Sándor Gál

Application of non-linear regression methods for the estimation of common kinetic parameters from several thermoanalytical curves

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.ZusammenfassungAuf der Basis bekannter nichtlinearer Parameter-Schätzungsverfahren (Adaption der Gauss-Newton-Marquardt-Regression und der direkten Integrationsmethode von Valkó und Vajda) wurden neue Methoden zur gemeinsamen Auswertung von zwei (oder mehr) thermogravimetrischen Kurven ausgearbeitet. Ihre Fähigkeit zur Schätzungen von gewöhnlichen kinetischen Parametern einiger TG (m-T)-oder DTG (dm/dt-T)-Kurven wurde für Kurvenpaare unterschiedlicher Aufheizgeschwindigkeit und für wiederholte Kurven bei gleicher Aufheizgeschwindigkeit an der Zersetzung von CaCO3 in einem offenen Ofen getestet. In diesen Fällen wurden Arrheniussche Ausdrücke und Modellfunktionenn-ter Ordnung vorausgesetzt. Die Fitting-Fähigkeit der Schätzungen für Einfachkurven und für Kurvenpaare mit einer unterschiedlichen Anzahl von Parametern wurde auf der Basis der residualen Deviationen (Sres) überprüft und mit der Standarddeviation der Messungen verglichen.Im Falle unterschiedlicher Aufheizgeschwindigkeiten konnten die zwei Kurven unter Annahme von drei gewöhnlichen Parametern nicht beschrieben werden, da die minimale residuale Deviation sehr hoch war. Die Anwendung von nur Aktivierungsenergie und präexponentiellem Faktor sowie von verschiedenen Exponenten für die beiden Kurven lieferte ein zufriedenstellendes Fitting unserer Methode. Dagegen konnten wir im Falle der wiederholten Kurven ein solches Tripel üblicher Parameter finden, welches eine vergleichbare residuale Deviation wie die Standarddeviation der Messungen aufweist.Aufgrund ihrer Flexibílität (unter Berücksichtigung der unterschiedlichen Anzahl gewöhnlicher Parameter und der flexiblen Form der Modellgleichungen) scheinen diese Methoden vielversprechende Mittel zur gemeinsamen Auswertung einiger verwandter thermoanalytischer Kurven zu sein.

Thermoanalytical studies on crown ether-alkali complexes

Solid samples prepared from benzo-15-crown-5, its nitro, acetylamino and decanoylamino derivatives (Group I), and chloro-dibenzo-aza-crown ethers (Group II) with alkali metal salts were studied. The existence of solid adducts between LiBr, NaSCN, KSCN and crown ethers of group I was proved by DSC. The melting points of adducts of the same ligand were found to increase in KSCN<NaSCN<LiBr order. DSC and TG results suggested a ligand scission mechanism of thermal decomposition for all the complexes except that of benzo-15-crown-5 and KSCN where a dissociation and evaporation process took place. The samples prepared from crown ethers belonging to group II were found to be mechanical mixtures of the alkali salts and crown compounds.

The effect of heat transport within the sample on the shape of thermoanalytical curves

Abstract Constant heating rate thermoanalytical curves were simulated for processes governed by a phase boundary reaction and the heat conduction inside the sample. The effects of thermal conductivity, the heat of the reaction, the sample size, etc., on the shape of the peak and on the kinetic parameters estimated without considering thermal resistance are described. Dimension analysis was applied to obtain quantitative expressions of: (a) the maximum difference between the temperature of the reacting interface and the program temperature, (b) the criteria of accurate estimation of kinetic constants without considering heat transport, on the basis of material and experimental parameters.

The application of empirical quantities describing the shape of thermoanalytical curves

Abstract Empirical parameters - related to peak position, width, sharpness and asymmetry - were used to describe the shape of thermoanalytical curves. The reproducibility of these parameters is shown on the example of Al/OH/ 3 DSC curves. A method is suggested for the estimation of kinetic parameters.

Description of the shape of thermoanalytical curves. Part 2. Simulation of Peak Shape from Kinetic equations

Abstract Differential thermoanalytical curves were simulated with the commonly used kinetic equation dα/dt = A exp (−E/RT)·(1 - α)n; noise and baseline components were added. Empirical parameters describing peak shape were calculated. Comparison of the results with those of experimental differential scanning calorimetric curves show that sufficiently different sets of the three kinetic parameters can be distinguished on the basis of peak shape. The effects of noise and baseline choice are discussed in detail.

Description of the shape of thermoanalytical curves. Part 3. A Method for estimating kinetic constants from parameters characterizing peak shape

Abstract The relationships between empirical parameters characterizing the shape of thermo-analytical curves and the constants of the kinetic equation, dα/d t = A exp (− E / RT )(1 − α) n , are studied. A procedure is developed for the estimation of the three constants of this equation from the empirical parameters. The efficiency of this method is compared to that of model fitting. In evaluation of the confidence intervals of estimated constants and in the case of identification, least-squares (or similar) fitting is shown to be inferior because of its low sensitivity to properties other than the position of the peak along the temperature axis. This lack of sensitivity may be a major cause of the apparent kinetic compensation effect often encountered in the field of thermal analysis.

Comprehensive kinetic studies on isothermal and non-isothermal reactions of some aluminium compounds

Residual differences after model fitting were investigated in both isothermal and non-isothermal kinetics in order to make numerical comparisons between several models and various parameter-estimating methods. Data from two independent experimental series were evaluated.A large data set, collected earlier under isothermal conditions from decompositions and hydrothermal reactions of aluminium hydroxides and oxides, was processed first. It showed that mechanical activation of the starting gibbsite affected reactivity of samples in several subsequent reactions for all model equations tried. The relative residual deviation concept is introduced, and statistics were applied to find a model that fits a certain reaction in most of the cases.In the second study, the sulphate decomposition step of aluminium sulphate octadecahydrate was investigated. TG curves were measured using a constant heating rate. Dynamic models were fitted by three mathematical methods, including a new general purpose one. Fitting ability of the methods with various complexity were compared on the basis of residual deviations obtained after integration of the model equations. As well as evaluating the best fit, this new parameter-estimating method provides a statistical analysis of the reliability of the whole model fitting process.ZusammenfassungFür einen numerischen Vergleich einiger Modelle und verschiedener Methoden zur Parameterschätzung wurden Restdifferenzen nach dem Modellfitting sowohl bei isothermer als auch nichtisothermer Kinetik untersucht. Daten aus zwei unabhängigen Versuchsreihen wurden ausgewertet.Zuerst wurde ein große Reihe von bereits früher, unter isothermen Bedingungen erfaßten Daten von Zersetzungs- und hydrothermischen Reaktionen von Aluminiumhydroxiden und-oxiden bearbeitet. Es zeigte sich, daß eine mechanische Aktivierung des Ausgangsmateriales Gibbsit für alle angewendeten Modellgleichungen die Aktivität der Probe in einigen Nachfolgereaktionen beeinflußte. Es wurden das Prinzip des relativen Restfehlers eingeführt und statistische Methoden eingesetzt, um ein Modell zu finden, welches im Falle einer bestimmten Reaktion für die meisten Fälle ein angemessenes Fitting bietet.In der zweiten Studie wird der Sulfatzersetzungsschritt von Aluminiumsulfat-Oktadekahydrat untersucht. Die TG-Kurven wurden bei konstanter Aufheizgeschwindigkeit erstellt. Das Fitting dynamischer Modelle erfolgte mittels dreier mathematischer Methoden. Die Fitting-Fähigkeit von Methoden verschiedener Komplexizität wurde auf der Grundlage von Restfehlern verglichen, welche man nach Integration der Modellgleichungen erhielt. Außer dem erhaltenen besten Fitting bringt diese neue Parameterschätzungsmethode eine statistische Analyse der Zuverlässigkeit des gesamten Modellfitting-Prozesses mit sich.

Dinamic mechanical analysis of paper samples

Abstract A clamping technique was worked out for dynamic mechanical analysis of thin cellulose and paper sheets. The technique has been applied in the study of original and aged papers.

A sample mounting technique for the dynaminc mechanical analysis of cellulose and paper sheets

Abstract A sample clamp assembly has been devised for the dynamic mechanical analysis of thin cellulose and paper sheets. The assembly, used with the DuPont 981 DMA, provides an arched sample cross-section to prevent buckling deformation of the sample. The applicability of this technique is demonstrated by measurements on original and thermally-aged newsprints.

Aluminum sulphate hydrates

Three different calculation methods of deriving kinetic parameters (activation energy and preexponential factor) from dynamic TG data have been applied for the sulphate decomposition stage of the aluminum sulphate octadecahydrate. The constant rate experiments were carried out by Derivatograph and DuPont thermobalances. The three parameters estimation methods included a simple differential method, the classical Coats-Redfern and a new direct integral method. The fits of the curves obtained by these procedures were compared both graphically and numerically. It was found that the direct integral method gave the most satisfactory results. With the order type reaction models this method in each case produced the smallest residual deviation values and the best fitting curves compared to those obtained by the other two methods. The activation parameters calculated by the differential method were not acceptable at all, for the estimated curves were very far from the measured ones.ZusammenfassungFür den Sulfat-Zersetzungsschritt bei Aluminiumsulfat-Oktadekahydrat wurden an den DTG-Daten drei verschiedene Rechenmethoden zur Ermittelung der kinetischen Parameter (Aktivierungsenergie, präexponentieller Faktor) angewendet. Die Versuche mit konstanter Geschwindigkeit wurden mittels Derivatograf und DuPont Thermowaagen durchgeführt. Die drei Methoden zur Schätzung der Parameter waren eine einfache Differentialmethode, die klassische Coats-Redfern-Methode und eine neue direkte Integralmethode. Die Übereinstimmung der durch diese Verfahren erhaltenen Kurven wurde sowohl graphisch als auch numerisch verglichen. Man fand, daß die direkte Integralmethode die besten Resultate lieferte. Verglichen mit den beiden anderen Methoden ergab diese Methode in allen Fällen den geringsten Nullpunktsfehler und die besten Kurvenübereinstimmungen. Die mit Hilfe der Differentialmethode berechneten Aktivierungsenergien waren vollständig unakzeptabel und lagen für die geschätzten Kurven sehr weit von den gemessenen Werten entfernt.