Self-organization of all-inorganic dodecatungstophosphate nanocrystallites

Article abstract of DOI:10.1021/ja070694c

The crystallinity and porosity of all-inorganic dodecatungstophosphate M₃PW₁₂O₄₀ (M = Cs, NH₄, Ag, denoted as MPW) particles are controlled by the changes in the synthetic temperatures and countercations. The MP

Full text of DOI:10.1021/ja070694c

Published on Web 05/17/2007
Self-Organization of All-Inorganic Dodecatungstophosphate
Nanocrystallites
Keigo Okamoto, Sayaka Uchida, Takeru Ito, and Noritaka Mizuno*
Contribution from the Department of Applied Chemistry, School of Engineering, The UniVersity
of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Received January 31, 2007; E-mail: tmizuno@mail.ecc.u-tokyo.ac.jp
Abstract: The crystallinity and porosity of all-inorganic dodecatungstophosphate M
3 4
PW12O40 (M ) Cs, NH ,
Ag, denoted as MPW) particles are controlled by the changes in the synthetic temperatures and
countercations. The MPW particles can be classified into three groups by the crystallinity and porosity: (i)
mesoporous “disordered” aggregates, (ii) microporous “self-organized” aggregates, and (iii) nonporous single
crystals. The formation and growth mechanism of MPW particles is expressed by three steps: formation
of nanocrystallites, assembly of the nanocrystallites to form aggregates, and the growth of aggregates by
the attachment of nanocrystallites. The time courses of the turbidity of the synthetic solution, the concentration
of the nanocrystallites, and the average particle sizes of MPW particles are well reproduced by the calculation
based on the mechanism.
to form the structure of bone tissue, in nature.6 The
morphologies (cubic, dodecahedron, or sphere) of molybdenum
Introduction
Self-organization is the spontaneous aggregation of molecules
or particles into patterns or structures.1-9 The driving forces of
the self-organization are van der Waals interaction, hydrophobic
interaction, aromatic interaction, hydrogen-bonding, electrostatic
interaction, etc.1 For example, in the synthesis of inorganic
metal oxide molecular sieves, the metal oxide framework
precursors are formed by the progressive hydrolysis and
condensation of metal aquo ions,10,11 and the organization of
the pore structure is achieved by the electrostatic interaction
between the precursors and the structure-directing organic
molecules.4 In the self-organization of inorganic particles
such as metals, metal oxides, and metal sulfides, the control of
the shape and size is achieved also by the addition of organic
oxide particles are controlled by the use of polyethylene oxide
homopolymer with different molar masses, which act as a
structure-directing reagent. The self-organization of all-
inorganic aggregates without the aid of organics is reported only
1
6
-4
1
7
18
for copper sulfate pentahydrate, calcium carbonate, silica
19
20
carbonate, and tin oxide. While the thermodynamic morphol-
ogy of the aggregates can be predicted from their crystal
structures, most shapes are empirically controlled by changing
2
1,22
the extent of supersaturation.
In addition, the crystallinity
and porosity of all-inorganic aggregates have not yet been
controlled and the mechanism of the formation and growth is
still unclear.
,12
Polyoxometalates are inorganic metal oxide anion nanoclus-
or organometallic molecules, which act as precursors or
ters that show unique chemical properties such as catalysis by
structure-directing reagents.2
,3,5,6,12-16
For example, the inorganic
changes in the constituent elements and countercations.2
3-31
The
hydroxyapatite crystallizes along the organic collagen fibers
dodecatungstophosphoric acid H3PW12O40 is a well-known solid
acid, and the partial substitution of protons with alkali metal
(
(
(
(
1) Whitesides, G. M.; Grzybowski, B. Science 2002, 295, 2418.
2) C o¨ lfen, H.; Mann, S. Angew. Chem., Int. Ed. 2003, 42, 2350.
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Misono, M.; Monson, P. A.; Pez, G.; Scherer, G. W.; Vartuli, J. C.; Yaghi,
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Kranendonk, M. J.; Welham, N. J. Science 2003, 302, 1194.
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UK, 2002.
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2
89.
(
(
(
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Lett. 2006, 6, 1505.
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(
(
(
10) Livage, J. Stud. Surf. Sci. Catal. 1994, 85, 1.
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Phys. Chem. B 1999, 103, 11021, and references therein.
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(
(
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J. AM. CHEM. SOC. 2007, 129, 7378-7384
10.1021/ja070694c CCC: $37.00 © 2007 American Chemical Society

All-Inorganic Dodecatungstophosphate Nanocrystallites
A R T I C L E S
Table 1. Properties of Various MPW Particlesa
synthetic
solubility
size of organized
form (nm)
ED
BET surface
area (m2 g-1)
d(BET)
(nm)
L(XRD)
(nm)
organized
form
(10- mol dm-3)
5
pattern
major pore
sample
temperature (K)
CsPW
298
0.221
1.30
1.22
5.20
250
3-10
ring
spot
spot
spot
spot
spot
spot
mesopore
micropore
micropore
micropore
none
148
82
91
51
9
6
12
11
19
1.1 × 10
2.4 × 10
2.4 × 10
13
24
27
59
9.3 × 10
7.7 × 10
5.6 × 10
i
ii
ii
ii
iii
iii
iii
2
2
2
3
5
3
4
368
1 × 10 to 3 × 10
2
NH4PW
298
1 × 10 to 4 × 10
2
3
4
68
73
3 × 10 to 1 × 10
4
2
2
2
2
2
2
2 × 10 to 1 × 10
2
AgPW
298
68
149
254
5 × 10 to 3 × 10
none
none
4
4
3
3
2 × 10 to 1 × 10
a
Size of organized form was measured from the SEM image. d(BET) (nm) is the average size of nanocrystallites calculated from the BET surface area
assuming a spherical shape. L(XRD) is the length of coherent ordered structure calculated by Scherrer’s equation from the 222 diffraction. Organized forms
are (i) mesoporous disordered nanocrystallites, (ii) microporous self-organized aggregates of nanocrystallites, and (iii) nonporous single crystals.
Figure 1. SEM images and ED patterns of (a) CsPW-298, (b) CsPW-368, (c) NH4PW-298, (d) NH4PW-368, (e) NH4PW-473, (f) AgPW-298, and (g)
AgPW-368.
ions or ammonium ions increases the surface area and
(M ) NH4, Cs, denoted as MPW) are self-organized aggregates
of 5-10 nm nanocrystallites, while the self-organization is not
porosity.4
,32-35
For example, Cs2.5H0.5PW12O40 possesses high
4
,41-43
porosity and surface acidity and is more active than the parent
acid for acid-catalyzed reaction such as alkylation, acylation,
controllable and the mechanism is still unclear.
On the
other hand, ring-shaped polyoxometalate clusters are formed
by the self-organization of several tens to more than a hundred
3
2,34,35
and hydrolysis.
Recently, self-organized aggregates of
36-43
38
polyoxometalates have been reported.
Porous M3PW12O40
molybdenum atoms in acidic solution with reducing reagents
3
9
or under UV irradiation. These molybdenum oxide clusters
further assemble with ionic interactions to form vesicles of ca.
(
(
(
32) Nishimura, T.; Okuhara, T.; Misono, M. Appl. Catal. 1991, 73, L7.
33) Lapham, D.; Moffat, J. B. Langmuir 1991, 7, 2273.
4
0
34) Essayem, N.; Coudrier, G.; Fournier, M.; Vedrine, J. C. Catal. Lett. 1995,
50 nm in size.
3
4, 223.
In this work, we demonstrate the successful control of the
self-organization of all-inorganic ionic nanocrystallites by using
MPWs and elucidate the self-organization mechanism.
(
(
(
35) Corma, A.; Martinez, M.; Martinez, C. J. Catal. 1996, 164, 422.
36) Long, D. L.; Cronin, L. Chem.-Eur. J. 2006, 12, 3698.
37) Rhule, J. T.; Neiwert, W. A.; Hardcastle, K. I.; Do, B. T.; Hill, C. L. J.
Am. Chem. Soc. 2001, 123, 12101.
(38) M u¨ ller, A.; Shah, S. Q. N.; B o¨ gge, H.; Schmidtmann, M. Nature 1999,
Experimental Section
3
97, 48.
(
39) Yamase, T.; Prokop, P. V. Angew. Chem., Int. Ed. 2002, 41, 466.
40) Liu, T.; Diemann, E.; Li, H.; Dress, A. W. M.; M u¨ ller, A. Nature 2003,
Materials. H
3
PW12
O
40‚nH
2
O (n ≈ 25) was synthesized and purified
(
44
4
26, 59.
by extraction with diethyl ether and recrystallization from water. The
(41) Mizuno, N.; Misono, M. Chem. Lett. 1987, 967.
(42) Ito, T.; Inumaru, K.; Misono, M. J. Phys. Chem. B 1997, 101, 9958.
(43) Okuhara, T.; Watanabe, H.; Nishimura, T.; Inumaru, K.; Misono, M. Chem.
Mater. 2000, 12, 2230.
-1
IR spectrum of H
(44) Bailar, J. C., Jr. Inorg. Synth. 1939, 1, 132.
J. AM. CHEM. SOC. VOL. 129, NO. 23, 2007 7379
3
PW12
O
40‚nH
2
O (KBr: 1079, 982, 892, and 800 cm )
9

A R T I C L E S
Okamoto et al.
Figure 2. TEM image and ED pattern of CsPW-298 nanocrystallites.
Figure 4. Time course of the SAXS profiles of the synthetic solution of
NH4PW-293. Inset: the relative signal intensity at 2θ ) 2.52° in the SAXS
profile. The solid line shows the concentration of [B] calculated with eq 9.
The SAXS profiles were the averaged data for (a) 13-33 min, (b) 38-58
min, (c) 62-82 min, (d) 87-107 min, and (e) 112-132 min.
mL) of H
15 mL) of Cs
93 K.
Characterization. The scanning electron microscopy (SEM) images
3
PW12
O
40‚nH
O (0.001 mol dm-3) to an aqueous solution
2
-
3
(
2
2 3
CO (0.0015 mol dm ) in a single step with stirring at
were obtained with an S-4700 (Hitachi) without metal coating. The
transmission electron microscopy (TEM) images and electron diffraction
(
ED) patterns were measured with a JEM-4000FX II (JEOL). The TEM
image and ED pattern of Cs-298 were measured with a JEM-2100
JEOL) at 77 K: CsPW-298 was dispersed in a resin and the resin
was sliced with a microtome to a thickness of 50 nm. N adsorption/
(
2
desorption isotherms of MPW were measured with an ASAP-2010
automatic adsorption apparatus (Micromeritics). Powder X-ray diffrac-
tion patterns were recorded with a MultiFlex diffractometer (Rigaku
Corporation) using Cu KR radiation.
Figure 3. Time courses of the photographs of the synthetic solution of
NH4PW-293 and turbidity. Solid squares and solid line show the experi-
mental and calculated data with eq 3, respectively.
The solubility of MPW was estimated as follows: MPW was
3-
dispersed in water at 298 or 368 K, and the quantity of PW12O40 in
the supernatant was estimated with the absorbance of the 260 nm band
of the Keggin anion (ligand-to-metal charge transfer (OfW) band).
The solubility in water at 368 K was also estimated by using the surface
free energy ( γj ) at 298 K. The value of γj was calculated with the
agreed with that reported in the literature.44 NH
was recrystallized in a water-ethanol mixed solvent. Cs
and AgNO (Wako) were used without further purification. Water was
purified by Milli-RX12R (Millipore Corporation).
Synthesis. MPWs (M ) NH , Cs, and Ag) were synthesized as
follows: A stoichiometric amount of an aqueous solution of NH HCO
(0.075 mol dm of M) was added dropwise to an
HCO
3
(Nacalai Tesque)
CO (Merck)
4
2
3
3
equation rcn ) 2 γj V/(kT ln(a/a
0
)), where rcn, k, T, and V are the size of
-
23
-1
the critical nuclei, Boltzmann constant (1.38066 × 10
J K ),
4
-27
3
46
temperature, and molecular volume (4.189 × 10 m ), respectively.
4
3
,
-
3
Concentrations were used in place of approximated activities (a
0
, initial
3
concentration of H PW12O40 (0.025 mol dm ); a, solubility of MPW).
Cs
aqueous solution of H
for 5 min with stirring to form a white colloidal solution. During
this procedure, the solution was kept at 298 or 368 K. NH PW-473
was synthesized under hydrothermal conditions as described
2 3 3
CO , or AgNO
-3
-
3
3-
3
PW12
O
40‚nH
2
O (0.025 mol dm of PW12
O
40
)
The estimated values of the solubility approximately agreed with the
experimental values (e.g., experimental (estimated) solubility of Cs-
4
-
3
3
68: 17.5 (13.0) µmol dm ).
4
5
Small-angle X-ray scattering (SAXS) measurements of the synthetic
before. For the mechanistic study, the synthetic solution of NH
4
PW
solution were carried out to detect nanocrystallites with a NANO-
Viewer diffractometer (Rigaku Corporation). The solution was sealed
in a quartz capillary (2 mm φ), and the SAXS spectra were measured
with Cu KR radiation (40 kV, 20 mA).
was prepared by adding an aqueous solution (15 mL) of H
3
PW12
O
40
‚
3
-3
nH
2
O (0.005 mol dm ) to an aqueous solution (15 mL) of NH
4
HCO
0.015 mol dm- ) in a single step with stirring at 293 K. The synthetic
3
(
solution of CsPW was prepared by adding an aqueous solution (15
45) Ito, T.; Hashimoto, M.; Uchida, S.; Mizuno, N. Chem. Lett. 2001, 1272.
(
46) Stumm, W. Chemistry of the Solid-Water Interface; Wiley: New York,
(
1992.
7
380 J. AM. CHEM. SOC. VOL. 129, NO. 23, 2007
9

All-Inorganic Dodecatungstophosphate Nanocrystallites
A R T I C L E S
Figure 5. (a) Schematic model of a nanocrystallite of ca. 3 nm in size and
(
b) the calculated X-ray diffraction pattern. Gray polyhedron shows the
3-
WO6 unit of PW12O40
.
UV-vis spectra of the synthetic solution were measured in the range
00-800 nm with a Fiberspec S-2450 (Soma). The absorbance (A)
2
was converted to the turbidity (τ) with the equation τ ) 2.303A. The
turbidity (τ) of the solution is defined by
I
I0
Figure 6. Time course of the particle size distribution of NH PW-293.
4
The average particle size is shown by the arrow. Each graph shows the
size distribution of 450-550 particles in the SEM images.
)
exp(-τl)
(1)
where I/I
light pass, respectively. According to Rayleigh-Gans theory
turbidity of the solution containing spherical particles is defined by
0
and l are the transmittance of light and the length of the
In order to apply eq 2 to a wide range of particle sizes, f(R)was
multiplied by eq 2 for the correction.51 Equation 3 was obtained by the
substitution of the parameters in eq 2:
4
7
48,49
the
3
2
2
τ
c
4πR m - 1
λd
53
2
p
)
(2)
τ ) 1.54 × 10 × V [C] × f(R)
(3)
(
2
)
m + 2
where [C] is particle concentration. The values of f(R) were obtained
from ref 51 and were approximated as a linear equation of R,
where c, d, λ, a, and m are the concentration of the particle [g cm-3],
density of the particle, wave length in water, relative particle size, and
relative refractive index, respectively. The density of the particle,
relative particle size, and relative refractive index are defined by d )
-
-
0.42R + 1.12 (0 < R < 2)
0.172R + 0.63 (2 e R < 2.5)
3
M/V
Avogadro’s number), R ) 2πr/λ, and m ) µ
of water (1.33); µ , refractive index of particle (1.68)), respectively.
p
N
A
(M, molecular weight; V
p
, volume of particle ()4/3πr ); N
A
,
1
/m
2
1
(µ , refractive index
f(R) ) -0.069R + 0.36 (2.5 e R < 4)
(4)
5
0
2
-
-
0.030R + 0.21 (4 e R < 5)
0.012R + 0.12 (5 e R < 6)
{
}
(
47) Atkins, P. W. Physical Chemistry; Oxford University Press: Oxford, 1990;
Chapter 17.
(
(
(
48) Lord Rayleigh. Proc. R. Soc. 1911, A84, 25.
49) Gans, R. Ann. Phys. 1925, 76, 29.
50) The best fit for the calculation of the turbidity of the NH
(51) Tabibian, R. M.; Heller, W.; Epel, J. N. J. Colloid Sci. 1956, 11, 195:
Theoretical turbidity calculated by eq 2 is compared to the experimental
one for polymer solution, of which the concentration and particle size are
known. The deviation between the theretical and experimental values are
corrected by the multiplication of f(R).
4
PW solution was
2
obtained with µ ) 1.68. The value agreed fairly well with the refractive
index of typical metal oxides (µ ) ca. 1.5) (American Institute of Physics
Handbook, 3rd ed.; McGrawHill: New York, 1973).
J. AM. CHEM. SOC.
9
VOL. 129, NO. 23, 2007 7381

A R T I C L E S
Okamoto et al.
Figure 7. Time course of the average particle size of NH4PW-293. Solid
squares and solid line show the experimental and calculated data with eq
1
4, respectively.
Results and Discussion
Systematic Control of Crystallinity and Porosity of MPW
Particles with Temperature and Countercations. Table 1 and
Figure 1 show the properties and SEM images of MPW
particles, respectively. The morphology (SEM) and crystallinity
(
ED) of the MPW particles systematically changed with
changes in the synthetic temperatures and the kinds of coun-
tercations as follows: CsPW synthesized at 298 K (designated
as CsPW-298) consisted of fine nanocrystallites of <10 nm in
size (Figure 1a). The nanocrystallites formed spherical ag-
gregates of 50-100 nm in size and were crystallographically
disordered, as indicated by the ring-patterned electron
diffractogram (ED). The ED of the nanocrystallites
showed discrete spots, indicating that the nanocrystallites are
crystalline (Figure 2). The intercrystallite spaces behaved as
mesopores.4 By increasing the synthetic temperature to 368
K (CsPW-368), the sizes of spherical particles were increased
to 100-300 nm (Figure 1b). The particles showed discrete spots
in the ED, indicating that the nanocrystallites are crystallo-
graphically ordered in the spherical particles (i.e., self-organized
aggregates).
Figure 8. Time courses of the (a) turbidity of the synthetic solution and
(b) averag particle size of CsPW-293. Solid squares and solid lines show
the experimental and calculated data, respectively.
1,43
grown under hydrothermal conditions showed a cubic cell
4
5
(space group, Pn3-m), and the powder XRD patterns of the
other MPWs were indexed to the same structure. In the unit
cell, polyoxometalates were placed at the vertices of the cube
and were positioned diagonally. Therefore, the density of the
{110} planes was higher than that of {100}, suggesting that
the crystal growth along the {110} planes to form a dodeca-
hedron is thermodynamically more stable than that along the
+
+
By changing the countercation from Cs to NH4 , spherical
particles of 100-400 nm in size were formed at 298 K (NH4-
2
-1
PW-298) (Figure 1c). The large BET surface area (91 m g )
indicates that the spherical particles are aggregates of
nanocrystallites of ca. 10 nm in size. The ED of NH4PW-298
showed discrete spots, indicating that the nanocrystallites are
crystallographically ordered in the same way as that of CsPW-
{
100} planes to form a cube. The BET surface area of NH4-
2
-1
PW-368 was 51 m g and still had a large micropore volume.
3
68.
By increasing the synthetic temperature to 368 K, dodeca-
hedral particles were formed and the sizes were increased to
.3-1 µm (Figure 1d). The dodecahedron was formed by 12
Nonporous dodecahedral single crystals of 25 µm in size were
grown under hydrothermal conditions (NH4PW-473, Figure
45
1
e).
0
+
By changing the countercation to Ag , nonporous dodeca-
equivalent planes of {110} of a cubic lattice. Generally, the
hedral particles of 0.5-3 µm in size were formed even at 298
K (AgPW-298) (Figure 1f). By increasing the synthetic tem-
perature to 368 K (AgPW-368), the particle size was increased
to 2-10 µm (Figure 1g). Thus, MPW particles can be classified
into three groups by their crystallinity and porosity: (i)
mesoporous “disordered” aggregates (CsPW-298), (ii) mi-
croporous “self-organized” aggregates (CsPW-368, NH4PW-
morphology of self-organized aggregates of a material with
a cubic lattice is either a cube52 formed by six equivalent
planes of {100} or a dodecahedron53 formed by 12 equivalent
planes of {110}. In the case of NH4PW, the single crystal
(
52) Lu, W.; Fang, J.; Stokes, K. L.; Lin, J. J. Am. Chem. Soc. 2004, 124, 11798.
53) Trikalitis, P. N.; Rangan, K. K.; Bakas, T.; Kanatzidis, M. G. J. Am. Chem.
Soc. 2002, 126, 12255.
(
7382 J. AM. CHEM. SOC.
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VOL. 129, NO. 23, 2007

All-Inorganic Dodecatungstophosphate Nanocrystallites
A R T I C L E S
cloudy with time. The turbidity showed an induction period and
then increased with time, in good agreement with the photo-
graphs.
Figure 4 shows the reproducible changes in the SAXS profiles
of the synthetic solution as a function of time. The intensity of
the 2θ ) 2-3° region (d ) 3-4.5 nm) initially increased,
reached a maximum around 50 min, and then decreased. This
peak position approximately agreed with that calculated with
dodecahedral NH4PW-293 nanocrystallites of 3 nm in size
(Figure 5). Therefore, the initial increase in the intensity of the
2θ ) 2-3° region suggests that the nanocrystallites are initially
formed and then the amount decreased with time.
The increase in the turbidity after the induction period
in Figure 3 and the decrease in the signal intensity of 2θ )
2
-3° suggest that the formation and growth of particles take
place by the consumption of the nanocrystallites. Figure 6 shows
the time course of the particle size distribution of NH4PW-293.
The size increased, while the distribution remained almost
unchanged with time, showing that the particles are monodis-
persed.
Kinetics and Mechanism. On the basis of the above results,
it is probable that the formation and aggregation of nanocrys-
tallites proceeds according to eqs 5-7; nanocrystallites are
3
-
+
formed with free PW12O40 and M (eq 5) and assemble to
form aggregates (eq 6), and then the aggregates grow by
attaching nanocrystallites (eq 7) (Scheme S1).
k1
A
9
8 B (nucleation)
(5)
(6)
(7)
k2
B + B
98 C (formation)
k3
B + C
98 C (growth)
where A, B, and C stand for the free ions (NH4 , PW12O403-),
+
nanocrystallites, and aggregates, respectively. According to eqs
5
-7, the following rate equations were obtained:
d[A]
dt
2
)
-k [A]
(8)
(9)
1
d[B]
dt
k
1
2
2
)
[A] - 2k [B] - k [B][C]
Figure 9. SEM images of NH4PW-298 particles: (a) as prepared and after
keeping in water (b) at 298 K for 1 week and (c) at 368 K for 24 h.
2
3
nB
d[C]
dt
2
2
98, and NH4PW-368), and (iii) nonporous single crystals
) k [B]
(10)
2
54
(NH4PW-473, AgPW-298, and AgPW-368).
5
7
Formation and Growth of NH4PW Particles.56 The turbid-
where k and k are rate constants, k is time dependent, and
nB is the average number of [PW12O40] in the nanocrystallite.
A], [B], and [C] could be calculated by solving eqs 8-10
1
2
3
3
-
ity of the synthetic solution of NH4PW-293 can be used as a
measure of the aggregation since NH4PW-293 are white particles
of 100-400 nm in size and scatter visible light. Figure 3 shows
the photographs of the synthetic solution of NH4PW-293 and
the turbidity. The solution was initially clear and then became
[
consecutively with ∆t ) 0.02 s, and the time courses of the
turbidity of the synthetic solution of NH4PW-293 (Figure 3),
the concentration of the nanocrystallites (inset in Figure 4), and
the average particle size of NH4PW-293 (Figure 7) were well
-
1
-1
3
-1 -1
reproduced by k1 ) 1.2 [s mol dm ], k2 ) 2.5 × 10 [s
(54) While MPW particles of groups ii and iii have an epitaxial connection
-
1
3
6
-1
-1
3
of nanocrystallites and the formation and growth of these particles would
mol dm ], and k3′ ) 9.9 × 10 [s mol dm ] (see the solid
lines). The results suggest that the formation and aggregation
of the nanocrystallite is much slower than the growth of the
particle (k1, k2 , k3). All these results support eqs 5-7. The
increase in the turbidity after the induction period (Figure 3)
and decrease in the signal intensity of 2θ ) 2-3° in the SAXS
profile (Figure 4) show that the particle growth by the
5
5
be regarded as the crystal growth, the nanocrystallites are randomly
oriented (disordered) in the MPW particles of group i. Therefore,
the formation and growth of MPW particles in part includes the crystal
growth.
(
55) Markov, I. Crystal Growth for Beginners; World Scientific: Hackensack,
NJ, 2003.
(
56) The formation and growth of the aggregates was made slower by lowering
the concentration of the ions in the synthetic solution of NH
investigate the mechanism in more detail.
4
PW to
J. AM. CHEM. SOC.
9
VOL. 129, NO. 23, 2007 7383

A R T I C L E S
Okamoto et al.
attachment of the nanocrystallites (eq 7) becomes dominant after
a certain period (ca. 50 min).
The time courses of the turbidity (Figure 8a) and average
particle size (Figure 8b) of CsPW-293 were also well reproduced
form, and the mesopores were left between the nanocrystallites
probably because the dissolution and reprecipitation of the
nanocrystallites hardly occur. As for the compounds in group
ii with medium solubility, the epitaxial interfaces were formed
to give a thermodynamically stable morphology (i.e., dodeca-
hedron), and certain amounts of micropores were left between
the nanocrystallites. As shown in Figure 9, by keeping NH4-
PW-298 in water (at 298 K for 1 week or at 368 K for 24 h),
the morphology of the particle changed from sphere to dodeca-
hedron with a fair maintenance of the particle size. Therefore,
epitaxial interfaces are formed by the slight dissolution and
reprecipitation of the nanocrystallites. As for the compounds
with high solubility (group iii), nonporous dodecahedral crystals
were formed probably because the dissolution and reprecipitation
of the nanocrystallites easily occur.
2
-1
-1
3
by the calculation with k1 ) 2.5 × 10 [s mol dm ], k2 )
-
1
-1
3
8
-1
-1
3 62
6
.5 [s mol dm ], and k3′ ) 8.1 × 10 [s mol dm ].
Thus the mechanism could also be applied to the formation of
CsPW particles.
On the basis of the mechanism described above and the
reverse reactions (solubilization), the decreases in the crystal-
linity (crystallographic coherence) and the increases in the
porosity (BET surface area) of MPWs with the decrease in the
solubility (Table 1) were explained.63 CsPW-298, with the
lowest solubility (group i), did not aggregate into the crystalline
(
57) On the assumption that the growth of the aggregates by attaching
nanocrystallites is a diffusion-controlled reaction, the rate of the consump-
tion of nanocrystallites by the attachment to an aggregate is expressed by
Conclusion
The self-organization of all-inorganic nanocrystallites was
successfully controlled by the changes in the synthetic temper-
atures and countercations. The formation and growth mechanism
of MPW particles was elucidated by the mechanism that
consisted of three steps: formation of nanocrystallites, assembly
of the nanocrystallites to form aggregates, and the growth of
aggregates by the attachment of nanocrystallites.
3 A A
k ) 4π(r + rnano)DN (11), where r, rnano, N , and D are the average
radius of aggregates, average radius of nanocrystallites (rnano ) 3 nm),
5
8
Avogadro’s number, and the diffusion constant, respectively. According
to the Stokes-Einstein equation, the diffusion constant D is expressed by
5
9
D ) kT/6πη(1/r + 1/rnano) (12), where η is the viscosity of water. The
average number of nanocrystallites (n
C
) in a monodispersed particle is given
t
by n
C
) (∫ k
3
[B][C] dt)/[C] (13), where V is the volume of the synthetic
0
6
0
solution. Thus, the average radius of the aggregate is expressed by r )
1/3
nano
r n
C
× 1.2 (14). By the use of eq 14, eq 15 is derived from eq 11 as
follows: k
3
) k
3
′(r + rnano)(1/r + 1/rnano) (15), where k
3
′ is (2kTN A)/3η
A
and A is a coefficient taking the reverse reaction of eq 7 (dissolution of the
aggregate) into account.
Acknowledgment. Mr. Tsunakawa (Univ. of Tokyo) is
acknowledged for the measurements of ED patterns. Mr. Endo
(
(
(
(
(
58) Atkins, P. W. Physical Chemistry; Oxford University Press: Oxford, 1990;
Chapter 28.
(JEOL) is acknowledged for the measurements of TEM and
59) Atkins, P. W. Physical Chemistry; Oxford University Press: Oxford, 1990;
Chapter 25.
ED patterns of Cs-298. Mr. Hoshino (Rigaku Corporation) is
acknowledged for the measurements of SAXS patterns. This
work was supported in part by the Core Research for Evolutional
Science and Technology (CREST) program of the Japan Science
and Technology Agency (JST) and a Grant-in-Aid from the
Ministry of Education, Culture, Sports, Science, and Technology
of Japan.
60) The constant 1.2 in eq 14 was calculated with (0.58)-1/3, where 0.58 is the
6
1
typical filling factor of the random packing of spheres.
61) Privman, V.; Goia, D. V.; Park, J.; Matijevi, E. J. Colloid Sci. 1999, 213,
3
6.
′ ) 9.9 × 10 [s mol-1 dm ] for NH
6
-1
3
62) The fitting of the turbidity gave k
3
4
-
9
-1
-1
3
PW, and the value was smaller than 1.9 × 10 [s mol dm ], which
3 A
was calculated by k ′ ) 2kTN /3η on the assumption that the reverse
reaction of eq 7 is negligible (i.e., A ) 1). The discrepancy was probably
due to the contribution of the dissolution of the aggregates (i.e., reverse
8
reaction of eq 7). On the other hand, the k
3
value (8.1 × 10 ) for CsPW
9
agreed fairly well with the calculated value (1.9 × 10 ).
Supporting Information Available: Scheme S1 shows a
schematic illustration of the formation and aggregation of
nanocrystallites according to eqs 5-7. This material is available
free of charge via the Internet at http://pubs.acs.org.
(63) The solubility of MPW in water increases with the increase in the hydration
enthalpy of the countercation (Huheey, J. E. Inorganic Chemistry; Harper
&
Row Publishers: New York, 1983; Chapter 3). The hydration enthalpy
is proportional to the square of the charge and the inverse of the ionic
radius. Therefore, the solubility of MPWs would decrease in the order
+
+
+
AgPW (Ag , 1.29 Å) > NH
which agreed with the experimental results.
4 4
PW (NH , 1.51 Å) > CsPW (Cs , 1.81 Å),
JA070694C
7384 J. AM. CHEM. SOC.
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VOL. 129, NO. 23, 2007