Application of neural networks in analysis of thermal decomposition of CoSO4·7H2O

Article abstract of DOI:10.1023/B:JTAN.0000005197.33066.f5

Thermal decomposition of CoSO₄·7H₂O was investigated by simultaneous DTA-TG techniques and XRD method. Neural networks were used for DTA-TG curves analysis. Additionally, the network architecture (GRNN - Generalized Regression Neural

Full text of DOI:10.1023/B:JTAN.0000005197.33066.f5

Journal of Thermal Analysis and Calorimetry, Vol. 74 (2003) 583–588
APPLICATION OF NEURAL NETWORKS IN ANALYSIS
OF THERMAL DECOMPOSITION OF CoSO 7H O
4
2
*
Elübieta Tomaszewicz and M. Kotfica
Technical University of Szczecin, Faculty of Chemical Engineering, Institute of Chemistry and
Environment Protection, al. Piastów 42, 71-065 Szczecin, Poland
Abstract
4 2
Thermal decomposition of CoSO ·7H O was investigated by simultaneous DTA-TG techniques and
XRD method. Neural networks were used for DTA-TG curves analysis. Additionally, the network
architecture (GRNN - Generalized Regression Neural Networks) and its statistical parameters were
calculated. This method permits to generate DTA-TG curves without using kinetic models.
4 2
Keywords: CoSO ·7H O thermal decomposition, DTA-TG methods, neural networks
Introduction
Kinetics of thermal decomposition processes of solids in the case of conventional
methods is described by the equation:
dα
=
k(T ) f (α)
(1)
dt
where: α – degree of conversion, t – time, f(α) – function dependent of kinetic model
for given reaction, k(T) – rate constant of the reaction.
Kinetic constant of the reaction is expressed by Arrhenius equation and each
stage of the reaction is treated as an independent reaction. After determining the f(α)
function on the base of experimental data, a detailed formula of kinetic equation is
obtained for each stage. About forty kinetic models are known based on various as-
sumptions concerning the process mechanism [1]. Present discussions concern also
being justifiable of the classic kinetics methods for the description of thermal decom-
position processes of solids as well as the accuracy of obtained results [2–6]. The ap-
plication of conventional methods requires a separate distinguishing of individual
process stages and next their describing by complex expressions. In this work neural
networks were applied for the description of cobalt(II) sulfate(VI) hydrate decompo-
sition. Such networks enable a description of given process without a necessity of di-
viding it into stages, they are easy to handle and result in a very good accuracy of ap-
proximating the experimental data.
*
Author for correspondence: E-mail: tomela@ps.pl
1
388–6150/2003/ $ 20.00
Akadémiai Kiadó, Budapest
©
2003 Akadémiai Kiadó, Budapest
Kluwer Academic Publishers, Dordrecht

5
84
TOMASZEWICZ, KOTFICA: NEURAL NETWORKS
Experimental
For DTA-TG investigations CoSO ·7H O was used after obtaining it as a result of a slow
4
2
crystallisation from a saturated solution of CoSO . The solution was prepared using
4
CoSO ·nH O (pure, product of POCh Gliwice). The obtained crystals of CoSO ·7H O
4
4
2
2
were dried in acetone and ground in an agate mortar. The DTA-TG measurements were
carried out applying the apparatus SDT 2960 of TA Instruments. They were performed in
–1
air atmosphere (air flow – ca. 100 ml min ) with the use of open corundum crucibles and
portion masses of CoSO ·7H O within the 21–37 mg range. DTA-TG studies were made
4
2
–1
at the following heating rates: 2, 4, 6, 8 and 10 K min . For each heating rate three, inde-
pendent DTA-TG measurements were carried out. For all heating rates a very good
reproducibility of experimental data was obtained. In order to establish some, intermedi-
ate and final solid products of CoSO ·7H O decomposition, separate samples of this salt
4
2
were heated in air atmosphere for 4 h, at temperatures chosen on the base of the TG
curves, i. e. at 400, 800 and 1000ºC. On completion of heating the samples were rapidly
cooled to ambient temperature. Such obtained preparations were subjected to XRD ex-
amination. These investigations were carried out by means of DRON-3 diffractometer,
applying the radiation CoK (λ=0.179021 nm).
α
For calculations the program Statistica Neural Network [7] was used. In this pro-
gram the neural network is constructed by means of the tool IPS (Intelligent Problem
Solver). After completion of the calculations the IPS creator establishes a set of net-
works best fitted to given problem, gives the number of variables taken into account
and the accuracy of calculations. Quality of a network in the STNN program is as-
sessed on the base of the indicators: Data Mean – average value of the target output
variable; Data S.D. – standard deviation of the target output variable; Error
Mean – average error (residual between target and actual output values) of the output
variable; Abs.E. Mean – average absolute error (difference between target and actual
output values) of the output variable; Error S.D. – standard deviation of errors for the
output variable; S.D. Ratio – determined as the error divided by data standard devia-
tion ratio; Correlation – the standard Pearson-R correlation coefficient between the
target and actual output values. The indicators describing the quality of the network
are determined independently for the sets: training Tr, verification Ve and testing Te.
While estimating given network mainly the last two indicators were considered.
Results and discussion
Figure 1 presents experimental DTA and TG curves recorded for the heating rate of
–1
10 K min . On the basis of the quantitative results obtained from the thermogravimetric
investigations (Table 1.) and literature information about a dehydration of sulfates(VI) of
d-elements [8–13], the following mechanism of dehydration could be proposed:
I
CoSO ·7H O =CoSO ·6H O +H O
2
(2)
(3)
4
2
(s)
4
2
(s)
(g)
incongruent melting CoSO ·7H O DCoSO ·6H O +L
4
2
(s)
4
2
(s)
(sat)
J. Therm. Anal. Cal., 74, 2003

TOMASZEWICZ, KOTFICA: NEURAL NETWORKS
585
J. Therm. Anal. Cal., 74, 2003

5
86
TOMASZEWICZ, KOTFICA: NEURAL NETWORKS
–1
Fig. 1 Experimental DTA and TG curves recorded for the heating rate of 10 K min
Fig. 2 Comparison of calculated and experimental TG curves
isothermal boiling
L(sat)→CoSO ·6H O +H O
(4)
(5)
(6)
4
2
(s)
2
(g)
II
CoSO ·6H O =CoSO ·H O +5H O
(s)
4
2
(s)
4
2
2
(g)
III
CoSO ·H O =CoSO +H O
4 2 (s) 4(s) 2 (g)
On the base of the mass loss observed on the TG curves and presented in Table
, XRD investigations and literature information [14–16] desulphurization can be
distinguished:
1
IV
V
3CoSO4(s)=Co O4(s)+3SO2(g)+O2(g)
3
(7)
(8)
Co O =3CoO +1/2O
2(g)
3
4(s)
(s)
On the ground of XRD investigations, the solid products obtained after the third,
fourth and fifth were determined. For description of the course of TG and DTA
curves applying the neural networks, independent variables were temperature and
heating rate, whereas a dependent variable was reduced mass m/m (TG curves) and
0
in the case of DTA curves – differential of temperature with respect to time. The re-
sults of TG and DTA measurements formed two separate sets of data. For the TG data
set the network GRNN 2/1515 was selected (two independent variables and 1515 hid-
den neurones) of the following parameter values: S.D. Ratio for the set Tr 0.033; for
the set Ve 0.041; for the set Te 0.041, correlation coefficient for all sets 0.99915. Fig-
J. Therm. Anal. Cal., 74, 2003

TOMASZEWICZ, KOTFICA: NEURAL NETWORKS
587
Fig. 3 Comparison of calculated and experimental DTA curves
ure 2 presents a comparison of the calculated TG curves with the experimental ones.
Lower plot in Fig. 2 shows a difference between these curves. The obtained result in-
dicates that by one neurone model all curves were described obtained at various heat-
ing rates and various masses of sample portions.
In a similar way the set of data concerning the DTA curves was worked out. In this
case the network GRNN 2/1515 was also selected, for which the following values of pa-
rameters were obtained: S.D. Ratio for the set Tr 0.113; for the set Ve 0.139; for the set
Te 0.121, correlation coefficient; 0.9937; 0.9905 and 0.9931, respectively. Figure 3 pres-
ents the calculated and experimentally determined DTA curves. Upper plot in this figure
shows a difference between the curves. As it can be seen from Fig. 3, also in this case a
very good accuracy of approximating the experimental data was attained.
Conclusions
The present study reports results of research conducted by DTA-TG methods for
CoSO ·7H O. Mechanism of decomposition has been established for this salt on the
4
2
base of TG and XRD investigations. This enabled determining the intermediate and
final solid products of decomposition of cobalt(II) sulfate(VI) hydrate. Neural net-
works were applied here to describe the course of CoSO ·7H O thermal decomposi-
4
2
tion. It has been established that the best approximation of the experimental curves
TG and DTA is attained by applying the same neurone model GRNN 2/1515 for de-
scription of their shape. Application of neural networks makes possible obtaining
very good reproducibility of DTA-TG experimental data.
References
1
M. Brown, D. Dollimore and A. K. Galwey, Reactions in the Solid State. Comprehensive
Chemical Kinetics, Vol. 22, Elsevier, Amsterdam 1980.
2
3
4
5
6
S. Vyazovkin and Ch. A. Wight, Thermochim. Acta, 340–341 (1999) 53.
D. F²tu, J. Therm. Anal. Cal., 66 (2001) 549.
J. J. Pysiak and Y. A. Albadwi, J. Therm. Anal. Cal., 68 (2002) 169.
J. J. Pysiak and Y. A. Albadwi, J. Therm. Anal. Cal., 70 (2002) 423.
K. S. Khairou, J. Therm. Anal. Cal., 69 (2002) 583.
J. Therm. Anal. Cal., 74, 2003

5
88
7
TOMASZEWICZ, KOTFICA: NEURAL NETWORKS
P. Wójtowicz, Polish version of STATISTICA Neural Networks.
http://www.statsoft.pl/czytelnia/neuron/pwesnn.html
8
9
F. Paulik, Special trends in thermal analysis, Wiley & Sons Ltd., New York 1995.
J. Straszko, M. Olszak-Humiennik and J. Mozejko, J. Therm. Anal. Cal., 59 (2000) 935.
1
1
1
1
1
1
1
0 E. Ingier-Stocka, J. Therm. Anal. Cal., 65 (2001) 561.
1 B. MaÓecka, E. Dróüdü-Cieíla and A. MaÓecki, J. Therm. Anal. Cal., 68 (2002) 819.
2 V. Jordanovska, B. Boyanow and Lj. Pejov, J. Therm. Anal. Cal., 71 (2003) 629.
3 V. Jordanovska, P. Naumow, B. Boyanow and R. Trojko, J. Therm. Anal. Cal., 59 (2000) 859.
4 V. Petkova and Y. Pelovski, J. Therm. Anal. Cal., 64 (2001) 1037.
5 V. Petkova and Y. Pelovski, J. Therm. Anal. Cal., 64 (2001) 1025.
6 Y. Pelovski, V. Petkova and S. Nikolov, Thermochim. Acta, 274 (1996) 273.
J. Therm. Anal. Cal., 74, 2003