The kinetic parameters of thermal decomposition of Cu(II) and Zn(II) salts of carboxylic acids were investigated on the basis
of the respective thermal curves. The values of the activation energy (Ea) of thermal decomposition, reaction order (n), frequency factor (A) and velocity constant (k) (in the Arrhenius kinetic equation), established from thermal data, were compared. Based on the initial decomposition temperature,
the following sequences of stabilities of the studied compounds have been proposed:
The apparent kinetic parameters of the thermal decomposition of theβ-cyclodextrin-water complex were estimated from thermogravimetric data. Various calculation methods were used and the results compared. All methods except the Kissinger method gave a reaction order near to zero and an activation energy in the range 60 to 65 kJ/mol. Some trials were made to extrapolate the activation energy values to semi-isothermal conditions (65.7 kJ/mol). The loss in weight indicated the presence of 11 water molecules in the complex. This was liberated in single stage, despite its occurrence as two distinct types, as shown by crystallographic studies.
The theoretical curves in the coordinates a vs. time for isothermal, and avs. temperature for non-isothermal experiments are calculated as functions of three kinetic parameters: activation energyE, pre-exponentical factorA and theg(α) function describing the mechanism of thermal decomposition of solids. The results show that conclusions not taking into consideration all three parameters can lead to information of little value concerning the mechanism of the decomposition and kinetic calculations. A correlation between non-isothermal and isothermal experiments, important for determination of the thermal stabilities of the compounds, is impossible without a knowledge of theg(α) function.
A critical assessment of the so-called “peak temperature methods” (originally proposed by Kissinger) is presented. The two ingredients of peak temperature methods, namely, Kissinger's assumption and transformation equations, are considered. First it is argued that Kissinger's assumption although not being valid for DTA holds for DSC. Then it is shown that the only way to use kinetic parameters obtained from non-isothermal experimental data to describe both iso- and anisothermal kinetics is to take the same reaction rate equation for the two kinetics, as previously done by Henderson.
The mathematical error in the method proposed by Bae for the determination of kinetic parameters from DTA curves has been corrected. The proposed equation does not contain thermal constants of the apparatus, and can be applied to DTA curves by an iterative method. The results obtained by the application of this equation to experimental DTA curves for the decomposition of sodium bicarbonate compared well with those from isothermal measurements, even when the DTA sample holder assembly was of the isolated cup-type instead of the block-type assembly recommended by Bae.
Authors:M. Reading, D. Dollimore, and R. Whitehead
Following previous work on the measurement of meaningful activation energies and the application of Constant Rate Thermal Analysis (CRTA) to the determination of kinetic parameters [1, 2], here we further examine sources of error in determining activation energies and go on to consider the form of the alpha function and the value ofA. Using theoretical arguments based on transition state theory, we conclude that allowing significant pressures of product gas to appear in the reaction environment will lead to very high values for apparent activation energies. We note that, although this is observed in practice for calcium carbonate, it in no way invalidates the application of the Arrhenius equation to solid state decomposition reactions, provided care is taken to avoid this type of distortion of experimental results. We attempt to determine the alpha function for the decomposition of calcium carbonate using data gathered from a variety of different types of temperature programme and reaction conditions. We find that the apparent alpha function depends on the method adopted and the experimental conditions used. We propose an explanation of why this occurs and tentatively introduce a new way of looking at the development of a reaction interface for this type of reaction. We review the literature and conclude that, while significant variations for the activation energy for the decomposition of calcium carbonate exist, a critical appraisal leads to good agreement amongst values that follow good experimental practice and reliable methods of data reduction. The apparent divergence of results can be explained in the light of the theoretical arguments advanced and the easily understood sources of experimental error.
Dependence of kinetic parameters (activation energy and pre-exponential factor) and procedural factors (sample mass and heating
rate) independent of the reversibility and the type of reactions in non-isothermal thermogravimetry have been established.
Tris(ethylenediamine)nickel(II) oxalate dihydrate has been selected as a model complex and experiments were carried out at
different heating rates and sample masses to study the dependence quantitatively. The kinetic parameters calculated using
mechanistic and non-mechanistic equations show a systematic decrease with increase in either sample mass or heating rate for
the dehydration and deamination reactions. For the decomposition reaction, the kinetic parameters are not influenced by the
procedural factors. Mathematical correlations of high reliability are established between kinetic parameters and heating rate/sample
mass using both mechanistic and non-mechanistic equations for dehydration and deamination reactions. The quantification follows
an exponential decay of second order relation with respect to heating rate and a sigmoidal relation with regard to sample
mass for both the dehydration and deamination reactions. No quantitative correlation is possible for the final decomposition
stage. Thus, it is found that independent of the type of reaction (deamination or dehydration) the kinetic parameters have
a particular dependence on the procedural variables. The equations for exponential decay and sigmoidal dependence can be represented
respectively, where y represents kinetic parameters (E or A) and x represents the procedural variables (φ or m). Mechanism of the dehydration reaction is found to be random nucleation with the formation of one nucleus on each particle
and the deamination is a phase boundary reaction. It is observed that the mechanism of these reversible reactions is not affected
by the variation in sample mass and heating rate.
Authors:I. Roşca, N. Foca, E. Stefancu, D. Sutiman, A. Cailean, I. Rusu, D. Sibiescu, and M. Vizitiu
This paper reports the synthesis and study of some Co(II) coordination polymers with the following acids as ligands: 2,8-dimethylphenoxyphosphinic,
diphenyloxyphosphinacetic, diphenylthiophosphinacetic and dihexylphosphinic acids. The study was performed by means of chemical
analysis, gel chromatography, IR spectroscopy, ESR, X-ray diffraction, thermogravimetry and electric resistance measurements.
The experimental results were used to propose the structural formulae of these compounds and to calculate the kinetic parameters
of the thermal decomposition reactions.
Authors:J. Zsakó, I. Szilágyi, Á. Simay, Cs. Várhelyi, and K. Kerekes
A number of 7 complexes of the [Co(DH)2(amine)2)]I type (DH2 stands for dimethyloxime) have been studied by means of thermogravimetry and differential scanning calorimetry in nitrogen atmosphere, by using heating rates of 2.5, 5 and 10 K min–1. In all cases an endothermal deamination reaction occurs leading to the relatively stable [Co(DH)2I(amine)] intermediate. For this reaction apparent kinetic parameters have been derived. The influence of heating rate is discussed. The validity of a linear and a non-linear kinetic compensation law was verified.
Novel methods of unified evaluation of two (or more) thermogravimetric curves have been worked out on the basis of known non-linear
parameter estimating procedures (Gauss-Newton-Marquardt-type regression and the direct integral method of Valkó and Vajda
were adapted). Their ability to provide estimate for common kinetic parameters of several TG (m−T) or DTG (dm/dt-T) curves were tested for pairs of curves of different heating rates, and for repeated curves of the same heating rate, obtained
for the decomposition of CaCO3 in open crucible. In these cases the Arrhenius terms and then-th order model functions were assumed. The fitting ability of estimations made for single curves and for pairs of curves
sharing different number of parameters, was judged on the base of residual deviations (Sres) and compared to the standard deviation of the measurements.
In the case of different heating rates, the two curves could not be described with the assumption of three common parameters,
because of the minimum residual deviation was very high. However, sharing of activation energy and preexponential term only,
and applying different exponents for the two curves, provided a satisfactory fit by our methods. Whilst in the case of repeated
curves, we could find such a common three-parameter set, which has a residual deviation comparable with the standard deviation
of the measurements.
Because of their flexibility (taking into account the variable number of common parameters and the versatile forms of model
equations), these methods seem to be promising means for unified evaluation of several related thermoanalytical curves.