Quantitative correlation of kinetic parameters and procedural factors in non-isothermal thermogravimetry-dependence of heating rate and sample mass

Article abstract of DOI:10.1007/s10973-009-0670-7

Dependence of kinetic parameters (activation energy and pre-exponential factor) and procedural factors (sample mass and heating rate) independent of the reversibility and the type of reactions in non-isothermal thermogravimetry have been established. Tris(ethylenediamine)nickel(II) oxalate dihydrate has been selected as a model complex and experiments were carried out at different heating rates and sample masses to study the dependence quantitatively. The kinetic parameters calculated using mechanistic and non-mechanistic equations show a systematic decrease with increase in either sample mass or heating rate for the dehydration and deamination reactions. For the decomposition reaction, the kinetic parameters are not influenced by the procedural factors. Mathematical correlations of high reliability are established between kinetic parameters and heating rate/sample mass using both mechanistic and non-mechanistic equations for dehydration and deamination reactions. The quantification follows an exponential decay of second order relation with respect to heating rate and a sigmoidal relation with regard to sample mass for both the dehydration and deamination reactions. No quantitative correlation is possible for the final decomposition stage. Thus, it is found that independent of the type of reaction (deamination or dehydration) the kinetic parameters have a particular dependence on the procedural variables. The equations for exponential decay and sigmoidal dependence can be represented as y = y0 + A ₁e-^-x/t1 + A₂e^-x/t2 and y = A ₁-A₂/1+e(x-x₀)/dx + A₂ respectively, where y represents kinetic parameters (E or A) and x represents the procedural variables (φ or m). Mechanism of the dehydration reaction is found to be random nucleation with the formation of one nucleus on each particle and the deamination is a phase boundary reaction. It is observed that the mechanism of these reversible reactions is not affected by the variation in sample mass and heating rate. Akademiai Kiado, Budapest, Hungary 2010.

Full text of DOI:10.1007/s10973-009-0670-7

J Therm Anal Calorim (2010) 100:909–916
DOI 10.1007/s10973-009-0670-7
Quantitative correlation of kinetic parameters and procedural
factors in non-isothermal thermogravimetry-dependence
of heating rate and sample mass
K. S. Rejitha Suresh Mathew
•
Received: 21 April 2009 / Accepted: 18 December 2009 / Published online: 12 January 2010
Ó Akad e´ miai Kiad o´ , Budapest, Hungary 2010
A1ꢀA2
Abstract Dependence of kinetic parameters (activation
energy and pre-exponential factor) and procedural factors
y ¼
þ A2 respectively, where y represents kinetic
ðxꢀx Þ=dx
1
þe
0
parameters (E or A) and x represents the procedural variables
(u or m). Mechanism of the dehydration reaction is found to be
random nucleation with the formation of one nucleus on each
particle and the deamination is a phase boundary reaction. It is
observed that themechanism of these reversible reactions is not
affected by the variation in sample mass and heating rate.
(sample mass and heating rate) independent of the reversibility
and the type of reactions in non-isothermal thermogravimetry
have been established. Tris(ethylenediamine)nickel(II) oxalate
dihydrate has been selected as a model complex and experi-
ments were carried out at different heating rates and sample
masses to study the dependence quantitatively. The kinetic
parameters calculated using mechanistic and non-mechanistic
equations show a systematic decrease with increase in either
sample mass or heating rate for the dehydration and deami-
nation reactions. For the decomposition reaction, the kinetic
parameters are not influenced by the procedural factors.
Mathematical correlations of high reliability are established
betweenkineticparameters andheating rate/sample massusing
both mechanistic and non-mechanistic equations for dehydra-
tion and deamination reactions. The quantification follows an
exponential decay of second order relation with respect to
heating rate and a sigmoidal relation with regard to sample
mass for both the dehydration and deamination reactions.
No quantitative correlation is possible for the final decompo-
sition stage. Thus, it is found that independent of the type of
reaction (deamination or dehydration) the kinetic parameters
have a particular dependence on the procedural variables. The
equations for exponential decay and sigmoidal dependence
can be represented as y ¼ y0 þ A1eꢀ þ A2eꢀx=t2 and
Keywords Exponential decay ꢁ Kinetic parameters ꢁ
Thermal decomposition ꢁ
Tris(ethylenediamine)nickel(II) oxalate dihydrate
Introduction
Thermal decomposition studies of oxalate systems present
an interesting problem and have long been studied. Oxalate
compounds give well defined decomposition pattern on
heating and hence it is always used as model compounds to
investigate the influence of many experimental variables
[1]. Recently, thermal decomposition studies of various
oxalate compounds have been reported [2, 3]. Precursor
nano synthesis and the dielectric studies of CaCu Ti O
4 12
3
have also been reported [4]. Mathew et al. have investi-
gated the deamination kinetics of nickel amine complex [5]
and the effect of procedural parameters like sample mass
and heating rate on the kinetics and mechanism of
solid state decomposition using diaquobis(ethylenedia-
mine)copper(II) oxalate as the model system [6].
x=t1
Electronic supplementary material The online version of this
article (doi:10.1007/s10973-009-0670-7) contains supplementary
material, which is available to authorized users.
It is well known that the results from TG curves are
affected by procedural parameters like furnace heating rate,
furnace atmosphere, geometry of the sample holder and
furnace, sensitivity of recording mechanism, composition of
sample container, amount of sample etc. Amongst these, the
K. S. Rejitha ꢁ S. Mathew (&)
School of Chemical Sciences, Mahatma Gandhi University, P.D.
Hills, Kottayam 686 560, Kerala, India
e-mail: sureshmathews@sancharnet.in
123

9
10
K. S. Rejitha, S. Mathew
major experimental variables are heating rate and sample
mass. Investigations on the effect of these experimental
variables are very important and the results are often used to
optimise the experimental conditions in quality assessment
of petroleum products [7]. Although the dependence of E and
A on the sample mass and heating rate is well known [8–11],
not much work has been done so far to study the dependence
quantitatively.
12
1
000
10
800
600
8
4
00
6
4
2
200
0
In this paper, we report the results of our attempts to
evolve a mathematical correlation between the procedural
factors and the kinetic parameters for three reaction types
viz., reversible deamination, reversible dehydration and the
irreversible decomposition reaction. Kinetic parameters
derived from both the mechanistic (model fitting) and non-
mechanistic equations from non-isothermal analysis is
utilised for the investigation.
–200
0
100
200
300
400
500
600
°
Temperature/ C
Fig. 1 TG/DTA plot for the decomposition of tris(ethylenedia-
-
mine)nickel(II) oxalate dihydrate (u = 10 °C min
1
)
In the present work, tris(ethylenediamine)nickel(II)
oxalate dihydrate was used as the model complex, which
gave non-overlapping and clear cut stoichiometric reac-
tions of three reaction types, i.e. a reversible dehydration,
followed by a reversible deamination, followed by a non-
reversible decomposition reaction.
the loss of two water molecules to give tris(ethylenedia-
mine)nickel(II) oxalate. The second stage corresponds to
the loss of two en molecules to give mono ethylenediamine
complex. The final stage corresponds to the decomposition
of mono(ethylenediamine)nickel(II) oxalate to give NiO as
the final residue. The intermediates were separated and
identified by means of XRD and SEM. The stages of
thermal decomposition are as shown below. Under oxi-
dising condition, ethylenediamine is oxidised instanta-
neously and the oxides of nitrogen and carbon are evolved
as the gaseous products and the exothermicity due to oxi-
dation is seen in the DTA.
Experimental
The complex was synthesized as per the procedure reported
in the literature [12] and was characterised by various
spectral and chemical means. Nickel content in the com-
plex was determined by means of gravimetry [13].
Â
Ã
Â
Ã
NiðenÞ C2O4ꢁ2H2O ! NiðenÞ C2O4 þ 2H2O
3
3
Instrumentations
Â
Ã
NiðenÞ C2O4 ! NiðenÞC2O4 þ 2en
3
Thermogravimetric analyses were carried out using Shi-
madzu DTG-60 instrument connected to a TA-60 online
analyser. The experiments were conducted in flowing air
NiðenÞC2O4 ! NiO þ en þ CO2 þ CO
The shapes of the TG curves remain unchanged with
increase in either heating rate or sample mass while there is
a noticeable increase in the temperature of inception (Ti)
-
1
with a flow rate of 50 mL min . In order to study the
effect of heating rate, eight experiments were conducted at
different heating rates (1, 2, 5, 10, 15, 20, 50 and
and final temperature (T ). The decomposition starts at low
f
-
1
9
0 °C min ). Samples were loaded in a platinum crucible
temperature for slow heating rate and ends at low
temperature. It is observed that the reaction interval
(T - T ) is increased with increase in heating rate. For
of cylindrical geometry with a diameter of 5 mm and the
mass was kept constant around 10 ± 0.1 mg. To investi-
gate the effect of sample mass, seven sample masses (2.5,
f
i
all three decomposition stages, T increases with sample
f
5
, 7, 10, 12, 15.6, 20 mg) were used and the heating rate
mass and heating rate. With increase in sample mass there
is an increase in the concentration of the gaseous products
in the surrounding atmosphere, which in turn retards the
forward reaction thereby shifting the reaction to higher
temperature. Also, the increase of the mass leads to a larger
change of the temperature profile due to the self-cooling (or
self-heating) process, caused by the heat of the reaction
[14]. Since the furnace heating rate is linear, there is a
resultant increase in the value of Tf [15]. The
phenomenological data for the thermal decomposition of
the model complex are given in Table 1.
-
1
was kept constant (10 °C min ). All the samples were
loaded in a platinum crucible in a uniform manner. The
particles were sieved through a Fisher sub-sieve sizer to
make the particle size uniform so that the effect of particle
size can be avoided. The average particle size was 50 lm.
Results and discussion
-
1
The TG/DTA plot for the complex at 10 °C min is given
in Fig. 1. The first stage of decomposition corresponds to
1
23

Quantitative correlation of kinetic parameters and procedural factors
911
Table 1 Phenomenological data for the thermal decomposition of
Ni(en)
(a) 200
[
3
]C
2 4
O ꢁ2H
2
O
CR
1
1
1
80
60
40
MKN
HM
MT
Dehydration/°C
Deamination/°C
Decomposition/°C
T
i
T
f
T
s
T
i
T
f
T
s
T
i
T
f
T
s
Sample mass/mg
120
100
80
2
5
7
1
1
1
2
.5
77 138
80 152
90
98
242 317 290
248 326 310
250 330 313
252 332 313
256 335 314
263 341 316
268 348 330
318
327
331
333
336
342
349
380
387
397
400
407
412
422
370
378
390
392
396
398
406
82 158 103
82 161 105
81 165 109
60
0
2
0
20
40
60
80
100
–
1
°
Heating rate/ C min
5.6 81 170 112
85 174 114
(
b)210
0
CR
MKN
MT
-
1
200
Heating rate, u/°C min
1
1
1
90
80
70
1
2
5
1
1
2
5
9
58 106
61 115
66 106
82
84
97.7 247 308 298
224 283 274
284
340
360
387
404
410
418
475
520
325
358
380
396
408
412
470
450
HM
234 302 300.5 303
309
332
345
351
160
150
0
5
0
0
0
74 136 101
76 140 113
78 144 115
81 164 142
80 184 153
250 331 312
255 344 322
258 350 334
1
1
1
40
30
20
276 373 348.5 374
280 402 375 403
0
20
40
60
80
100
°
–1
Heating rate/ C min
Fig. 2 Variation of activation energy with heating rate for
a dehydration and b deamination reaction
Kinetic parameters
The kinetic parameters were calculated using four non-
mechanistic equations viz., Coats–Redfern, MacCallum–
Tanner, Horowitz–Metzger and MKN [16–19] equations.
The order parameter n was determined using the Coats–
Redfern equation by an iteration method. Linear plots of
a) 180
(
MT
CR
HM
MKN
1
1
1
70
60
50
2
ln[g(a)/T ] vs. 1/T were plotted by least square method,
140
taking a and T values from the TG curve. Linear curves
were drawn for different values of n ranging from 0 to 2, in
increment of 0.01. The value of n was selected from the
best fit having maximum correlation coefficient. The order
parameters for each stage were chosen by taking the
average of all values obtained for both heating rate and
sample mass variations. With the values of n thus obtained,
the kinetic parameters were computed using four non-
mechanistic equations for deamination and dehydration
reactions [6].
1
1
1
30
20
10
100
2
4
6
8
10 12 14 16 18 20 22
Sample mass/mg
(
b) 190
CR
MT
HM
MKN
1
1
1
1
1
85
80
75
70
65
The variations of the kinetic parameters with heating
rate and sample mass for the dehydration and deamination
stages are given in Figs. 2, 3, 4 and 5. From the figures, it
can be seen that the activation energy (E) and pre-
exponential factor (A) are found to decrease with increase
in sample mass or heating rate. Thus, as far as the kinetic
parameters are concerned, an increase in heating rate at
constant sample mass has the same quantitative trend as an
increase in the sample mass at constant heating rate.
Whereas for the final decomposition reaction no particular
trend is observed, i.e. the variations are irregular.
160
155
150
145
2
4
6
8
10 12 14 16 18 20 22
Sample mass/mg
Fig. 3 Variation of activation energy with sample mass for
a dehydration and b deamination reaction
123

9
12
K. S. Rejitha, S. Mathew
(
a) 28
(a)
2
2
2
4
2
0
MKN
CR
MT
2
2
2
2
1
1
1
1
1
6
4
2
0
8
6
4
2
0
CR
MKN
HM
MT
HM
18
1
1
1
6
4
2
8
6
4
0
20
40
60
80
100
2
4
6
8
10 12 14 16 18 20 22
°
–1
Heating rate/ C min
Sample mass/mg
(
b) 16
(b) 14.5
MT
CR
MKN
HM
MT
CR
MKN
HM
1
1
1
4.0
3.5
3.0
1
1
1
1
1
1
5
4
3
2
1
0
12.5
12.0
11.5
11.0
10.5
9
8
7
10.0
0
20
40
60
80
100
2
4
6
8
10 12 14 16 18 20 22
–1
°
Heating rate/ C min
Sample mass/mg
Fig. 4 Variation of log A with heating rate for a dehydration and
b deamination reaction
Fig. 5 Variation of log A with sample mass for a dehydration and
b deamination reaction
values with heating rates for the dehydration and the
deamination reaction can be represented as an exponential
decay of 2nd order.
The regular trend of these kinetic parameters relative to
changes in heating rate and sample mass for the dehydra-
tion and deamination reactions makes the data amenable to
statistical analysis. Standard types of curve fits such as
exponential decay of 1st, 2nd and 3rd orders, exponential
growth and sigmoidal (Boltzmann) were tried and the best
fit was chosen (Figs. 2, 3, 4, 5). It is found that for all the
four non-mechanistic equations the variation of E and A
ꢀ
u=t1
þ A2eꢀu=t2
E ¼ y þ A e
0
1
ꢀ
1
u=t1
þ A2eꢀu=t2
where y , A , A , t and t are fit parameters for exponential
log A ¼ y þ A e
0
0
1
2
1
2
decay of order two and represents offset, amplitudes and
Table 2 Curve fit constants for the reversible reactions (exponential decay second order equation) using non-mechanistic equations
Dehydration Deamination
y
0
A
1
A
2
t
1
t
2
y
0
A
1
A
2
t
1
t
2
Correlation with E
CR
35.4
128.7
128.6
127.8
81.2
60
173.1
172.4
172.1
128.7
0.47
0.47
0.45
0.84
-7.9
-2.2
-6.2
-1.7
7.9
56.9
57.1
54.2
57.5
2.7
7.6
6.5
9.4
9.1
MKN
MT
35.7
34.7
43.1
60
2.2
5.4
1.7
9.1
8.1
7.3
59.7
64.7
HM
Correlation with log A
CR
3.9
4.4
3.8
6.6
17.7
19.6
17.5
14.6
40.9
40.9
43.1
14.5
43.8
42.8
41.1
36.9
0.37
0.36
0.35
0.69
10.9
10.9
10.3
10.3
-1.4
-1.4
-2.3
-3.3
5.9
5.9
5.4
3.3
-122.5
-122.5
-111.1
-110.3
9.5
9.5
9.8
MKN
MT
HM
11.1
1
23

Quantitative correlation of kinetic parameters and procedural factors
913
2
Table 3 Curve fit constants for the reversible reactions (sigmoidal)
equation using non-mechanistic equations
Table 4 The fisher constant, chi square (v ) and coefficient of
determination (R ) for the various fits between heating rate
2
(u)/sample mass (m) with activation energy for the dehydration
reaction using four non-mechanistic equations
Dehydration
Deamination
A
1
A
2
x
0
dx
A
1
A
2
x
0
dx
Fits
Activation energy, E
Correlation with E
CR 164.2 101.5
MKN 164.3 101.4
Heating rate
Sample mass
13.1
13.1
13.2
13.3
3.1 170.4 148.8 8.6 2.8
3.1 170.4 148.8 8.6 2.8
3.4 168.2 145.2 7.6 3.1
2.8 189.3 169.5 8.9 2.7
2
2
2
R
2
F
R
v
F
v
Exponential decay I
MT
HM
164.5 102.3
171.8 112.9
CR
685.8
685.8
671.1
581.2
0.9778
0.9778
0.9778
0.9722
46.13
46.13
46.13
58.31
581.2
580.2
571.1
502.1
0.9624
0.9731
0.9745
0.9545
24.01
17.19
16.65
27.63
MKN
MT
Correlation with log A
CR
26.6
26.6
8.9
8.9
9.1
10.5
10.5
10.4
6.8
6.8
5.9
12.8
12.9
12.4
14.4
10.3 9.9 2.7
10.7 9.2 2.8
10.2 7.2 2.9
12.3 8.9 2.2
HM
MKN
MT
Exponential decay II
23.4
CR
1047.2
1047.2
1025.3
1016.7
0.9997
0.9997
0.9998
0.9989
0.8950
0.8944
0.8943
4.56
–
–
–
HM
167.5
6.7 -4.5 23.7
MKN
MT
HM
decay constants respectively for a second order exponential
decay curve and u is the heating rate.
The variation of E and A values with sample mass for
the dehydration and deamination reaction can be best
represented as a sigmoidal (Boltzman fit) curve of the type
Exponential decay III
CR
1044.6
1044.6
1035.2
1016.7
0.9997
0.9997
0.9997
0.9987
2.55
2.54
–
–
–
MKN
MT
2.54
HM
13.68
A1 ꢀ A2
Exponential growth
E ¼ 1
þ e
þ A2
ðmꢀx0Þ=dx
CR
MKN
MT
685.8
685.8
690.1
581.2
0.9778
0.9778
0.9776
0.9722
46.13
46.01
47.31
58.31
621.1
621.1
613.4
582.2
0.9624
0.9731
0.9745
0.9545
24.01
17.19
16.65
27.63
A1 ꢀ A2
log A ¼ 1
þ A2
ðmꢀx0Þ=dx
þ e
HM
where A , A , x , and dx are fit parameters which represents
0
1
2
Sigmoidal
CR
the initial value, final value, centre (point of inflection) and
time constant (the change in X corresponding to the most
significant change in Y values), respectively, of a sigmoidal
curve and m is the sample mass. The fit constants that are
different for the four non-mechanistic equations and are
given in Tables 2 and 3. The fitted curves are given in
Figs. 2, 3, 4 and 5.
674
0.9774
0.9774
0.9773
0.9718
58.71
58.56
59.01
73.8
654.1
653.5
650.2
632.1
0.9862
0.9861
0.9877
0.9870
11.74
11.84
11.89
10.50
MKN
MT
674
674
HM
572.9
2
The reliability of the fits were assessed by means of R
2
invoking equation. The kinetic parameters obtained for
mechanism invoking equation for different heating rates and
sample masses are given in Tables 8 and 9.
(
coefficient of determination) and chi square (v ) value.
Chi square test is to measure the discrepancy existing
between the observed and the expected frequencies. The
2
The correlation coefficients obtained are very close to
unity in almost all cases, indicating nearly perfect fit. A
choice of the probable mechanism from the best fit curve
thus becomes difficult. In such a situation, Satava [22] has
chosen the function g(a) which yield kinetic parameters in
agreement with those kinetic parameters by numerical
method. In the present case, comparison with the values
obtained from Coats–Redfern method is more appropriate
as this method was also used for solving the exponential
integral. It is found that the rate controlling process for
dehydration reaction is random nucleation while the rate
controlling process for the deamination process is phase
boundary reaction. Kinetic parameters were also calculated
from the mechanistic equations. For the dehydration and
smaller the value of chi square the better will be the fit. R
is a statistics that will give information about the goodness
2
of a model. An R of 1.0 indicates a perfect fit [20, 21]. The
goodness of the models was also checked by F test. The
fisher constant at 99% confidence level, the values of chi
2
square and R for various fits are given in Tables 4, 5, 6
2
and 7. The fit with higher R and lower chi square values is
selected as the best fit.
Mechanism of the reactions
Quantitative correlations between the kinetic parameters and
procedural factors have also been obtained using mechanism
123

9
14
K. S. Rejitha, S. Mathew
2
2
Table 5 The fisher constant, chi square (v ) and coefficient of
determination (R ) for the various fits between heating rate
Table 6 The fisher constant, chi square (v ) and coefficient of
determination (R ) for the various fits between heating rate
2
2
(u)/sample mass (m) with log A for the dehydration reaction using
four non-mechanistic equations
(u)/sample mass (m) with activation energy for the deamination
reaction using four non-mechanistic equations
Fits
Log A
Fits
Activation energy, E
Heating rate
Sample mass
Heating rate
Sample mass
2
2
2
R
2
2
2
2
2
F
R
v
F
v
F
R
v
F
R
v
Exponential decay I
Exponential decay I
CR 123.6 0.9640
MKN 124.2 0.9637
CR
461.4
466.1
453.2
306.4
0.9805
0.9805
0.9801
0.9661
0.9539
0.9539
0.9831
1.73
521.2
521.1
518.2
472.3
0.9831
0.9831
0.9878
0.9859
0.33
39.76
40.22
41.01
17.75
624.3 0.9745
624.4 0.9748
620.9 0.9788
602.1 0.9712
2.17
2.16
2.34
2.16
MKN
MT
0.33
0.43
MT
HM
131.1 0.9641
78 0.9791
HM
0.2508
Exponential decay II
Exponential decay II
CR
657.5
657.5
612.3
462
0.9997
0.9997
0.9989
0.9849
0.1851
0.1851
0.15
534.2
532.1
530.6
521.1
0.9831
0.9831
0.9845
0.9859
0.6541
0.33
CR
230.2 0.9794
37.93
38.21
38.21
29.88
625.1 0.9745
624.3 0.9748
618.2 0.9812
588.4 0.9712
4.35
4.31
3.21
4.33
MKN
MT
MKN 232.4 0.9793
0.143
0.3759
MT
HM
228.1 0.981
78 0.9791
HM
1.29
Exponential decay III
Exponential decay III
CR 229.2 0.9793 114.59
MKN 216.4 0.9771 123.59
CR
640.2
466.1
524.2
416.6
0.9902
0.9902
0.9896
0.9849
0.2418
0.2418
1.78
516.1
517.9
510.0
482.1
0.9831
0.9831
0.9832
0.9859
–
–
–
–
625.1 0.9745
624.3 0.9748
618.2 0.9732
588.4 0.9712
–
–
–
–
MKN
MT
MT
HM
225.5 0.9791 120.9
78 0.9693 190.1
HM
3.77
Exponential growth
Exponential growth
CR
CR
MKN
MT
461.4
466.1
420.3
306.4
0.9805
0.9805
0.9801
0.9661
0.9539
0.9539
1.73
521.7
521
0.9831
0.9831
0.9878
0.9859
0.33
123.6 0.9640
39.76
40.22
39.8
625.1 0.9745
624.3 0.9748
618.2 0.9744
2.17
2.16
2.17
0.33
MKN 124.2 0.9637
513.2
498.7
0.43
MT
HM
120.5 0.9645
78 0.935
HM
2.98
0.2508
46.2
588.4 0.0.9712 2.16
Sigmoidal
CR
Sigmoidal
CR
452.7
466.1
403.2
300.9
0.9801
0.9801
0.9834
0.9657
6.23
1.54
7.89
2.19
576.2
576.3
570.9
555.2
0.9847
0.9847
0.9894
0.9859
0.39
120.7 0.9638
40.02 1014.2 0.9973
39.76 1014.2 0.9974
0.305
0.301
0.31
MKN
MT
0.39
MKN 121.4 0.9641
0.23
MT
HM
118.6 0.9637
50.2 0.9335
50.1
60.9
100.2 0.9978
989.7 0.9959
HM
0.1879
0.406
deamination reaction the kinetic parameters decrease with
increase in heating rate or sample mass (Tables 8, 9). The
mechanism of these reversible reactions remains unchan-
ged with the change in sample mass and heating rate.
Where as the kinetic parameter obtained from the mecha-
nism invoking equation for the decomposition reaction is
not affected by either sample mass or heating rate.
Exponential decay of order 2 can be represented as
E ¼ 14:1 þ 519:8eðꢀu=0:49Þ þ 112:8e
ðꢀu=82:9Þ
ðꢀu=19:7Þ
ðꢀu=1:3Þ
ðꢀu=117:9Þ
ðꢀu=10:2Þ
log A ¼ ꢀ1:4 þ 71:2e
þ 0:56e
E ¼ ꢀ4:4 þ 4:4e
þ 54:8e
ðꢀu=11:2Þ
þ 2:6eðꢀu=1:8Þ
log A ¼ 2:6 ꢀ 5:3e
Regular variations of the kinetic parameters obtained
from mechanistic equation were subjected to statistical
analysis as in the case of non-mechanistic equations.
Equations corresponding to exponential decay of order 1,
Sigmoidal equations are
1
88:8
E ¼ 1
ꢀ 41:5
ðmꢀ28:4Þ=10:4
þ e
3
12:7
2
, 3, exponential growth and sigmoidal relations were tried
log A ¼ 1
E ¼ 1
ꢀ 200:7
þ eðmꢀ129:9Þ=142:6
18:9
þ eðmꢀ8:2Þ=2:6
for curve fitting. The variation of kinetic parameters with
heating rate for the dehydration and deamination reaction
can be represented as exponential decay of order two while
the variation of kinetic parameters with sample mass for
the dehydration and deamination reaction can be repre-
sented as sigmoidal curve.
þ 154
2
:2
log A ¼ 1
þ 14
þ eðmꢀ9:5Þ=2:9
1
23

Quantitative correlation of kinetic parameters and procedural factors
915
2
Table 7 The fisher constant, chi square (v ) and coefficient of
determination (R ) for the various fits between heating rate
Table 8 Kinetic parameters for reversible reactions at various heat-
ing rates obtained from mechanistic equations
2
(
four non-mechanistic equations
u)/sample mass (m) with log A for the deamination reaction using
Heating rate, Dehydration (Mampel
-
Deamination (phase
boundary equation)
1
u/°C min
equation)
Fits
Log A
-
1
-1
A/s
-1
E/kJ mol
-1
A/s
E/kJ mol
Heating rate
Sample mass
3
0
18
18
17
16
14
14
13
12
1
195.7
133.8
116.9
115.7
109.6
105.8
72.4
1.5 9 10
3.9 9 10
9.9 9 10
5.6 9 10
5.6 9 10
1.7 9 10
2.7 9 10
192.7
189.9
184.8
166.7
145.7
147.2
134.3
5.3 9 10
1.9 9 10
8.5 9 10
1.4 9 10
1.3 9 10
1.6 9 10
1.2 9 10
1.2 9 10
2
2
2
2
F
R
v
F
R
v
20
2
17
17
16
16
11
8
Exponential decay I
5
CR
92.7
92.9
90.7
73.1
0.9766
0.9766
0.9763
0.9747
0.2054
0.2054
0.2031
0.2028
635.1
635.3
628.8
592.4
0.9684
0.9723
0.9732
0.9531
0.039
0.025
0.031
0.045
10
15
20
50
90
MKN
MT
HM
Exponential decay II
53.3
8 9 10 125.4
CR
141.8
141.9
129.1
73.1
0.9833
0.9833
0.9834
0.9747
0.2439
0.2431
0.2434
0.3379
635.1
635.3
628.8
592.4
0.9684
0.9723
0.9732
0.9531
0.078
0.051
0.045
0.091
MKN
MT
HM
Exponential decay III
CR
137.9
136.5
132.1
73.1
0.9823
0.9823
0.9822
0.9747
0.7755
0.7755
0.7745
1.01
635.1
635.3
628.8
592.4
0.9684
0.9723
0.9732
0.9531
–
–
–
–
MKN
MT
Table 9 Kinetic parameters obtained for the reversible reactions at
various sample masses from mechanistic equations
HM
Sample mass/mg Dehydration (Mampel
equation)
Deamination (phase
boundary equation)
Exponential growth
CR
MKN
MT
92.9
92.9
89.9
73.1
0.9766
0.9766
0.9765
0.9727
0.2054
0.2054
0.21
635.1
635.3
628.8
592.4
0.9684
0.9723
0.9732
0.9531
0.0395
0.0252
0.0231
0.0453
-1
-1
-1
-1
E/kJ mol
A/s
E/kJ mol
A/s
2
2
9 9 10 189.9
2
2.2 9 10 163.3
1
8.3 9 10 158.6
1
5.6 9 10 166.7
0
1.9 9 10 147.8
1
9.6 9 10 164.2
1
2.1 9 10 148
18
15
15
16
14
15
13
2.45
5.14
6.96
10
135.8
134.2
119
7.6 9 10
7.7 9 10
1.9 9 10
1.4 9 10
1.7 9 10
4.3 9 10
9.6 9 10
1
HM
0.2028
7
Sigmoidal
CR
7
90.6
90.1
89.7
73.1
0.9764
0.9764
0.9764
0.974
0.2589
0.2589
0.261
978.2
978.2
967.5
911.2
0.9946
0.9959
0.9959
0.9896
0.009
115.7
134.9
104.8
75.4
2
MKN
MT
0.005
12.09
15.55
20.09
5
0.0034
0.0134
1
HM
0.1525
Table 10 The curve fit constants for the reversible reactions (exponential decay second order equation) using the mechanistic equations
2
R
2
y
0
A
1
A
2
t
1
t
2
F
v
Dehydration (Mampel equation)
Correlation with E
14.1
519.8
71.2
112.8
0.56
0.49
82.9
656
621
0.9969
0.9959
12.8
0.4
Correlation with log A
-1.4
19.7
117.9
Deamination (phase boundary equation)
Correlation with E
-4.4
4.4
54.8
2.6
1.3
10.2
1.8
215.2
231
0.9735
0.9766
0.1241
0.1342
Correlation with log A
2.6
-5.3
11.2
The curve fit constants for the dehydration and deami-
nation reaction using mechanism based equations (Mam-
pel and phase boundary equations) are given in Tables 10
and 11.
Dependence of procedural factors
The investigation reveals that independent of reversibility
and type of the reaction, the kinetic parameters have a
123

9
16
K. S. Rejitha, S. Mathew
Table 11 The curve fit constants for the reversible reactions (sigmoidal) equation using the mechanistic equations
2
2
A
1
A
2
x
0
dx
F
R
v
Dehydration (Mampel equation)
Correlation with E
147.3
112
-41.5
28.4
10.4
650.3
567.3
0.9873
0.9776
2.12
Correlation with log A
-200.7
129.9
142.6
12.1
Deamination (Phase boundary equation)
Correlation with E
172.9
16.2
154
14
8.2
9.5
2.6
2.9
670
0.9987
0.9921
0.2921
0.2112
Correlation with log A
643.2
dependence on the procedural variables. Mathew et al. [6]
have evolved mathematical correlation between activation
parameters and procedural factors and its dependence on
reaction type. It is found that for both the dehydration and
deamination reactions, quantitative correlation can be
evolved between a particular procedural variable (u or m)
and kinetic parameters.
3. Su TT, Zhai YC, Jiang H, Gong H. Studies on the thermal
decomposition kinetics and mechanism of ammonium niobium
oxalate. J Therm Anal Calorim. 2009;98:449–455.
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. Thomas P, Dwarakanath K, Varma KBR, Kutty TRN. Synthesis
4 12
of nanoparticles of the giant dielectric material, CaCu Ti O
3
from a precursor route. J Therm Anal Calorim. 2009;95:267–72.
. Rejitha KS, Mathew S. Thermal deamination kinetics of
tris(ethylenediamine)nickel(II) sulphate in the solid-state. J
Therm Anal Calorim. 2008;93:213–7.
. Mathew S, Nair CGR, Ninan KN. Quantitative correlations of
activation parameters and procedural factors-dependence on
reaction type. Thermochim Acta. 1991;184:269–94.
. Shishkin YL. The effect of sample mass and heating rate on DSC
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Conclusions
The effect of kinetic parameters on procedural parameters
like heating rate and sample mass during the thermal
decomposition have been studied using tris(ethylenedia-
mine)nickel(II) oxalate dihydrate as a model complex. The
complex yields clear cut thermal decomposition pattern
consists of reversible dehydration, reversible deamination
and irreversible decomposition. For the dehydration and
deamination reaction the kinetic parameters decrease with
increase in sample mass or heating rate while for the
decomposition reaction the variations are irregular. The
mechanism of these reversible reactions remains unchanged
with variations in procedural factors(heating rate and sample
mass). Quantitative correlations between the kinetic
parameters and procedural variables, independent of the type
of the reaction have been evolved. The dependence of kinetic
parameters on heating rate can be best described as a second
order exponential decay for the deamination and dehydration
reaction. While the dependence of kinetic parameters on
sample mass can be expressed as a sigmoidal equation for the
deamination and dehydration reaction. No quantitative cor-
relation is possible for decomposition reaction.
8. Bigda R, Mianowsky A. Influence of heating rate on kinetic
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