Lumped parameter equation and thermoanalytical curves

The importance of knowing either an approximate value of the activation energy or the reaction mechanism prior to the analysis of DSC curves using the relation $ln?g(\alpha )?ln?p(x)=ln?\frac{ZE}{\beta R}$ is emphasised on the basis of the results obtained for the decomposition of sodium bicarbonate. The iteration of activation energy in the neighbourhood of an approximate value determined independent of the reaction mechanism eliminates the necessity to carry out a separate isothermal experiment to determine the reaction mechanism. A computer program suitable for the purpose is presented. Comparison of theoretical curves based on the above equation, with experimental α vs. T curves, shows good agreement for α values greater than 0.1. The conclusions, although derived from DSC curves, are general in nature since the treatment is based on α vs. T curves.     

Description of the shape of thermoanalytical curves

Empirical parameters were chosen for the characterization of peaks (or steps) of thermoanalytical curves. The parameters were applied in studies on the repeatability, the relationship between kinetic constants and peak shape, the effect of sample thermal resistance. Kinetic constants can be estimated on the basis of peak shape parameters. Besides, approximate criteria were formulated for experiments allowing kinetic evaluation with the neglect of the heat transport within the sample. The empirical parameters were also used in checking the suitability of DSC data for purity analysis and in detecting changes of the thermal decomposition of papers caused by ageing.Zur Beschreibung von Peaks bzw. Stufen thermoanalytischer Kurven wurden emperische Parameter ermittelt, die bei der Untersuchung der Reproduziertbarkeit, der Beziehung zwischen kinetischen Konstanten und Peakform so wie des Einflusses des thermischen Wiederstandes der Probe angewendet wurden. Kinetische Konstanten können auf der Basis von Peakformparametern geschÄtzt werden. Weiterhin wurden Kriterien für Experimente ermittelt, die eine kinetische NÄherungslösung unter VernachlÄssigung des WÄrmetransportes innerhalb der Probe ermöglichen. Die empirischen Parameter wurden au\erdem bei der Untersuchung der Eignung von DSC-daten zur Reinheitsanalyse angewendet, weiterhin zum Nachweis von alterungsbedingten Änderungen der thermischen Zerzetzung von Papier.

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The authors express their thanks to Mrs E. Tóth for her valuable technical help. The permission to reproduce Figs 2–6 and 8–10 from Analytica Chimica Acta and Thermochimica Acta (Elsevier, Amsterdam) is also acknowledged.     

The problems of reaction kinetics calculations based on thermoanalytical curves

The work, results and estimations are summarized which are related to reaction kinetic calculations using thermoanalytical curves. Mathematical operations applied to the calculations are studied. Calculation methods are evaluated on the basis of our test results. The effect of test conditions on reaction kinetic parameters is analysed. Calculation of half-period is also investigated in the study.     

Some demonstrations of the effect of the heating rate on thermoanalytical curves

Thermoanalytical curves of two parallel competitive reaction systems and of two systems in which two mutually independent reactions occur concurrently are made by simulation, as well as isothermal curves of the systems. From these curves, an effect of heating rate is illustratively shown; one peak is observed in a derivative thermoanalytical curve at one heating rate, while a shoulder or two peaks appear in another derivative curve of the same reaction system at another heating rate. An advantage of thermal analysis over isothermal experiments, and its limitations, are discussed.     

Kinetic evaluation of non-isothermal thermoanalytical curves in the case of independent thermal reactions

A least squares curve-fitting method was developed for the following thermo-analytical problem: “Find the kinetic parameters and the unknown initial amounts of the reactants from non-isothermal thermoanalytical curves in the case of two or more independent or quasi-independent thermal reactions”. From a numerical point of view this problem differs from the non-linear least squares techniques used in other areas of reaction kinetics. The special difficulties which have arisen in such calculations were eliminated by parameter transformations and by separating the linear and non-linear parts of the problem. The method can be applied at any T(t) functions. Thermo-analytical curves differing in temperature program can be evaluated simultaneously.     

Influence of pressure reduction on the shapes of thermoanalytical curves of red muds

The effect of reduction of pressure on the shapes of the TG, DTG and DTA curves and the mass-spectra of hydroxide and carbonate phases was investigated in some typical Hungarian red muds. The pressure change caused different decomposition rates of the phases and resulted in better separation of the overlapping thermal curves; this led to advantages as regards phase analysis. For phase analysis the red muds were extracted with water, and the extracts and solid residues were identified by IR- and X-ray methods.

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Zusammenfassung Die Wirkung der Druckänderung auf die Form der TG-, DTG- und DTA-Kurven, sowie der MS-Spektra der Hydroxid- und Carbonatphasen in einigen typischen ungarischen Rotschlamm-Sorten wurde geprüft. Die Druckänderung verursachte verschiedene Zersetzungsgeschwindigkeiten der Phasen, führte zur besseren Auftrennung der sich überlappenden thermischen Kurven, und war ausserdem auch hinsichtlich der Phasenanalyse vom Vorteil. Zur Phasenanalyse wurden die Rotschlämme mit Wasser extrahiert und die Extrakte und festen Rückstände mittels IR- und Röntgenmethoden identifiziert.

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Résumé On a étudié dans quelques espèces typiques de boues rouges de Hongrie l'effet des variations de pression sur la forme des courbes TG, TGD et ATD ainsi que les spectres de masse des phases hydroxyde et carbonate. La variation de la pression entraîne des vitesses de décomposition différentes. Il en résulte une meilleure séparation des phénomènes dans le cas où ceux-ci se chevauchent ainsi que des avantages du point de vue de l'analyse des phases. L'analyse des phases présentes dans les boues rouges a été effectuée par extraction à l'eau. Les extraits et les résidus solides ont été identifiés par spectrométrie infrarouge et par diffraction des rayons X.

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Paper presented at the Scientific Session on Thermal Analysis held at Balatonfüred, Hungary, on 14–16 October 1976.     

Utilization of the affine transformation of thermoanalytical curves for the determination of kinetic parameters

A method is suggested for the affine transformation of thermoanalytical curves, by means of which their comparison with one another becomes feasible. It is demonstrated that the results obtained by the traditional methods of non-isothermal kinetics depend on the heating rate, whereas the results attained by affine transformation are independent of the heating rate. They are consistent with the results obtained by Merzhanov's dmethod, which is also a non-aprioristic method.

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Zusammenfassung Eine Methode zur Affintransformierung thermoanalytischer Kurven wird vorgeschlagen, wodurch ihr Vergleich miteinandere rmöglicht wird. Es wird gezeigt, daß die durch traditionelle Methoden der nicht-isothermen Kinetik erhaltenen Ergebnisse von der Aufheizgeschwindigkeit abhängig sind, während die durch Affintransformierung erhaltenen von der Aufheizgeschwindigkeit unabhängig sind. Sie sind in Übereinstimmung mit den nach der Methode von Merzhanov erhaltenen Ergebnissen, die ebenfalls eine nicht-aprioristische Methode ist.

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Résumé On propose une méthode pour la transformation affine des courbes d'analyse thermique, qui permet leur comparaison. On montre que les résultats obtenus par les méthodes traditionnelles de cinétique non-isotherme dépendent de la vitesse du chauffage, tandis que les résultats obtenus par la transformation affine n'en dépendent pas. Ils sont en accord avec les résultats de la méthode de Merzhanov.

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Analysis of complex thermoanalytical curves: The thermodynamic and kinetic parameters of isopropylammonium nitrate

A method is presented to determine thermodynamic and kinetic parameters from complex thermoanalytical curves. Such curves are obtained when thermoanalytical events like phase transition and chemical decomposition overlap.Isopropylammonium nitrate was taken as an example to demonstrate how these parameters were determined from non-isothermal TG and DSC curves by constructing DSC-DTG sum curves.

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Zusammenfassung Es wird ein Verfahren zur Bestimmung thermodynamischer und kinetischer Parameter von komplexen thermoanalytischen Kurven beschrieben. Kurven dieser Art entstehen bei der Überlappung thermoanalytischer Ereignisse wie z.B. Phasenumwandlungen und chenliche Zersetzungen.Am Beispiel von Isopropylammoniumnitrat wird demonstriert, wie die einzelnen Parameter der nicht-isothermen TG und DSC Kurven durch Konstruktion von DSC-DTG-Summenkurven ermittelt werden.

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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 (S _res ) 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.     

Thermolysis under vacuum: Essential influence of the residual pressure on thermoanalytical curves and the reaction products

This paper examines the influence of residual pressures in the range from 10^–5 to 5 torr on the course of thermal analysis. With the help of examples concerning in particular the thermolysis of gibbsite, A1(OH)₃, it is shown that a) the control of residual pressure is of virtually no use unless the rate of decomposition isalso controlled (otherwise, the TG curves represent a composite phenomenon, which is practically unintelligible); b) the influence of residual pressure may be unexpectedly high both on the shape of the TG curves (and therefore on the apparent kinetic parameters) and on the nature (porosity, structure) of the products.

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Zusammenfassung Der Einfluß von Restdrücken zwischen 10^–5 und 5 torr auf thermische Zersetzungen wird geprüft. An Hand von Beispielen, insbesondere hinsichtlich der Thermolyse von Gibbsit A1(OH)₃ wird gezeigt, daß a) eine Regelung des Restdruckes nur dann von Nutzen ist, wenn auch die Zersetzungsgeschwindigkeit geregelt werden kann (ansonsten stellen die TG-Kurven ein nicht zu entzifferndes komplexes Phänomen dar) und daß b) die Wirkung des Restdruckes äußerst bedeutend sein kann, sowohl hinsichtlich der Gestalt der TG-Kurven (also der scheinbaren kinetischen Parameter), als auch der Beschaffenheit (Porosität, Struktur) des Produkts.

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Résumé On examine l'influence des pressions résiduelles comprises entre 10^–5 et 5 torrs sur le cours des décompositions thermiques. Grâce à des exemples concernant en particulier la thermolyse de la gibbsite A1(OH)₃ on montre: a) qu'un contrôle de la pression résiduelle n'est utile que si l'on peutaussi contrôler la vitesse de décomposition (sans quoi les courbes de TG représentent un phénomène composite inextricable); b) que l'effet de la pression résiduelle peut être extrêmement important, aussi bien sur la forme des courbes de TG et donc sur les paramètres cinétiques apparents) que sur la nature (porosité, structure) des produits

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Paper presented at the Scientific Session on Thermal Analysis held at Balatonfüred, Hungary, on 14–16 October 1976.     

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

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.     

Kaolinite-genetic and thermoanalytical parameters

Different genetic types of kaolinite were investigated from the point of view of crystallinity. The measurements were carried out by means of different methods of thermal analysis, infrared spectroscopy and X-ray diffraction. The different parameters of the degree of crystallinity based on a series of 85 nearly monomineralic samples were critically studied. The estimated parameters of the different methods show relatively bad correlation. The reason for the difference in the data come from the fact that the methods give information about different parts and/or features of the mineral structure. The results are better if several parameters are simultaneously used. In the present paper the results of thermal parameters are summarized.     

Advances in thermoanalytical techniques

Journal of Thermal Analysis and Calorimetry - Thermogravimetry coupled with chemometrics has proved to be a rapid and cost-effective diagnostic tool for β-thalassemia screening. This model,...     

A simple method for estimating activation energy from derivative thermoanalytical curves and its application to thermal shrinkage of polycarbonate

Activation energy can be estimated by a new simple method, in which logarithm of maximum rate of conversion observed at different heating rates is plotted against reciprocal absolute temperature, because the conversion at the maximum rate is approximately independent of the heating rate. The method is applied to thermal shrinkage of polycarbonate, and the estimated activation energy is in good agreement with those obtained by conventional methods.

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Zusammenfassung Die Schätzung der Aktivierungsenergie kann mittels einer neuen Methode erfolgen, bei welcher der Logarithmus der für verschiedene Aufheizgeschwindigkeiten gemessenen maximalen Konversionsgeschwindigkeit als Funktion der reziproken Temperatur aufgetragen wird, da die Konversion bei der maximalen Geschwindigkeit inetwa unabhängig von der Aufheizgeschwindigkeit ist. Das Verfahren wurde beim thermischen Schrumpfen von Polycarbonat angewendet und die geschätzte Aktivierungsenergie liegt in guter Übereinstimmung mit den in herkömmlichen Verfahren ermittelten Werten.

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Dedicated to Professor Dr. H. J. Seifert on the occasion of his 60^th birthday     

Quantitative parameters by thermoanalytical methods

The conditions and premises of the kinetic evaluation of thermoanalytical curves on the basis of chemical kinetics are demonstrated, and the limits of their availability are pointed out. For reactions with an unclear structural and chemical course, some appropriate definitions of terms are proposed.The possibilities of the use of the inflection points of the reaction rate versus time curve are presented. New methods of determination of kinetic parameters are described, including the ratio of the degrees of reactionx, the ratio of the reaction ratesx and the ratio of the tangent slopesx at these points.

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Zusammenfassung Bedingungen und Voraussetzungen der kinetischen Auswertung thermoanalytischer Meßkurven auf der Basis der chemischen Kinetik werden dargestellt, gleichzeitig wird auf die Grenzen ihrer Gültigkeit hingewiesen. Für Reaktionen mit unklarem chemischem oder strukturellem Ablauf werden geeignete neue Bezeichnungen definiert.Die Möglichkeit zur Verwendung der Wendepunkte der Kurve Reaktionsgeschwindigkeit gegen Zeit vorgestellt. Neue Methoden werden beschrieben, die zur Bestimmung kinetischer Parameter das Verhältnis der Umsätzex ₁ x ₂, das Verhältnis der Reaktionsgeschwindigkeitenx ₁/x ₂, und das Verhältnis der Tangentensteigungenx ₁/x ₂ an den Wendepunkten verwenden.

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Historical development of thermoanalytical methods

Thermal tests in antiquity and in the Middle Ages. Blowpipe tests. Measuring temperature and the development of thermometers. Latent heat. The nature of heat. Amount of heat. Differential thermal analysis. Differential scanning calorimetry. Heat treatment of precipitates. Thermobalances. Thermoanalytical methods associated with determination of evolved gas. Thermometry, enthalpimetry.     

A thermoanalytical assessment of an organoclay

High resolution thermogravimetric analysis (TG) has attracted much attention in the synthesis of organoclays and its applications. In this study, organoclays were synthesised through ion exchange of a single cationic surfactant for sodium ions, and characterised by methods including X-ray diffraction (XRD) and TG. The changes of surface properties in montmorillonite (MMT) and organoclays intercalated with surfactant were determined using XRD through the changes in the basal spacing. The TG was applied in this study to investigate more information of the configuration and structural changes in the organoclays with thermal decomposition. There are four different decompositions steps in differential thermogravimetric curves. The obtained TG steps are relevant to the arrangement of the surfactant molecules intercalated in MMT and the thermal analysis indicates the thermal stability of surfactant modified clays. This investigation provides new insights into the properties of organoclays and is important in the synthesis and processing of organoclays for environmental applications.