Study on the non-isothermal kinetics of decomposition of 4Na 2SO4?2H2O2?NaCl

Article abstract of DOI:10.1007/s10973-005-7127-4

The non-isothermal decomposition kinetics of 4Na₂SO ₄?2H₂O₂?NaCl have been investigated by simultaneous TG-DSC in nitrogen atmosphere and in air. The decomposition processes undergo a single step reaction. The multivariate nonlinear regression technique is used to distinguish kinetic model of 4Na₂SO ₄?2H₂O₂?NaCl. Results indicate that the reaction type Cn can well describe the decomposition process, the decomposition mechanism is n-dimensional autocatalysis. The kinetic parameters, n, A and E are obtained via multivariate nonlinear regression. The n ^th-order with autocatalysis model is used to simulate the thermal decomposition of 4Na₂SO₄?2H₂O ₂?NaCl under isothermal conditions at various temperatures. The flow rate of gas has little effect on the decomposition of 4Na ₂SO₄?2H₂O₂?NaCl.

Full text of DOI:10.1007/s10973-005-7127-4

Journal of Thermal Analysis and Calorimetry, Vol. 89 (2007) 2, 531–536
STUDY ON THE NON-ISOTHERMAL KINETICS OF DECOMPOSITION
OF 4Na2SO4·2H2O2·NaCl
Z. Hong-Kun*, T. Cao, Zh. Dao-Sen, X. Wen-Lin, W. Ya-Qong and Q. Qi-Shu
College of Chemistry and Chemical Engineering, YangZhou University, 225002 YangZhou, PR China
The non-isothermal decomposition kinetics of 4Na2SO4·2H2O2·NaCl have been investigated by simultaneous TG-DSC in nitrogen
atmosphere and in air. The decomposition processes undergo a single step reaction. The multivariate nonlinear regression technique
is used to distinguish kinetic model of 4Na2SO4·2H2O2·NaCl. Results indicate that the reaction type Cn can well describe the
decomposition process, the decomposition mechanism is n-dimensional autocatalysis. The kinetic parameters, n, A and E are
obtained via multivariate nonlinear regression. The nth-order with autocatalysis model is used to simulate the thermal decomposition
of 4Na2SO4·2H2O2·NaCl under isothermal conditions at various temperatures. The flow rate of gas has little effect on the
decomposition of 4Na2SO4·2H2O2·NaCl.
Keywords: kinetics, multivariate nonlinear regression, sodium sulfate-hydrogen peroxide-sodium chloride, thermal
decomposition
Introduction
first and then the Avrami-Eroveef (n=2) model.
However, only one dynamic curve was given in their
studies. In this paper the thermal decomposition
kinetics of the adduct were carried out by using
multiple dynamic TG-DSC technique. The objective
of the present paper is to determine the thermal
decomposition kinetics of 4Na2SO4·2H2O2·NaCl in
nitrogen atmosphere and in air.
Sodium sulfate–hydrogen peroxide–sodium chloride
adduct with formula 4Na2SO4·2H2O2·NaCl, which is
also named PSC, is a known chemical entity which is
useful as a peroxygen bleaching agent. The adduct can
be obtained by reacting in aqueous solution, sodium
sulfate, sodium chloride and hydrogen peroxide. The
4Na2SO4·2H2O2·NaCl is an inclusion compound and
is very stable [1, 2]. The crystalline compound has
good properties as a whitener, dissolves quickly and
its solubility in cold water is high. In addition, it is
prepared from non-toxic starting materials that are
abundant, cheap and used regularly in washing powder
formulations. For a detailed description of this product,
including its preparation and application in bleaching,
reference is made to DE2530529 [3], GB1480884 [4],
US3739312 [5], US3739313 [6], US4005182 [7],
US440367 [8], JP6051611 [9], EP1258454A1 [10]
and EP1258455A1 [11]. Recently, H.K. Zhao studied
the phase diagram of the quaternary system
Na2SO4+NaCl+H2O2+H2O [12].
Cosgrove [13] studied the thermal decomposition
of 4Na2SO4·2H2O2·NaCl in nitrogen atmosphere with
the heating rates of 10 K min–1, and a N2 flow of
25 mL min–1. Combined TG-MS was performed using a
heating rate of 30 K min–1 and DSC was performed with
an argon gas flow of 30 mL min–1, and a heating rate of
10 K min–1. These results indicated that the thermal
decomposition of 4Na2SO4·2H2O2·NaCl corres-
ponded to obedience to the contracting circle model at
Experimental
The preparation method of the 4Na2SO4·2H2O2·NaCl
was also described elsewhere [13]. Using laboratory
grade reagents, a solution of 0.42 g NaCl in 8 g of
0.30 g mL–1 H2O2 was added dropwise to a solution of
4.09 g of Na2SO4 in 20 g of 0.30 g mL–1 H2O2. The re-
sulting solution was allowed to evaporate in air and
yielded well-formed crystal of 4Na2SO4·2H2O2·NaCl.
These were ground. Analytical results show that the
H2O2 content of the sample is 9.78%, corresponding
to the two H2O2 per formula unit (expected 9.8%).
The experimental measurements were carried out
on apparatus Netzsch STA 409PC Luxx simultaneous
TG-DSC connected to a Greatwall computer under
same experimental conditions, the heating rates 2.1,
4.2, 6.5 and 8.9 K min–1 in nitrogen atmosphere and
2.1, 4.2, 6.5, 8.9 and 11.3 K min–1 in air, the dynamic
nitrogen or air (dry gas, 20 mL min–1), the sample mass
8-10 mg. Calibration of this instrument was performed
with standard indium, lead, zinc and naphthalene
*
Author for correspondence: hkzhao@zzu.edu.cn
1388–6150/$20.00
Akadémiai Kiadó, Budapest, Hungary
Springer, Dordrecht, The Netherlands
© 2007 Akadémiai Kiadó, Budapest

HONG-KUN et al.
samples of known temperatures and enthalpies of
melting. The metals possess over 99.99% purity and
the organic compounds over 99.95%. The measured
TG-DTG and TG-DSC curves are shown in Figs 1–4.
Figures 1–4 show the effect of heating rates on
TG, DTG and DSC curves. It can be seen that there
are same characteristics on TG-DTG and TG-DSC
curves in nitrogen atmosphere and in air. The
apparent decomposition temperatures become higher
with increasing heating rate. The amplitude of the
DSC and DTG peak decrease with heating rate
decreasing. The measured TG-DSC curves further
illustrate that there is an endothermic process, the
whole decomposition process undergoes a single step.
The slight decrease in TG curves corresponds to
physical desorption of hydrogen peroxide absorbed
on surface of the product of thermal decomposition of
4Na2SO4·2H2O2·NaCl. The second peaks on DSC
curves correspond to the transition temperature of
crystal form. Analytical results indicate that the
residue of thermal decomposition of the titled
compound are Na2SO4(III) and NaCl.
Fig. 3 Simultaneous TG-DTG curves of 4Na2SO4·2H2O2·NaCl
in air, b increasing from left to right
Fig. 4 Simultaneous TG-DSC curves of 4Na2SO4·2H2O2·NaCl
in air, b increasing from left to right
Theoretical background
For kinetic analysis of the reaction (1) under non-
isothermal conditions, Eq. (2) is generally
assumed [14].
Fig. 1 Simultaneous TG-DTG curves of 4Na2SO4·2H2O2·NaCl
in nitrogen atmosphere, b increasing from left to right
A(s)®B(s)+B(g)
(1)
(2)
da
dT
1
= kf (a )
b
where: T temperature/K, b heating rate, a mass loss,
f(a) an expression describing the kinetic model.
The kinetic analyses are based on formal kinetic
models. These models include one-, two-, or multi-step
processes, in which the individual steps are linked as
independent, parallel, competitive or consecutive
reactions. The intermediate and final products are to be
viewed as pseudo-components and may comprise a
whole variety of chemical species. Arrhenius equation
was used for the temperature-dependent rate constants.
The following irreversible reaction type turned out to
Fig. 2 Simultaneous TG-DSC curves of 4Na2SO4·2H2O2·NaCl
in nitrogen atmosphere, b increasing from left to right
532
J. Therm. Anal. Cal., 89, 2007

NON-ISOTHERMAL KINETICS OF DECOMPOSITION OF 4Na2SO4·2H2O2·NaCl
Table 1 Reaction types and corresponding reaction equations da/dt=Aexp(–E/RT)f(a)
Code
f(a)
Reaction type
F1
F2
Fn
1–a
First-order reaction
Second-order reaction
nth-order reaction
(1–a)2
(1–a)n
D1
D2
D3
D4
1/2a
One-dimensional diffusion
Two-dimensional diffusion
Three-dimensional diffusion (Jander's type)
Three-dimensional diffusion (Ginstling-Brounstein type)
–(1/ln(1–a))
3(1–a)2/3/2[1-(1–a)1/3
3/2[(1–a)–1/3–1]
]
R2
R3
2(1–a)1/2
Two-dimensional phase boundary reaction
Three-dimensional phase boundary reaction
3(1–a)2/3
B1
Bna
a(1–a)
Simple Prout-Tompkins equation
Expanded Prout-Tompkins equation(na)
an(1–a)n
First-order reaction with autocatalysis through the reactants, X
X=a product in the complex model, frequently X=a
(1–a)(1+Kcat.X)
(1–a)n(1+Kcat.X)
C1–X
Cn–X
nth-order reaction with autocatalysis through the reactants, X
A2
A3
An
2(1–a)[–ln(1–a)]1/2
3(1–a)[–ln(1–a)]2/3
n(1–a)[–ln(1–a)]1–1/n
Two-dimensional nucleation
Three-dimensional nucleation
n-dimensional nucleation/nucleus growth according to Avrami-Erofeev
be applicable for the kinetic description of the
decomposition of 4Na2SO4·2H2O2·NaCl:
the choice of an appropriate model considerably and
improves the model validity.
da
dT
1
E
æ
ö
÷
= k exp –
f (a )
(3)
ç
0
b
RT
è
ø
Results and discussion
The f(a)represents a function depending on the
kinetic model. The f(a) functions corresponding to the
kinetic models most commonly used in the literature
are listed in Table 1 [14]. This list contains classic
homogeneous reactions and typical solids reactions.
In comparison to the known reaction types, the list is
extended with the combined autocatalytic types C1 and
Cn, which, on careful examination, already represent
parallel reactions with the same activation energy.
The kinetic parameters were fitted by running
the optimization routine according to the technique of
multivariate nonlinear regression, which was success-
fully used to determine the kinetic model for decom-
position of solid [14–16]. The task of nonlinear
regression is the iterative calculation of the minimum
sum of least squares. In case the multivariate regression
technique is applied, the total LSQ yields a sum of LSQ
calculated with data from the different experimental runs
Different models are evaluated to describe the total
mass loss of the STA experiments. The material bal-
ance of the STA sample holder yields for each model,
a set of ordinary differential equations. The crucible
contents are described as a dynamic system with con-
centrated parameters. The simultaneous numerical solu-
tion of the ordinary differential equations system and the
estimation of the kinetic parameters by the least squares
(LSQ) method were done using Thermokinetics
(Netzsch GmbH, Germany). Netzsch Thermokinetics
is a software module for the evaluation of thermokinetic
experiments. The differential equations are calculated
using a fifth-degree Runge-Kutta embedding method
with automatic optimization of the interpolation
nodes for numerical solution of the reaction equations
(Prince-Dormand method). To minimize the deviance
of LSQ, an improved version of the hybrid procedure
described in Marquardt [16] is used. This is a combi-
nation of a derivation-free, regularized Gauss-New-
ö2
÷
Ns
s
Ù
æ
LSQ=
Y –Y
(4)
j,k
ç
åå
j,k
ton procedure (Marquardt procedure) with
a
j= l k=l
è
ø
step-length optimization. Related details can be found
in reference [17, 18]. The results of multivariate nonl-
inear regression on TG curves are shown in Tables 2
and 3.
The experimental values yj,k are the normalized
mass, y=m(T)/m0(t=0) from STA. Data for all heating
rates have been used simultaneously. The model values
Ù
Y
result from the numerical solution of the respective
j,k
Tables 2 and 3 show the multivariable nonlinear
regression results. It can be seen from Tables 2 and 3
that the LSQ of CnB model is smallest and corresponds
to Fexp=1. (A detailed description of the F-Test can be
found in reference [18]). That is to say, the
decomposition mechanism of 4Na2SO4·2H2O2·NaCl
ordinary differential equations. The multivariate analysis
bases on the assumption that the kinetic parameters
have to be identical for all experimental conditions in
the modelled parameter range. This constraint facilitates
J. Therm. Anal. Cal., 89, 2007
533

HONG-KUN et al.
Table 2 Results of nonlinear regression on TG curves for different models (in nitrogen atmosphere)
Reaction
type(s)
E/kJ mol–1
lgA
LSQ
Corr. coeff.
0.99949
Parameter(s)
Fexp
CnB
174.84
16.91
15.69
1.00
n=0.88567
lgK=0.59734
lgK=0.69127
n=1.54617
C1B
An
Fn
173.853
172.283
188.548
209.57
16.769
16.979
18.635
20.77
16.389
18.031
42.928
69.494
82.9
0.999457
0.999388
0.998528
0.99732
1.043
1.147
2.732
n=0.14985
R2
A2
R3
F1
4.415
152.33
14.744
21.814
24.318
27.295
13.189
33.55
0.997012
0.996253
0.994058
0.990416
0.985111
0.98291
5.267
220.159
237.843
264.202
138.44
95.213
148.28
237.97
412.959
424.977
458.08
466.551
472.034
1587.51
6.049
9.421
F2
15.12
A3
D1
D2
D4
D3
B1
26.237
27.001
29.104
29.642
29.991
100.862
323.65
363.577
378.9
37.829
38.924
41.337
14.315
0.981245
0.980827
0.980592
0.944101
400.239
138.691
Table 3 Results of nonlinear regression on TG curves for different models (in air)
Reaction
type(s)
E/kJ mol–1
lgA
LSQ
Corr. coeff.
0.9994
Fexp
Parameter(s)
CnB
152.86
14.22
21.29
1.0
n=0.4529
lgK=0.5277
lgK=9404
C1B
An
Fn
150.64
150.37
168.61
144.01
200.37
208.94
217.28
224.56
134.61
382.71
367.11
354.98
315.56
137.08
13.84
14.33
16.28
13.64
19.48
20.26
21.64
22.33
12.61
38.55
36.87
36.18
32.05
13.98
52.65
101.29
103.61
125.77
284.15
334.43
388.00
446.68
495.03
716.19
719.05
727.13
783.47
2201.77
0.9986
0.9972
0.9971
0.9966
0.9921
0.9907
0.9892
0.9876
0.9863
0.9799
0.9799
0.9797
0.9781
0.9379
2.47
4.75
n=1.7589
n=8.03·10–5
4.86
A2
R2
R3
F1
5.89
13.31
15.67
18.18
20.93
23.19
33.55
33.69
34 06
36.70
103.15
F2
A3
D3
D4
D2
D1
B1
in nitrogen atmosphere and in air is all nth-order with
autocatalysis. But in nitrogen atmosphere, the Fexp
values for models C1B and An are very closer to that
of 4Na2SO4·2H2O2·NaCl in air. The conclusion can be
made that the reaction type CnB can well describe the
decomposition of 4Na2SO4·2H2O2·NaCl in nitrogen
atmosphere and air. The decomposition mechanism of
4Na2SO4·2H2O2·NaCl is n-dimensional autocatalysis,
which can be expressed as
of
model
CnB.
The
decomposition
of
4Na2SO4·2H2O2·NaCl can also be described with
model An, this result is in accordance with the
literature [13]. However, the case is different in air.
The value Fexp for model An is 4.75 times of model
CnB, the model An can not describe the decomposition
da
=k(1–a )n (1+Kcat.a )
(5)
dt
534
J. Therm. Anal. Cal., 89, 2007

NON-ISOTHERMAL KINETICS OF DECOMPOSITION OF 4Na2SO4·2H2O2·NaCl
Table 4 Kinetic parameters resulting from multiple-curve
analyses from TG measurement with a noise
level of 0.2%
Gas
E/kJ mol–1
lgA
n
lgkcat.
Nitrogen
Air
174.84
152.86
16.91
14.22
0.8857
0.4529
0.5974
0.5277
Fig. 7 Prediction of isothermal decomposition of
4Na2SO4·2H2O2·NaCl in nitrogen; 1 – 428 K, 2 – 433 K,
3 – 438 K, 4 – 443 K, 5 – 448 K, 6 – 453 K
Fig. 5 Fit of TG measurements, simulated with reaction type
CnB and a noise level of 0.2% for the heating rates 2.1,
4.2, 6.5 and 8.9 K min–1 in nitrogen atmosphere, to
reaction type CnB. Signs measured, —calculated
Fig. 8 Prediction of isothermal decomposition of
4Na2SO4·2H2O2·NaCl in air; 1 – 413 K, 2 – 423 K,
3 – 433 K, 4 – 443 K, 5 – 453 K, 6 – 463 K
NaCl undergoes a single step reaction in nitrogen
atmosphere and in air, and the mechanism is nth
autocatalytic. The conversion curves as a function of
time with temperature as a parameter are given in
Figs 7 and 8. The temperature range is from 413 to
463 K. Figures 7 and 8 show that the decomposition
rate is slower in air than that in nitrogen atmosphere.
For example, the decomposition process finishes in
240 min at 433 K in nitrogen atmosphere, but in air,
the conversion is only 77% for 300 min at the same
temperature. This is because the reaction order in
nitrogen atmosphere (n=0.8857) is much greater than
that in air (n=0.4529).
In order to explicit the effect of gas flow rate of
the decomposition of 4Na2SO4·2H2O2·NaCl, further
experiments were carried out at the heating rate of
8 K min–1 in nitrogen atmosphere. The flow rates of
nitrogen are 10, 20, 30 and 50 mL min–1, respectively.
The simultaneous TG-DSC curves are shown in
Fig. 9. It indicates that, under different flow rates, the
Fig. 6 Fit of TG measurements, simulated with reaction type
CnB and a noise level of 0.2% for the heating rates 2.1,
4.2, 6.5, 8.9 and 11.3 K min–1 in air, to reaction type
CnB. Signs measured, — calculated
The kinetic parameters, n, A and E are obtained
via multivariate nonlinear regression, which are listed
in Table 4. The decomposition processes of 4Na2SO4·
2H2O2·NaCl in nitrogen atmosphere and in air are
simulated (Figs 5, 6). Figures 5, 6 indicate that a satis-
factory fit is possible with model CnB for the com-
mon analysis of the TG measurements.
Using these kinetic parameters obtained, the
isothermal decomposition process at any temperature
in nitrogen atmosphere or in air can be predicted. This
procedure is done with Netzsch Thermokinetics soft-
ware. The decomposition process of 4Na2SO4· 2H2O2·
J. Therm. Anal. Cal., 89, 2007
535

HONG-KUN et al.
various temperatures. The decomposition rate is slower
in air than that in nitrogen atmosphere. The reason is
that the reaction order in nitrogen atmosphere
(n=0.8857) is much greater than that in air (n=0.4529).
Acknowledgements
We gratefully acknowledge the High Education Natural Science
Foundation of Jiangsu Province (Grant No. HK051087) and the
Open Project Program of the Key Laboratory of Physical
Chemistry, Yangzhou University, China for their support. Also
the authors like to express their sincere thanks to the editors and
anonymous reviewers for their constrictive suggestions.
Fig. 9 Effect of flow rate of nitrogen on the decomposition of
4Na2SO4·2H2O2·NaCl. The flow rates of nitrogen ,
1 – 10, 2 – 20, 3 – 30 and 4 – 50 mL min–1; heating
rate, 8 K min–1
References
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respectively, the decomposition reaction of 4Na2SO4·
2H2O2·NaCl start at a temperature of 440 K. Compar-
ison with Fig. 2, the decomposition process of
4Na2SO4·2H2O2·NaCl and peak temperature are very
closer under different conditions. The flow rate of
nitrogen has little effect on the decomposition of
4Na2SO4·2H2O2·NaCl.
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decomposition process undergoes a single step reaction.
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transition temperature of crystal form. Further
experiments show that the flow rate of gas has little
effect on the decomposition of 4Na2SO4·2H2O2·NaCl.
The multivariate nonlinear regression technique
is used to distinguish kinetic model of 4Na2SO4·
2H2O2·NaCl. The reaction type Cn can well describe
the decomposition process, the decomposition
mechanism is n-dimensional autocatalysis. The results
are not in accordance with that in the literature [13].
The kinetic parameters, n, A and E are obtained via
multivariate nonlinear regression. Based on these
kinetic parameters, the nth-order with autocatalysis
model is used to simulate the thermal decomposition
of 4Na2SO4·2H2O2·NaCl under isothermal conditions at
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Received: June 21, 2005
Accepted: January 23, 2007
OnlineFirst: April 29, 2007
DOI: 10.1007/s10973-005-7127-4
536
J. Therm. Anal. Cal., 89, 2007