Kinetic study of the thermal decomposition of the compound of terbium(III) trifluoromethanesulfonate and hexamethylphosphoramide (HMPA) employing both Zsako?'s and nonlinear methods

Article abstract of DOI:10.1016/S0925-8388(00)00621-6

Terbium trifluoromethanesulfonate compound with hexamethylphosphoramide was synthesized and characterized. Thermogravimetric data with three heating rates were used to obtain kinetic parameters such as activation energy (E_a), reaction order (n) and preexponential factor (k₀). The results obtained by two different methods, Zsa?'s and a nonlinear one, are compared.

Full text of DOI:10.1016/S0925-8388(00)00621-6

Journal of Alloys and Compounds 303–304 (2000) 142–145
L
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Kinetic study of the thermal decomposition of the compound of
terbium(III) trifluoromethanesulfonate and hexamethylphosphoramide
´
(HMPA) employing both Zsako’s and nonlinear methods
*
´
M.F.F. Pedrosa, D.M. Araujo Melo , H. Scatena Jr., F.M.M. Borges, L.B. Zinner, A.O. Silva
´
Departamento de Quımica, CCET, UFRN, C.P. 1662, CEP 59078-970, Natal, RN, Brazil
Received 24 March 1999; accepted 6 October 1999
Abstract
Terbium trifluoromethanesulfonate compound with hexamethylphosphoramide was synthesized and characterized. Thermogravimetric
data with three heating rates were used to obtain kinetic parameters such as activation energy (Ea), reaction order (n) and preexponential
´
factor (k0). The results obtained by two different methods, Zsako’s and a nonlinear one, are compared.
2000 Elsevier Science S.A.
All rights reserved.
´
Keywords: Rare earth elements; Thermal decomposition; Trifluoromethanesulfonate; Kinetic parameters; Zsako’s and nonlinear methods
1. Introduction
sition process through nonisothermal thermogravimetric
(TG) data, and first three ligands leaving process employ-
ing two different methods.
The coordination chemistry of rare earths underwent an
enormous progress during the last decade. These studies
are generally based on the determination of factors which
have an influence on the formation of the complex species,
on stoichiometry coordination number, ion–ligand inter-
action nature, etc. [1]. The trifluoromethanesulfonate anion
presents a low coordination capacity and thermal stability
[2].
Hexamethylphosphoramide (HMPA) was initially used
as a solvent, catalyst and organic reaction environment. It
is a colorless, water soluble liquid, miscible with polar or
nonpolar organic solvents. HMPA has a larger basic
character than DMF and dimethyl sulfoxide (DMSO) [3],
having also a high ‘‘donation number’’ [4].
There are few references in the literature on kinetic
approaches about rare earth complexes’ thermal decompo-
sition [5,6] in spite of some work on ligands loss without
kinetic parameters determination.
This paper studies the synthesis and characterization of
terbium trifluoromethanesulfonate with HMPA and the
acquisition of kinetic parameters of the thermal decompo-
2. Experimental
The compound was prepared by dissolving the hydrated
trifluoromethanesulfonate in absolute ethanol and acetone
and treatment with HMPA (molar ratio 1:6). The solution
was mixed, left to react on a water-bath and later at room
temperature for precipitation.
Terbium ion was determined by complexometric titra-
tion with EDTA [7]. Analysis of carbon, hydrogen and
nitrogen was performed by usual microanalytical pro-
cedures. Fourier transform infrared spectra were recorded
on a Perkin-Elmer 16 PC spectrophotometer using KBr
plates.
TG curves with heating rates 5, 10, 15 K min21 under
50 ml min21 nitrogen were obtained in a TGA-50H
Shimadzu System.
´
Zsako’s [8] and nonlinear [9] methods were used in
order to obtain kinetic parameters of the thermal decompo-
sition reactions in nonisothermal processes from TG data.
Temperature ranges for the kinetic parameters of the
*Corresponding author. Tel./fax: 155-84-215-3826.
´
E-mail address: dmelo@summer.com.br (D.M. Araujo Melo)
0925-8388/00/$ – see front matter
PII: S0925-8388(00)00621-6
2000 Elsevier Science S.A. All rights reserved.

M.F.F. Pedrosa et al. / Journal of Alloys and Compounds 303–304 (2000) 142–145
143
first weight loss (two ligands leaving) and the second are,
respectively, 300–489 K and 453–587 K.
3. Theory
´
Zsako’s method is one of the most frequently used to
obtain kinetic parameters of thermal decomposition re-
actions in nonisothermal processes from TG data.
To begin, a kinetic equation:
2 Ea
]
dw
dt
n
S
Dw
5 2 k0 exp
(1)
RT
where w is the compound’s sample weight at time t, k0 and
Ea are preexponential factor and activation energy, respec-
tively, T is temperature and n is reaction order. In a linear
program t and T are related by:
Fig. 1. First derivatives of thermogravimetric curves for Tb(CF3SO3)3?
6HMPA. Thermal decomposition at three different heating rates.
dT
dt
5 b
(2)
where b is the heating rate.
Eq. (1) becomes:
lated weight versus observed weight for the nonlinear
method.
2 k0
]
2 Ea
]
dw
dT
n
expS
Dw
5
(3)
(4)
b
RT
4. Results and discussion
which, under integration, becomes:
w9
T 9
The analytical results for Ln, C, H and N confirm the
general formula Tb(CF3SO3)3?6(HMPA). The TG curves,
in Fig. 2, were obtained at three different heating rates. In
both Figs. 1 and 2, it is seen that the weights drop slowly
but linearly with temperature after 1000 K. TG curves
indicate that the compounds are anhydrous. The final
residue is TbF3. The presence of fluoride was proved by
the glass corrosion test with concentrated H2SO4 [11].
The integral methods present results easier to understand
when compared to parameters obtained by differential
2 k0
]
2 Ea
]
dw
wn
expS
DdT 5 g(T)
f(w) 5
E
5
E
b
RT
w
T
0
0
It is not really necessary to do T0 50 K, but it is usual.
Integration of the right side of the Eq. (4), (called
temperature integral) was numerically obtained by a Gauss
quadrature method with 48 points collected from T0 as the
temperature onset for each studied process.
By applying logarithms on both sides of Eq. (4), the
optimized value of Ea can be found when the slope is unity
and preexponential factor achieved through linear coeffi-
cient.
The nonlinear method used in this work takes the weight
increase for ith point, Dwi, of Eq. (1), and relates it to the
calculated weight of the ith point, wi:
wi11 5 wi 1 Dwi
(5)
The objective function, F, to be minimized is:
N
2
wi,calc
]
F 5
O
1 2
(6)
F G
wi,obs
i51
where calc and obs are indices which represent calculated
and observed weights. N is data’s number.
An algorithm of Simplex’s [10] type was used to
minimize F. It is necessary, for nonlinear methods to
introduce germen values for Ea, n and k0, as input.
For reasons of comparison, a correlation was made of
Fig. 2. Thermogravimetric curves of Tb(CF3SO3)3?6HMPA. Thermal
´
log f(w) versus log g(T) for Zsako’s method and calcu-
decomposition at three different heating rates.

144
M.F.F. Pedrosa et al. / Journal of Alloys and Compounds 303–304 (2000) 142–145
Table 1
´
Kinetic parameters for the first thermal decomposition of Tb’s compound by Zsako’s and nonlinear methods: np is the number of points used and r is the
correlation
Method
b
Ea
k0
Ti
(K)
Tf
(K)
np
r
(K min-1)
(kJ mol-1)
(min-1)
2.1?103
1.0?105
1.5?104
327
336
336
459
461
475
160
155
186
0.9902
0.9925
0.9916
´
Zsako
5
10
15
52.5
64.2
57.8
Nonlinear
5
10
15
64.8
73.2
62.7
6.1?108
4.7?109
1.3?108
300
349
322
463
461
489
196
140
226
0.9990
0.9990
0.9980
methods in the case of kinetic parameters of nonisothermal
thermal decomposition processes due to low dispersion. A
possible explanation is that the data obtained with robust
instrumentation, computer managed, can show noise. De-
rivatives of these data increase the noise and, the data plot
results in a pronounced dispersion.
5. Conclusion
The comparison between the nonlinear method de-
veloped by our group and Zsako’s is not made with the
´
intention to be a substitute of an already well known
method but to show that it can be used with the same
reliability and also to show that in the present case as also
in other situations [9] better dispersions and correlations
are obtained.
Concerning the kinetic aspects of the ligand decomposi-
tion, it can be observed that in both cases activation
energies are quite similar. The reaction order (always 1)
well characterizes the complex decomposition, beginning
with HMPA ligands loss and not the salt.
The integral methods damp off these noises. Of the
´
integral methods, Zsako’s is the best known since it is not
necessary to do any approximation to calculate the tem-
perature integral. The results presented in Tables 1 and 2
were acquired using onset temperatures as the ones pre-
sented in the Ti column. All reaction orders were unit and
errors in Ea less than 0.1 kJ mol21
.
The correlations presented by the nonlinear method are
´
closer to unit than those obtained from Zsako’s method.
The number of points used in the parameters calculation by
nonlinear methods was the same or more than those used
Acknowledgements
´
for Zsako’s method. For both methods the activation
energies are comparable for each decomposition and the
same is true for the preexponential factor. The weight loss
first derivative is easier to calculate for a nonlinear method
M.F.F. Pedrosa acknowledges an I.C. CNPq.PIBIC
fellowship. Financial Support: CAPES, CNPq.
´
than for Zsako’s and this is a very important factor of
choice in an Arrhenius equation type calculation.
The derivative of weight with respect to temperature is
represented in Fig. 1 for the first and second decomposi-
tions by two sealed peaks. They shift to higher tempera-
tures with the heating rates increase.
References
[1] L.B. Zinner, G. Vicentini, J. Inorg. Nucl. Chem. 43 (1981) 193.
[2] A.O. Silva, D.M.A. Melo, L.B. Zinner, An. Assoc. Bras. Quim. 44
(4) (1995) 10–13.
Table 2
´
Kinetic parameters for the second thermal decomposition of Tb’s compound by Zsako’s and nonlinear methods: np is the number of points used and r is the
correlation
Method
b
Ea
k0
Ti
(K)
Tf
(K)
np
r
(K min21
)
(kJ mol21
)
(min21)
1.4?105
3.6?105
1.6?105
453
472
478
572
571
587
143
120
146
0.9952
0.9981
0.9985
´
Zsako
5
10
15
88.1
91.2
87.8
Nonlinear
5
10
15
86.1
111.6
103.4
6.1?108
1.6?1011
1.4?1010
453
472
478
573
571
587
143
120
146
0.9990
0.9998
0.9998

M.F.F. Pedrosa et al. / Journal of Alloys and Compounds 303–304 (2000) 142–145
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