Facile surfactant-free synthesis of monodisperse Ni particles via a simple solvothermal method and their superior catalytic effect on thermal decomposition of ammonium perchlorate

Article abstract of DOI:10.1039/c0nj00987c

Successful synthesis of monodisperse nickel particles with narrow particle size distributions is reported for the first time via a simple solvothermal method with ultrasonic treatment using no surfactants. The Ni products are characterized by X-ray powder diffraction, scanning electron microscopy, and transmission electron microscopy. The as-synthesized monodisperse Ni particles show a spherical morphology with the mean particle size of 46.2, 60.1 and 113.7 nm for the reaction time of 0.5, 1 and 3 h, respectively at a low temperature of 100 °C. The catalytic effect is investigated for the Ni particles on the thermal decomposition of ammonium perchlorate (AP) using differential thermal analysis and thermogravimetry. For the purpose of comparison, as-prepared and commercial non-monodisperse Ni particles are used for examining the catalytic effect. The monodisperse Ni particles show a superior catalytic effect over the non-monodisperse Ni counterparts with a similar mean particle size. The surface areas of Ni particles are measured by Brunauer-Emmett-Teller (BET) technique. A theoretical consideration is also presented for analysis of the surface areas of monodisperse and non-monodisperse particles. Both the BET and theoretical results show that the surface area of monodisperse particles is higher than that of non-monodisperse counterparts. Consequently, the catalytic effect of Ni particles on thermal decomposition of AP is explained in terms of the surface areas. The Royal Society of Chemistry and the Centre National de la Recherche Scientifique.

Full text of DOI:10.1039/c0nj00987c

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PAPER
Facile surfactant-free synthesis of monodisperse Ni particles via a simple
solvothermal method and their superior catalytic effect on thermal
decomposition of ammonium perchlorate
ab
a
ab
a
Xiao-Jun Shen, Jiao-Ping Yang, Yu Liu, Yong-Song Luo* and
ac
Shao-Yun Fu*
Received (in Montpellier, France) 16th December 2010, Accepted 25th March 2011
DOI: 10.1039/c0nj00987c
Successful synthesis of monodisperse nickel particles with narrow particle size distributions is
reported for the first time via a simple solvothermal method with ultrasonic treatment using no
surfactants. The Ni products are characterized by X-ray powder diffraction, scanning electron
microscopy, and transmission electron microscopy. The as-synthesized monodisperse Ni particles
show a spherical morphology with the mean particle size of 46.2, 60.1 and 113.7 nm for the
reaction time of 0.5, 1 and 3 h, respectively at a low temperature of 100 1C. The catalytic effect is
investigated for the Ni particles on the thermal decomposition of ammonium perchlorate (AP)
using differential thermal analysis and thermogravimetry. For the purpose of comparison,
as-prepared and commercial non-monodisperse Ni particles are used for examining the catalytic
effect. The monodisperse Ni particles show a superior catalytic effect over the non-monodisperse
Ni counterparts with a similar mean particle size. The surface areas of Ni particles are measured
by Brunauer-Emmett-Teller (BET) technique. A theoretical consideration is also presented for
analysis of the surface areas of monodisperse and non-monodisperse particles. Both the BET and
theoretical results show that the surface area of monodisperse particles is higher than that of
non-monodisperse counterparts. Consequently, the catalytic effect of Ni particles on thermal
decomposition of AP is explained in terms of the surface areas.
2
2
the added advantage from the applied point of view.
Surfactants are generally used to synthesize monodisperse Ni
1
. Introduction
Transition metal and alloy fine particles have attracted much
attention owing to their promising potential applications in
magnetic storage, medical diagnosis, magnetic fluid, and
6,16,17,19–24
particles,
resulting in fine particles with narrow size
distributions. Nonetheless, the particles are coated with a layer
of surfactant, which is undesirable in practical applications.
In addition, it will increase the prime cost in industrial
production. On the other hand, big particles with broad
1
–5
catalysis. Of these fine particles, Ni particles are important
magnetic materials that are expected to find applications as
6
catalysts for hydrogenation of nitrobenzene and thermal
size distributions are often obtained under no surfactant
18,25
7
–10
decomposition of ammonium perchlorate (AP),
12
fillers for magnetic inks or ferrofluids. Thus, various
methods have been reported for synthesis of Ni fine particles,
as well
conditions.
synthesize monodisperse Ni fine particles without using any
However, it is still a challenging task to
1
1
26
surfactants. Li et al. reported successful synthesis of mono-
1
3,14
such as chemical vapor deposition,
1
decomposition, microwave-assisted polyol process, and
sonochemical
disperse Ni nanoparticles via a solvothermal method using
6
oleylamine as the surfactant. In the present work it is first
5
16
1
7–26
chemical reduction.
Synthesis of monodisperse Ni fine
reported that monodisperse Ni fine particles are obtained via
the solvothermal method without using any surfactants under
mild conditions, and the difference between the present work
particles has attracted great interest due to the dependence
of their physical properties on their size and surface area and
6
and the literature is briefly described.
a
As a key energetic material for rocket technologies,
ammonium perchlorate (AP) is the most common oxidizer in
Technical Institute of Physics and Chemistry, Chinese Academy of
Sciences, Beijing 100190, China. E-mail: syfu@mail.ipc.ac.cn,
ysluo@mail.ipc.ac.cn
Graduate School, Chinese Academy of Sciences, Beijing 100039,
China
International Centre for Materials Physics, Chinese Academy of
Sciences, Shenyang 110016, China
7
composite solid propellants (CSPs). The characteristic of the
b
thermal decomposition of AP is believed to influence the
performance of CSPs and is remarkably sensitive to additives.
Transition metal oxides are frequently used as a burning rate
c
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New J. Chem., 2011, 35, 1403–1409 1403

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2
7–30
modifier for CSPs.
Recently, new catalysts based on fine
sealed again and heated at 100 1C for 3 h and then allowed to
cool to room temperature. To investigate the effects of
reaction time and reaction temperature, various reaction times
and temperatures were employed in synthesis of Ni products.
When the reaction finished, the black fluffy solid product was
separated from the solution by centrifugation, washed for
several times with ethanol.
particles have been reported in the thermal decomposition of
AP. For example, Ni, Cu, Al, Ni/Ag, Ni/CNTs, NdCrO3,
Cr O , Ni/Zn, Ni/TiO particles were reported as the
2
3
2
7
–10,31–36
additives. An important goal in the emerging field of
nanotechnology is to make fine particles with a very large
3
7,38
surface area
and thus the ratio of surface atoms to non-
surface atoms is much larger than in a bulk material, and
finally surface species display local geometry differing from the
The phase purity of the products was examined by X-ray
diffraction (XRD) on a X-ray diffractometer with Cu-Ka
radiation (l = 1.5418 A). Scanning electron microscopy
3
9
˚
bulk and strongly influencing chemical reactivity. On the
other hand, for fine particles, the surface area depends on their
size distribution. Nonetheless, no theoretical consideration has
been made yet for the dependence of the surface area on the
particle size distribution. In this work a simple model is
developed to demonstrate that monodisperse particles would
have a relatively higher surface area compared to non-
monodisperse counterparts. It is thus inferred that mono-
disperse Ni particles would show a superior catalytic effect
on the thermal decomposition of AP over non-monodisperse
Ni particles.
(SEM) images were obtained using a Hitachi S-4300 micro-
scope (Japan). Transmission electron microscopy (TEM)
observations were carried out on a JEOL JEM-2010 instru-
ment in bright field. The Ni particle size was measured by the
software SemAfore 4.0 as did in our previous work on
4
0
measurement of carbon nanotube diameter. The surface
areas for Ni particles were measured via Brunauer-Emmett-
Teller (BET) technique by nitrogen adsorption isotherms at
77 K using a Quadrasorb SI-MP analyzer.
To test the catalytic effect of Ni particles on the thermal
decomposition of AP, the fine Ni particles were mixed with AP
in ethanol by the ultrasonic technique for several minutes and
the sample was put into a vacuum drying chamber, which was
then dried at room temperature for 24 h. Finally, the powder
mixture was ground carefully for 10 min and some of the
sample was detected by DTA and TG at a heating rate of
Herein the solvothermal method is first reported for facile
synthesis of monodisperse Ni particles with ultrasonic
treatment without using any surfactants. The as-prepared
monodisperse Ni particles show a spherical morphology with
the mean size of 46.2, 60.1 and 113.7 nm respectively for the
reaction time of 0.5, 1 and 3 h at 100 1C. A possible reduction
reaction during the solvothermal process can be formulated as
follows:
ꢀ1
ꢀ1
20 1C min in a 20 ml min N atmosphere by a BY DTU-1A
2
instrument with a-Al O as the reference material. The Ni
2
3
particle content in the mixture was 5 wt%. For the purpose of
comparison, non-monodisperse Ni particles were prepared at
2
+
ꢀ
Ni + N H + 4OH - 2Ni(s) + N (g) + 4H O
2 4 2 2
2
6
The structural and morphological characterization of the Ni
particles is conducted using X-ray powder diffraction,
scanning electron microscopy, and transmission electron
microscopy. The catalytic effect of the as-prepared Ni particles
is investigated on the thermal decomposition of AP. For the
purpose of comparison, as-prepared and commercial non-
monodisperse Ni particles are used to examine their catalytic
effect. It is demonstrated that the as-prepared monodisperse
Ni particles show a superior catalytic effect on the thermal
decomposition of AP over the non-monodisperse Ni counter-
parts. The surface areas of Ni particles are measured by
100 1C for 3 h using the simple stirring method without
ultrasonic treatment also using no surfactants. Moreover,
commercial non-monodisperse Ni particles with a mean size
of 110.3 nm purchased from Beijing Nachen S&T Ltd were
used for studying the catalytic effect to justify the advantages
of monodisperse particles.
3. Results and discussion
3
.1 Characterization of Ni particles
Brunauer-Emmett-Teller (BET) technique. Meanwhile,
a
Fig. 1a shows the SEM image of the Ni particles prepared at a
reaction temperature of 100 1C for 3 h. Fig. 1a clearly
demonstrates the formation of monodisperse Ni particles with
a high yield. The as-prepared Ni particles have a spherical
morphology and their mean particle size is about 113.7 nm.
Fig. 1b shows the TEM image of the as-synthesized Ni
particles, which displays that the Ni particles have a narrow
particle size distribution and is consistent with the SEM results
(Fig. 1a). Moreover, the corresponding electron diffraction
(SAED) pattern of the selected area of the as-synthesized Ni
particles is displayed in the inset of Fig. 1b. Three ring patterns
corresponding to plane distances of 0.203 nm, 0.176 nm, and
0.124 nm can be observed, suggesting that the Ni spheres are
polycrystalline. And the results are consistent with the indices
simple model is developed for analysis of the surface areas
of monodisperse and non-monodisperse particles. The results
for the surface areas are then used to explain the catalytic
activity of Ni particles.
2
. Experimental
All the chemicals were analytic grade without further
purification. In a typical synthetic route, 2.8 mmol of
Ni(CH
the mixture was treated with the ultrasonic technique for
0 min. After this, the mixture was transferred into a 50 ml
3
COO)
2
2
ꢁ4H O was dissolved in 35 ml of ethanol, then
2
Teflon-sealed autoclave and maintained at 85 1C for 3 h, then
naturally cooling to room temperature. In addition, 1.75 mmol
of NaOH and 1.4 ml of hydrazine hydrate were added to the
above solution and the resulting mixture was treated with the
ultrasonic technique for another 10 min. The autoclave was
1
111, 200, and 222 of the face-centered cubic (fcc) Ni phase.
Fig. 1c shows the typical high-resolution transmission electron
microscopy (HRTEM) image of the part of an individual Ni
particle and the enlarged image of the area marked by a
1
404 New J. Chem., 2011, 35, 1403–1409
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the Ni particles synthesized at 100 1C, respectively for 0.5 h,
1
h and 3 h. The monodisperse Ni particles are obtained with
the mean diameter of 46.2, 60.1 and 113.7 nm, respectively. It
can be observed that the as-prepared Ni particles have
spherical morphology and their mean particle size increases
with the reaction time. To get further information about the
microstructure of these spherical Ni particles, the products
were investigated by TEM. Fig. 2d–f shows the TEM images
of the Ni particles prepared at 100 1C for 0.5 h, 1 h and 3 h.
From the TEM observations, it can be seen that the Ni
particles exhibit a spherical morphology and their mean
particle size gradually increases with increasing the reaction
time. Moreover, the size distribution of Ni particles becomes
more uniform and narrower as the reaction time increases,
possibly due to the Ostwald ripening (phase coarsening)
4
1
effect, which can be confirmed from the data for the standard
deviations (see Fig. 3). The absolute standard deviations
(4.9, 5.7 and 7.1 nm) correspond to the relative standard
deviations of 10.5%, 9.4% and 6.3% for the reaction time of
Fig. 1 (a) SEM image of monodisperse Ni particles, (b) TEM image
of monodisperse Ni particles and the inset is the corresponding SAED
result, (c) HRTEM image of the part of an individual Ni particle and
the enlarged image of the area marked by a rectangle in panel and
(d) XRD pattern of the as-prepared nickel particles.
0.5 h, 1 h and 3 h, respectively. The monodisperse Ni particles
prepared via a solvothermal method have much narrower size
rectangle in panel (c) with a lattice spacing of about 0.176 nm.
The XRD pattern of the as-synthesized Ni particles is
displayed in Fig. 1d. The two peaks detected for the sample
are assigned to diffractions from the (111) and (200) planes
of the face-centred cubic (fcc) structured Ni particles,
respectively. This is consistent with the data in the standard
card (JCPDS card No. 4-485) for Ni. Broadening of the peaks
compared to the standard card exhibits the fine crystalline nature
of the sample. No impurity peaks were detected in the experi-
mental range, indicating the formation of pure Ni particles.
In order to study the variance of the size of monodisperse Ni
particles with the reaction time, the time-dependent experi-
ments were carried out and the samples were collected at
different time intervals. Fig. 2a–c shows the SEM images of
distributions compared to the previously reported Ni particles
prepared via the hydrothermal method without using
18,25
surfactants.
Moreover, as shown in Fig. 4 for XRD
patterns of as-prepared samples, the peak intensity increases
with increasing the reaction time, indicating that the crystalline
degree becomes higher as the reaction time increases.
6
The difference between the present work and the literature
is briefly described here. Monodisperse Ni particles were
successfully prepared by Li et al. via the solvothermal method
using oleylamine as the surfactant by vigorously stirring the
suspension before being transferred into a Teflon cup in a
6
stainless steel-lined autoclave. The present work without
using any surfactants has employed the ultrasonic technique
instead of the simple stirring method during processing, also
leading to successful synthesis of monodisperse Ni particles.
The high power during the ultrasonic treatment might play a
role in size control of Ni particles. It was reported that the
sonication role could contribute to the sonocrystallization,
allowing the reduction of particle size and the increase in the
particle size homogeneity owing to control of the local nucleus
4
2
population. This is confirmed by Fig. 5 showing that the
as-prepared Ni product using the simple stirring method
without ultrasonic treatment is the non-monodisperse Ni
Fig. 2 SEM and TEM images of the as-prepared monodisperse Ni
particles at 100 1C for the reaction time of (a, d) 0.5 h, (b, e) 1 h, and
Fig. 3 The mean particle size and standard deviation of the nickel
particles prepared at 100 1C for the various reaction time of 0.5 h, 1 h,
and 3 h, respectively.
(c, f) 3 h, respectively.
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SEM images of the Ni particles synthesized at various reaction
temperatures are shown in Fig. 7. The mean diameter is
estimated to be 113.7, 118.1, 112.2 and 119.6 nm respectively
for the Ni particles synthesized at 100, 160, 190 and 220 1C.
This indicates that the reaction temperature has no obvious
effect on the particle size for the reaction time of 3 h. Since the
relatively low reaction temperature (100 1C) is preferred in
practical applications, the details for other cases of higher
reaction temperatures will not be discussed here.
3
.2 Catalytic effect of Ni particles on thermal decomposition
of ammonium perchlorate
Fig. 4 XRD patterns of the as-prepared nickel particles at 100 1C for
the reaction time of (a) 0.5 h, (b) 1 h and (c) 3 h, respectively.
It is known that the thermal decomposition of the pure AP has
three stages as shown in Fig. 8. In the first stage, the
endothermic peak at 258.0 1C is attributed to its transition
4
3,44
from orthorhombic form to cubic form.
In the second
stage, the exothermic peak appears at 314.1 1C, which is
ascribed to the partial decomposition of AP and the formation
4
5
of an intermediate product. In the third stage, the exothermic
peak appears at 410.6 1C. When Ni particles were added to
AP, all samples have the similar endothermic peaks at about
2
58.0 1C, indicating that the Ni particles have little effect on
the crystallographic transition temperature of AP. But in the
relatively high temperature region, the samples containing Ni
particles have dramatic changes in the exothermic peaks of AP
decomposition. When 5 wt% Ni particles were added to AP,
the original exothermic peak of pure AP at 410.6 1C
disappeared and only one exothermic peak was obtained.
The exothermic peak temperature was 307.2 1C, 300.7 1C
and 300.2 1C for the monodisperse Ni particles of 113.7 nm,
Fig. 5 SEM image of non-monodisperse Ni particles prepared at
100 1C for 3 h using the simple stirring method without ultrasonic
treatment. The mean size of the as-prepared non-monodisperse Ni
particles is measured to be 115.6 ꢂ 33.9 nm.
particles. The as-prepared non-monodisperse Ni particles with
a wide size distribution have a mean size of 115.6 nm ꢂ 33.9 nm,
which is very close to that (113.7 ꢂ 7.1 nm) for the mono-
disperse Ni particles with a narrow size distribution prepared
at 100 1C for 3 h with ultrasonic treatment. Moreover, the
6
0.1 nm and 46.2 nm in their diameter, respectively. And the
exothermic peak temperature was 330.4 1C for the as-prepared
non-monodisperse Ni particles with a diameter of 115.6 ꢂ 33.9 nm
and 340.1 1C for the commercial non-monodisperse Ni
particles (see Fig. 9) with a diameter of 110.3 ꢂ 99.2 nm
purchased from Beijing Nachen S&T Ltd.
6
reaction time of 3 and 6 h in the literature corresponds to the
mean particle size of 45 and 100 nm while the reaction time of
The above results indicate that Ni particles have a signifi-
cant effect on the decomposition temperature of AP. For the
monodisperse Ni particles, the decomposition temperature of
AP decreases as the particle size decreases. Namely, smaller Ni
particles would lead to higher catalytic effect, which is
0.5 and 3 h in the present work corresponds to the mean
particle size of about 46 and 114 nm.
Furthermore, the Ni particles were also synthesized at the
temperature of 100 1C for 12 and 24 h. The result revealed that
the particles undergo no obvious change on further prolonging
the reaction time, as shown in Fig. 6. The mean diameter of the
synthesized Ni particles after the reaction time of 12 and 24 h
is respectively 114.3 and 113.5 nm, which are approximately
equal to that after the reaction time of 3 h. Except the reaction
temperature 100 1C, other reaction temperatures such as 160,
1
90 and 220 1C were also employed for the reaction time of 3 h.
Fig. 6 SEM images of the monodisperse Ni particles at 100 1C for the
reaction time of (a) 12 h and (b) 24 h, respectively.
Fig. 7 SEM images of pure Ni spheres synthesized at the reaction temp-
erature of (a) 100 1C, (b) 160 1C, (c) 190 1C and (d) 220 1C, respectively.
1
406 New J. Chem., 2011, 35, 1403–1409
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Fig. 8 DTA curves of the AP samples after addition of various Ni
particles: (a) pure AP and (b) wt% 110.3 nm commercial
Fig. 10 TG patterns of the AP samples after addition of various Ni
particles: (a) pure AP, (b) 5 wt% 110.3 nm commercial non-
monodisperse Ni particles, (c) 5 wt% 115.6 nm as-prepared non-
monodisperse Ni particles, (d) 5 wt% 113.7 nm Ni monodisperse
particles, (e) 5 wt% 60.1 nm Ni monodisperse particles, (f) 5 wt%
5
non-monodisperse Ni particles, (c) 5 wt% 115.6 nm as-prepared
non-monodisperse Ni particles, (d) 5 wt% 113.7 nm Ni monodisperse
particles, (e) 5 wt% 60.1 nm Ni monodisperse particles, (f) 5 wt% 46.2 nm
monodisperse Ni particles.
4
6.2 nm Ni monodisperse particles.
1
13.7 nm), 292.5 1C (monodisperse Ni particles of 60.1 nm)
and 291.7 1C (monodisperse Ni particles of 46.2 nm), respec-
tively. And their final thermal decomposition occurs at
457.2 1C, 378.6 1C, 365.3 1C, 343.8 1C, 325.1 1C and 322.5 1C,
respectively. Obviously, the final decomposition temperature
is decreased by about 78.6 1C, 91.9 1C, 113.4 1C, 132.1 1C and
1
34.7 1C, respectively for the above five cases containing Ni
particles compared to the pure AP case. Obviously, the
decrease in the final decomposition temperature of AP in the
present study by the addition of monodisperse Ni particles is
much larger than that by the addition of non-monodisperse Ni
particles with the similar mean size. This result suggests that
monodisperse Ni particles with narrow size distribution are
advantageous over non-monodisperse Ni particles in the
catalytic effect on the thermal decomposition of AP. It is
known that the catalytic activity of metal particles is a
Fig. 9 SEM image of the commercial non-monodisperse Ni particles
with the mean size of 110.3 ꢂ 99.2 nm.
4
6
consistent with the literature. This is due to the fact that the
surface area of relatively smaller Ni particles is larger due
to its relatively smaller particle size and thus there are more
reaction sites on the surfaces of smaller particles. This can be
confirmed by the BET results. The BET surface areas
measured for the Ni particles of 113.7 nm, 60.1 nm and
4
7
function of their surface area. The BET results shown above
have confirmed that monodisperse Ni particles have a higher
surface area compared to non-monodisperse counterparts and
thus would have more surface reaction sites for catalytic
activity. The surface areas of monodisperse and non-
monodisperse fine particles are also derived below based on
the simple assumption of uniform particle size distribution.
It is assumed that the fine particles have a uniform size
distribution with the minimum size a and the maximum size
b at the two extremes, which is defined as system one. The
radius of the spherical particles is assumed to be r. Then, the
particle size distribution function f(r) can be expressed by
1/(b ꢀ a). Thus, the mean particle size is given by:
2
ꢀ1
2
ꢀ1
2
ꢀ1
4
6.2 nm are 10.109 m g , 17.011 m g and 18.972 m g ,
respectively. Moreover, the monodisperse Ni particles show a
lower decomposition temperature of AP compared to the
non-monodisperse Ni counterparts with similar diameters
(
see curves b–d of Fig. 8), indicating that the monodisperse
Ni particles have a higher catalytic effect than the non-
monodisperse Ni particles. This can also be explained in terms
of their surfaces areas. The BET surface areas measured for
the as-prepared and commercial non-monodisperse Ni
2
ꢀ1
2
ꢀ1
particles are respectively 7.487 m g and 5.806 m g , lower
ꢀ1
2
than that (10.109 m g ) of the as-prepared monodisperse Ni
particles with a similar mean size.
b
Z
1
r ¼ rfðrÞ dr ¼ ða þ bÞ
ð1Þ
Furthermore, the weight loss of AP is determined from the
TG curves of different samples (Fig. 10). Fig. 10a exhibits
two weight loss steps while Fig. 10b–d exhibit only one weight
loss step. The results are in agreement with those of the
exothermic peaks of the DTA curves in Fig. 8. The initial
thermal decomposition takes place at 305.5 1C (pure AP),
2
a
Similarly, we can get the mean particle size when the minimum
and maximum particle size is respectively c and d, which is
defined as system two:
d
Z
3
03.2 1C (commercial non-monodisperse Ni particles of
10.3 nm), 302.1 1C (as-prepared non-monodisperse Ni
1
r ¼ rfðrÞ dr ¼ ðc þ dÞ
ð2Þ
1
2
particles of 115.6 nm), 300.3 1C (monodisperse Ni particles of
c
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It is assumed that the two particle systems have the same mean
particle size. Thus, we can get from the above two equations:
The thermal decomposition of AP has been investigated for
both monodisperse and non-monodisperse Ni particles. The
results indicated that the monodisperse Ni particles had the
superior catalytic activity over non-monodisperse Ni counter-
parts. A simple theoretical consideration was proposed for the
comparison in the surface area of monodisperse and non-
monodisperse fine particles, which is in agreement with the
BET results. Finally, it was concluded that the excellent
catalytic effect could be ascribed to the narrow-sized nature
of monodisperse Ni particles with a higher surface area
compared to non-monodisperse Ni particles.
a + b = c + d
(3)
Moreover, the particle content (or particle volume) is also
assumed to be the same for the two systems with different
particle size distributions. Then, we can get:
b
Z
1
3
3
2
2
r ¼ r fðrÞ dr ¼ ða þ bÞða þ b Þ
ð4Þ
4
a
and:
Acknowledgements
d
Z
1
3
3
2
2
r ¼ r fðrÞ dr ¼ ðc þ dÞðc þ d Þ
ð5Þ
We gratefully acknowledge the financial support from the
National Basic Research Program of China (no. 2010CB934500),
Beijing Municipal Natural Science Foundation (Nos. 2091004
and 2082023) and China Postdoctoral Science Foundation
Funded Project. The assistance in preparing Ni products from
Mr Xiao-Jun Dai and Dr Lu-Ping Zhu is appreciated.
4
c
From eqn (3)–(5), we can get:
2
a + b = c + d
2
2
2
(6)
The surface area of a sphere is proportional to the square of
the particle size. Thus, a comparison is presented between the
mean value of the square of the particle size. We can obtain for
system one:
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2
2
2
2
r ¼ r fðrÞ dr ¼ ða þ ab þ b Þ
ð7Þ
¨
¨
cker, N. C. Bigall, P. Olk,
3
¨
a
3
4
´
´
and for system two:
2
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Z
1
2
2
2
2
r ¼ r fðrÞ dr ¼ ðc þ cd þ d Þ
ð8Þ
4
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We compare the difference in the mean value of the square of
the particle size ranging from a to b and from c to d. It is
assumed that the size span (d ꢀ c) for non-monodisperse
particles is much greater than the size span (b ꢀ a) for
monodisperse particles. Since a + b = c + d, it is easy to
deduce in terms of algebra that the product of (aꢁb) would be
much greater than the product of (cꢁd). Thus, it can be
concluded from eqn (7) and (8) that the surface area of the
monodisperse particles is much greater than that of non-
monodisperse particles with the same mean particle size at a
fixed particle volume. This is in agreement with the BET
results stated above. The relatively larger surface area would
supply more reaction sites on the surfaces of fine particles
for the catalytic activity. Consequently, it can be easily under-
stood why the as-prepared monodisperse Ni particles in the
present work show a superior catalytic effect on thermal
decomposition of AP compared to the non-monodisperse Ni
counterparts
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