In order to identify the kinetic process of self-heating in DSC experiment for Ti+3Al→TiAl3 reaction, two approaches, linear-fitting approach developed from Semenov"s theory of spontaneous ignition and variation of
Friedman method, were carried out with cylindrical Ti-75 at% Al samples. Following these approaches, two identical activation
energies are obtained as 16915 kJ mol-1 and 1705 kJ mol-1, respectively. Compared with the activation energies of reactions and interdiffusions between Ti and Al, the possible rate-controlling
process of self-heating in DSC experiment for Ti+3Al→TiAl3 reaction is the interdiffusion between Ti and Al through TiAl3-layer.
The activation energies of the same process are often reported to have different values, which are usually explained by the
differences in experimental conditions and sample characteristics. In addition to this type of uncertainty, which is associated
with the process (ΔEprocess) there is an uncertainty related to the method of computation of the activation energy (ΔEmethod). For a method that uses fitting single heating rate data to various reaction models, the value of ΔEmethod) method is large enough to explain significant differences in the reported values of the activation energy. This uncertainty
is significantly reduced by using multiple heating rate isoconversional methods, which may be recommended for obtaining reference
values for the activation energy.
Activation energy is calculated from a single curve of a derivative of mass loss perturbed by a sinusoidal modulation of a
temperature-time relationship. The method is based on a prediction of a hypothetical derivative of mass loss that corresponds
to the absence of this modulation (perturbation). Simple considerations show that the unperturbed derivative coincides with
the modulated derivative at inflection points of the modulated temperature-time relationship. The ratio of the perturbed and
unperturbed derivatives at the points of time corresponding to maxima and minima of the sinusoidal component of the modulated
temperature immediately leads to activation energy. Accuracy of the method grows with decreasing in the amplitude of the modulation.
All illustrations are prepared numerically. It makes possible to objectively test the method and to investigate its errors.
Two-stage decomposition kinetics with two independent (parallel) reactions is considered as an example. The kinetic parameters
are chosen so that the derivative of mass loss would represent two overlapping peaks. The errors are introduced into the modulated
derivative by the random-number generator with the normal distribution. Standard deviation for the random allocation of errors
is selected with respect to maximum of the derivative. If the maximum of the derivative is observed within the region from
200 to 600C and the amplitude of the temperature modulation is equal to 5C, the error in the derivative 0.5% leads to the
error in activation energy being equal to 2-6 kJ mol-1. As the derivative vanishes, the error grows and tends to infinity in the regions of the start and end of decomposition.
With the absolute error 0.5% evaluations of activation energy are impossible beyond the region from 5 to 95% of mass loss.
Recently, model free kinetic analysis of sinusoidal modulated TG-curves has been presented. In this contribution we compare
the activation energies resulting from model free analysis of modulated TG-curves and from Vyazovkin's model free kinetic
analysis of non-modulated TG-curves. We used polytetrafluorethylene and manganese oxide as samples. As a result we find, that
both methods deliver similar activation energies for polytetrafluorethylene. However, the activation energies of manganese
oxide deviate substantially.
The main purpose of kinetic analysis is its potential for predictions of the temporal behavior of materials under certain
thermal conditions. Analysis of modulated TG-curves allows a model free determination of the temperature dependence of the
activation energy. However, in order to make predictions, one still has to rely on kinetic models such as e.g. first order
kinetics. This is in contrast to Vyazovkin's approach, which allows a model free description of kinetic processes in terms
of a conversion dependent activation energy. This function can then be used to make kinetic predictions without any further
assumptions with respect to reaction models. In this paper we further discuss this fundamental difference.
The activation energy associated with the glass transition relaxation of an epoxy system has been determined by using the
three-point bending clamp provided in the recently introduced TA Instruments DMA 2980 dynamic mechanical analyzer. A mathematical
expression showing the dependency of modulus measurements on the sample properties and test conditions has also been derived.
The experimental results showed that the evaluation of activation energy is affected by the heating rate and test frequency,
as well as the criterion by which the glass transition temperature (Tg) is established. It has been found that the activation energy based on the loss tangent (tanδ) peak is more reliable than
on the loss modulus (E2) peak, as long as the dynamic test conditions do not cause excessive thermal lags.
Recently, Órfão obtained two simple equations for the estimation of the relative error in the activation energy calculated
by the integral methods . In this short communication, the validity of the equations has been evaluated by comparing the
results calculated by the equations with the results calculated by the equation from theoretical derivation without introducing
From the peak reaction temperatures as a function of heating rate, the activation energies were obtained for a system consisting of an epoxy resin (Badgen=0) and a curing agent (isophorone diamine), using a Perkin Elmer DSC7 operated in the dynamic mode. At the same time, the Arrhenius law was used to calculate rate constants.
A differential isoconversional non-linear procedure for evaluating activation energy from non-isothermal data is suggested.
This procedure was applied to model reactions (simulations) and to the dehydration of CaC2O4⋅H2O. The results were compared with those obtained by other isoconversional methods.
The differential and integral isoconversional methods for evaluation the activation energy, described in the first note of
this series, were applied for:
a) simulated data for two successive reactions;
b) dehydration of calcium oxalate monohydrate.
It was shown that for these systems the activation energy depends on the conversion degree as well as on the method of evaluation.
The results of determination of activation energies (EA) of polymeric cable insulations obtained by conventional methods (usually based on the evaluation of changes of mechanical
properties of insulations after their ageing in thermal chamber at different temperatures) have been compared with results
obtained by methods employing the differential scanning calorimetry (DSC). Three DSC methods have been tested: the method
according the ASTM E 698; measuring of DSC characteristics in the isothermal mode at several different temperatures; and the
method based on evaluation of DSC characteristics of insulations after their thermal ageing in thermal chamber. The last method
— which can be called as a modified conventional method, because instead of mechanical properties, the DSC characteristics
are determined — has been found as most acceptable and giving similar values of EA as the other conventional methods.