Kinetic analysis of thermal decomposition of some Co-complexes of three unsymmetrical vic-dioximes ligands: Model fitting and model-free method

Article abstract of DOI:10.1007/s10973-005-7019-7

The thermal decomposition of three new reagent cyclohexylamine-p- tolylglyoxime (L₁H₂), tertiarybutyl amine-p-tolylglyoxime (L₂H₂) and secondary butylamine-p-tolylglyoxime (L ₃H₂ and their Co-complexes were studied by both isothermal and nonisothermal methods. As expected, the complex structure of Co-complexes, different steps with different activation energies were realized in decomposition process. Model-fitting and model-free kinetic approaches were applied to nonisothermal and isothermal data. The kinetic triplet (f(α), A and E) related to nonisothermal model-fitting method can not be meaningfully compared with values obtained from isothermal method. The complex nature of the multi-step process of the studied compounds was more easily revealed using a wider temperature range in nonisothermal isoconversional method.

Full text of DOI:10.1007/s10973-005-7019-7

Journal of Thermal Analysis and Calorimetry, Vol. 89 (2007) 1, 123–131
KINETIC ANALYSIS OF THERMAL DECOMPOSITION OF SOME
Co-COMPLEXES OF THREE UNSYMMETRICAL Vic-DIOXIMES LIGANDS
Model fitting and model-free method
O. Sahin*, E. Tas and H. Dolas
Department of Chemistry, Harran University, S.Urfa, Turkey
The thermal decomposition of three new reagent cyclohexylamine-p-tolylglyoxime (L1H2), tertiarybutyl amine-p-tolylglyoxime
(L2H2) and secondary butylamine-p-tolylglyoxime (L3H2 and their Co-complexes were studied by both isothermal and
nonisothermal methods. As expected, the complex structure of Co-complexes, different steps with different activation energies
were realized in decomposition process. Model-fitting and model-free kinetic approaches were applied to nonisothermal and
isothermal data. The kinetic triplet (f(a), A and E) related to nonisothermal model-fitting method can not be meaningfully compared
with values obtained from isothermal method. The complex nature of the multi-step process of the studied compounds was more
easily revealed using a wider temperature range in nonisothermal isoconversional method.
Keywords: Arrhenius parameter, Co(II) complexes, kinetic analysis, model-fitting and model-free methods, vic-dioxime
da
dt
Introduction
=k(T ) f (a )
(1)
The chemistry of oxime/oximato metal complexes has
been investigated actively since the time of the first
It is usually assumed that the basic kinetic
equation for solid-state decomposition process under
non-isothermal condition or in other words the
temperature dependence of the rate constant can be
expressed as a function of the fractional conversion in
the following form [7].
synthesis,
e.g.
preparation
of
nickel(II)
dimethylglyoximato and recognition of the chelate
five-membered character of this complex by
Chugaev [1]. Oximes are widely recognized as
versatile synthons for a variety of heterocycles [2].
The exceptional stability and unique electronic
properties of these complexes can be attributed to
their planar structure which is stabilized by hydrogen
bonding [3]. When asymmetrical dioximes such as
phenylglyoxime or methylglyoxime are employed as
starting ligands, a mixture of fac- and mer-isomers
was obtained. However, in some cases one of them
was isolated individually [4]. The synthetic chemistry
of MN4 core containing vic-dioxime compounds has
been described previously [5]. Recently, metal
containing oxime complexes are utilized in medicine
as well, technetium(V) and copper(II) complexes
containing vicinal dioxime currently are used as
cerebral and myocardial perfusion imaging
agents [6].
da
dt
E
æ
ö
÷
= Aexp –
f (a )
(2)
ç
RT
è
ø
where A (the pre-exponential factor) and E (the
activation energy) are the Arrhenius parameters and R
is the gas constant. Arrhenius parameters, together
with the reaction model are called the kinetic triplet.
da
Since
in Eq. (2) can be difficult to measure
dt
accurately, temperature dependence in Eq. (2) can be
rewritten in the form of:
da
dt
A
E
æ
ö
÷
= exp –
f (a )
(3)
ç
b
RT
è
ø
T –T0
where b=
is the heating rate.
t
By separation of variable and integration, the
following equation obtained:
Kinetic computations
a d(a ) A T
E
The kinetic analysis of solid state decomposition is
usually based on a single kinetic equation (0<a<1)
æ
ö
=
dT
÷
(4)
g(a )=ò
òexp –
ç
f (a ) bT
RT
è
ø
0
0
*
Author for correspondence: osahin@harran.edu.tr
1388–6150/$20.00
Akadémiai Kiadó, Budapest, Hungary
Springer, Dordrecht, The Netherlands
© 2007 Akadémiai Kiadó, Budapest

SAHIN et al.
For nonisothermal conditions, there are several
The most common of p(x) function lead to
relationship used to compute Arrhenius parameters
each of which is based on an approximate form of the
temperature integral [8]. One such approximation is
given by Coats-Redfern [9] as following:
expression of the type
exp(–x)
p(x)=
Q(x)
(8)
x2
where Q(x) is a function with several particular
forms. Q(x) can be considered the series expansion
as given following
æ
ö
g(a )
T 2
æ AR ö 2RT
E
æ
ç
ö
÷
ç
1–
÷
÷
–
ln
=ln
(5)
ç
ç
÷
ç
÷
bE
E
RT
è
ø
è
ø
è
ø
2
3
where T is the mean experimental temperature. This
method is reported [10] to be one of the most fre-
quently used to evaluate nonisothermal data.
Arrhenius parameters determined from the plot
RT
Q(x)=1!–2! +3!
RT
E
RT
E
æ
ö
÷
æ
ö
÷
–4!
...
(9)
ç
ç
E
è
ø
è
ø
Q(x) function can also be expressed in the ratio
of two forth order polynomials [14] as given below:
g(a )
1
æ
ö
ln
vs. . This kind of calculation of kinetic
ç
÷
T 2
x4 +18x3 +86x2 +96x
T
è
ø
Q(x)=
(10)
x4 +20x3 +120x2 +240x+120
triplet is called as model-fitting method.
Model fitting approach, Arrhenius parameters
are found by form of g(a) assumed. Since in a
nonisothermal experiment both T and a vary
simultaneously, the model-fitting approach generally
fail to achieve a clean separation between the
temperature dependence k(T) and the reaction model,
g(a). For this reason, the model fitting methods tent
to procedure highly uncertain value of Arrhenius
parameters. The second reason of deviation from
model-fitting method between the assumed form of
g(a) and the true reaction model are revealed in
decomposition of solid compound having several
steps. This means that the effective activation energy
determined from thermal analysis experiments will
also be a function of temperature and extend of
conversion. Thus, the application of model-fitting
methods is aimed at extracting a single value of
activation energy for an overall process.
The experimental data can be analyzed by other
approximation such as temperature integral method,
isoconversion method and model free-method [11, 12],
since the integral of Eq. (4) in the right-hand side has
not exact analytical solution. In all mentioned approx-
imation, the value of integral between 0 and T0 is neg-
ligible, since the starting temperature is near room
temperature and the activation energy is not too low.
In this case Eq. (4) becomes
All, p(x)-linear isoconversion methods involve the
plotting of 1/T vs. a logarithmic function which depends
on the heating rate and temperature. The Q(x) function
shows an approximation for the temperature integral
used which is different for the different p(x)-linear
isoconversion methods. Therefore the approximation
of the temperature integral is the key to understanding
the different methods. The linear isoconversion
method equation used in this study can be obtained by
combining Eqs (7), (8) at constant fraction transformation
as given following
ART 2
g(a )=
Q(x)exp(–x)
(11)
bE
For constant g(a), Eq. (11) becomes
b
AR
E
æ
ö
÷
=
exp –
(12)
ç
T 2Q(x)
Eg(x)
RT
è
ø
Taking the logarithm of both sides of Eq. (11)
gives
b
æ
ö
AR E
ln
=ln
–
÷
(13)
ç
ç
÷
T 2Q(x)
Eg(a ) RT
è
ø
In this study, the first three terms in Eq. (9) was
considered as Q(x) function
Iterative procedure is used to approach the exact
value of E in Eq. (12) as following:
AT
E
æ
ö
g(a )=
dT
÷
(6)
b òexp –
ç
RT
è
ø
b
1
0
• Plotting ln
vs. under the assumption of
T 2Q(x)
T
Equation (6) can be rewritten by taking x= E/RT
Q(x)=1 to determine the initial value of E1.
• Using E1 to calculate the value of Q(x) function,
a
da
AE ¥ exp(–x)
AE
g(a )=
=
dx=
p(x) (7)
ò
ò
x2
f (a ) bR
bR
b
1
0
x
then plotting ln
vs.
to calculate a new
T 2Q(x)
T
The p(x) function on the right hand side is
generally termed as temperature integral [13] which
can be approximated in different ways.
value of E2 in slope.
124
J. Therm. Anal. Cal., 89, 2007

Co-COMPLEXES OF THREE UNSYMMETRICAL Vic-DIOXIMES LIGANDS
Synthesis of the cobalt(II) complexes
• Comparing
step
E1
En–En–1<0.01 Kcal mole–1, the last value of En is the
with
E2,
when
0.5 mmol L1H2, 0.5 mmol L2H2 and 0.5 mmol L3H2 was
dissolved in EtOH (25 cm3). A solution 0.25 mmol of
the metal salt [CoCl2·6H2O] in 10 mL of ethanol was
added drop-wise with continuous stirring. The stirred
mixture was heated at reflux for 60 min and was
maintained at this temperature. The pH of solutions
was about 1.5–3.0 and was adjusted to 4.5–5.5 by the
addition of a 1% NaOH solution in ethanol. After
cooling to room temperature, the complexes were
filtered and washed with hot water (3·5 mL). Finally,
washed with diethylether and dried at 90°C for 5 h.
The Co-complexes shown in Fig. 1, was prepared
by the reaction of cyclohexylamine, tertiary
butylamine and secondary butylamine with
anti-p-tolylchloroglyoxime which was prepared by
treating a suspension of anti-p-tolylchloroglyoxime in
absolute THF with 15.8 mmol in solution of
Et3N(triethylamine) in absolute THF at –15°C. Ex-
cess Et3N(triethylamine) was used to neutralize the
HCI liberated in the reaction. The ligand has one
cyclohexyl ring, one p-tolyl group and two oxime
groups for L1H2, one p-tolyl group, one tertiary group
and and two oxime groups for L2H2 and one p-tolyl
group, one secondary group and and two oxime groups
for L3H2, respectively. Mononuclear complexes have
been synthesized from L1H2, L2H2 and L3H2 with salts
of Co(II). Co(II) mononuclear complexes have a
metal-ligand ratio of 1:2 and ligands are coordination
only by N,N’ atoms of vicinal dioximes. In additional
to this the cobalt(II) complex has two additional coor-
exact value of activation energy.
This kind of approximation have been applied by
Guan and et al. [15]
The present paper is aimed at preparation,
characterization and thermal decomposing kinetics
based on model-fitting and model free method of
three different ligands and their Co complexes.
Experimental
Materials
Cyclohexylamine, tertiary butylamine and secondary
butylamine (Fluka Chemical Company, Taufkirchen,
Germany) and tetra-n-butylammonium perchlorate
(n-Bu4NClO4, Fluka Chemical Company, Taufkirchen,
Germany) were used as received.
Synthesis of the ligands L1H2, L2H2 and L3H2
Anti-p-tolylchloroglyoxime was synthesized as described
in the literature [16]. A solution of 15.8 mmol of
cyclohexylamine, 15.8 mmol tertiary butylamine and
15.8 mmol secondary butylamine in 30 cm3 of absolute
THF was added to a solution of 15.8 mmol of Et3N in
10 cm3 of absolute THF. This mixture was cooled to
–15°C and kept at this temperature, and a solution of
15.8 mmol anti-p-tolylchloroglyoxime in 50 cm3 ab-
solute THF was added dropwise under a N2 atmo-
sphere with continuous stirring. The addition of the
anti-p-tolylchloroglyoxime solution was carried out
over 1.5 h. The mixture was stirred for 1 h more and
the temperature rose to 20°C. Precipitated Et3NHCI
chloride was filtered and the filtrate was evaporated
to remove THF. The oily products were dissolved in
10 cm3 of CH2Cl2 and 200 cm3 of n-hexane were
added to precipitate the compound. This process was
then repeated several times. The products were
filtered and dried in vacuum.
Fig. 1 The structure of the Co(II) complexes
Fig. 2 TG and DTG curves of L1–3H2 ligands
J. Therm. Anal. Cal., 89, 2007
125

SAHIN et al.
Results and discussion
The thermal behavior of L1H2, L2H2, L3H2 and their
Co-complexes at heating rate of 5°C min–1 are presented
in Figs 2 and 3, respectively. As seen in Figs 2 and 3,
each TG curve for both ligands and their
Co-complexes, exhibits one and two steps,
respectively. However, the DTG curve corresponding
to the ligands and for first TG steps of Co-complexes
have
a
clear shoulder. Thus, both thermal
decomposition of ligands and the first TG step of
Co-complexes corresponding to a complex process
consisting in minimum two consecutive or
simultaneous reactions. In this work, thermal
decomposition of both ligands and the first step of
Co-complexes were treated as if they comprised one
stage and the kinetic parameters were calculated as
for one stage. The character of first step of
decomposition of Co-complexes indicates that the
process occurs with a narrow range of temperature, in
contrast to a second one, which is rather moderate rate
in broad temperature. Since L1H2 and L3H2 ligands
contain the moisture, the thermal decomposition of
these ligands appear at two steps each of them ended
about 100°C. The thermal decomposition products, the
temperature range concerned and the estimated and the
calculated mass loss are listed in Table 1 for both used
three ligands and their Co-complexes.
Fig. 3 TG and DTG curves of Co(L1H)2·2H2O,
Co(L2H)2·2H2O and Co(L3H)2·2H2O
Nonisothermal study
dinated water molecules. Consequently, these
vic-dioximes is capable of forming mononuclear
complexes [17, 18].
Inserting various g(x) models into Eq. (5) results in a
set of Arrhenius parameters determined from the plot
g(x)
T 2
æ
ö
ln
vs. T–1. The set of Arrhenius parameters ob-
ç
÷
Methods
è
ø
tained the best four reaction models for the thermal
decomposition of both used ligands and their Co-com-
plexes are shown in Tables 2, 3. For each model and
heating rate, the goodness of fit is estimated by correla-
tion coefficient, r2. The thermal decomposition of used
compounds were performed at nonisothermal condition
In experiments, a Setaram TG/DTA/DSC-16 instru-
ment were used for thermal analysis of ligands and
their Co complexes. Thermogravimetric tests were
performed at nitrogen flow of 0.850 mL s–1 and at con-
stant heating rates of 5, 10, 15 and 20°C min–1.
Table 1 Mass losses of used ligands and their Co-complexes in different temperature ranges
Mass loss%
Decomposition
product lost
Compound
Temp. range/°C
55–478
Final product
–
Found
100
Calcd.
100
Ligand, L1H2
C15H21N3O2
Co(L1H)2·2H2O
64–342
342–892
C20H31O3
C10H13N6
C10H13N6OCo
CoO
54.59
31.32
54.71
33.66
Ligand, L2H2
42–748
C13H19N3O2
–
100
100
Co(L2H)2·2H2O
152–312
312–847
C22H40N2O2
C4N4O3
C4O4N4Co
CoO
61.53
25.62
61.59
25.71
Ligand, L3H2
47–521
C13H19N3O2
–
100
100
Co(L3H)2·2H2O
59–325
325–892
C7H11N5O4Co
CoO
51.35
36.03
51.27
36.04
C19H29NO2
C7H11N5O3
126
J. Therm. Anal. Cal., 89, 2007

Co-COMPLEXES OF THREE UNSYMMETRICAL Vic-DIOXIMES LIGANDS
J. Therm. Anal. Cal., 89, 2007
127

SAHIN et al.
128
J. Therm. Anal. Cal., 89, 2007

Co-COMPLEXES OF THREE UNSYMMETRICAL Vic-DIOXIMES LIGANDS
at constant heating rate of 5, 10, 15 and 20°C min–1,
since a single step of nonisothemal (a, T, t) data give
similarly satisfactory fits to most of many equations.
This set is conventionally taken as the group of kinetic
models that are characteristic of decomposition reaction
of solid. The apparent magnitude of the Arrhenius pa-
rameters, however vary significantly with each alter-
native kinetic model compared [19].
As seen in Table 2, the nonisothermal kinetic pa-
rameters obtained by CR method for L1H2, L2H2 and
L3H2 ligands can be represented by four different kinetic
models with respect to r2 values, but the apparent acti-
vation energy is far from each other for each ligand.
In this case, there is no adequate criterion for distin-
guishing the best set of kinetic parameters at
nonisothermal condition. Also, in Table 3, the thermal
decomposition steps of Co-complexes are represented
by four different models. The difference between r2
values is very small, but the apparent activation en-
ergy values changes by a factor x 2 or more. This kind of
result has been given in literature by Vyazovkin [20].
The general result for data given in Tables 2, 3 obtained
by CR method can be summarized as following
Fig. 4 Prediction of isothermal decomposition data of
Co(L3H)2·2H2O for both Step I and Step II from
nonisothermal TG curves
• CR approach to kinetic analysis is generally
unsuitable for determination of kinetic triplex.
• The interrelationship between the exponent n and
activation energy found by CR method in Table 3 is
effectively unable to separate the individual
contributions to the composite function.
E
–
g(a )
RT
i
ki = Ae
=
(15)
ta
where ta is the time to reach the extent of conversion
a at the constant temperature of Ti.
Figure 4 represents the isothermal decomposition
data obtained from nonisothermal TG curves for
Co(L3H)2·2H2O complex. As can be seen in Fig. 4, the
changes of conversion with time is nearly parallel for
both decomposition steps of Co(L3H)2·2H2O separately.
For different reaction model, the rate constants are
evaluated at several temperatures as given in Eq. (14),
the Arrhenius parameters are determined by using the
Arrhenius equation in its logarithmic form,
Isothermal study
Rearrangement and integration of Eq. (1) for isothermal
condition gives
a
da
gi (a )=
=ki (T )t
(14)
ò
f (a )
0
The subscript i has been introduced to emphasize
that substituting a particular reaction model into Eq. (14)
results in calculation the suitable rate constant determined
from the slope of a plot of g(a) vs. t. In this study, the
statistical equivalent kinetic triplets determined from
nonisothermal data using the model fitting method have
been used to determine isothermal data [21] as follow:
Ei
ln(ki )=ln(A)–
(16)
RTi
Figure 5 depicts a plot of ln(k) vs. 1/T. Arrhenius
parameters found for the isothermal decomposition of
used Co-Complexes by the model fitting method are
illustrated in Table 4. It is believed that the analysis of
Table 4 Arrhenius parameters for isothermal decomposition of used Co-complexes determined using the model-fitting method
Compound
Co(L1H)2·2H2O
Model
E/kJ mol–1
A/min–1
R2
I step
II step
D2
n=1
43.7
42.3
13.681
15.799
0.983
0.964
I step
II step
D2
n=2
46.7
105.6
114.663
51149.535
0.982
0.966
Co(L2H)2·2H2O
Co(L3H)2·2H2O
I step
II step
D2
n=1
77.1
119.7
178974.748
255505.701
0.999
0.962
J. Therm. Anal. Cal., 89, 2007
129

SAHIN et al.
Fig. 6 Dependence of the activation energy of L1H2 ligand and
Fig. 5 Arrhenius plots of the thermal decomposition of
their Co(L1H)2·2H2O complex conversion determined
using the model-free isoconversional method for the
nonisothermal data
Co-complexes
isothermal kinetic parameters is more reliable, since
the temperature is held constant during experiments.
Therefore, the results of nonisothermal experiments
are expected to agree with isothermal data. As seen in
Table 4, the activation energy values obtained by iso-
thermal methods and the best model represented ther-
mal decomposition of the Co-complexes data are very
differ from that is obtained from nonisothermal
method. This inaccuracy between two methods was
explained in nonisothemal study section. On the other
hand, it must be taken into account that in the isother-
mal condition the reaction are very slow at the low tem-
perature, so that the experiments will be limited by
long terms, while for high temperature the reaction
will be too fast. As a result of this restriction, it can be
said that the isothermal experimental is limited by
temperature.
Fig. 7 Dependence of the activation energy of L4H2 ligand and
their Co(L2H)2·2H2O complex conversion determined
using the model-free isoconversional method for the
nonisothermal data
Model-free linear isoconversional method study
Model fitting methods are designed to extract a single
step of global Arrhenius parameters for the whole
process and are therefore unable to reveal this type of
complexity in solid state reactions. The values
obtained in such a way are averages that do not reflect
changes in the mechanism and kinetics with the
temperature and extend of conversion. The
model-free isoconversional method allows for
unmistakable detecting multi-stage kinetics as
dependence of the activation energy on the extend of
conversion. Furthermore, it was shown that revealing
the dependence of the activation energy on the
conversion not only helps to disclose the complexity
of a process, but also helps to identify its kinetics
scheme. Thus, it is possible to obtain information
about the mechanism of a process and predict its
kinetic without the knowledge of both the reaction
model and the pre-exponential factor.
Fig. 8 Dependence of the activation energy of L3H2 ligand and
their Co(L3H)2·2H2O complex conversion determined
using the model-free isoconversional method for the
nonisothermal data
activation energy, E is found for each value of
conversion (a), in order to find the dependence of the
activation energy on the extent of conversion.
Figures 6–8 show the activation energy dependencies
determined for the nonisothermal decomposition of
L1H2, L2H2 and L3H2 ligands and their Co-complexes.
For a set of experiments conducted at different
heating rates, the activation energy can be calculated
at any particular value of a in Eq. (13). The best value of
130
J. Therm. Anal. Cal., 89, 2007

Co-COMPLEXES OF THREE UNSYMMETRICAL Vic-DIOXIMES LIGANDS
As shown in Figs 6–8, the value of the activation
reaction mechanism. The obtained activation energies
values for L1H2, L2H2 and L3H2 ligands are
approximately constant, since decomposition of used
ligands realized at single step.
energy increases or decreases with the degree of
conversion for used complexes. Variation in the value of
activation energy may be a hint of change in reaction
mechanism with reaction progressing in some cases. If
activation energy values are not constant with
conversion for any decomposition, then one is
probably dealing with either a change in mechanism
as the reaction proceeds or a more complex situation
such as a mutually independent multiple, competitive
or consecutive reaction system, reversible
reaction [22–25].
First step of the nonisothermal decomposition of
Co(L1H)2·2H2O complex gives an E–a dependence
(Fig. 6) that rises from about 140 kJ mol–1 at a=0.4
and decrease at high conversion to nearly 40 kJ mol–1.
For second step of same Co-complex, the activation
energy decreases monotonically to 40 kJ mol–1 near
the end of reaction.
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energy (Fig. 7) for both steps increase with increasing
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Conclusions
The application of the model fitting method to a
multi-step decomposition of Co(L1H)2·2H2O,
Co(L2H)2·2H2O and Co(L3H)2·2H2O complexes results
to be unsuitable for the nonisothermal data. For
isothermal data model-fitting method gives rise to
apparently reliable results that are likely to conceal the
kinetic complexity. A variable alternative to the
model-fitting method is the model-free isoconversional
method. By this method nonisothermal data can be
easily be analyzed and the activation energy, E vs.
conversion, a plots can reveal complexities in the
reaction kinetics. The thermal decomposition of L1H2,
L2H2 and L3H2 ligands and their Co-complexes was
carried out by the general known method named
model fitting and isoconversional method to
determine the Arrhenius kinetic parameters and the
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Received: March 25, 2005
Accepted: December 28, 2006
OnlineFirst: April 29, 2007
DOI: 10.1007/s10973-005-7019-7
J. Therm. Anal. Cal., 89, 2007
131