Thermal kinetic TG-analysis of metal oxalate complexes

Article abstract of DOI:10.1016/S0040-6031(03)00221-1

The TG/DSC curves of K₃[Cr(C₂O₄) ₃]·3H₂O, K₃[Al(C₂O ₄)₃]·3H₂O, K₃[Fe(C ₂O₄)₃]·3H₂O and K ₂[Cu(C₂O₄)₂]·2H₂O in nitrogen were determined at the heating rate of 15, 10, 5, and 2°C min^-1, respectively. A non-linear optimization was applied for different reaction models to perform single and overall steps optimizations. Kinetic parameters were given, and the most probable mechanism functions were suggested.

Full text of DOI:10.1016/S0040-6031(03)00221-1

Thermochimica Acta 406 (2003) 77–87
Thermal kinetic TG-analysis of metal
oxalate complexes
Li Jun∗, Zhang Feng-Xing, Ren Yan-Wei, Hun Yong-Qian, Nan Ye-Fei
Department of Chemistry, Northwest University, Key Laboratory of Physicoinorganic Chemistry,
TaiBai Road 229, Xi’an 710069, Shaanxi Province, PR China
Received 19 September 2002; received in revised form 25 March 2003; accepted 3 April 2003
Abstract
The TG/DSC curves of K3[Cr(C2O4)3]·3H2O, K3[Al(C2O4)3]·3H2O, K3[Fe(C2O4)3]·3H2O and K2[Cu(C2O4)2]·2H2O in
nitrogen were determined at the heating rate of 15, 10, 5, and 2 ◦C min−1, respectively. A non-linear optimization was applied
for different reaction models to perform single and overall steps optimizations. Kinetic parameters were given, and the most
probable mechanism functions were suggested.
© 2003 Elsevier B.V. All rights reserved.
Keywords: Thermal analysis; Kinetic; Metal oxalate complexes
1. Introduction
lg A of each steps by means of Ozawa–Flynn–Wall,
Friedman and ASTME698 methods [12]. But the ki-
netic studies of the type K3[M(C2O4)3]·3H2O and
K2[Cu(C2O4)2]·2H2O are rarely reported until now. In
this article, a non-linear optimization was applied for
different reaction models to perform single and over-
all steps optimizations and kinetic parameters were
given, the most probable mechanism functions were
suggested for the complexes of K3[Cr(C2O4)3]·3H2O,
K3[Al(C2O4)3]·3H2O, K3[Fe(C2O4)3]·3H2O and
K2[Cu(C2O4)2]·2H2O.
2−
C2O4 is a good ligand and can be coordinated
with many transition and non-transition metals. Their
thermal decomposition processes are relatively com-
plicated because of the reduction property of C2O4
2−
.
So their thermal analysis studies are often in at-
tention. A review on the thermal decomposition of
some solid oxalates has been given by Harris and
co-workers [1]. The kinetics and mechanisms of ther-
mal decomposition of solids have been reviewed by
L’vov [2]. The thermal decomposition of the type
K3[M(C2O4)3]·3H2O (where M = Co, Cr, Fe, Ga)
and K2[Cu(C2O4)2]·2H2O (where M = Cu, Zn, Pd,
Pt) were studied [3–11]. Recently, we also studied
the thermal decomposition of K3[Cr(C2O4)3]·3H2O,
K3[Al(C2O4)3]·3H2O, K3[Fe(C2O4)3]·3H2O and
K2[Cu(C2O4)2]·2H2O in nitrogen, and obtained Ea,
2. Experimental
2.1. Reagents
K2C2O4·H2O, H2C2O4·2H2O, K2Cr2O7, Al2(SO4)3,
FeCl3·6H2O and CuSO4·5H2O are all A.R. or G.R.
from China.
∗
Corresponding author.
E-mail address: junli@nwu.edu.cn (L. Jun).
0040-6031/$ – see front matter © 2003 Elsevier B.V. All rights reserved.
doi:10.1016/S0040-6031(03)00221-1

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L. Jun et al. / Thermochimica Acta 406 (2003) 77–87
Table 1
The selective 15 mechanism functions for evaluation of the kinetic equations
Name of functions
Kinetics mechanisms
Form of functions
Symbol
f(α)
G(α)
First order
Second order
Nth order
Parabola law
Valensi equation
(1 − α)
F1
F2
Fn
D1
D2
Formal chemical reaction
(1 − α)2
(1 − α)n
0.5α−1
(1 − α)−1
[1 − (1 − α)1−n ]/(1 − n)
One-dimensional diffusion
Two-dimensional diffusion
α2
−1/ln(1 − α)
α + (1 − α)ln(1 − α)
−1
2
Jander equation
Three-dimensional diffusion
Three-dimensional diffusion
1.5(1 − α)2/3[1−(1−α)1/3
1.5[(1 − α)−1/3 − 1]−1
]
[1−(1 − α)1/3
]
D3
D4
Ginstling–Brounshtein
((1 − 2α)/3)−(1 − α)2/3
Contracting sphere
Cylindrical symmetry
Spherical symmetry
Phase boundary reaction
Phase boundary reaction
2(1 − α)1/2
3(1 − α)2/3
1−(1 − α)1/2
1−(1 − α)1/3
R2
R3
Prout–Tompkins equation
(1 − α)α
(1 − α)nαa
ln[α/(1 − α)]
B1
Expanded Prout–
Tompkins equation
Auto-catalysis,
Ramiform nucleation
Bna
(1 − α)(1 + Kα)
C1
A2
Avrami–Erofeev equation
Two-dimensional
(1 − α)[−ln(1 − α)]1/2
[−ln(1 − α)]1/2
[−ln(1 − α)]1/3
[−ln(1 − α)]1/n
nucleation and growth
Three-dimensional
nucleation and growth
N-Dimensional
3(1 − α)[−ln(1 − α)]2/3
A3
An
n(1 − α)[−ln(1 − α)](n−1)/n
nucleation and growth
2.2. Preparation
where α is fractional extent of reaction in time t,
β the heating rate, Ea the activation energy, A the
pre-exponential factor, and f(α) is kinetic differential
function. Its integral form is as follows:
K3[Al(C2O4)3]·3H2O, K3[Cr(C2O4)3]·3H2O, K3
[Fe(C2O4)3]·3H2O and K2[Cu(C2O4)2]·2H2O were
prepared according to the literature [13].
ꢀ
ꢁ
ꢂ
ꢂ
α
T
dα
A
β
−Ea
G(α)
=
exp
dT
(2)
f(α)
RT
2.3. Thermal analysis
0
0
Fifteen mechanism functions in Table 1 were used to fit
kinetics curves. The kinetics software from NETZSCH
was adopted.
NETZSCH STA449C thermal analysis instrument
(made in Germany). An alumina crucible container
was used in nitrogen. The rate of heating was 15, 10,
5, and 2 ◦C min−1, and sensitive of the instrument is
0.1 ␮g. The sample mass is 3–6 mg.
3. Results and discussion
2.4. The theory base of the kinetics estimation
of the thermal decomposition
3.1. Thermal decomposition processes
According to non-isothermal kinetic models, the ki-
netic equation of solid thermal decomposition is given
as follows:
The thermal decomposition processes of K3[Al(C2
O4)3]·3H2O, K3[Cr(C2O4)3]·3H2O, K3[Fe(C2O4)3]·
3H2O and K2[Cu(C2O4)2]·2H2O have been reported
previously by [12]. There, some data were given in
Table 2.
ꢀ
ꢁ
dα
dT
A
β
−Ea
=
f(α)exp
(1)
RT

L. Jun et al. / Thermochimica Acta 406 (2003) 77–87
79
Table 2
The thermal decomposition processes of the complexes K3M(C2O4)3·3H2O (M = Al, Cr, Fe) and K2Cu(C2O4)2·2H2O
Steps
K3Al(C2O4)3·3H2O
K3Cr(C2O4)3·3H2O
K3Fe(C2O4)3·3H2O
K2[Cu(C2O4)2]·2H2O
I
↓ −3H2O
↓ −3H2O
↓ −3H2O
↓ –2H2O
K3Al(C2O4)3
K3Cr(C2O4)3
K3Fe(C2O4)3
K2[Cu(C2O4)2]
II
↓ −1/2(3CO2 + 6CO)
1/2Al2O3 + 3/2K2CO3
↓ −1/10(16CO + 9CO2)
↓ −(CO2 + 1/2CO)
↓ −(3/2CO2 + 1/2CO)
1/2Cu2O + K2C2O4
3/2K2C2O4 + 1/5(Cr3O4 + Cr2(CO3)3
1/2K2CO3 + K2[FeC2O4]2
II
↓ −1/30(37CO + 23CO2)
↓ −5/2CO
↓ −CO
3/2K2CO3 + 1/3Cr3O4
3/2K2CO3 + FeCO3
K2CO3 + 1/2Cu2O
IV
↓ CO2 + 1/6O2
3/2K2CO3 + 1/6Fe3O4 + 1/2Fe
Fig. 1. The TG curve of K3Al(C2O4)3·3H2O at the heating rate of 15, 10, 5, and 2 ◦C min−1, respectively (a); the first step (b) and the
second step (c) were the best fit to mechanism functions. The solid line is the fit curve.

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L. Jun et al. / Thermochimica Acta 406 (2003) 77–87
Fig. 1. (Continued ).
Table 3
The optimized mechanism functions and kinetics parameters of K3M(C2O4)3·3H2O (M = Cr, Fe, Al) and K2Cu(C2O4)2·2H2O
Complexes
Steps
Mechanism
Ea (kJ mol−1
)
lg A (s−1
)
Reaction
order n
Exponent a
Correction
coefficient
K3[Al(C2O4)3]·3H2O
I
Fn
Fn
88.56
227.49
11.39
30.54
0.36
3.65
0.99944
II
Bna
Fn
107.03
150.49
6.15
8.72
21.68
8.91E−02
2.57
0.60
0.78
0.82
0.18
0.99861
K3[Cr(C2O4)3]·3H2O
K3[Fe(C2O4)3]·3H2O
I
II
III
Fn
Bna
Fn
81.87
297.71
361.78
9.94
18.78
16.02
0.99816
0.99943
0.99856
I
Bna
Bna
63.67
79.51
8.13
9.78
1.20
1.54
0.23
0.81
0.99846
0.99888
0.99834
0.99978
0.99988
0.99961
II
III
IV
I
Fn
Bna
60.90
99.80
3.08
8.08
0.19
1.14
0.84
1.34
R3
Bna
344.00
168.42
23.25
12.32
20.66
Fn
Fn
194.39
185.25
11.07
9.66
0.89
0.75
K2[Cu(C2O4)2]·2H2O
Bna
Bna
193.52
72.02
26.48
8.59
2.06
0.65
0.56
0.65
II
A3
D3
190.51
390.12
15.82
35.85

L. Jun et al. / Thermochimica Acta 406 (2003) 77–87
81
3.2. Thermal kinetic TG-analysis of
K3[Al(C2O4)3]·3H2O
good. So, we base the change of activation energy with
the reacted fraction α, and try to use multireaction
mechanisms to fit. The results were satisfied (Fig. 1).
From Table 3, we see that the dehydration of
K3[Al(C2O4)3]·3H2O adopted the A → B → C se-
quential reaction, and the reaction mechanism was
Fn–Fn. The activation energy of the later was larger
than the former; the second step adopted A → B and
TG kinetic of K3[Al(C2O4)3]·3H2O were analyzed.
The TG data for the first step and second step of
K3[Al(C2O4)3]·3H2O were non-line fit to 15 mecha-
nism functions which were given in Table 1. Single
reaction mechanism was tried to fit, but it do not fit
Fig. 2. The TG curve of K3Cr(C2O4)3·3H2O at the heating rate of 15, 10, 5, and 2 ◦C min−1, respectively (a); the first step (b), the second
step (c) and the third step (d) were the best fit to mechanism functions. The solid line is the fit curve.

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L. Jun et al. / Thermochimica Acta 406 (2003) 77–87
Fig. 2. (Continued ).
C → D reaction mode, and the reaction mechanism
tried to fit, but it does not fit good. This demonstrated
that three steps of K3[Cr(C2O4)3]·3H2O were a single
reaction mechanism. So single reaction mechanism
was used, and the results were shown in Fig. 2 and
Table 3.
was Bna–Fn.
3.3. Thermal kinetic TG-analysis of
K3[Cr(C2O4)3]·3H2O
The optimized mechanism functions of the three
steps were Fn, Bna and Fn, respectively. Rele-
TG kinetic of three steps of K3[Cr(C2O4)3]·3H2O
were analyzed, respectively, and each step was
non-line fit to 15 mechanism functions which were
given in Table 1. The multireaction mechanism was
vant Ea were 77.79, 284.16, and 261.25 kJ mol−1
,
and lg A were 9.468, 18.78, and 16.02 s−1. Com-
pared with optimized multireaction mechanism of

L. Jun et al. / Thermochimica Acta 406 (2003) 77–87
83
K3[Al(C2O4)3]·3H2O, the correction coefficient of
step was non-line fit to 15 mechanism functions which
were given in Table 1. Single reaction mechanism was
tried to fit, but it does not fit good. So multireaction
mechanism was used, and the results were shown in
Fig. 3 and Table 3.
The four steps TG of K3[Fe(C2O4)3]·3H2O were
optimized. They adopted A → B → C, A → B and
C → D, A → B and C → D, A → B → C reaction
single reaction mechanism was not so good.
3.4. Thermal kinetic TG-analysis of
K3[Fe(C2O4)3]·3H2O
Similarly, TG kinetic of four steps of K3[Fe(C2
O4)3]·3H2O were also analyzed, respectively, and each
Fig. 3. The TG curve of K3Fe(C2O4)3·3H2O at the heating rate of 15, 10, 5, and 2 ◦C min−1, respectively (a); the first step (b), the second
step (c), the third step (d) and the fourth step (e) were the best fit to mechanism functions. The solid line is the fit curve.

84
L. Jun et al. / Thermochimica Acta 406 (2003) 77–87
Fig. 3. (Continued ).

L. Jun et al. / Thermochimica Acta 406 (2003) 77–87
85
mode, and the optimized mechanism functions were
Bna–Bna, Fn–Bna, R3–Bna and Fn–Fn, respec-
tively. The activation energies of the first and second
steps are larger than that of the third and the fourth
steps.
The multireaction mechanism was used to optimize
the mechanism function, and the results were shown
in Fig. 4 and Table 3.
The results show that the dehydration of K2[Cu(C2
O4)2]·2H2O adopted the A → B → C sequential
reaction, and the reaction mechanism was Bna–Bna.
The second step also adopted A → B → C re-
action mode, and the reaction mechanism was
A3–D3. Compared with K3[Al(C2O4)3]·3H2O and
K3[Fe(C2O4)3]·3H2O, the correction coefficient of
K2[Cu(C2O4)2]·2H2O is more close to 1.
3.5. Thermal kinetic TG-analysis of
K2[Cu(C2O4)2]·2H2O
TG kinetic of the first and the second steps of
K2[Cu(C2O4)2]·2H2O were analyzed, respectively.
Fig. 4. The TG curve of K2Cu(C2O4)2·2H2O at the heating rate of 15, 10, 5, and 2 ◦C min−1, respectively (a); the first step (b) and the
second step (c) were the best fit to mechanism functions. The solid line is the fit curve.

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L. Jun et al. / Thermochimica Acta 406 (2003) 77–87
Fig. 4. (Continued ).
3.6. Discussion
mal chemical reaction (Fn) takes second place, and
three-dimensional nucleation and growth (A3) takes
the third, phase boundary reaction contracting sphere
(R3) and diffusion three-dimensional diffusion (D3)
have the largest activation energies.
3.6.1. The process of dehydration
The dehydration reaction of K3[Al(C2O4)3]·3H2O
undergoes two same chemical reaction mechanisms
(Fn) with different Ea, n and lg A (Table 3) and the
later mechanism has the larger activation energy.
For K3[Cr(C2O4)3]·3H2O, the dehydration mecha-
nism is also formal chemical reaction (Fn) with Ea,
4. Evaluation of models
n and lg A being 81.87 kJ mol−1, 1.8, and 9.94 s−1
,
The multireactions mechanism and single reac-
tion mechanism have been used to optimized for
each step of these complexes. The results show that
the multireactions mechanism are better than sin-
gle reaction mechanism for K3[Al(C2O4)3]·3H2O,
K3[Fe(C2O4)3]·3H2O and K2[Cu(C2O4)2]·2H2O. We
suppose there may exist two or even more reaction
mechanisms in a step of thermal decomposition of
solids. Of course, some times the parameters gained
from optimizing were not good, such as reaction order.
respectively. Difference from K3[Al(C2O4)3]·3H2O
and K3[Cr(C2O4)3]·3H2O, the dehydration re-
action mechanisms of K3[Fe(C2O4)3]·3H2O and
K2[Cu(C2O4)2]·2H2O are auto-catalysis (Bna) and
both also undergo two processes with different Ea, n,
a and lg A (Table 3). These can be explained by that
the dehydration reactions start on some local place,
such as on the crystal lacuna. Subsequently, these
dehydration products get together and form a new
nuclear. Later, the new nuclear occur phase bound-
ary reaction, and the reactant graduate away and the
products grow until the reaction accomplish.
Acknowledgements
3.6.2. Mechanism functions and activation energies
Analyzing the mechanism functions and activation
energies of each steps, we see that auto-catalysis (Bna)
corresponds to the smallest activation energies, for-
We are very grateful for the financial support from
The National Natural Science Foundation of China
and The National Science Foundation of Shaanxi
Province.

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87
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