Tibor Dubaj

The mathematical incorrectness of the integral isoconversional methods in case of variable activation energy and the consequences

Kinetic parameters resulting from the application of isoconversional methods mostly depend on the degree of conversion. This paper shows that the integral isoconversional methods are mathematically incorrect if the activation energy depends on conversion. In this case, the incorrectness resides in improper separation of variables in the general rate equation. As a consequence, non-sensical snake-like shape of the conversion versus time curves is observed when the kinetic results are extrapolated to lower temperatures.

An incremental isoconversional method for kinetic analysis based on the orthogonal distance regression

The parameters obtained from a kinetic analysis of thermoanalytical data often exhibit a conversion‐dependent behavior. A novel incremental isoconversional method able to deal with this phenomenon is proposed. The kinetic model is directly fitted to the experimental data using nonlinear orthogonal least squares procedure. The data are processed without transformations, so their error distribution is preserved. As the objective function is based on a maximum likelihood approach, reliable uncertainties of the parameters can be estimated. In contrast to other methods, the activation energy and the pre‐exponential factor are treated as equally important kinetic parameters and are estimated simultaneously. Validity of the method is verified on simulated data, including a dataset with local nonlinearity in the temperature variation. A practical application on the nonisothermal cold crystallization of polyethylene terephthalate is presented.

Equivalence of the Arrhenius and non-Arrhenian temperature functions in the temperature range of measurement

In this paper, it is demonstrated that the Arrhenius, Harcourt–Esson and Berthelot–Hood temperature functions describe kinetic data equivalently in the temperature range of measurement. The reason for this finding resides in the fact that, in a narrow temperature range, 1/T, ln T and T are linearly related to each other. The equivalence of the temperature functions enables a recalculation of the kinetic parameters from one function to another. The equivalence holds for the incremental and differential isoconversional methods only; the integral isoconversional methods give incorrect results due to their mathematical incorrectness. It is reasoned that the temperature functions are equivalent not only in the case of the isoconversional methods but also for the model-fitting methods.

Thermooxidative stability of poppy seeds studied by non-isothermal DSC measurements

Papaver somniferum L. is an important crop cultivated mostly for seed production. Poppy seeds have a high nutritive value and are used as a food and as a source of edible oil. This oil is a rich source of polyunsaturated fatty acids. It is well known that the unsaturated fatty acids easily undergo oxidation reactions, which lead to the reduction of shelf life, nutritional quality, development of unpleasant tastes and odors. The goal of this study was to develop the methodology for testing the stability of poppy seeds using non-isothermal DSC. For the treatment of the experimental data a method based on non-Arrhenian temperature function has been applied and the values the kinetic parameters have been obtained. In order to assess the durability of the commercial poppy seeds, the lengths of induction periods have been calculated.

Imatinib mesylate cocrystals: synthesis, screening, and preliminary characterization

Drug–drug cocrystals of imatinib mesylate with several cocrystal formers, i.e. 5-chlorouracil, 5-fluorouracil, hydroxyurea, 5-fluorocytosine, N-acetylcytosine, chlorogenic acid, dacarbazine, curcumin, creatine, orotic acid, l-cysteine, glutathione, and caffeic acid, were prepared from mixtures by cogrinding or solvent cocrystallization. The samples prepared were analyzed by FTIR, DSC, and XRPD. Formation of cocrystals with different stoichiometry was observed. Novel cocrystals of imatinib mesylate with 5-fluorouracil or hydroxyurea were identified, characterized, and selected by the solid form screening approach. These cocrystals were non-hygroscopic and chemically and physically stable to thermal stress under the testing conditions.Graphical Abstract

Estimation of the curing rate of acrylamide used as a consolidant in heritage sandstone conservation

An investigation of the curing (polymerisation) rate of acrylamide was carried out using isothermal and non-isothermal DSC in order to estimate the time for complete conversion of monomer at ambient temperatures. The non-isothermal data were used to model the rate using integral isoconversional and incremental isoconversional kinetic methods. Applying the equations for integral isoconversional methods and extrapolating to ambient temperatures resulted in non-sensical conversion–time curves, where the time estimated decreased for increasing degree of conversion to be reached. This odd behaviour was attributed to the incorrectness of the integration where the kinetic parameters (e.g. the activation energy) are a function of conversion. The problem was addressed by applying incremental methods which provided more reasonable results as the integration is carried out over small conversion increments where the kinetic parameters are assumed to be constant. Estimates of the conversion were compared to isothermal measurements and, although isothermal DSC produced significant variability in the data, extrapolated estimates from non-isothermal kinetic analysis produced, at best, an upper boundary for the estimation of the time to reach a fixed degree of conversion.

Edaravone cocrystals: synthesis, screening, and preliminary characterization

Cocrystals constructed of edaravone (a neuroprotective agent) and phenolic acids (phytochemicals) are investigated. Edaravone and cocrystal formers were coground, slurried, and cocrystallized from solvent at 1:1, 2:1, and 1:2 molar ratios. The physicochemical characteristics of the products were studied using elemental analysis, optical microscopy, Fourier transform infrared spectroscopy, differential scanning calorimetry, and X-ray powder diffraction. Edaravone cocrystals were prepared at various molar ratios. For three cocrystals, i.e., edaravone:gallic acid (2:1), edaravone:protocatechuic acid (1:1), and edaravone:trimesic acid (1:1), two polymorphs have been identified. Representative samples of the cocrystals were exposed to accelerated oxidative and thermal stress to investigate their stability. From the stability screening, protocatechuic acid and gallic acid cocrystals were identified as development candidates because they provide stable cocrystal forms.Graphical abstract

Equivalence of the Arrhenius and Non-Arrhenian Temperature Functions in the Temperature Range of Measurement and Its Application in Isoconversional Kinetics

It is shown that the kinetic data can be equivalently described in the temperature range of measurement by the Arrhenius, Harcourt–Esson and Berthelot–Hood temperature functions. The reason is that, in a narrow temperature range, 1/T, ln T and T are linearly related to each other. Therefore, the kinetic parameters obtained from one function can be recalculated to the parameters from another one. This equivalence holds for the incremental and differential isoconversional methods only; due to their mathematical incorrectness, the equivalence does not take place for the integral isoconversional methods. It is reasoned that the temperature functions are equivalent not only in the case of the isoconversional methods, but also for the model-fitting methods. An incremental isoconversional method without any approximations or transformations of the experimental data and with a statistically well-grounded and physically justified objective function based on the maximum likelihood approach is mentioned.

A new phenomenon of various polarity observed in p-menthane-1,2,4-triol

A new phenomenon was observed for p-menthane-1,2,4-triol, i.e., the substance with the same molecular structure occurs in two forms with different polarity. The form with a lower polarity is eluted with ethyl acetate in column chromatography; the form with a higher polarity is eluted with methanol. The crystals isolated by ethyl acetate elution exhibit polymorphism; whereas no polymorphism was observed for the crystals isolated by methanol elution. The crystals isolated differed in melting temperature and optical rotation. The structure of p-menthane-1,2,4-triol was confirmed by two independent methods, i.e., by the single-crystal X-ray diffraction and NMR spectra.Graphical abstract.