Model-fitting and model-free analysis of thermal decomposition of palladium acetylacetonate [Pd(acac)2]

Article abstract of DOI:10.1007/s10973-008-9118-8

The non-isothermal decomposition process of the powder sample of palladium acetylacetonate [Pd(acac)₂] was investigated by thermogravimetric (TG) and the X-ray diffraction (XRD) techniques. Model-free isoconversional method of Tang, applied to the investigated decomposition process, yield practically constant apparent activation energy in the range of 0.05≤α≤0.95. It was established, that the Coats-Redfern (CR) method gives several statistically equivalent reaction models, but only for the phase-boundary reaction models (R2 and R3), the calculated value of the apparent activation energy (E) is nearest to the values of E obtained by the Tang's and Kissinger's methods. The apparent activation energy value obtained by the IKP method (132.4 kJ mol^-1) displays a good agreement with the value of E obtained using the model-free analysis (130.3 kJ mol^-1). The artificial isokinetic relationship (aIKR) was used for the numerical reconstruction of the experimental integral model function, g(α). It was established that the numerically reconstructed experimental function follows R3 reaction model in the range of α, taken from model-free analysis. Generally, decomposition process of Pd(acac)₂ starts with initial nucleation which was characterized by rapid onset of an acceleratory reaction without presence of induction period.

Full text of DOI:10.1007/s10973-008-9118-8

Journal of Thermal Analysis and Calorimetry, Vol. 94 (2008) 2, 395–403
MODEL-FITTING AND MODEL-FREE ANALYSIS OF THERMAL
DECOMPOSITION OF PALLADIUM ACETYLACETONATE [Pd(acac)2]
B. Jankoviº* and S. Mentus
Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12-16, P.O. Box 137, 11001 Belgrade, Serbia and Montenegro
The non-isothermal decomposition process of the powder sample of palladium acetylacetonate [Pd(acac)2] was investigated by
thermogravimetric (TG) and the X-ray diffraction (XRD) techniques. Model-free isoconversional method of Tang, applied to the in-
vestigated decomposition process, yield practically constant apparent activation energy in the range of 0.05£a£0.95. It was estab-
lished, that the Coats–Redfern (CR) method gives several statistically equivalent reaction models, but only for the phase-boundary
reaction models (R2 and R3), the calculated value of the apparent activation energy (E) is nearest to the values of E obtained by the
Tang’s and Kissinger’s methods.
The apparent activation energy value obtained by the IKP method (132.4 kJ mol–1) displays a good agreement with the value
of E obtained using the model-free analysis (130.3 kJ mol–1). The artificial isokinetic relationship (aIKR) was used for the numerical
reconstruction of the experimental integral model function, g(a). It was established that the numerically reconstructed experimental
function follows R3 reaction model in the range of a, taken from model-free analysis. Generally, decomposition process of
Pd(acac)2 starts with initial nucleation which was characterized by rapid onset of an acceleratory reaction without presence of
induction period.
Keywords: decomposition, model-fitting, model-free, non-isothermal kinetics, palladium acetylacetonate
Introduction
an endotherm at approximately 196°C, at the conclu-
sion of which a product containing 75% palladium
was found, the remainder comprised of carbon, hy-
drogen and oxygen [12]. They were found, that in oxi-
dizing atmosphere at the same heating rate, Pd(acac)2
decomposes exothermically at 180°C yielding essen-
tially pure palladium. Continued heating in oxygen,
to 800°C results in pure PdO. At 900°C, the PdO de-
composes yielding pure palladium.
Organometallic complexes have gained widespread
use in catalysis over the past few decades. In particu-
lar, precious metal complexes have been used exten-
sively as catalysts in many synthetic organic reactions
[1–8] including industrial-scale reactions. Metal cata-
lysts often contain organic ligands, and standard anal-
yses of metals by ion selective electrodes (ISEs) and
other electrochemical techniques are, however, for
metal ions free of organic ligands [9–11]. The organic
ligands usually need to be decomposed or removed to
free the metals prior to their qualitative and quantita-
tive analysis.
Our principal objective is the kinetic analysis of
non-isothermal decomposition of palladium acetyl-
acetonate (Pd(acac)2) (determination of full kinetic
triplet: pre-exponential factor (A), apparent activation
energy (E) and analytical form of reaction model
function (f(a)) by applying model-fitting and model-
free approaches [13]. In the modern literature, there is
no information about the non-isothermal decomposi-
tion of palladium acetylacetonate from the point of
view of solid-state kinetics.
Poston and Reisman [12] are investigated the
relative stabilities of palladium acetylacetonate and
palladium hexafluoroacetylacetonate using DTA and
mass loss analysis. In general, the acetylacetonates
decompose in the solid-state at relatively low temper-
atures (100–200°C), with several of them exhibiting
appreciable vapor pressures at temperatures below
which their decomposition rate is significant. At the
heating rates employed, £2°C min–1, palladium ace-
tylacetonate tends to decompose upon heating in ei-
ther an inert or oxidizing atmosphere before signifi-
cant quantities volatilize. Heating palladium acetyl-
acetonate in argon, at £2°C min–1, shows the onset of
Experimental
Materials and methods
Palladium acetylacetonate was synthesized by precip-
itation from the solution of PdCl2 and acetylacetone
in ethanol. The precipitate was washed by ethanol and
*
Author for correspondence: bojanjan@ffh.bg.ac.yu
1388–6150/$20.00
Akadémiai Kiadó, Budapest, Hungary
Springer, Dordrecht, The Netherlands
© 2008 Akadémiai Kiadó, Budapest

JANKOVI‡, MENTUS
dried under vacuum of approximately 10 mbar at
room temperature.
Thermal decomposition of acetylacetonate sam-
Model-free methods
However, due to the complexity of the kinetic de-
scription concerning the solid-state decomposition
processes it is usually assumed that the apparent acti-
vation energy is not a constant value but depends on a
[15, 16]. Therefore, in order to establish if such de-
pendence exists or not, the kinetic procedure adopted
in this work was first based on two multi-heating rate
methods. Both approaches determine the apparent ac-
tivation energy using thermal analysis data carried out
at different fixed heating rates without choosing a pri-
ori a defined model function. In particular, the first ki-
netic method used was the isoconversional method of
Tang et al. [17], that is based on Eq. (3), with approxi-
mate formula of high accuracy for Arrhenius tempera-
ture integral [17] in linear form:
ples was studied by thermogravimetric technique us-
ing a TA SDT 2960 thermobalance. The average mass
of samples was about 4 mg. Purging gas was a nitro-
gen (99.9995 vol%) at a flowing rate of 90 mL min–1.
The flow of pure filtered nitrogen carrier gas was sup-
plied from a high-pressure (HP) cylinder. The furnace
temperature rose linearly at the following heating
rates (b): b=2, 5, 10, 15 and 30°C min–1, in the tem-
perature range from an ambient one up to 350°C. The
microphotograph of the samples upon decomposition
was taken by scanning electron microscope of type
JEOL JSM-6460. The X-ray powder diffrac-
tion (XRPD) patterns were collected using a
Philips PW-1050 automatic diffractometer with a
CuK line of 1.5418 nm.
b
AE
a1,2
ln
=ln
+3.635041-
T 1.894661
Rg(a )
E
Kinetic analysis
1.894661lnE-1.001450
(4)
RT
Kinetics of solid-state reactions is usually described
by the following equation:
At any selected value of a, from the slope of the
related regression straight line derived by the
ln(b/T1.894661) vs. 1/T plot, the corresponding E value
is derived as a function of a. The present kinetic study
was also performed using the Kissinger method
[18, 19] that uses the following equation:
da
dt
E
æ
ç
è
ö
÷
ø
= Aexp -
f (a )
(1)
RT
where a is the extent of conversion defined as a=
(m0–mt)/(m0–mf) (mt represents the mass of the sample
at arbitrary time t (or temperature T), whereas m0 and
mf are the mass of the sample at the beginning and at
the end of the process, respectively), A is the pre-ex-
ponential factor, E is the apparent activation energy,
R is the gas constant and f(a) is the reaction model
function. Moreover, taking into account that under
non-isothermal condition the heating rate is b=dT/dt,
then from Eq. (1) we have Eq. (2):
æ
ç
ç
è
ö
÷
÷
ø
æ
ö
ö
÷
÷
ø
b
AR
E
E
R
1
æ
ç
è
ö æ
+ -
ç
ln
=ln
(5)
÷ ç
ø è
÷
2
Tp
ç
Tp
ø
è
where Tp is the DTG peak temperature at a given heat-
ing rate. From the slope of Eq. (5) a single apparent
activation energy value (E) for each step of mass loss
is given.
Model-fitting methods
da da dt æ A ö
exp -
E
æ
ç
ö
÷
ø
=
dT dt dT
=
f (a )
(2)
ç
÷
ç
÷
For non-isothermal experiments, model-fitting in-
volves fitting different models to a–T curves and si-
multaneously determining E and A [20]. Subse-
quently, TG data derived by a single linear heating
rate experiment were fitted to some of the integral
model functions g(a) reported in the literatures
[20–22] using the Coats–Redfern (CR) method [23].
This method makes the assumption that the integral
model function
b
RT
è
è
ø
Most of the methods that describe the kinetics of
reactions in solids use Eq. (2) as well as several ap-
proximation of its integral form:
AT
b òexp -
E
RT
æ
æ
ç
è
ö
dT =
÷
ø
g(a )=
0
æ
ö¥ exp(- )
x
ö
AE
AE
dx=
p(x)
(3)
ç
ç
÷
ç
÷÷ò
øx
ç
è
÷
x2
bR
bR
è
ø
g (a )
A R Ej
ö
j
é
ê
ë
ù
ú
û
æ
ç
ç
è
j
÷
ln
=ln
-
(6)
T 2
÷
where g(a) is the integral form of the model function
and p(x) represents the ‘temperature integral’, which
can not be analytically integrated, where x=E/RT. To
overcome this difficulty, the ‘temperature integral’
has been solved using approximation methods, series
expansions, and numerical solution methods [14].
bE
RT
ø
where the subscript j is related to the selected reaction
model. From the slope of the linear regression ob-
tained by plotting ln[gj(a)/T2] vs. 1/T, the correspond-
ing kinetic parameters Ej and Aj are obtained for each
396
J. Therm. Anal. Cal., 94, 2008

THERMAL DECOMPOSITION OF PALLADIUM ACETYLACETONATE [Pd(acac)2]
Results and discussion
model function j. These kinetic parameters related to
all the different model function j of the same process
are linearly correlated (compensation effect).
TG and DTG curves of the decomposition process of
palladium acetylacetonate ([Pd(acac)2]) samples ob-
tained at the different heating rates (b=2, 5, 10, 20 and
30°C min–1) are shown in Figs 1 and 2.
It has been observed that the same experimental
curve a=a(T) can be described by the different model
function (f(a)). Further, the values of the apparent ac-
tivation energy obtained for various f(a) for the single
non-isothermal curve are correlated through the com-
pensation effect [24, 25]. These observations form the
basis of the IKP –invariant kinetic parameter method.
In order to apply this method, a=a(T) curves are ob-
tained at the different heating rates (bv, v=1, 2, 3, ...)
using TG technique. For each heating rate, the pairs
(Avi, Evi) (where i corresponds to a particular extent of
conversion), are determined using the CR equation
(Eq. (6)). For constant value of b, a plot of ln[g(a)/T2]
vs. 1/T is a straight line whose slope allows the evalu-
ation of the apparent activation energy Ev and inter-
cept, the pre-exponential factor Av, for different reac-
tion models g(a). The same procedure is repeated to
obtain the pairs (Ev, Av) for different heating rates. In
addition, the calculation of the invariant activation
parameters is done using the compensation relation
[25–27]
The observed TG curves show an asymmetric
character and were moved to a higher values of exper-
imental temperature with increase in heating rate
(Fig. 1). The total mass loss for considered process at
all heating rates was found to be 71.47%. The ob-
served DTG curves manifested the similar behaviour
as TG curves, where the peak temperature (Tp) values
increasing with increase in heating rate, b (Table 1).
Figure 3 shows the rate–temperature (da/dt–T)
curves for decomposition process of palladium ace-
tylacetonate at the different heating rates.
lnAv =a * +b* Ev
(7)
The above Eq. (7) represents a linear relationship
between lnA and E and any increase in the magnitude
of one parameter is offset, or compensated, by the
appropriate increase of the other. Plotting lnAv vs. Ev
for the different heating rates, the compensation
effect parameters a* and b* are obtained. These
parameters follow an equation
a * =lnA-b* E
(8)
Fig. 1 TG curves for the non-isothermal decomposition
process of palladium acetylacetonate samples in
nitrogen atmosphere
The plot of a* and b* gives the true values of ki-
netic parameters (A, E).
Numerical reconstruction of the experimental model
function
The integrated model function g(a) can be numeri-
cally reconstructed using an artificial isokinetic
relationship (aIKR) [28] if Ea were practically inde-
pendent of a. Once the values of lnAa and Ea are
determined the integrated model function g(a) is
reconstructed by substituting the selected estimates of
Aa and Ea in Eq. (3). The explicit form of the model
function can be determined by comparing the selected
numerical dependence of g(a) vs. a with corres-
ponding model dependencies.
Fig. 2 DTG curves for the non-isothermal decomposition
process of palladium acetylacetonate samples in
nitrogen atmosphere
J. Therm. Anal. Cal., 94, 2008
397

JANKOVI‡, MENTUS
Table 1 Values of Tp and ap for the non-isothermal
decomposition process of palladium acetylacetonate
(Pd(acac)2), determined by thermogravimetric
analysis at the different heating rates
b/°C min–1
Tp/°C
ap
2
5
215
235
240
250
255
0.73
0.73
0.69
0.70
0.72
10
20
30
Fig. 4 The dependence of da/dt vs. a for the decomposition
process of palladium acetylacetonate at the different
heating rates. Short solid lines represents themaximums
of the curves which corresponds to ap values
trolled reactions (mechanisms: R2 (0.73£ap£0.74) or
R3 (ap=0.69)). It can be pointed out, that this ap-
proach is useful for the basic classification of possible
kinetic model, but it is not sufficient for an unambigu-
ous determination of true reaction model. The non-
isothermal decomposition process of palladium ace-
tylacetonate was analyzed by Tang (T) isoconver-
sional method. For all sets of a values, the linear
isoconversional plots result in a linear correlation co-
efficients larger than 0.99. The dependences of E and
ln[A/g(a)] values on a are displayed in Fig. 5.
Fig. 3 Experimental reaction rate curves (da/dt vs. T) for the
decomposition process of palladium acetylacetonate
under the nitrogen atmosphere at the different heating
rates
As shown in Fig. 5, the value of apparent activa-
tion energy hardly varies with the extent of conver-
sion (a). Practically constant E values around
130.3±1.9 kJ mol–1 were found (changes lie within the
associated uncertainties). Alternatively, ln[A/g(a)]–a
plot demonstrates an identical manner (Fig. 5), which
it may suggest that both the apparent activation en-
ergy (E) and the pre-exponential factor (A) are practi-
As can be seen from Fig. 3, the maximal rate of
the investigated process increases with increase in
heating rate. The maximums of the rate–temperature
curves were moved to a range of higher values of tem-
perature (Fig. 3) and this behaviour coincides with
behaviour of DTG curves (Fig. 2). The both, DTG and
rate-temperature curves exhibited the one clearly
peak at all heating rates. From these results, we may
concluded, that the investigated decomposition pro-
cess can follow the single-step reaction mechanism.
However, this observation is some roughly, and be-
cause of that, the further analysis is necessary.
Figure 4 shows the dependence of da/dt vs. a for
the investigated decomposition process of palladium
acetylacetonate at the considered heating rates.
It can be seen from Fig. 4, that the values of a
which corresponds to the maximum values of rate of
process (ap) falls in the range of 0.69£ap£0.73
(Table 1). From the Dollimore’s procedure for the
identification of reaction mechanism [29–31], which
is based on the theoretical positions of ap values in a
scale for the various types of solid-state mechanisms,
we can conclude that the investigated decomposition
process belongs to the group of phase-boundary con-
Fig. 5 The dependence of the apparent activation energy (E)
and ln[A/g(a)] values on the extent of conversion (a)
(T-method) for the non-isothermal decomposition
process of palladium acetylacetonate
398
J. Therm. Anal. Cal., 94, 2008

THERMAL DECOMPOSITION OF PALLADIUM ACETYLACETONATE [Pd(acac)2]
The value of the apparent activation energy ob-
tained by the Kissinger’s method is higher than value
of obtained by the Tang (T) method
E
(130.3 kJ mol–1). It can be pointed out, that the differ-
ence between E values calculated from the above
mentioned methods does not large (DE<10 kJ mol–1),
which represent a satisfactory result. The kinetic pa-
rameters for the decomposition process of Pd(acac)2
are also determined by CR method for all model func-
tions used in this work, and given in Tables 2 and 3
with their linear correlation coefficient (r)
values [32]. The validity of reaction model functions
was tested by a statistical F-test [33, 34].
A single function can not be discriminated since
the five phase-boundary (R2; R3) and two- and three-
dimensional diffusion models (D2; D3; D4) seem to
be statistically equivalent fitting models. It can be ob-
served, that only for R2 and R3 models, the calculated
value of the apparent activation energy is nearest to
the values of E obtained by the Tang’s and
Kissinger’s methods, separately at the 10°C min–1.
In order to apply the IKP method, the conversion
range in which the value of E is practically constant
has to be determined and that has been done through
the above methods. For determining the compensa-
tion effect parameters (a*, b*), CR method has been
Fig. 6 Kissinger plot for the decomposition process of
palladium acetylacetonate
cally independent on the extent of conversion. On the
other hand, from the slope of the regression line ob-
tained by fitting the ln(b/Tp2 ) experimental data vs.
Tp–1 (Fig. 6) according to Eq. (4), the apparent activa-
tion energy of the investigated decomposition process
equal to 138.0±2.2 kJ mol–1 is found. The value of
pre-exponential factor (A), for the considered decom-
position process is the following: A= 7.00·1013 min–1.
Table 2 Arrhenius parameters related to the decomposition process of Pd(acac)2 at 2 and 5°C min–1 obtained by the
Coats–Redfern method for the most commonly used model functions
b=2°C min–1
b=5°C min–1
Model
lnA
E/kJ mol–1
r
F-testb
lnA
E/kJ mol–1
r
F-testb
P1
2.42
5.46
25.1
36.0
–0.9976
–0.9980
–0.9983
–0.9986
–0.9986
–0.9997a
–0.9986
–0.9941
–0.9811
–0.9632
–0.9255
–0.9938
–0.9935
–0.9929
–0.9922
–0.9987
–0.9999a
–0.9987
–0.9999a
1476.386
1761.532
2080.180
2561.149
2434.622
10799.658
2571.612
585.256
2.21
4.95
22.2
32.3
–0.9839
–0.9867
–0.9888
–0.9909
–0.9905
–0.9988
–0.9997a
–0.9972
–0.9816
–0.9570
–0.9100
–0.9970
–0.9969
–0.9966
–0.9962
–0.9912
–0.9965
–0.9997a
–0.9981
273.597
331.070
394.967
490.605
465.546
3606.960
13022.744
1580.618
237.961
97.911
P2
P3
11.29
44.61
28.11
32.28
33.74
38.97
46.20
54.56
73.81
24.31
16.88
9.30
58.0
10.18
39.80
25.16
29.54
31.18
36.99
45.67
56.02
79.82
23.25
16.28
9.17
52.6
P4
189.6
123.8
141.8
148.7
164.2
191.3
222.7
295.4
106.8
78.2
174.1
113.3
132.8
140.7
158.9
192.6
233.0
326.5
103.2
75.3
R1
R2
R3
F1
F3/2
F2
180.387
89.829
F3
41.793
43.338
A3/2
A2
A3
A4
D1
D2
D3
D4
560.144
1510.327
1441.140
1306.208
1176.099
503.427
1262.179
14063.192
2426.415
535.469
49.5
487.457
47.5
5.40
35.1
441.282
5.49
33.6
60.97
66.06
72.03
67.00
255.4
277.1
305.3
286.4
2626.037
52341.542
2680.983
30618.464
54.31
59.48
66.13
60.61
234.9
257.6
289.5
267.9
aStatistically equivalent models, bStatistical F-distribution function [33, 34]
J. Therm. Anal. Cal., 94, 2008
399

JANKOVI‡, MENTUS
400
J. Therm. Anal. Cal., 94, 2008

THERMAL DECOMPOSITION OF PALLADIUM ACETYLACETONATE [Pd(acac)2]
applied in the range of the extent of conversion where
E is independent on a (0.05£a£0.95). The apparent
compensation effect is observed for each heating rate
for the process under investigation and presented in
Fig. 7.
obtained
using
the
model-free
analysis
(130.3 kJ mol–1). From Table 4, it can be seen that the
isokinetic temperature (Tiso) increasing with increase
in heating rate, and all Tiso lies in the region of the ex-
perimental temperatures. The E value from model-
free analysis can be used to calculate numerically the
actual model functions, f(a) or g(a). Comparison of
the numerically reconstructed kinetic function with
those of the theoretical models can provide a much
clearer picture of the reaction mechanism and can in-
dicate whether the mechanism changes during the
course of the reaction. To reconstruct the model nu-
merically, we must evaluate the pre-exponential fac-
tor, A. Vyazovkin and Lesnikovich [36] were the first
to evaluate the pre-exponential factor by use the arti-
ficial isokinetic relationship (aIKR). Such an analysis
shows that the values of lnA are linearly related to the
values of E obtained from fitting to different models.
As a consequence, A for the model-free approach may
be calculated as a function of the extent of conver-
sion. Figure 8 shows the dependence of lnA values
calculated from the model-free approach on the extent
of conversion (a), for the non-isothermal decomposi-
tion process of palladium acetylacetonate (the calcu-
lations are done for b=10°C min–1).
A compensation effect of this kind is classified
as artificial compensation effect which occurs on fit-
ting the various reaction models to the same set of
non-isothermal kinetic data [35]. The values of a* and
b* were calculated from the intercepts and the slopes
of the straight lines obtained in Fig. 7. The values of
the apparent compensation effect parameters (a*, b*)
obtained at the different heating rates (b) are pre-
sented in Table 4.
A linear regression from the straight-line plot of
a*=lnA–b*E allows computation of the kinetic param-
eters (A, E). From Eq. (8) one obtains: A=1.10·
1013 min–1 and E=132.4 kJ mol–1. Table 4 also shows
the values of isokinetic temperatures (Tiso= 1/Rb*) at
considered heating rates. From the established results,
we can see that the value of E obtained by the IKP
method (132.4 kJ mol–1) is very close to the value of E
It can be observed that lnA values follow the
same trend as the E values which were calculated us-
ing Tang’s method (Fig. 5). With knowledge of E and
A, the experimental kinetic function, g(a), can be cal-
culated using Eq. (3) [36]. The numerically recon-
structed experimental kinetic function, g(a), is shown
in Fig. 9. The lines were calculated according to R2,
R3, D2, D3 and D4 models. Because the kinetic func-
tion, g(a), depends only on a, the construction of
these lines does not require knowledge of E or A. The
lines are constructed from knowledge of the individ-
ual kinetic function itself.
The superposition of experimental g(a) function
(the full circles) obtained from the model-free analy-
sis, indicated that the kinetics of decomposition pro-
cess of palladium acetylacetonate could be described
by a single model function. It can be easily seen from
Fig. 7 Artificial compensation effect observed between the
apparent activation energy and pre-exponential factor
evaluated by applying the CR method, for the
decomposition process of palladium acetylacetonate
under the nitrogen atmosphere
Table 4 Values of compensation effect parameters with
corresponding values of isokinetic temperatures
(Tiso), at five different heating rates for the non-iso-
thermal decomposition process of palladium acetyl-
acetonate (Pd(acac)2)
b/
°C min–1
a*/
min–1
b*/
mol kJ–1
Tiso/
r
°C
2
5
–3.2079
–2.6515
–1.8962
–1.1078
–0.7295
0.2523
0.2446
0.2411
0.2356
0.2328
203.5
218.5
225.7
237.3
243.5
0.9991
0.9988
0.9988
0.9989
0.9989
Fig. 8 The dependence of lnA values calculated from the
model-free approach on the extent of conversion (a),
for the non-isothermal decomposition process of
palladium acetylacetonate
10
20
30
J. Therm. Anal. Cal., 94, 2008
401

JANKOVI‡, MENTUS
Fig. 9 Reconstruction of g(a) vs. a plots from model-free
Fig. 11 X-ray diffractogram of palladium (Pd) obtained by the
thermal decomposition process of [Pd(acac)2].
The dashed lines represent the ASTM data for
palladium
analysis (lines are calculated from the considered
theoretical models). Key: (·) values calculated for
decomposition process of Pd(acac)2 from the E and A
values derived from model-free analysis
The film thickens by sampling Pd atoms deliber-
ated during the decomposition of the rest of
Pd(acac)2, primarily at the places of close contact. It is
not excluded that the film grows partly via Pd(acac)2
evaporation–decomposition [37–39], but however
this way may not be dominant, since the mass loss
caused by the sample evaporation have not been reg-
istered by TG curves. The diffractogram of the de-
composition product (Fig. 11) corresponds essentially
to that of Pd, with somewhat enlarged elementary
cell. The width of diffraction lines indicates low de-
gree of crystallinity. Accordingly, the mean crystal
diameter calculated by means of the Scherer’s
formula amounts to value of 18 nm.
Fig. 9 that the kinetic process for Pd(acac)2 decompo-
sition is the most probably described by R3 model
with accommodated exponent n=3:
1
g(a )=1-(1-a )3
(9)
The contracting geometry models are based on
an initial rapid (instantaneous) dense nucleation
across all, or some specific, crystal faces. Close spac-
ing of nuclei results in the rapid (low a) generation of
a coherent reaction zone that advances inwards at a
constant rate in the absence of diffusion effects.
On the basis of established TG curves, we can
conclude that the decomposition of Pd(acac)2 is a sin-
gle-step process, which can be presented simply by
the formula:
Generally, the decomposition process starts with
initial nucleation which was characterized by rapid
onset of an acceleratory reaction behavior without
presence of induction period. Furthermore, the con-
sidered process was characterized by Pd particles
growth in three dimensions, probably generating the
spherical reaction zone.
Pd(acac)2 ®Pd+2acac
(10)
An accompanying destruction of the ligand, if al-
ready occurs does not play significant role to the ki-
netics of the overall investigated process. According
to the SEM microphotographs (Fig. 10), thermal de-
composition commences at the outer crystal surface,
yielding the ragged Pd-film, which surrounds the rest
of Pd(acac)2 crystal.
Conclusions
The kinetics of the non-isothermal decomposition of
palladium acetylacetonate (Pd(acac)2) was accurately
determined from a series of thermoanalytical experi-
ments at the different constant heating rates. The phys-
ical characterization of decomposition product of the
investigated process was analyzed by the SEM and
X-ray diffraction experiments. It was established, that
by applying the Tang’s model-free method, the decom-
position process of Pd(acac)2 can be described by the
single step of mass loss with negligible change in the E
values (E=130.3±1.9 kJ mol–1). It was concluded, that
the Coats–Redfern (CR) method give several statis-
tically equivalent reaction models, but only for R2 and
R3 models, the calculated value of E is nearest to the
values of E obtained by the Tang’s and Kissinger’s
Fig. 10 SEM microphotograph of palladium (Pd) obtained by
the thermal decomposition process of palladium
acetylacetonate [Pd(acac)2]
402
J. Therm. Anal. Cal., 94, 2008

THERMAL DECOMPOSITION OF PALLADIUM ACETYLACETONATE [Pd(acac)2]
16 S. Vyazovkin and C. A. Wight, Annu. Rev. Phys. Chem.,
methods. The use of the IKP method for the range where
48 (1997) 125.
E is practically independent of a, led to the invariant
activation parameters, which were used for the nume-
rical evaluation of the model function, f(a). The appar-
ent activation energy value (132.4 kJ mol–1) obtained by
the IKP method displays a very good agreement with
the value of E obtained using the model-free analysis.
The artificial isokinetic relationship was used for
numerical reconstruction of the experimental integral
model function, g(a). It was established that the numeri-
cally reconstructed experimental function follows the
R3 reaction model in the considered range of a, taken
from the model-free analysis.
17 W. J. Tang, Y. W. Liu, H. Zhang and C. X. Wang,
Thermochim. Acta, 408 (2003) 39.
18 H. E. Kissinger, Anal. Chem., 29 (1957) 1702.
19 P. Budrugeac and E. Segal, J. Therm. Anal. Cal.,
88 (2007) 703.
20 S. Vyazovkin and C. A. Wight, J. Phys. Chem. A,
101 (1997) 5653.
21 A. Khawam and D. R. Flanagan, J. Phys. Chem. B,
110 (2006) 17315.
22 A. Khawam and D.R. Flanagan, J. Pharm. Sci.,
95 (2006) 472.
23 A. W. Coats and J. P. Redfern, Nature, 201 (1964) 68.
24 A. K. Galwey, Thermochim. Acta, 399 (2003) 1.
25 P. Budrugeac and E. Segal, Int. J. Chem. Kinet.,
30 (1998) 673.
Acknowledgements
26 P. Budrugeac, C. Popescu and E. Segal, J. Therm. Anal.
Cal., 64 (2001) 821.
The study was partially supported by the Ministry of Science
and Environmental Protection of Serbia, under the following
Projects 142025 and 142047 (Professor S. Mentus).
27 P. Budrugeac, J. Therm. Anal. Cal., 89 (2007) 143.
28 S. Vyazovkin, Int. J. Chem. Kinet., 28 (1996) 95.
29 D. Dollimore, T. A. Evans, Y. F. Lee and F. W. Wilburn,
Thermochim. Acta, 188 (1991) 77.
30 D. Dollimore, T. A. Evans, Y. F. Lee, G. P. Pee and
F. W. Wilburn, Thermochim. Acta, 196 (1992) 255.
31 Y. F. Lee and D. Dollimore, Thermochim. Acta,
323 (1998) 75.
References
1 J. Halpern, Precious Met., 19 (1995) 411.
2 S. S. Stahl, Science, 309 (2005) 1824.
3 R. F. Heck, Palladium Reagents in Organic Synthesis,
Academic Press, New York 1985.
32 C. Popescu, E. Segal and C. Oprea, J. Therm. Anal. Cal.,
38 (1992) 929.
33 N. L. Johnson and F. C. Leone, Statistics and
Experimental Design in Engineering and the Physical
Sciences, Wiley and Sons, New York 1977, Vol. I.
34 D. L. Massart, B. G. M. Vandeginste, L. M. C. Buydens,
S. de Jong, P. J. Lewi and J. Smeyers-Verbke, Handbook
of Chemometrics and Qualimetrics, Part A, Elsevier,
Amsterdam 1997.
4 R. Singh, M. S. Viciu, N. Kramareva, O. Navarro and
S. P. Nolan, Org. Lett., 7 (2005) 1829.
5 J. Terao, A. Oda and N. Kambe, Org. Lett., 6 (2004) 3341.
6 B. M. Trost and J. Xu, J. Am. Chem. Soc.,
127 (2005) 17180.
7 R. T. Jacobsen, Chem. Eng. Prog., 101 (2005) 20.
8 C. G. Anderson and S. M. Nordwick, Precious Met.,
19 (1995) 123.
35 S. Vyazovkin and W. Linert, Chem. Phys.,
193 (1995) 109.
36 S. Vyazovkin and A. I. Lesnikovich, Thermochim. Acta,
128 (1988) 297.
9 M. Aghamohammadi and N. Alizadeh, Anal. Chim. Acta,
480 (2003) 299.
37 P. P. Semyannikov, V. M. Grankin, I. K. Igumenov and
A. F. Bykov, J. Phys., 4 (1995) 205.
10 J. Wang and K. Varughese, Anal. Chim. Acta,
199 (1987) 185.
38 A. G. Nasibulin, P. P. Ahonen, O. Richard,
E. I. Kauppinen and I. S. Altman, J. Nanopart. Res.,
3 (2001) 385.
11 G. Raber, K. Kalcher, C. G. Neuhold, C. Talaber and
G. Kolbl, Electroanalysis, 7 (1995) 138.
12 S. Poston and A. Reisman, J. Electr. Mater.,
18 (1989) 553.
39 A. G. Nasibulin, I. S. Altman and E. I. Kauppinen, Chem.
Phys. Lett., 367 (2003) 771.
13 S. Vyazovkin and C. A. Wight, Thermochim. Acta,
340–341 (1999) 53.
14 J. H. Flynn, Thermochim. Acta, 300 (1997) 83.
15 A. K. Galwey and M. E. Brown, Thermal Decomposition
of Ionic Solids, Elsevier, Amsterdam 1999.
DOI: 10.1007/s10973-008-9118-8
J. Therm. Anal. Cal., 94, 2008
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