Syntheses, structures, and luminescent properties of two cadmium(II) entangled frameworks based on 5-bromoisophthalic acid and bipyridyl ligands

Article abstract of DOI:10.1002/zaac.201100373

Two cadmium(II) entangled frameworks, Cd(BIPA)(bpe)_1.5 (1) and Cd(BIPA)(bpp)(H₂O) (2), were prepared by hydrothermal reactions based on rigid 5-bromoisophthalic acid (H₂BIPA) and two flexible bipyridyl ligands 1, 2-bis(4-pyridyl)ethane (bpe) and 1, 3-bis(4-pyridyl)propane (bpp). The complexes were characterized by elemental analysis, IR spectroscopy, thermogravimetric analysis, and single-crystal X-ray diffraction. Complex 1 is a rare example of a polycatenated array of 1D nanotubes, whereas complex 2 exhibits a three-dimensional twofold interpenetrating diamondoid network. The analysis results reveal that the flexibility of the bipyridyl ligands plays a significant role in the structure of the final products. Moreover, the luminescent properties of the complexes were investigated. Copyright

Full text of DOI:10.1002/zaac.201100373

ARTICLE
DOI: 10.1002/zaac.201100373
Syntheses, Structures, and Luminescent Properties of two Cadmium(II)
Entangled Frameworks Based on 5-Bromoisophthalic Acid and Bipyridyl
Ligands
[a]
[a]
[a]
Guang-Xiang Liu,* Xiao-Feng Wang, and Hong Zhou
Keywords: Cadmium; Coordination polymers; 5-Bromoisophthalic acid; Entangled frameworks; Luminescence
Abstract. Two cadmium(II) entangled frameworks, Cd(BIPA)(bpe)1.5
1) and Cd(BIPA)(bpp)(H O) (2), were prepared by hydrothermal reac-
tions based on rigid 5-bromoisophthalic acid (H BIPA) and two flexi-
ble bipyridyl ligands 1,2-bis(4-pyridyl)ethane (bpe) and 1,3-bis(4-pyr-
tal X-ray diffraction. Complex 1 is a rare example of a polycatenated
(
2
array of 1D nanotubes, whereas complex 2 exhibits a three-dimen-
sional twofold interpenetrating diamondoid network. The analysis re-
sults reveal that the flexibility of the bipyridyl ligands plays a signifi-
2
idyl)propane (bpp). The complexes were characterized by elemental cant role in the structure of the final products. Moreover, the lumines-
analysis, IR spectroscopy, thermogravimetric analysis, and single-crys-
cent properties of the complexes were investigated.
Introduction
We are focused on the construction of MOFs based on flexi-
ble organic ligands.[
21–23]
For instance, we successfully con-
The current interest in metal-organic frameworks (MOFs) trolled the flexible 4,4Ј-dicarboxybiphenyl sulfone in the syn-
II
not only stems from their potential applications in microelec- thesis of Zn complexes by tuning the reaction tempera-
24]
tronics, nonlinear optics, porous materials, and catalysis, but tures.[ Although there is much more difficulty in predicting
also from their intriguing variety of topologies and entangle- and designing the assembly process, the versatile coordination
ment motifs.[
1–8]
However, there are too many factors that have modes of the functional groups of flexible ligands provide
great influences on the formation and functional behavior of more opportunity to form some particular structures and prop-
MOFs, and so far it is still a challenge for chemists and mate- erties. Several complexes with interesting topology such as
rial scientists to realize the structural control and functional 2DǞ3D polycatenation or 2DǞ3D polythreading based on
tuning of MOFs. Much effort has been paid to investigate the the flexible bis(imidazole) ligands were designed and success-
important influences of metal ions, organic multitopic ligands, fully isolated in our previous studies.[
24,25]
Compared with un-
pH values, solvents, templates, reaction temperature etc. on substituted isophthalate, isophthalates substituted in 5-position
the construction of MOFs.[
9–16]
As to the rational design and may result in the different electronic effect and the steric hin-
synthesis of MOFs, a widely used strategy is based on the drance to change the coordination modes of carboxylate groups
careful selection of metal atoms and ligands.[
17,18]
[26–30]
For the lin- in the assembly process.
In order to get further under-
ear organic ligands, the spacer lengths, flexibility, coordination standing of possible factors that can affect the formation of
modes or configurations, steric hindrance effects have great MOFs, we now expand our research attention to the flexible
influence on the structure of the final MOFs. Elaborately tun- bipyridyl ligands and the rigid 5-bromoisophthalic acid ligand
ing of the experiment conditions may result in various products system.
with interesting entangled structures such as polycatenation or
polythreading. As known, entangled frameworks are now cent properties of two cadmium(II) entangled frameworks
drawing great interest from scientists not only because it is an Cd(BIPA)(bpe)1.5 (1) and Cd(BIPA)(bpp)(H O) (2) [H BIPA =
Herein, we describe the synthesis, structure, and lumines-
2
2
important factor that contributing to the diversities of crystal 5-bromoisophthalic acid, bpp = 1,3-bis(4-pyridyl) propane, and
structures, but also due to its intensive relationship with bio- bpe = 1,2-bis(4-pyridyl)ethane].
logical systems.[
19,20]
Experimental Section
*
Dr. G.-X. Liu
Materials and General Methods: All chemicals purchased were of
regent grade and used without further purification. Elemental analyses
(C, H and N) were performed with a Vario EL III elemental analyzer.
Infrared spectra were performed with a Nicolet AVATAR-360 spectro-
photometer with KBr pellets in the 4000–400cm region. The lumi-
nescence spectra for the powdered solid samples were measured at
room temperature with a Hitachi F-4500 fluorescence spectrophotome-
Fax: +86-25-86178260
E-Mail: njuliugx@gmail.com
[
a] Department of Chemistry
Nanjing Xiaozhuang University
Nanjing 211171, P. R. China
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/zaac.201100373 or from the au-
thor.
–1
Z. Anorg. Allg. Chem. 2012, 638, (2), 455–460
© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
455

G.-X. Liu, X.-F. Wang, H. Zhou
ARTICLE
ter with a xenon arc lamp as the light source. In the measurements of
emission and excitation spectra the pass width is 5 nm. All the mea-
gram.[33] All of the non-hydrogen atoms were refined anisotropically.
The hydrogen atoms of the ligands were placed in the geometrically
surements were carried out under the same experimental conditions. calculated positions. The crystal data and structure refinement of com-
Thermogravimetric analyses (TGA) were performed with a Netzsch plexes 1 and 2 are summarized in Table 1. Selected bond lengths and
STA-409PC instrument in flowing nitrogen with a heating rate of bond angles for 1 and 2 are listed in Table 2 and Table 3, respectively.
–
1
1
0 K·min .
Crystallographic data (excluding structure factors) for the structures in
Preparation of Complex Cd(BIPA)(bpe)1.5 (1): A mixture containing this paper have been deposited with the Cambridge Crystallographic
Cd(NO ·4H O (61.6 mg, 0.2 mmol), H BIPA (49.0 mg, 0.2 mmol), Data Centre, CCDC, 12 Union Road, Cambridge CB21EZ, UK. Copies
bpe (36.8 mg, 0.2 mmol), and LiOH·H O (16.8 mg, 0.4 mmol) in de-
ionized water (15 mL) was sealed in a 25 mL Teflon lined stainless
3
)
2
2
2
2
of the data can be obtained free of charge on quoting the depository
numbers CCDC-809276 and CCDC-809278 (Fax: +44-1223-336-033;
steel container and heated at 140 °C for 3 days under autogenous pres- E-Mail: deposit@ccdc.cam.ac.uk, http://www.ccdc.cam.ac.uk).
sure. Cooling the reactor subsequently to room temperature at a rate
–
1
Supporting Information (see footnote on the first page of this article):
TG curves and PXRD patterns of complexes 1 and 2.
of 10 K·h , colorless block crystals of 1 were collected by filtration
and washed with water and ethanol several times with a yield of 63%.
C
26
H
21
N
3
O
4
BrCd: calcd. C 49.43; H 3.35; N 6.65%; found: C 49.51;
H 3.38; N 6.62%. IR (KBr): ν˜ = 3443 (m), 3060 (w), 2927 (m), 1611
Results and Discussion
(
(
s), 1550 (m), 1505 (m), 1427 (s), 1368 (s), 1222 (m), 1078 (w), 1017
m), 829 (m), 774 (m), 726 (m), 545 (m), 520 (w) cm .
–1
Syntheses
Preparation of Complex Cd(BIPA)(bpp)(H
cedure with 1 was followed to prepare 2 except bpe was replaced by
bpp (yield 56%). C21 BrCd: calcd. C 44.12; H 3.35; N 4.90%;
found: C 44.09; H 3.38; N 4.91%. IR (KBr): ν˜ = 3446 (m), 3074 (w),
946 (w), 2866 (w), 1612 (s), 1560 (m), 1501 (w), 1424 (m), 1400
m), 1350 (s), 1226 (m), 1098 (w), 1069 (w), 1014 (w), 819 (m), 772
2
O) (2): An identical pro-
Because the mixing of metal salts and carboxylate solutions
in traditional aqueous reactions usually resulted in precipitates,
which made the growth of crystals difficult, the hydrothermal
method was adopted in these reactions. The use of hydrother-
mal conditions causes the reaction to shift from the kinetic to
the thermodynamic domain. By performing parallel experi-
ments it was found that different bases play an important role
in the isolation of the two complexes, as is the case for some
other metal polycarboxylate coordination polymers reported.
19 2 5
H N O
2
(
(
–1
m), 732 (m), 722 (m), 572 (w) cm .
X-ray Crystallography: Single crystal X-ray diffraction data for com-
plexes 1 and 2 were recorded with a Bruker Smart Apex II CCD dif-
fractometer using Mo-K
empirical absorption corrections were applied.
solved by direct methods using the SHELXS-97 program
α
radiation (λ = 0.71073 Å) at 293(2) K. The
Complexes 1 and 2 were prepared when LiOH·H O was used
[
31]
2
The structures were
[
32]
to adjust the pH value; single crystals were not obtained by
using the other bases. However, we found that the above reac-
tions were not sensitive to the reaction temperature. If the reac-
tion temperature was set 10 °C above or below, the intended
crystals still formed.
and re-
2
fined by full-matrix least-squares on F using the SHELXL-97 pro-
Table 1. Crystal data and structure refinement for 1 and 2.
1
2
Empirical formula
Molecular weight
Crystal system
Space group
a /Å
b /Å
c /Å
α /°
β /°
C
26
H
21
N
3
O
4
BrCd
C
21 19 2 5
H N O BrCd
Crystal Structure Descriptions
631.77
triclinic
P1
571.69
monoclinic
C2/c
The bipyridyl ligand bpe with a –CH CH – linker was em-
2
2
¯
ployed in the synthetic reaction and complex 1 was isolated.
Structural analysis shows that complex 1 crystallizes in the
10.1548(15)
10.8976(16)
13.884(2)
109.243(3)
99.624(3)
109.615(2)
1298.0(3)
2
293(2)
1.616
2.416
626
14.2797(18)
18.8445(18)
16.5121(18)
90
100.608(3)
90
4367.4(8)
8
293(2)
1.739
¯
triclinic space group P1 and the asymmetric unit consists of
II
2–
one crystallographically unique Cd ion, one BIPA ligand,
and one and a half bpe ligands, as illustrated in Figure 1a. The
crystal structure of complex 1 consists of cationic [Cd(bpe)4]
γ /° 3
V /Å
Z
8+
squares with Cd···Cd separations of 13.884(2) and
13.961(5) Å; The bpe ligand acts as an exo-bidentate ligand in
T /K
–3
D
calc /g·cm
anti conformation, and the dihedral angle between two pyr-
–1
μ /mm
2.864
2256
idine rings is 47.08°. These square units are joined by anionic
F(000)
Maximum / minimum
transmission
θ range /°
Reflections collected
Independent reflections
2–
BIPA bridges to give one-dimensional nanotubes containing
0.8686 / 0.6436
0.7250 / 0.5981
large cubelike boxes of approximate dimensions
10.15ϫ11.88ϫ13.96 Å (Figure 1b). The Cd ion is coordi-
II
1.64–25.00
6509
1.81–25.50
11219
nated in distorted pentagonal bipyramidal arrangement to four
oxygen atoms from two different BIPA ligands and three nitro-
gen atoms from three bpe ligands. Two carboxylate groups of
4487 (0.0208)
4048 (0.0582)
int
(R )
Restraint / parameters2
0 / 316
1.030
0.0432
0.1117
2 / 279
0.944
0.0402
0.0585
2–
the BIPA ion adopt a chelating coordination mode to link
Goodness-of-fit on F
a)
II
R
1
[I Ͼ 2σ(I)]
two Cd ions (Scheme 1a). Four coordinated oxygen atoms
b)
wR
2
[I Ͼ 2σ(I)]
together with one pyridyl nitrogen atom define the equatorial
positions, whereas the axial positions are occupied by two pyr-
= |Σw(|F 2 |2)|/Σ|w(F
2 1/2
a) R
1
o
c o 2 o c o
= Σ||F |–|F ||/Σ|F |. b) wR | –|F ) | .
4
56
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© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Z. Anorg. Allg. Chem. 2012, 455–460

CdII Frameworks with 5-Bromoisophthalic Acid and Bipyridyl Ligands
Table 2. Selected bond lengths /Å and angles /° for complex 1.
Cd(1)–O(4)#1
Cd(1)–O(1)
Cd(1)–N(3)
2.291(4)
2.298(3)
2.325(4)
2.373(4)
Cd(1)–N(1)
Cd(1)–O(3)#1
Cd(1)–O(2)
2.376(4)
2.553(4)
2.572(4)
Cd(1)–N(2)#2
O(4)#1–Cd(1)–O(1)
O(4)#1–Cd(1)–N(3)
O(1)–Cd(1)–N(3)
O(4)#1–Cd(1)–N(2)#2
O(1)–Cd(1)–N(2)#2
N(3)–Cd(1)–N(2)#2
O(4)#1–Cd(1)–N(1)
O(1)–Cd(1)–N(1)
84.21(13)
138.22(14)
137.44(13)
95.51(16)
93.13(15)
86.73(15)
90.16(15)
88.98(14)
88.01(14)
174.13(14)
53.11(13)
N(3)–Cd(1)–O(3)#1
N(2)#2–Cd(1)–O(3)#1
O(1)–Cd(1)–O(3)#1
N(1)–Cd(1)–O(3)#1
O(4)#1–Cd(1)–O(2)
O(1)–Cd(1)–O(2)
N(3)–Cd(1)–O(2)
N(2)#2–Cd(1)–O(2)
N(1)–Cd(1)–O(2)
85.52(13)
86.88(16)
137.01(13)
95.31(14)
137.11(13)
52.93(12)
84.66(13)
86.33(15)
90.58(14)
168.35(12)
N(3)–Cd(1)–N(1)
N(2)#2–Cd(1)–N(1)
O(4)#1–Cd(1)–O(3)#1
O(3)#1–Cd(1)–O(2)
Symmetry transformations used to generate equivalent atom: #1: x+1, y, z; #2 x, y, z–1.
Table 3. Selected bond lengths /Å and angles /° for complex 2.
Cd(1)–O(3)#1
Cd(1)–O(2)
Cd(1)–N(2)
2.211(3)
2.223(3)
2.270(3)
Cd(1)–O(1W)
Cd(1)–N(1)
Cd(1)–O(1)
2.334(4)
2.353(3)
2.624(3)
O(3)#1–Cd(1)–O(2)
O(3)#1–Cd(1)–N(2)
O(2)–Cd(1)–N(2)
O(3)#1–Cd(1)–O(1W)
O(2)–Cd(1)–O(1W)
N(2)–Cd(1)–O(1W)
O(3)#1–Cd(1)–N(1)
N(1)–Cd(1)–O(1)
130.34(12)
90.04(13)
139.47(12)
80.72(14)
90.03(12)
93.98(12)
91.50(12)
89.35(11)
O(2)–Cd(1)–N(1)
N(2)–Cd(1)–N(1)
O(1W)–Cd(1)–N(1)
O(3)#1–Cd(1)–O(1)
O(2)–Cd(1)–O(1)
N(2)–Cd(1)–O(1)
O(1W)–Cd(1)–O(1)
88.33(11)
94.83(12)
168.25(14)
176.67(11)
52.90(9)
86.68(11)
98.92(13)
Symmetry transformations used to generate equivalent atom: #1: x, –y+1, z+1/2.
idyl nitrogen atoms. The coordination bond lengths that in- products. Different topological structures may be obtained by
II
volve the Cd atom are in the range 2.325(4)–2.376(4) Å for rational design and tuning of the length and the flexibility of
Cd–N bonds and 2.291(4)–2.572(4) Å for Cd–O bonds, which the auxiliary bipyridyl ligands. Thus, a bpp ligand with the
are all in good agreement with those typically observed longer linker –CH CH CH – was engaged in the construction
2
2
2
34]
(
Table 2).[ A large number of molecular squares were thor- of complex 2. X-ray crystallographic analysis reveals that
[35]
oughly investigated to date,
all of them were held together complex 2 crystallizes in the monoclinic space group C2/c
II
by van der Waals interactions except in one case, in which with one Cd ion, one BIPA ligand, one bpp ligand, and one
cationic squares were interconnected by axial chloride bridges ligated water molecule in the asymmetric unit. The local coor-
into a 3D network.[ Therefore, to the best of our knowledge, dination environment of the Cd ion in 2 is illustrated in Fig-
36]
II
II
this is the rare nanosized tubular structure constructed by the ure 2a. Each Cd ion is octahedrally coordinated to two nitro-
covalent linkage of molecular squares.
gen atoms from two bpp ligands, three oxygen atoms from two
The most fascinating and peculiar structural feature of 1 is different BIPA ligands, and a ligated water molecule. The Cd–
that each nanotube, which is aligned parallel to the a axis, is N bond lengths are 2.270(3) and 2.353(3) Å and the Cd–O
interlocked in a parallel fashion (along the b axis) with the two bond lengths are in the range 2.211(3)–2.624(3) Å. Further
nearest neighboring ones to give rise to a 2D polycatenated studies of the structure of 2 reveal that two carboxylate groups
layer (Figure 1c). This kind of entanglement is still quite un- of the BIPA ligand adopt monodentate and chelating coordina-
common and the known examples are based exclusively on tion modes different from those in 1 (Scheme 1b), whereas the
infinite 1D molecular ladders.[
37,38]
Therefore, complex 1, be- bpp ligand adopts cis conformation linking the Cd ions to a
II
sides providing a remarkable new structural motif, represents 3D network. This is because the two C–C single bonds be-
the novel example of a 2D array of such motifs polycatenated tween the two pyridyl groups in the bpp ligand are longer than
in a parallel manner. It is also a rare example having both those in the bpe ligand and enable a greater flexibility to show
polyrotaxane and polycatenane characteristics and could different configurations. Topological analyses of 2 were car-
equally well be considered as formed by interconnected 1D ried out using the TOPOS program, and the results show that
polyrotaxane columns.[
39,40]
complex 2 has a typical 3D twofold interpenetrating dia-
As it is known, the flexibility of the bipyridyl ligand has mondoid framework containing adamantanoid cages as shown
important influence on the resulting structures of the final in Figure 2b. As known, large voids in MOFs are usually occu-
Z. Anorg. Allg. Chem. 2012, 455–460
© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.zaac.wiley-vch.de
457

G.-X. Liu, X.-F. Wang, H. Zhou
ARTICLE
in 2 causes twofold interpenetration and the final 3D twofold
interpenetrating diamondoid network is shown in Figure 2c.
For 2, the bpp ligand exhibits cis configuration with a dihedral
angle of 84.00° between the two pyridyl planes. This means
that the two pyridyl planes of a bpp ligand are almost perpen-
dicular to each other, which is further validated as the ligand
II
II
link the Cd ions into 1D zigzag chains. Meanwhile, the Cd
ions are also linked by the BIPA ligand into 1D chains and the
two kinds of chains intersect with each other to make up a 3D
diamond network. The dihedral angle in 2 is much larger than
that in 1 due to the longer flexible C–C single bonds between
the two pyridyl groups.
Reactions of Cd(NO ) , 5-bromoisophthalic acid, and two
3
2
different flexible linear bipyridyl ligands under hydrothermal
conditions afford two different interesting entangled networks.
The results clearly indicate that the flexibility of the bipyridyl
ligands has important influence on the structure of the final
products. Obviously, the two bipyridyl ligands involved in the
construction of two entangled complexes have the same pyr-
idyl group and a similar bis(monodentate) bridging coordina-
tion mode. The length and flexibility of the two ligands is
different, which cause different configuration of the two li-
II
gands when coordinating to the Cd ions and finally result in
two distinct entangled frameworks. On the other hand, two
complexes are different from other complexes in the litera-
ture,[
25–30]
because the –Br substituent of the isophthalate
group causes different electronic effects and steric hindrance
that change the coordination modes of carboxylate groups in
the complexes. This gives useful information for further under-
standing the possible factors that direct the formation of en-
tangled frameworks.
Thermogravimetric Analyses
To characterize the thermal stabilities of the two complexes,
we carried out TGA analyses (Figure S1, Supporting Infor-
mation). The experiments were performed on samples con-
sisting of numerous single crystals of 1 and 2 in a nitrogen
–1
atmosphere with a heating rate of 10 K·min . The weight of
complex 1 remains stable to approx. 320 °C, finally leading to
the formation of stoichiometric amount of CdO as the residue
Figure 1. (a) Perspective view of the coordination environments of the
Cd atom in 1 with thermal ellipsoids at 30% probability. (b) Portion
(found 19.65%; calcd. 20.32%). The TGA curve of 2 shows
II
that the first weight loss of 3.10% between 75 and 130 °C
corresponds to the loss of one ligated water molecule per for-
mula unit (calcd. 3.15%), afterwards it is stable up to 290 °C.
The framework collapsed in the temperature range 290–550 °C
before the final formation of a metal oxide (found 21.77%;
calcd. 22.46%).
of two cubelike boxes of a single nanotube in 1. (c) Schematic view
of the parallel polycatenation of three different nanotube motifs in 1.
Luminescent Properties
Coordination polymers with central d10 metal atoms and or-
ganic ligands are promising candidates for photoactive materi-
Scheme 1. Coordination modes of BIPA2– ligands.
als with potential applications.
[41–44]
In this paper, the solid
state luminescent properties of complexes 1 and 2 were inves-
pied by guest molecules or filled through interpenetrating with tigated in the solid state at room temperature. As depicted in
other motifs. The capacious space of the adamantanoid cages Figure 3, complexes 1 and 2 exhibit intense blue fluorescent
4
58
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© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Z. Anorg. Allg. Chem. 2012, 455–460

CdII Frameworks with 5-Bromoisophthalic Acid and Bipyridyl Ligands
emissions are observed at 454, 419, and 425 nm for the free
H BIPA, bpe and bpp ligands, respectively. The enhancement
2
of the emissions for complexes 1 and 2 compared with those
of the free ligands may be ascribed to the increase in the ligand
II
conformational rigidity due to their coordination to Cd ion
resulting in a decrease in the nonradiative decay of intraligand
excited states.[ They appear to be good candidates for novel
hybrid inorganic organic photoactive materials.
45]
Figure 3. Solid-state emission spectra of complexes 1 and 2 at room
temperature.
Conclusions
We have successfully synthesized two novel coordination
polymers under hydrothermal conditions. Complex 1 is a rare
example of a polycatenated array of 1D nanotubes, whereas
complex 2 exhibits a three-dimensional twofold interpenetrat-
ing diamondoid network. The analysis results reveal that the
flexibility of the bipyridyl ligands plays a significant role on
the structure of the final frameworks. In addition, the emission
in the blue region indicates that complex 1 and 2 appear to be
good candidates for promising blue-light-emitting materials.
Acknowledgement
This work was supported by the National Natural Science Foundation
of China (Nos. 20971004, 21171097), the Key Project of Chinese Min-
istry of Education (No. 210102), and the Natural Science Foundation
of Anhui Province (No. 11040606M45).
Figure 2. (a) Perspective view of the coordination environments of the
Cd atom in 2 with thermal ellipsoids at 30% probability. (b), (c)
II
Schematic views of a single adamantanoid cage in 2. (d) Schematic
representation of the twofold interpenetrating diamond network in 2.
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Z. Anorg. Allg. Chem. 2012, 455–460
© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.zaac.wiley-vch.de
459

G.-X. Liu, X.-F. Wang, H. Zhou
ARTICLE
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Received: August 18, 2011
Published Online: December 5, 2011
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