G. Singh et al. / Thermochimica Acta 511 (2010) 112–118
117
Table 4
Set of reaction models applied to describe thermal decomposition of solids.
Model no.
Reaction model
f(˛)
g(˛)
1/4
1.
2.
3.
4.
5.
6.
7.
8.
Power law
Power law
Power law
Power law
One-dimensional diffusion
Mampel (first order)
Avrami-Erofeev
Avrami-Erofeev
Avrami-Erofeev
Contracting sphere
Three-dimensional diffusion
Contracting cylinder
Prout-Tompkins
Ginstling-Brounshtein
4˛3/4
˛
1/3
3˛2/3
˛
1/2
2˛1/2
˛
3/2
2/3˛−1/2
˛
2
1/2˛−1
˛
1 − ˛
−ln(1 − ˛)
4(1 − ˛)[−ln(1 − ˛)]3/4
3(1 − ˛)[−ln(1 − ˛)]2/3
2(1 − ˛)[−ln(1 − ˛)]1/2
3(1 − ˛)2/3
[−ln(1 − ˛)]1/4
[−ln(1 − ˛)]1/3
[−ln(1 − ˛)]1/2
1 − (1 − ˛)1/3
9.
10.
11.
12.
13.
14.
2(1 − ˛)2/3[1 − (1 − ˛)1/3
2(1 − ˛)1/2
]
[1 − (1 − ˛)1/3
1 − (1 − ˛)1/2
ln(˛/1 − ˛)
]
−1
2
˛/(1 − ˛)
3/2[(1 − ˛)−1/3 − 1]−1
[1 − (2˛/3)] − (1 − ˛)2/3
Table 5
Activation energy (Ea), Arrhenius parameters and correlation coefficient (r) for the isothermal decomposition of AP and AP with CdFe2O4 and Cd.
Model
AP
AP+CdFe2O4
AP+Cd
Ea (kJ mol−1
)
−ln A
r
Ea (kJ mol−1
)
−ln A
r
Ea (kJ mol−)
−ln A
r
1
2
3
4
5
6
7
8
9
10
11
12
13
14
94.7
95.0
95.6
98.4
99.4
98.0
97.0
95.6
96.3
97.7
100.2
97.6
102.0
88.5
13.8
14.1
14.3
14.6
14.4
15.1
14.6
14.4
14.7
13.8
12.8
14.2
0.9619
0.9622
0.9627
0.9646
0.9648
0.9641
0.9646
0.9626
0.9631
0.9640
0.9625
0.9640
0.9801
0.9288
59.3
59.5
60.2
63.4
64.8
62.9
61.3
60.3
61.0
62.6
65.8
62.4
59.4
65.4
7.4
7.6
7.9
8.3
8.2
8.7
8.1
8.0
8.4
7.5
6.5
7.8
9.5
6.3
0.9156
0.9171
0.9232
0.9349
0.9403
0.9329
0.9250
0.9209
0.9242
0.9314
0.9436
0.9306
0.9164
0.9425
78.6
78.8
79.4
82.4
83.7
82.0
80.5
79.5
80.2
81.6
84.9
81.4
86.2
70.8
11.3
11.4
11.7
12.0
11.9
12.5
11.8
11.7
12.1
11.2
10.3
11.5
14.8
7.3
0.9954
0.9956
0.9960
0.9973
0.9977
0.9971
0.9967
0.9960
0.9963
0.9961
0.9611
0.9970
0.9736
0.9675
Isoconversional kinetic analysis has also been carried out by
Lang and Vyazovkin [31] to detect changes in the effective activa-
tion energy of the thermal decomposition of AP by using DSC, TGA,
and high pressure DSC (HP-DSC) techniques. It has been reported
that the initial stages of decomposition characterize by a change
(isoconversional method) is a better method of obtaining reliable
and consistent kinetic information.
Acknowledgements
in the effective activation energy from ∼100 to ∼60 kJ mol−1
.
The authors are grateful to Head, Chemistry Department of DDU
Gorakhpur University for laboratory facility; IIT Roorkee for TG-
DSC; STIC, Cochin for XRD and Punjab University for TEM images.
Thanks are also due to financial assistance by CSIR for providing
Emeritus Scientist to G. Singh, JRF to Reena Dubey and RA to Dr.
Pratibha Srivastava.
It is inferred that solid AP decompose via two major chan-
sublimation products. In addition, model free and model fitting
decomposition of HMX and ammonium dinitramide have also been
reported in detail [32] by applying an F-test to check the signifi-
cance of the difference of different kinetic models.
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CdFe2O4 and Cd nanocrystals were prepared and characterized
by XRD and TEM. These show good catalytic effect on the ther-
mal decomposition of AP, HTPB and CSPs, though CdFe2O4 is better
than that of the Cd nanocrystals. The burning rate of CSPs was also
found to be enhanced. Though model fitting method using a set of
reaction model applied to isothermal data but model free approach