
(OTf)2] and the triphenylphosphanyl-substituted precursor sors occupy every vertex of an octahedron, whereas the four
2 [Pd(PPh3)(OTf)2] can be easily prepared by ion exchange triangular ligands alternatively occupy the eight faces of the
reactions between [Pd(dppf)Cl2] or [Pd(PPh3)Cl2] and Ag- octahedron. The ratio of faces to corners must be 4:6 with
OTf. [Pd(dppf)Cl2] and [Pd(PPh3)Cl2] are two common Su- a total number of 10 subunits to obtain a closed octahedral
zuki and Heck reaction palladium catalysts and can be eas- cage structure.
ily obtained. Thus, by suspending the tritopic ligand 3 in
an acetone solution of the precursor 1 or 2 in the ratio of identified by H NMR spectroscopic analysis. In Figure 1
2:3, we obtained the assembled M6L4 complex 4 or 5. Al- (a), the H NMR spectrum of 4 shows only one set of pro-
The formation of a single product, 4, was qualitatively
1
1
though the ferrocenyl-substituted cage complex 4 is remark- ton signals, in good agreement with its highly symmetric
ably soluble in organic solvents such as acetone, acetoni- structure. The peak at δ = 9.02 ppm was assigned to Py Ha
trile, nitromethane, dimethyl sulfoxide (DMSO), and so on, (peak a, Py = pyridinyl) and the peak at δ = 8.06 ppm was
attributed to the Py Hb of the triazine ligand core of the
cage. The peaks c, d and e correspond to the three protons
of the phenyl group of the PdII metal subunit. The proton
signals Hf and Hg at δ = 4.94 and 4.85 ppm, respectively,
characterized two protons in the ferrocenyl-substituted
group. The integration ratio of the seven protons (Ha–g) was
approximately 24:24:48:24:48:24:24 (Ha/Hb/Hc/Hd/He/Hf/
Hg), in accordance with the stoichiometric ratio 6:4 of 1
and 3. Similar results were obtained for 5. Elemental analy-
sis of 4 and 5 provided further evidence to support the iden-
tification of the current cage structures.
The diffusion coefficient is often used to determine the
size of molecules,[15] as the self-diffusion coefficient of a
molecule depends not only on the viscosity of the solvent
but also the effective size of individual molecule/supramole-
cule. We carried out 1H NMR diffusion-ordered spec-
troscopy (DOSY) experiments for both 4 and 5 in [D6]acet-
one solution. In Figure 1 (b), all proton signals of 4 give
only one diffusion coefficient at 5.62ϫ10–9 m2 s–1 (logD =
Scheme 1. Self-assembly reactions to prepare multifunctional octa-
hedral complexes M6L4 4 and 5 with six appended functional moie-
ties.
–8.25). The diameter of 4 was estimated as 3.1 nm based on
the Stokes–Einstein equation.[16] Similarly, complex 5 was
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(Figure S2–3). In the calculations, the optimized geometries
of 4 and 5 clearly displayed a highly symmetric octahedral
structure. Taking 4 for example, the interior diagonal Pd–
Pd distance was calculated to be 1.9 nm and the Pd–Pd dis-
tance for the triangular facial windows was 1.4 nm. From a
stick model, an approximate diameter of 3.3 nm was de-
rived for the overall size of 4, and the distance between
neighbouring ferrocene units was 2.0 nm (Figure S2). The
calculated diameter of 4 was in good agreement with those
obtained from the DOSY deduced results and AFM obser-
vations.
The single-electron-accepting character of 5 is supported
by theoretical calculations. Owing to the rather high sym-
metry of the structure of 5, a few of the occupied orbitals
near the highest occupied molecular orbital (HOMO) are
degenerate. The same situation happens for several unoccu-
pied molecular orbitals near the lowest unoccupied molecu-
lar orbital (LUMO). Interestingly, the electronic population
densities of the HOMO and LUMO are located in the Pd–
bis(triphenylphosphane) part and the tritopic triazine part,
respectively (Figures 3 and S4). This phenomenon indicates
that the HOMO–LUMO transition leads to an electroni-
cally excited state with strong intramolecular charge-trans-
fer (CT) character. Furthermore, several similar CT states
1
Figure 1. a) H NMR spectrum (600 MHz, [D6]acetone, 298 K) of
4. Signals a and b denote Py Ha (Py = pyridinyl) and Py Hb of the
tritopic ligand; signals c, d, e and f, g denote phenyl and ferrocenyl
ring protons, respectively, and b) 1H DOSY spectrum of 4
(600 MHz, [D6]acetone, 298 K).
assembled from six 90° PdII-containing subunits 2 and four
tritopic ligand subunits 3. The diffusion coefficient deter-
mined by a DOSY experiment was 5.25ϫ10–9 m2 s–1 (logD
= –8.28) in [D6]acetone.
The molecular size of 4 was confirmed directly by AFM
(Figure 2), which clearly showed the diameter of 4 was ap-
proximately 3–4 nm. The results also revealed the stability
of the nanoparticles under AFM conditions. The frame-
work structures of 4 (DFT, B3LYP method) and 5 (PM6
method) were further studied by theoretical calculations Figure 3. HOMO and LUMO of octahedral cage 5.
Figure 2. AFM images of 4 on mica: a) 3D image, b) 2D image and c) height profile.
377
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should exist in the low excitation energy domain for such cesses was observed, as clarified by the 1H NMR spectra of
systems owing to the orbital degeneracy. As previously sug- 4 before and after the electrochemical reactions. As pro-
gested by Fujita et al.,[17] the presence of these low-lying posed by Stang et al.,[21] electrochemical reversibility indi-
CT states may allow us to perform the photocatalysis of cates that fast electron transfer processes occur among the
some oxidation/reduction reactions that do not take place six peripheral redox sites. Such fast heterogeneous electron
in ordinary chemical environments. Meanwhile, we presume transfer processes were caused by fast rotation or electron
that this CT feature of this type of system may also have hopping between the different subunits. The combination
potential use in artificial photosynthesis.[18]
of ferrocene functional moieties with transition metal com-
Despite extensive efforts, we have not been successful in plexes offered a marvellous chance to link the chemistry of
growing suitable X-ray quality crystals of the complexes. ferrocenes with supramolecular self-assembly, thus opening
This may be due to the large cavity size of the molecules new families of compounds to possible redox processes.
and the high solvent content of the crystals. However, the These novel assembly systems with multiredox groups could
physical and spectroscopic data are consistent with the oc- potentially be used as multielectron catalysts and sensors.
tahedral structures based on our experimental results and
theoretical calculations.
The electrochemical properties of the multiferrocene
complex 4 were also investigated. Cyclic voltammograms of
precursor 1 and complex 4 were recorded in 1.8 and 0.3 mm
acetone solutions, respectively, with 0.1 m nBu4NPF6 as
supporting electrolyte. The cyclic voltammograms of 1 ex-
hibited typical reversible redox curves from 0.2 to 1.6 V, as
shown in Figure S1. The cyclic voltammograms of 4 showed
a pair of quasireversible redox peaks, which indicated that
no interaction existed among the different ferrocene redox
centres (Figure 4). The potential difference (ΔEp) between
the oxidation peak potentials (Epa) and reduction peak po-
tentials (Epc) was 96Ϯ9 mV, which is larger than the theo-
retical value for an ideal quasireversible redox system
(59 mV at 298 K) owing to the resistance of the solution.[19]
Meanwhile, the oxidation and reduction peak currents of 4
increased linearly with respect to the square root of the
sweep rates from 25 to 200 mVs–1. The oxidation and re-
duction peak potentials were both slightly shifted with
higher sweep rates, which indicated the existence of a dif-
fusion-controlled quasireversible redox process. Cyclic vol-
tammograms of 4 displayed a considerably broad voltam-
metric peak, which was probably due to the simultaneous
statistical nature of the multielectron transfer processes, in
accordance with previously reported ones.[20] No decompo-
sition of the octahedral complex during these redox pro-
Conclusions
We have prepared nanoscale octahedral structures
through coordination self-assembly in a common organic
phase system. The coordination self-assembly allows for the
precise control of the shape, size and location of multiple
functional groups. When functional groups (such as ferro-
cenyl-substituted groups) are attached onto the vertices of
PdII metal subunits, such self-assembled complexes exhibit
interesting multiredox properties. Meanwhile, the func-
tional units retain their functional fidelity, and the large
discrete 3D supramolecular hollow structure provides an
ideal cavity for molecular recognition, inclusion phenomena
and catalysis. We are currently exploring the possibility of
oligopeptide encapsulation in the octahedral structures, in
which functional groups are expected to provide a new
means to characterize electron transfer from guest mole-
cules to the triazine ligands. We envision that the addition
of functional moieties and encapsulated moieties to the pe-
riphery and the interior of the nanocage, respectively, will
lead to many new materials with special electrochemical or
photochemical applications, such as multi-electron redox
catalysts, electrode modifiers and sensors.
Experimental Section
Material: Reagents were purchased from TCI Co. Ltd., WAKO
Pure Chemical Industries Ltd. and Sigma–Aldrich Co. Dichloro-
methane and acetone were distilled from calcium hydride prior to
use. All other chemicals were of reagent grade and were used with-
out any further purification.
[Pd(dppf)(OTf)2] (1): A Schlenk flask was charged with [Pd(dppf)-
Cl2] (225.1 mg, 0.307 mmol) and anhydrous CH2Cl2 (20 mL) to
give a dark red solution. To this solution was added AgOTf
(236.6 mg, 0.921 mmol), and the mixture was stirred at room tem-
perature for 8 h in darkness. The white precipitate was removed by
filtration, and the filtrate was reduced in volume to 3 mL. After
the addition of diethyl ether, the green product that precipitated
was collected by filtration, washed with diethyl ether and dried in
vacuo, yield 268.3 mg (91%), dark green solid. 1H NMR
(600 MHz, [D6]acetone, 298 K): δ = 8.01 (m, 8 H, Ph Ho), 7.82 (m,
4 H, Ph Hp), 7.66 (m, 8 H, Ph Hm), 4.89 (s, 2 H, ferrocene Hα),
4.84 (s, 2 H, ferrocene Hβ) ppm. DEPTQ 13C NMR (150 MHz,
[D6]acetone, 298 K): δ = 135.1 (CH), 134.5 (CH), 130.6 (CH), 128.9
Figure 4. Cyclic voltammetry of 4 at different scan rates (25–
200 mVs–1) at a 3 mm diameter glassy carbon working electrode in
0.3 mm acetone solution containing 0.1 m nBu4NPF6, vs. Ag/AgCl.
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(C), 122.6 (C), 79.7 (CH), 77.4 (CH), 69.9 (C) ppm. tained by electronic-structure calculations with the Gaussian pack-
C36H28F6FeO6P2PdS2 (958.92): calcd. C 43.46, H 3.24, S 6.45; age.[22] As the current systems are extremely large, the semi-empiri-
found C 43.52, H 3.31, S 6.49.
cal PM6 method was employed in the calculations of complex 5.
However, complex 4, which contains ferrocene groups, cannot be
described correctly at the PM6 level, thus we had to use the DFT
B3LYP level of theory and perform the calculations on a simplified
model system.
[Pd(PPh3)(OTf)2] (2): A Schlenk flask was charged with [Pd(PPh3)-
Cl2] (212.3 mg, 0.302 mmol) and anhydrous CH2Cl2 (20 mL) to
give a yellow solution. To this solution was added AgOTf
(226.5 mg, 0.882 mmol), and the mixture was stirred at room tem-
perature for 2 h. The white precipitate was removed by filtration,
and the filtrate was reduced in volume to 3 mL. After the addition
of diethyl ether, the brown precipitate was collected by filtration,
washed with diethyl ether and dried in vacuo, yield 261.3 mg
(93%), brown solid. 1H NMR (600 MHz, [D6]acetone, 298 K): δ =
7.72 (m, 18 H, Ho and Hp), 7.51 (m, 12 H, Hm) ppm. DEPTQ 13C
NMR (150 MHz, [D6]acetone, 298 K): δ = 135.6 (CH), 134.3 (CH),
130.5 (CH), 125.7 (C), 125.3 (C), 120.6 (C) ppm.
C38H30F6O6P2PdS2 (929.11): calcd. C 49.12, H 3.25, S 6.90; found
C 49.16, H 3.31, S 6.97.
Electrochemical Measurements: Electrochemical measurements
were made with a CHI 660D System. The working electrode was a
3 mm diameter glassy carbon electrode, a platinum wire as counter
electrode and an Ag/AgCl (3.0 m KCl) reference electrode. All elec-
trochemical experiments were performed in acetone solutions with
nBu4NPF6 (0.1 m) as supporting electrolyte; oxygen was removed
from the solutions by bubbling through high-purity argon before
the experiments. The concentration of redox molecules in solution
was 1.8 mm for 1 and 0.3 mm for4.
Supporting Information (see footnote on the first page of this arti-
cle): Cyclic voltammograms and molecular modelling procedures
are presented.
Cage 4: 2,4,6-Tris(4-pyridyl)-1,3,5-triazine 3 (9.9 mg, 0.032 mmol)
was suspended in an acetone solution (30 mL) of [Pd(dppf)-
(OTf)2] (1, 45.2 mg, 0.047 mmol), and the mixture was stirred at
room temperature for 30 min; the solution gradually turned clear
pink. After the solvent was evaporated, the resulting residue was
washed with diethyl ether three times and dried in vacuo to yield
4 (47.3 mg) as a pink solid in 87% yield. 1H NMR (600 MHz, [D6]-
acetone, 298 K): δ = 9.02 (d, J = 4.2 Hz, 24 H, pyridyl Hα), 8.06
(d, J = 6.0 Hz, 24 H, pyridyl Hβ), 7.99 (m, 48 H, Ph Ho), 7.72 (m,
24 H, Ph Hp), 7.64 (m, 48 H, Ph Hm), 4.94 (s, 24 H, ferrocene Hα),
4.85 (s, 24 H, ferrocene Hβ) ppm. Diffusion coefficient ([D6]acet-
one, 298 K): D = 5.62ϫ10–9 m2 s–1. DEPTQ 13C NMR (150 MHz,
[D6]acetone, 298 K): δ = 168.7 (C), 151.6 (CH), 144.3 (C), 134.3
(CH), 133.1 (CH), 130.0 (CH), 127.5 (C), 124.7 (CH), 120.3 (C),
Acknowledgments
This work was supported by the National Natural Science Founda-
tion of China (NSFC) (grant numbers 21103213, 51173199,
61107090), the Ministry of Science and Technology of China
(2010DFA52310), the Chinese Academy of Sciences (One Hundred
Talented Program, and KGCX2-YW-399+9-2), the Department of
Science and Technology of Shandong Province (2010GGC10345),
the Shandong Provincial Natural Science Foundation
(ZR2011BZ007), and the Qingdao Municipal Science and Technol-
ogy Program (11-2-4-22-hz). J. W. and Z. L. acknowledge the com-
puting resources from the super-computational centre in the insti-
tute and the Chinese Academy of Sciences.
77.3 (CH), 76.0 (CH), 69.0 (C) ppm.
O36P12Pd6S12 (7002.83): calcd. C 49.39, H 3.11, N 4.80, S 5.49;
found C 49.46, H 3.04, N 4.85, S 5.43.
C288H216F36Fe6N24-
Cage 5: 2,4,6-Tris(4-pyridyl)-1,3,5-triazine 3 (8.1 mg, 0.026 mmol)
was suspended in an acetone solution (30 mL) of [Pd(PPh3)-
(OTf)2] 2 (35.4 mg, 0.038 mmol), and the mixture was stirred at
room temperature for 2 h; the solution gradually turned colourless.
After the solvent was evaporated, the resulting residue was washed
with diethyl ether three times and dried in vacuo to yield 5
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1
(36.0 mg) as a white solid in 92% yield. H NMR (600 MHz, [D6]-
acetone, 298 K): δ = 9.26 (d, J = 4.2 Hz, 24 H, pyridyl Hα), 8.13
(d, J = 6.0 Hz, 24 H, pyridyl Hβ), 7.82 (m, 72 H, Ph Ho), 7.61 (m,
36 H, Ph Hp), 7.48 (m, 72 H, Ph Hm) ppm. Diffusion coefficient
([D6]acetone, 298 K): D = 5.25ϫ10–9 m2 s–1. DEPTQ 13C NMR
(150 MHz, [D6]acetone, 298 K): δ = 169.6 (C), 152.6 (CH), 145.0
(C), 135.4 (CH), 133.6 (CH), 130.6 (CH), 126.3 (C), 125.9 (C),
125.6 (CH), 123.4 (C) ppm. C300H228F36N24O36P12Pd6S12
(6823.97): calcd. C 52.80, H 3.37, N 4.93, S 5.64; found C 52.89,
H 3.45, N 4.95, S 5.56.
Structure Characterization: Various NMR (1H NMR, DEPTQ
NMR) spectra were recorded with a Bruker DRX-600 (600 MHz)
spectrometer. Tetramethylsilane (CDCl3 solution) in a capillary was
used as an external standard. The DOSY NMR spectra were ac-
quired with the standard pulse program from Bruker Topspin soft-
ware, ledbpgp2s, with a stimulated echo and longitudinal eddy cur-
rent delay, with bipolar sine-shaped gradient pulses and two spoil-
ing gradients. DOSY NMR spectra were recorded with 32000 time
domain data points in the t2 dimension and 16 t1 increments, 16
transients for each t1 increment and a relaxation delay of 1 s. Ele-
mental analysis was performed with a vario EL cube instrument.
The molecular structures of the cage complexes 4 and 5 were ob-
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Published Online: December 4, 2012
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