A Comparison of Catalytic Effect of Nano-Mn3O4 derived from MnC2O4.2H2O and Mn(acac)3 on Thermal Decomposition of Ammonium Perchlorate

Article abstract of DOI:10.1002/zaac.201700376

The formation and catalytic effect of Mn₃O₄ spinel nanoparticles on thermal decomposition of ammonium perchlorate (AP) were investigated and compared to two manganese precursors of MnC₂O₄·2H₂O and Mn(acac)₃. The catalytic effects of two coated precursors on AP thermal decomposition were measured by differential scanning calorimetric (DSC) and thermogravimetric analysis (TG). The MnC₂O₄·2H₂O@AP composite showed a decrease in the decomposition temperature of AP from 428.35 to 310.93 °C in one step, whereas for the Mn(acac)₃@AP composite, the thermal decomposition was seen in two steps at 288.04 and 323.875 °C. The kinetic triplet of activation energy (E_a), frequency factor (log A) and model of mechanism function [f(α)] of thermal decomposition for pure ammonium perchlorate,MnC₂O₄·2H₂O@AP and Mn(acac)₃@AP were investigated via two model-free (FWO, KAS and Starink) and model-fitting (Starink) methods at different conversions of α (α = 0.05–0.95). Also, the thermodynamic parameters were obtained via activation energy and frequency factor for different concentrations of catalysts.

Full text of DOI:10.1002/zaac.201700376

Title: A comparison of catalytic effect of nano-Mn3O4 derived from
MnC2O4.2H2O and Mn(acac)3 on thermal decomposition of
ammonium perchlorate
Authors: Mohammad Mahdavi
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To be cited as: Z. anorg. allg. Chem. 10.1002/zaac.201700376
Link to VoR: http://dx.doi.org/10.1002/zaac.201700376

10.1002/zaac.201700376
Zeitschrift für anorganische und allgemeine Chemie
A comparison of catalytic effect of nano-Mn3O4 derived from
MnC2O4.2H2O and Mn(acac)3 on thermal decomposition of ammonium
perchlorate
Mohammad Mahdavi,*[a] Hossein Farrokhpour[b], Marjan Tahriri[a]
decomposition of AP. They mixed catalyst with AP which
decreased the high-temperature peak of AP about 98°C [14-16].
Abstract: The formation and catalytic effect of Mn3O4 spinel
nanoparticles on thermal decomposition of ammonium perchlorate (AP)
were investigated and compared to two Manganese precursors of
In this study the sol-gel method was used to achieve the ultrafine
and active nano-Mn3O4 particles for catalytic decomposition of AP,
using manganese precursors which can be easily broken down
before or during the AP decomposition to produce the Mn3O4 nano-
particles in the gaseous phase. Manganese precursors were prepared
by oxalic acid and acetyl acetone. In this study, MnC2O4.2H2O@AP
and Mn(acac)3@AP shell–core composites were prepared by a sol-
gel method and their catalytic effects on AP thermal decomposition
were investigated.
MnC2O4.2H2O and Mn(acac)3. The catalytic effects of two coated
precursors on AP thermal decomposition were measured by differential
scanning calorimetric (DSC) and thermogravimetric analysis (TG). The
MnC2O4.2H2O@AP composite showed a decrease in the decomposition
temperature of AP from 428.35°C to 310.93°C in one step, whereas for
the Mn(acac)3@AP composite, the thermal decomposition was seen in
two steps at 288.04°C and 323.875°C. The kinetic triplet of activation
energy (Ea), frequency factor (logA) and model of mechanism function
(f(α))
of
thermal
decomposition
for
pure
ammonium
perchlorate,MnC2O4.2H2O@AP and Mn(acac)3@AP were investigated
via two model-free (FWO, KAS and Starink) and model-fitting (Starink)
methods at different conversions of α (α = 0.05-0.95). Also, the
thermodynamic parameters were obtained via activation energy and
frequency factor for different concentrations of catalysts.
Experimental procedure
Materials
The materials such as manganese nitrate [Mn(NO3)2·6H2O]
(99.9%), oxalic acid (C2H2O4) (99.9%), acetylacetone (C5H8O2)
(99.5%), potassium permanganate (KMnO4) (97%), ethanol
(C2H5OH) (99.5%) were purchased from Sigma-Aldrich company.
Ammonium perchlorate (NH4ClO4) (99.5%, 150 µm), was
purchased from Sinopharm company (China) and used without
further purification.
Introduction
The solid fuel rockets are widely used in the fields of aerospace,
universal exploration, and satellite launching. The ammonium
perchlorate (AP) has been considered as an energetic material and
main cause for the oxidizing agent of rocket fuel [1, 2]. Pure AP has
two steps thermal decomposition, namely low-temperature
decomposition (LTD) and high- temperature decomposition (HTD).
This two steps reaction causes reduction of engine thrust. Many
types of research explore to improve the thermal decomposition by
using catalysts [3-7]. Among these catalysts, metal oxides (MOs)
are widely studied for this purpose [8]. Accordingly, the majority of
researchers have focused their attentions on the coating of MOs
catalysts rather than mechanical mixing, to avoid agglomeration and
non-uniform distribution of the catalyst on AP [9,10]. In previous
studies, MOs catalysts have been covered on the surface of AP
using solvent/non-solvent method, but the morphology of AP
changed in this manner [11].
Preparation of MnC2O4.2H2O catalyst
In order to synthesis MnC2O4.2H2O, an aqueous solution of oxalic
acid (H2C2O4) was added to Mn(NO3)2·6H2O aqueous solution with
the ratio of 1:2 under stirring to produce gel solution. To obtain a
homogeneous gel, it was stirred slowly for 30 minutes at 25°C by a
magnetic stirrer and then the water was removed by centrifuging.
The precipitate was washed several times with ethanol to remove
water. Finally, an ethanolic gel of MnC2O4.2H2O was achieved
[17].
Preparation of Mn(acac)3 catalyst
Seemingly, to synthesis Mn(acac)3, an aqueous solution of 5g of
KMnO4 in 20 ml of distilled water was added to 10 ml of
Situ formation of MOs catalysts, simultaneous with the exothermic
decomposition of AP, can prevent agglomeration, poor mixing of
AP-MO and morphology variation of AP. Chen et al. considered the
catalytic effect of α-MnO2 nanowires (21 nm thickness) on the
thermal decomposition of AP. The α-MnO2 nanowires displaced the
high-temperature peak of AP to a lower temperature by about 98°C
[12]. Kishore et al. considered the catalytic effect of MnO2 (48 μm)
on the thermal decomposition of AP. The MnO2 nanowires
decreased the high-temperature peak of AP about 80°C [13]. Singh
et al. considered the mechanical mixing of MnC2O4 on the thermal
acetylacetone with continuous stirring to make
a dark and
homogeneous gel of Mn(acac)3. It was stirred slowly for 30 minutes
at 25°C by a magnetic stirrer and then cooled in an ice bath to
ensure maximum precipitation of the product. The precipitates were
filtered and washed several times with ethanol to remove water.
Eventually, an ethanolic gel of Mn(acac)3 was achieved [18].
Preparation of MnC2O4.2H2O@AP and Mn(acac)3@AP
composites
In this stage, a new process was introduced for better dispersion of
the catalysts to prepare MnC2O4.2H2O@AP and Mn(acac)3@AP
core-shells. Accordingly, 9.6 grams of AP was added to each
ethanolic gel of catalysts (4 Wt.%) and the mixtures were stirred
slowly for 15 minutes in room temperature to obtain semi-dried
composites of MnC2O4.2H2O@AP and Mn(acac)3@AP which had
the core-shell structure. Finally, products were fully dried at room
temperature.
*
Mohammad Mahdavi, Ph.D of Inorganic Chemistry
Tel.: +98-314-591-2705; fax: +98-314-522-0420;
Email address: m.mahdavi@mut-es.ac.ir
[a] Department of chemistry Malek-ashtar University of Technology
Shahin-shahr P.O. Box 83145/115, IR Iran
[b] Department of Chemistry Isfahan University of Technology
Isfahan 84156, IR Iran
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10.1002/zaac.201700376
Zeitschrift für anorganische und allgemeine Chemie
Specifications
The morphology of pure AP, MnC2O4.2H2O@AP and
Mn(acac)3@AP core-shell composites was recorded by scanning
electron microscope (SEM) TESCAN VEGA3, Czech Republic.
The morphology of the solid products remained from thermal
decomposition of MnC2O4.2H2O@AP and Mn(acac)3@AP were
recorded by scanning electron microscope (SEM) MIRA3
TESCAN. In order to determine the crystal phase structure of the
MnC2O4.2H2O, Mn(acac)3, and solid products remained from
thermal decomposition of MnC2O4.2H2O@AP and Mn(acac)3@AP
(Mn3O4 particles) X-ray diffraction patterns were determined by
X'PertPro using Cu-Kα radiation (λ = 1.5406 Å) in the 2Ө range
from 10° to 80°. Before X-ray scanning, MnC2O4.2H2O@AP,
Mn(acac)3@AP were washed several times with distilled water until
AP in two composites was completely dissolved and finally just
MC2O4.2H2O and Mn(acac)3 particles remained which were dried at
70C. The influence of MnC2O4.2H2O and Mn(acac)3 coatings on
the thermal decomposition of AP were investigated by differential
scanning calorimetric (DSC) and thermo gravimetric (TG) analysis
(Perkin Elmer STA 6000) in Ar-O2 atmosphere over the
temperature range of 50–520°C and heating rate of 10°C/min. The
performance of (MnC2O4.2H2O/AP) and (Mn(acac)3/AP)
composites was evaluated by comparing the decomposition
temperatures during the thermal decomposition of AP.
Results and discussion
Morphology and structure of MnC2O4.2H2O@AP and
Mn(acac)3@AP
Figure 2: EDS images of MnC2O4.2H2O@AP (a) and Mn(acac)3@AP (b)
Figure 1 shows SEM images of the pure AP semi-spherical crystals
(a), AP coated with MnC2O4.2H2O (b), and AP coated with
Mn(acac)3 (c), which reveals that in comparison with the pure AP,
the surface of both MnC2O4.2H2O@AP and Mn(acac)3@AP
composites have a regular and rough coating of MnC2O4.2H2O and
Mn(acac)3. Also, EDS spectrums and EDS elemental maps of
MnC2O4.2H2O@AP and Mn(acac)3@AP composites were shown in
figures 2-4, respectively. The results of SEM and EDS techniques
indicated that composites of AP with two manganese precursors
have been prepared successfully by sol-gel method.
Figure 1: SEM images of pure AP (a), MnC2O4.2H2O@AP(b) and
Mn(acac)3@AP (c)
Figure 3: The EDS elemental maps of MnC2O4.2H2O@AP
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10.1002/zaac.201700376
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The preparation of nano-Mn3O4 spinel from precursor
of manganese coating
According to thermal analysis of the MnC2O4.2H2O (figure 6), there
are two distinct weight loss steps. The first weight loss is about
21.22% which happens at 140-160°C and is related to the
evaporation of crystallization water. The second weight loss is
about 49.41% which occurs at the temperature range of 250-350°C
and may be ascribed to the decomposition of manganese oxalate to
nano-Mn3O4 spinel particles [19].
Additionally, the thermal decomposition of Mn(acac)3 has three
step weight losses. The first step weight loss is about 20% at 50-
100°C, which is attributed to the transformation of Mn(acac)3 to
Mn(acac)2 via removing of one of the acetylacetonate ligands [20].
The second weight loss (41%) within 100–180 °C corresponds to
oxidation of –CH3 groups and oxidation of Mn2+ to Mn3+. The third
weight loss within 180–400°C which is contributed to a substantial
exothermic effect, corresponds to the formation of nano-Mn3O4
particles spinel [21].
Figure 4: The EDS elemental maps of Mn(acac)3@AP
The XRD patterns of MnC2O4.2H2O (a) and Mn(acac)3 (b) catalysts
at 10°-80° angles of 2Ө were depicted in figure 5. All diffraction
peaks can be perfectly indexed to the diffraction patterns (JCPDS
No: 32-0646) for MnC2O4.2H2O and (JCPDS No: 13-0736) for
Mn(acac)3 indicating the coatings are pure MnC2O4.2H2O and pure
Mn(acac)3, respectively.
Figure 6: TG curve of MnC2O4.2H2O (a) and Mn(acac)3 (b)
Based on XRD patterns and SEM images, the coating of
MnC2O4.2H2O and Mn(acac)3 can be converted directly to the
related manganese spinel’s nano-particles with very fine particles
and active sites, intimated with AP thermal decomposition (figures
7-9). All the diffraction peaks in 2Ө angles of 10°-80° correspond
well with Mn3O4 nano-particles in the tetragonal system (JCPDS
No: 01-1127). It can be mentioned that the size distributions of
nano-particles are smaller than 100 nm for both precursors.
Figure 5: XRD patterns of MnC2O4.2H2O
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10.1002/zaac.201700376
Zeitschrift für anorganische und allgemeine Chemie
Figure 9: SEM images of nano-Mn3O4 remained from Mn(acac)3
Figure 7: XRD patterns of the solid products remained from precursor
of MnC2O4.2H2O (a) and Mn(acac)3 (b).
The catalytic activity of MnC2O4.2H2O and Mn(acac)3
on thermal decomposition of AP
Thermal analysis study of pure Ap, MnC2O4.2H2O@AP, and
Mn(acac)3@AP composites were investigated by TG-DSC
measurements at heating rates of 10ºC/min. Figures 10 and 11 show
the thermal decomposition of AP which started at 300°C and
continued until 440°C [2]. Additionally, TG and DTG experiments
exhibit that the AP weight decreases over 300°C. So, it shows two
phenomena regarding AP weight loss during 2 steps. In the first
step, the weight loss is due to low-temperature decomposition at
330.92°C (LTD). In the second step, which is the full
decomposition in high temperature at 428.35°C (HTD), the whole
process is completed. Also, the DSC curve reveals three phenomena
relating to one endothermic peak and two exothermic peaks in high
and low temperature as follows:
a. The endothermic peak is observed at about 258.68°C,
which is assigned to the crystallographic transition of AP
from orthorhombic to cubic.
b. The first exothermic peak at 330.92°C is assigned to
partial decomposition of AP.
c. The second and great exothermic peak at about 428.35°C
is assigned to complete decomposition of AP (figure 11).
Figure 8: SEM images of nano-Mn3O4 remained from MnC2O4.2H2O
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10.1002/zaac.201700376
Zeitschrift für anorganische und allgemeine Chemie
Figure 10: TG&DTG curves of pure AP
Figure 13: TG and DTG curves of Pure AP (a), MnC2O4.2H2O@AP (b) and
Mn(acac)3@AP (c).
The MnC2O4.2H2O@AP composite has better catalytic performance
than Mn(acac)3@AP. Such an observation may be due to the
decomposition temperatures of MnC2O4.2H2O and Mn(acac)3 to
nano-Mn3O4 spinel particles. According to thermal analysis of the
MnC2O4.2H2O (figure 6), the second weight loss occurs at the
temperature range of 250-350°Cand relates to the decomposition of
manganese oxalate to nano-Mn3O4 particles, this is less than the
first and second exothermic decomposition peaks (330.92°C,
428.35°C) of pure AP. So, in this condition, the MnC2O4.2H2O
precursor was decomposed before the AP decomposition and the
catalytic effect can be related to Mn3O4 spinel. Accordingly, the
manganese precursor with lower decomposition temperature has a
better effect on decreasing the decomposition temperature of AP.
Therefore, the thermal decomposition of AP with MnC2O4.2H2O is
taken in one step. But, the thermal decomposition of AP with
Mn(acac)3 is taken in two steps.
Figure 11: DSC curve of pure AP
Figure 12 shows the catalytic effect of MnC2O4.2H2O and
Mn(acac)3 on the thermal decomposition of AP which the
MnC2O4.2H2O@AP system leads to reduction of the decomposition
temperature of AP from 428.35°C to 310.93°C. For Mn(acac)3@AP
system, the first decomposition temperature peak is observed at
288.04°C and the second temperature peak is observed at 323.87°C.
The catalytic activity of MnC2O4.2H2O with different
weight ratios on thermal decomposition of AP
Thermal catalytic decomposition of AP is also highly related to the
amounts of loaded catalyst. The catalytic outcome of the
MnC2O4.2H2@AP composite was studied with different weight
ratios of MnC2O4.2H2O to AP {MnC2O4.2H2O (x Wt.%)@AP, x=
1-4} by DSC method. The DSC curves (figure 14) indicate only one
obvious exothermic peak for 4% weight ratio, in comparison with
two exothermic peaks for pure AP. Based on figure 10, increasing
the ratio of MnC2O4.2H2O to AP will lead to a large decrease in
decomposition temperature and the thermal decomposition of AP is
taken in one step, thus 4% sample exhibited the best catalytic
performance for decreasing the thermal decomposition temperature
of AP. In conclusion, based on the results of the different
percentages of MnC2O4.2H2O, the catalytic effect of Mn(acac)3 was
investigated with 4% weight, too.
Figure 12: DSC curves of Pure AP (a), MnC2O4.2H2O@AP (b) and
Mn(acac)3@AP (c).
It is clear that nano-catalysts have no effects on the endothermic
peak of AP (crystallographic transition temperature 258.68°C),
while
a large decrease was observed in high-temperature
exothermic peak. TG and DTG curves exhibit one phenomenon of
weight losing regarding MnC2O4.2H2O@AP and two steps weight
lowering for Mn(acac)3@AP. As
a
result, the thermal
decomposition temperature of AP depressed about 117.42°C and
104.48°C for MnC2O4.2H2O@AP and Mn(acac)3@AP, respectively
(figure 13).
Figure 14: DSC curves of MnC2O4.2H2O@AP with various weight ratios (1%,
2%, 3% & 4%) at a heating rate of 10 °C/min.
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10.1002/zaac.201700376
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Catalytic mechanism of thermal decomposition of AP by
manganese precursors
Generally, speaking it is believed that solid phase reactions should
occur only at the interface, where reactants and catalysts meet with
each other. Therefore, it should be expected that an improvement in
the probability of the interactions between these species will
enhance the overall reaction rate. Remarkably, our results proved
clearly that the initial heat can transform both of the MnC2O4.2H2O
and Mn(acac)3 into Mn3O4 particles before or simultaneous with the
thermal decomposition of AP. In this condition, the created nano-
Mn3O4 particles are redistributed uniformly within the reaction
system and the thermal decomposition of AP occurs in the presence
of very fresh nano-catalyst.
The Mn3+ ions with d4 configuration in Mn3O4 spinel have too much
tendency to achieve the stable electron configuration of d5, so these
ions have a great affinity for absorption and stabilization of radicals
near the surface of the catalyst. Thus the probability of an electron
transfer mechanism increases considerably for thermal
decomposition of AP. On the other hand, various counter ions in
manganese precursors (oxalic acid and acetyl acetone) may have
different effects on catalytic performance. Since the acac ion is a
−
proton doner which makes C5H7O2 and H+ ions. Accordingly, the
acac leads to a proton transfer mechanism for decomposition of AP
-2
by the formation of HClO4 in the transition state. The C2O4 ions
are electron rich species and they can increase the lifetime of radical
species by electron injection to transition state. As a result, it seems
that these ions increase the probability of electron transfer
mechanism. Consequently, the mechanism of electron transfer in
Mn(acac)3@AP composite is weaker than MnC2O4.2H2O@AP
composite.
Kinetics
In this study, we used two model-free and model-fitting methods to
find out kinetic triplet such as the activation energy, frequency
factor and model of mechanism function of MnC2O4.2H2O and
Mn(acac)3 in catalytic thermal decomposition of AP , differential
thermal
gravimetric
(DTG)
analysis
of
pure
AP,
MnC2O4.2H2O(4Wt.%)@AP and Mn(acac)3(4 Wt.%)@AP was
investigated at heating rates of 5, 10, 15 and 20°C/min (figure 15).
The Flynn–Wall–Ozawa (FWO), Kissinger–Akahira–Sunose
(KAS), and Starink as model-free methods were used for
determination of activation energies (Ea). These methods are best
suited for a model-free approach [22] and were used in this study to
evaluate the activation energies.
The Kissinger–Akahira–Sunose modified or Starink as the model-
fitting method was used for determining the types of mechanism
functions g(α) and f(α).
The Flynn–Wall–Ozawa (FWO), Kissinger–Akahira–Sunose
(KAS), and Starink as model-free methods were used for
determination of activation energies (Ea). These methods are best
suited for a model-free approach [22] and were used in this study to
evaluate the activation energies.
Figure 15: DTG curves of pure AP (a), MnC2O4.2H2O(4 Wt.%)@AP (b) and
Mn(acac)3 (4 Wt.%)@AP (c) at different heating rates 5, 10, 15 and 20°C/min
The model-fitting method
The Kissinger–Akahira–Sunose modified or Starink as the model-
fitting method was used for determining the types of mechanism
functions g(α) and f(α).
According to the commendations of the International Confederation
for Thermal Analysis and Calorimetry (ICTAC) [22], one of the
suitable isoconversional model-fitting is called modified Kissinger-
Akahira-Sunose (KAS) or Starink method (Equation 1), that it could
be used to obtain the kinetic triplets.
The Starink method (Equation 1) can be utilized to determine the
activation energy parameter of a thermal decomposition at different
degrees of conversion, based on the linear relation between
decomposition temperature and heating rates (figure 16) [23].
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10.1002/zaac.201700376
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훽ꢀ
푇훼1.92
퐸푎,훼
푅푇훼
Equation (1)
The activation energy (Ea,α) and its corresponding regression
coefficients R2 of the regression line for conversion range from 0.05
to 0.95 degree of conversion were calculated by Starick method for
decomposition of pure AP, MnC2O4.2H2O(4 Wt.%)@AP and
Mn(acac)3(4 Wt.%)@AP were shown in tables 1, 2 and 3,
respectively. Since the activation energy of composites
{MnC2O4.2H2O(4 Wt.%)@AP and Mn(acac), 3(4 Wt.%)@AP }
have decreased, thermal decomposition of AP is done easier and
faster.
ln (
) = Const. −1.0008
Table 1. The defined activation energy (Ea,α) and regression
coefficients (R2) of Pure AP by Starink method
α
AP
Step(I)
Step(II)
Ea,α
Ea,α
R2
R2
0.1
0.2
0.3
0.4
0. 5
0.6
0.7
0.8
0.9
106.59
107.31
107.92
108.53
108.65
108.81
108.91
109.41
111.31
0.9882
0.9919
0.9937
0.9951
0.9962
0.9974
0.998
122.44
134.51
143.16
154.65
165.21
172.39
177.29
177.47
171.87
0.9127
0.9082
0.9373
0.9559
0.967
0.9731
0.9737
0.9684
0.963
0.9985
0.9985
Table 2. The defined activation energy (Ea,α) and regression coefficients (R2) of
MnC2O4.2H2O(4 Wt.%)@AP by Starink method
α
MnC2O4.2H2O@AP
Ea,α
R2
0.1
0.2
0.3
0.4
0. 5
0.6
0.7
0.8
0.9
120.37
115.82
108.27
101.98
96.21
91.18
86.72
82.78
78.92
0.9833
0.9941
0.9985
0.9999
0.9985
0.9963
0.9936
0.9911
0.9878
Figure 16: The curves of Ln(βi/Tα1.92) by1000/Tα for thermal decomposition of
pure AP (a), MnC2O4.2H2O(4 Wt.%)@AP (b) and Mn(acac)3(4 Wt.%)@AP (c).
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10.1002/zaac.201700376
Zeitschrift für anorganische und allgemeine Chemie
Table 3. The defined activation energy (Ea,α) and regression
coefficients (R2) of Mn(acac)3(4 Wt.%)@AP by Starink
method
α
Mn(acac)3@AP
Step(I)
Step(II)
Ea,α
R2
0.9763
Ea,α
R2
0.1
0.2
0.3
0.4
0. 5
0.6
0.7
0.8
0.9
74.63
77.41
78.93
79.91
80.45
80.91
81.42
81.95
82.89
94.08
0.9069
0.9232
0.9347
0.9425
0.9487
0.9491
0.9791
0.9179
0.9798
0.9876
0.994
100.81
105.27
108.51
110.82
106.09
110.31
110.09
107.16
0.9976
0.9994
0.9998
0.9991
0.9964
0.9906
Interestingly, the average of the activation energy (tables 1, 2 and 3)
equals 164.352 (kJ·mol−1) and 173.01 (kJ·mol−1) for pure
ammonium
perchlorate,
104.79
(kJ·mol−1)
for
the
MnC2O4.2H2O@AP system and for Mn(acac)3@AP system 75.09
(kJ·mol−1) and 112.41 (kJ·mol−1). The activation energy for pure
ammonium perchlorate is reported to be in the ranges of 120-243
(kJ·mol−1) [24-27]. Figure 17 shows conversion-temperature (α-T)
curves in the range of 0.05-0.95 for thermal decomposition pure
ammonium perchlorate and composites MnC2O4.2H2O@AP and
Mn(acac)3@AP at different heating rates. The α-T curves in all the
heating rates show Sigmoidal models. Sigmoidal curves α-T can
reflect two types of reaction models such as Avrami-Erofeev or
Prout-Tomkins [28-30].
Twenty seven of kinetic model functions (Table 4) in integral and
differential forms were used to predict the kinetic triplet [31, 32].
The difference between the theoretical and experimental f(α) was
calculated by means of a non-linear regression method using the
residual sum of squares (RSS) that should be a minimum according
to equation 2:
2
Equation (2)
(
)
푡ℎ푒표푟.
푅푆푆 = ∑(푓(훼)푒푥푝. − 푓 훼
)
Figure 17: The T-α curves for thermal decomposition of pure AP (a),
MnC2O4.2H2O (4 Wt.%)@AP (b) and Mn(acac)3(4 Wt.%)@AP (c) systems by
Starink method
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10.1002/zaac.201700376
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Table 4. Twenty seven types of mechanism functions g(α) and f(α) used in the present analysis
No
Symbol
Mechanism function name
g(α)
f(α)
Models related to chemical processes
1
2
3
4
5
F1/3
F3/4
F3/2
F2
one-third order
three-quarters order
one and a half order
second order
1-(1-α)2/3
1-(1-α)1/4
(1-α)-1/2 -1
(1-α)-1 -1
(1-α)- 2 -1
3/2(1-α)1/3
4(1-α)3/4
2(1-α)3/2
(1-α)2
F3
third order
1/2(1-α)3
Increasing speed models
6
7
P3/2
P1/2
P1/3
P1/4
E1
Mampel power law
Mampel power law
Mampel power law
Mampel power law
Exponential law
α3/2
α1/2
α1/3
α1/4
lnα
(2/3) α -1/2
2α 1/2
3α 2/3
4α 3/4
α
8
9
10
Speed models Sigmoidal
11
12
13
14
15
16
A1,F1
A3/2
A2
Avrami-Erofeev equation
Avrami-Erofeev equation
Avrami-Erofeev equation
Avrami-Erofeev equation
Avrami-Erofeev equation
Prout-Tomkins equation
-ln(1-α)
(1-α)
[-ln(1-α)]2/3
[-ln(1-α)]1/2
[-ln(1-α)]1/3
[-ln(1-α)]1/4
ln[α/(1-α)]
3/2(1- α)[-ln(1-α)]1/3
2(1- α)[-ln(1-α)]1/2
3 (1- α)[-ln(1-α)]2/3
4(1- α)[-ln(1-α)]3/4
α (1-α)
A3
A4
Au
Decreasing speed models
17
18
19
F0, R1
F1/2, R2
F2/3, R3
power law
power law
power law
α
(1- α)0
1-(1-α)1/2
1-(1-α)1/3
2(1- α)1/2
3(1- α)2/3
Intrusive mechanism
20
21
22
23
24
25
26
27
D1
D2
D3
D4
D5
D6
D7
D8
parabola law
α2
1/2α
Valensi equation
α +(1-α)ln(1-α)
[-ln(1-α)]-1
2
-1
Jander equation
[1-(1-α)1/3
]
3/2(1-α)2/3[1-(1-α)1/3
3/2[(1-α)-1/3-1]-1
]
Ginstling-Brounstein equation
Zhuravlev, Lesokin, Tampelman equation
anti-Jander equation
1-2α/3-(1-α)2/3
[ (1-α)-1/3-1]2
[(1+α) 1/3 -1]2
1+2α/3-(1+α)2/3
[(1+α)-1/3 -1]2
3/2(1-α)4/3[(1-α)-1/3-1]-1
3/2(1+α)2/3[(1+α)1/3-1]-1
3/2[(1+α)-1/3-1]-1
anti-Ginstling-Brounstein equation
anti-Zhuravlev, Lesokin, Tampelman equation
3/2(1+α)4/3[(1+α)-1/3-1]-1
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10.1002/zaac.201700376
Zeitschrift für anorganische und allgemeine Chemie
The mechanism function of reaction was obtained by the minimum
values of RSS in table 5 which shows that the functions of the
integral function of -ln(1−α) and the differential function of (1−α)
are the most probable models for the decomposition of pure
ammonium perchlorate, MnC2O4.2H2O (4 Wt.%)@AP and
Mn(acac)3(4 Wt.%)@AP systems at different heating rates. The
model-fitting method is used with various kinetic model functions
to predict the mechanism of solid-phase reactions. The predicted
function of f(α) is related to Avrami-Erofeev equation for the
decomposition mechanism of ammonium perchlorate [33].
The KAS method: Among mathematical solutions to calculate
the activation energy, the KAS method (Equation 4) is better than
FWO suited to a model-free approach, and was used in this study to
evaluate the activation energy of (figure 15) [38,39]:
훽ꢀ
푇푝2
퐸푎
Equation (4)
ln ( ) = 퐶표푛푠푡. −
푅. 푇푝
In this equation, βi is the constant heating rate (βi=dT/dt), Ea is the
activation energy, R is the gas constant, and Tp is the maximum
peak temperature of thermal decomposition. According to equation
2
2, a plot of ln(βi /Tp ) against 1000/Tp should be a straight line.
Table 5. The values of RSS for determining the type of mechanism function
From the slope of straight lines, we can estimate apparent activation
energy (figure 19).
Samples
Pure AP
Peak
I
Symbol
A1
RSS
0.6009
0.6050
0.6516
0.6834
1.4517
0.6552
0.6592
0.6947
0.7259
1.5356
A2
A3
A4
A3/2
A1
II
A2
A3
A4
Figure 19: The curves of KAS (ln(βi /Tp2) by 1000/Tp) for thermal decomposition
of pure AP (a), MnC2O4.2H2O(4 Wt.%)@AP (b) and Mn(acac)3(4 Wt.%)@AP (c).
A3/2
The Starink method: This method is the best model-free
method and is directly based on equation 5 [23]. It is easy to obtain
exact value of activation energy by plotting ln[βi/T1.92)p] against
1000/Tp for a constant linear slope.
The model-free method
The FWO method: The FWO method represents the activation
energy value by maximum peak temperature of thermal
decomposition. The activation energy determines by means of
reading the trend line slope was equal to -1.0518Ea/R which
indicates the dependence of the right side of equation 3 [34-36].
훽ꢀ
퐸푎
Equation (4)
ln[ (
)] = 퐶표푛푠푡. −1.0008 (
)
푇푝1.92
푅푇푝
The slope of each line is equal to -Ea/R for activation energy, βi is
the heating rate, Ea is apparent activation energy (kJ·mol−1), and R
is ideal gas constant. For Starink method, the plots of ln[βi/T1.92)p]
against 1000/Tp are straight lines for pure AP and composites
(figure 20).
퐸푎
Equation (3)
(
)
ln 훽ꢀ = Const. −1.0518
푅. 푇푝
The plot of lnβi versus 1000/Tp (figure 18) was obtained from
Differential Thermal Gravimetric (DTG) curves recorded at several
heating rates. This plot should be a straight line whose slope allows
evaluation of the activation energy, which indicated that thermal
decomposition of these samples follows the first order kinetic law
[37].
Figure 20: The curves of Starink [ln(βi/Tp1.92) by1000/Tp] for thermal
decomposition of pure AP (a), MnC2O4.2H2O(4 Wt.%)@AP (b) and Mn(acac)3(4
Wt.%)@AP (c).
Figure 18: The curves of FWO [ln(βi) by1000/Tp] for thermal decomposition of
pure AP (a), MnC2O4.2H2O(4 Wt.%)@AP (b) and Mn(acac)3(4 Wt.%)@AP (c).
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10.1002/zaac.201700376
Zeitschrift für anorganische und allgemeine Chemie
The relationship of activation energy calculated by three model-free
methods for decomposition of pure ammonium perchlorate,
MnC2O4.2H2O(4 Wt.%)@AP and Mn(acac)3(4 Wt.%)@AP is
shown in Tables 6 and 7, respectively. The thermal decomposition
of AP is done easier and faster as the activation energy decreases by
the catalyst.
reduction of frequency factor, the approaching of reactants by
means of catalyst leads to easier and faster thermal decomposition.
Table 8. The kinetic triplet of activation energy, frequency factor and model of
thermal decomposition for Pure AP, MnC2O4.2H2O(4 Wt.%)@AP and
Mn(acac)3(4 Wt.%)@AP systems via model-fitting and model-free methods
Samples
Pure AP
Peak
I
E0
logA
7.19
Mechanism function
Table 6. The determined Ea and R2 for Pure AP
by three methods.
103.83
Avrami-Erofeev
equation
methods
Peak
Pure AP
I
II
170.97
92.62
10.70
5.76
4.91
8.17
Avrami-Erofeev
equation
II
MnC2O4.2H2O@AP
Mn(acac)3@AP
Avrami-Erofeev
equation
FWO
Ea
R2
Ea
R2
Ea
R2
106.45
0.9987
102.37
0.9984
102.67
0.9984
103.83
172.60
0.9895
169.99
0.9880
170.32
0.9881
170.97
I
75.67
Avrami-Erofeev
equation
KAS
II
115.93
Avrami-Erofeev
equation
Starink
Average
The effect of catalysts on thermodynamic parameters of
thermal decomposition of ammonium perchlorate
After the kinetic parameters, Ea and A were obtained via model-
fitting and model-free methods, the thermodynamic parameters of
activation (∆G#, ∆H#, and ∆S#) were calculated from equations 7-
10, respectively. ∆G#, ∆H#, and ∆S# are free energy, enthalpy, and
entropy of the activation, respectively. [40-44]:
Table 7. The determined Ea and R2 for MnC2O4.2H2O(4 Wt.%)@AP
and Mn(acac)3(4 Wt.%)@AP by three methods.
−∆퐺≠
푅푇푝
methods
Peak
MnC2O4.2H2O(4Wt.%)@AP
I
Mn(acac)3(4 Wt.%)@AP
−퐸푎
푅푇푝
Equation (7)
퐴 exp (
) = 휗 exp(
)
II
푘푇푝
Equation (8)
휗 =
FWO
Ea
R2
Ea
R2
Ea
R2
95.64
0.9979
90.96
78.95
0.9775
73.88
118.26
0.9494
114.61
0.9407
114.91
0.9411
115.93
ℎ
∆퐻≠ = 퐸푎 − 푅푇푝
Equation (9)
Equation (10)
KAS
∆퐺≠ = ∆퐻≠ − 푇푝∆푆≠
0.9976
91.27
0.9712
74.19
Parameters k (1.3806488 9 10-23 J/k) and h (6.626069 9 10-34 Js)
are Boltzmann and Planck constant, respectively [24]. Table 9 gives
the computed thermokinetic parameters for pure AP,
MnC2O4.2H2O@AP, and Mn(acac)3@AP. The results clearly
represent that thermodynamic parameters of AP have a considerable
reduction in the presence of MnC2O4.2H2O and Mn(acac)3.
Starink
Average
0.9976
92.62
0.9715
75.67
Table 9. The thermodynamic parameters of activation (∆G#, ∆H#, and ∆S#) of
thermal decomposition for Pure AP, MnC2O4.2H2O(4 Wt.%)@AP and
Mn(acac)3(4 Wt.%)@AP
Seemingly, the pre-exponential constant (logA) was obtained from
equation 6 [25].
Samples
Pure AP
Peak
∆G#
∆H#
∆S#
훽퐸푎
퐸푎
Equation (4)
퐴 =
exp
푅푇푝2푓′
푅푇푝
I
149.45
180.12
154.59
142.96
151.24
99.01
165.17
87.77
71.08
111.04
-86.97
(훼)푝
II
-21.43
Obviously, in the above equation, Tp is the maximum temperature
exothermic peaks from DTG curves at different rates of 5, 10, 15
and 20 ºC/min, Ea is the average activation energies obtained from
the three model-free methods, β is different rates (5, 10, 15 and 20
ºC/s) and f '(max) is (-1) from the derivation of the differential
function of (1−α). Table 8 presents values of Ea and logA and
mechanism function obtained from the model-free and model-fitting
methods.
MnC2O4.2H2O@AP
Mn(acac)3@AP
-114.467
-130.25
-68.348
I
II
Because of decreasing the activation energy in both composites
(MnC2O4.2H2O@AP
and
Mn(acac)3@AP),
the
thermal
decomposition of AP is done easier and faster for two catalysts. Of
course, diminishing of logA may be related to adsorption of reactive
species on the fresh surface of spinel nano-catalysts, but despite the
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10.1002/zaac.201700376
Zeitschrift für anorganische und allgemeine Chemie
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Conclusion
To prevent the agglomeration of metal oxide catalysts, during the
mixing and solvent/non-solvent process, the MnC2O4.2H2O and
Mn(acac)3 catalysts were coated homogeneously on the surface of
AP by sol-gel method. By thermal decomposition, the coatings of
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Keywords: Ammonium Perchlorate; Nano-Mn3O4; Spinel;
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