The relationship between isothermal and non-isothermal kinetics for thermoset characterization

General relationships are developed for obtaining non-isothermal (dynamic) rate equation from a knowledge of the isothermal kinetics of the system. Applications to several important specific forms of the isothermal rate expressions are given.     

Novel theoretical and computer-assisted modeling of isothermal and non-isothermal depolymerization kinetics

A novel kinetic model accounting for the observed asymptotic approach of the degree of polymerization (DP) to a limiting value significantly greater than unity on prolonged degradation is derived and applied to the solid-state degradation of cellulose (Kraft paper) and poly(acrylic acid) (PAA) under isothermal and non-isothermal conditions. Experimental data were fitted using two iterative computer algorithms: one for isothermal DP data and the other for non-isothermal DP data obtained under a linear temperature ramp. The apparent activation energy for the solid-state recombination of chain radicals was found to be low in each case and was attributed to the proximity of free radicals being facilitated by restrictions imposed by the polymer matrix. The application of the model to non-isothermal DP yielded rate parameters that could be reconciled with those obtained from isothermal analyses, suggesting the novel approach has much merit for the future study of polymer degradation.     

Rational approach to thermodynamic rrocesses and constitutive equations in isothermal and non-isothermal kinetics

Isothermal and non-isothermal kinetics are classified according to the viewpoint of rational approach. The appropriate selection of basic quantities and constitutive equations is stressed. The extensive discussion recently focused to the meaning of the partial derivatives is reinvestigated and clarified considering the origin of following equation $$\alpha = f(T,t)$$ whereα is the extent of reaction,T andt are the temperature and time respectively, andf represents a function. The meaning of partial derivatives is demonstrated in details. The disagreement sometimes claimed between the data evaluated by means of isothermal and non-isothermal kinetics is also reviewed, but no fundamental differences are established.     

Model-free method for isothermal and non-isothermal decomposition kinetics analysis of PET sample

Pyrolysis, one possible alternative to recover valuable products from waste plastics, has recently been the subject of renewed interest. In the present study, the isoconversion methods, i.e., Vyazovkin model-free approach is applied to study non-isothermal decomposition kinetics of waste PET samples using various temperature integral approximations such as Coats and Redfern, Gorbachev, and Agrawal and Sivasubramanian approximation and direct integration (recursive adaptive Simpson quadrature scheme) to analyze the decomposition kinetics.The results show that activation energy (E_α) is a weak but increasing function of conversion (α) in case of non-isothermal decomposition and strong and decreasing function of conversion in case of isothermal decomposition. This indicates possible existence of nucleation, nuclei growth and gas diffusion mechanism during non-isothermal pyrolysis and nucleation and gas diffusion mechanism during isothermal pyrolysis. Optimum E_α dependencies on α obtained for non-isothermal data showed similar nature for all the types of temperature integral approximations.     

Thermal decomposition kinetics and compatibility studies of primaquine under isothermal and non-isothermal conditions

Primaquine (PQ) is the drug of choice for the radical cure of Plasmodium vivax malaria, and currently being administered in solid dosage form. In this study, the compatibility studies were carried out using differential scanning calorimetry (DSC), thermogravimetry (TG), and fourier transformed infrared (FT-IR). Non-isothermal and isothermal methods were employed to investigate kinetic parameters under nitrogen and air atmospheres using TG. The DSC investigations obtained by physical mixtures showed slight alterations in the melting temperatures of PQ with some excipients. The FT-IR confirmed the possible interactions obtained by DSC for the physical mixtures with PQ and lactose, magnesium stearate and mannitol. The results showed that the thermal decomposition followed a zero order kinetic in both atmospheres in non-isothermal method. The activation energy in both methods using nitrogen atmosphere was similar, and in air atmosphere the activation energy decreased.     

Thermal behavior study and decomposition kinetics of salbutamol under isothermal and non-isothermal conditions

The thermal decomposition of salbutamol (β₂ — selective adrenoreceptor) was studied using differential scanning calorimetry (DSC) and thermogravimetry/derivative thermogravimetry (TG/DTG). It was observed that the commercial sample showed a different thermal profile than the standard sample caused by the presence of excipients. These compounds increase the thermal stability of the drug. Moreover, higher activation energy was calculated for the pharmaceutical sample, which was estimated by isothermal and non-isothermal methods for the first stage of the thermal decomposition process. For isothermal experiments the average values were E _act=130 kJ mol⁻¹ (for standard sample) and E _act=252 kJ mol⁻¹ (for pharmaceutical sample) in a dynamic nitrogen atmosphere (50 mL min⁻¹). For non-isothermal method, activation energy was obtained from the plot of log heating rates vs. 1/T in dynamic air atmosphere (50 mL min⁻¹). The calculated values were E _act=134 kJ mol⁻¹ (for standard sample) and E _act=139 kJ mol⁻¹ (for pharmaceutical sample).     

Morphology, isothermal and non-isothermal crystallization kinetics of poly(methylene terephthalate)

The morphology of crystals, isothermal and non-isothermal crystallization of poly(methylene terephthalate) (PMT) have been investigated by using polarized optical microscopy and differential scanning calorimeter (DSC). The POM photographs displayed only several Maltese cross at the beginning short time of crystallization indicating that some spherulites had been formed. The crystal cell belonged to the Triclinic crystal systems and the cell dimensions were calculated from the WAXD pattern. The commonly used Avrami equation and that modified by Jeziorny were used, respectively, to fit the primary stage of isothermal and non-isothermal crystallization. The Ozawa theory was also used to analyze the primary stage of non-isothermal crystallization. The Avrami exponents n were evaluated to be in the range of 2-3 for isothermal crystallization, and 3-4 for non-isothermal crystallization. The Ozawa exponents m were evaluated to be in the range of 1-3 for non-isothermal crystallization in the range of 135-155 °C. The crystallization activation energy was calculated to be −78.8 kJ/mol and −94.5 kJ/mol, respectively, for the isothermal and non-isothermal crystallization processes by the Arrhenius’ formula and the Kissinger’s methods.     

Crystallization kinetics of isotactic polypropylene nucleated with octamethylenedicarboxylic dibenzoylhydrazide under isothermal and non-isothermal conditions

Octamethylenedicarboxylic dibenzoylhydrazide (TMC-300) was used as a nucleating agent for isotactic polypropylene (iPP) for the first time. The Avrami method and the Caze method were used to analyze the isothermal and non-isothermal crystallization kinetics of iPP incorporated with TMC-300, respectively. During isothermal crystallization, the half crystallization time at 130 °C reduces from 130 s of virgin iPP to 44 s after addition of TMC-300, which reflects that TMC-300 increased the crystallization rate of iPP obviously. The crystallization activation energy decreases from 382.5 kJ mol^?1 of virgin iPP to 275.3 kJ mol^?1 of iPP/TMC-300. During non-isothermal crystallization, the crystallization peak temperature of iPP nucleated with TMC-300 was increased by 5.1 °C when compared to that of virgin iPP at the cooling rate of 20 °C min^?1, and both the reduction of half crystallization time and the increase in peak crystallization temperature also justified that the addition of TMC-300 accelerated the crystallization of iPP.

     

Kinetic compensation effect between the isothermal and non-isothermal decomposition of solids

A “true” kinetic compensation effect was established using the most appropriate kinetic functionF(α) for the non-isothermal decomposition of solids at various heating rates. It is likely that the correct kinetic mechanismF(α) is responsible for the “true” kinetic compensation effect, whereas an inappropriateF(α) would lead to “false” one. An establishment of such a “true” compensation effect between the isothermal and nonisothermal decompositions of a solid implies thatF(α) used is appropriate for both the isothermal and non-isothermal decompositions.     

Thermal behaviour, compatibility study and decomposition kinetics of glimepiride under isothermal and non-isothermal conditions

In the present work, the thermal decomposition of glimepiride (sulfonylurea hypoglycemic agent) was studied using differential scanning calorimetry (DSC) and thermogravimetry/derivative thermogravimetry (TG/DTG). Isothermal and non-isothermal methods were employed to determine kinetic data of decomposition process. The physical chemical properties and compatibilities of several commonly used pharmaceutical excipients (glycolate starch, microcrystalline cellulose, stearate, lactose and Plasdone®) with glimepiride were evaluated using thermoanalytical methods. The 1:1 physical mixtures of these excipients with glimepiride showed physical interaction of the drug with Mg stearate, lactose and Plasdone®. On the other hand, IR results did not evidence any chemical modifications. From isothermal experiments, activation energy (E _a) can be obtained from slope of lnt vs. 1/T at a constant conversion level. The average value of this energy was 123 kJ mol^–1. For non-isothermal method E _a can be obtained from plot of logarithms of heating rates, as a function of inverse of temperature, resulting a value of 157 and 150 kJ mol^–1, respectively, in air and N₂ atmosphere, from the first stage of thermal decomposition.     

Deduction of channel-length distribution from isothermal thermogravimetry

A possible deduction is proposed of channel length distribution in one-dimensional porous materials from the kinetic data obtained in isothermal thermogravimetry (TG). The method utilizes the absorption/desorption of small molecules into one-dimensional nano-channel. In the surface-controlled absorption/desorption, the second derivative with respect to time is directly proportional to the channel-length distribution function. Even in the diffusion-controlled case, the second derivative with respect to the square root of time gives rough information on the distribution function.     

Crystallisation kinetics of some archetypal ionic liquids: isothermal and non-isothermal determination of the Avrami exponent

The properties of ionic liquids give rise to applications in diverse technology areas including mechanical engineering, mining, aerospace and defence. The arbitrary physical property that defines an ionic liquid is a melting point below 100 °C, and as such, an understanding of crystallisation phenomena is extremely important. This is the first report dealing with the mechanism of crystallisation in ionic liquids. Assuming crystallisation of the ionic liquids is a thermal or mass diffusion-controlled process, the values of the isothermal Avrami exponent obtained from three different ionic liquids with three different anions and cations all indicate that growth occurs with a decreasing nucleation rate (n=1.8-2.2). For one of the ionic liquids it was possible to avoid crystallisation by fast cooling and then observe a devitrification upon heating through the glass transition. The isothermal Avrami exponent of devitrification suggested growth with an increasing nucleating rate (n=4.1), compared to a decreasing nucleation rate when crystallisation occurs on cooling from the melt (n=2.0). Two non-isothermal methods were employed to determine the Avrami exponent of devitrification. Both non-isothermal Avrami exponents were in agreement with the isothermal case (n=4.0-4.15). The applicability of JMAK theory suggests that the nucleation event in the ionic liquids selected is a random stochastic process in the volume of the material. Agreement between the isothermal and non-isothermal techniques for determining the Avrami exponent of devitrification suggests that the pre-exponential factor and the activation energy are independent of thermal history. The heating rate dependence of the glass transition enabled the calculation of the fragility index, which suggests that the ionic liquid is a "strong" glass former. This suggests that the temperature dependence of the rate constant could be close to Arrhenius, as assumed by JMAK theory. More generally, therefore, it can be concluded that there is nothing unusual about the crystallisation mechanism of the ionic liquids studied here.     

The determination of coal combustion kinetics with thermogravimetry

This investigation concerns the determination of the kinetics of coal combustion. It is not well possible to use an exact analytical formula for the rate equation. For that reason a stepwise method is proposed, giving the activation energy as function of the reaction parameter , without assumption of any specific rate equation.

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Zusammenfassung Diese Arbeit beschäftigt sich mit der Kinetik der Kohleverbrennung. Für die Reaktionsgeschwindigkeit ist es jedoch nicht möglich, eine exakte analytische Gleichung anzuwenden. Aus diesem Grunde wird ein schrittweises Vorgehen vorgeschlagen, das die Aktivierungsenergie ohne Voraussetzung jeglicher spezifischer Geschwindigkeitsgleichungen als Funktion des Reaktionsparameters liefert.

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The authors wish to thank Mr. L. J. M. van der Valk for doing a lot of the experiments and Mr J. J. B. van, Hoist for making the drawings.     

The non-linear least squares method in non-isothermal kinetics

The non-isothermal least squares method for the evaluation of the kinetics parameters was generalized to non-isothermal kinetics of heterogeneous reactions.     

Philosophy of non-isothermal kinetics

The most debatable and discrepant viewpoints of non-isothermal kinetics are discussed in the form of twelve questions and answers. The reputation of non-isothermal kinetics when carried out by thermoanalysts; the consequences of simplified concepts transferred from the kinetics of homogeneous reactions; the physical meaning of basic kinetic parameters in solid-state processes; the kinetic compensative effect and interdependence of kinetic parameters using the Arrhenius rate constant; the mutual usefulness of differential and integral methods of kinetic data evaluation; their accuracy and correctness; the reliability of DTA measurements; non-isothermal versus isothermal investigations; equilibrium and kinetic data and their mutual effect; the extended discussion initiated by MacCallum and Tanner; non-isothermal data publication policy; and finally the use of computers.

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Zusammenfassung In der Form von zwölf Fragen und Antworten werden die meist umstrittenen und auseinandergehenden Aspekte der nicht-isothermen Kinetik diskutiert. Insbesondere das Ansehen der nicht-isothermen Kinetik bei Durchführung durch Thermoanalytiker, die Konsequenzen der vereinfachten von der Kinetik homogener Reaktionen übertragenen Konzepte, die physikalische Bedeutung der kinetischen Grundparameter in Festphasenprozessen, der kinetische Kompensationseffekt und die gegenseitige Abhängigkeit der kinetischen Parameter bei Anwendung der Geschwindigkeitskonstante nach Arrhenius, die gegenseitige Nützlichkeit der Differential- und Integralmethoden der Auswertung kinetischer Daten, ihre Genauigkeit und Richtigkeit, die Zuverlässigkeit der DTA-Messungen, nichtisotherme gegenüber von isothermen Untersuchungen, Gleichgewichts- und kinetische Daten und ihre gegenseitige Wirkung, die Ausbreitung der von MacCallum und Tanner initierten Diskussion Politik der Veröffentlichung nicht-isothermer Angaben und, endlich, Einsatz und Hilfeleistung der Computer.

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Résumé Les aspects les plus discutables de la cinétique non-isotherme sont traités sous forme de douze questions et réponses, en particulier: réputation de la cinétique non-isotherme appliquée par les thermoanalystes, conséquences des concepts simplifiés déduits de la cinétique des réactions en phase homogène, signification physique des paramètres cinétiques fondamentaux dans les processus en phase solide, effet de compensation cinétique et interdépendance des paramètres cinétiques lors de l'utilisation de la constante de vitesse d'Arrhenius, utilité mutuelle des méthodes différentielles et intégrales d'évaluation des données cinétiques, leur exactitude et leur degré de justesse, fiabilité des mesures par ATD, études non-isothermes vis-à-vis des méthodes isothermes, données à l'équilibre et en régime dynamique et leurs effets mutuels, extension de la discussion engagée par MacCallum et Tanner, politique de publication des données non-isothermes et finalement utilisation des ordinateurs et aide apportée par ceux-ci.

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Vaporation characteristics of low-melting nitrocompounds by isothermal thermogravimetry

Determination of vapor pressure is critical for accurate detection of trace volatile hazardous materials, ensuring human health and environmental security. 2,4,6-Trinitrotoluene (TNT), 3,4-Dinitrofurazanfuroxan (DNTF), and 2,4-Dinitroanisole (DNAN) are an important class of volatile low-melting nitrocompounds which are widely used in military, aerospace, and defense industry. In this study, the sublimation and evaporation characteristics of these three nitrocompounds were investigated for the first time by using isothermal thermogravimetry (TG) undergoing zero order, non-activated evaporation processes, analyzed with the Antoine and Langmuir equations, and confirmed with benzoic acid as a calibration material. The Clausius–Clapeyron equations of TNT, DNTF, and DNAN at both sublimation and evaporation processes are established using the temperature dependence of vapor pressure. The enthalpies of sublimation and evaporation are determined. The results of TNT are well consistent with literatures, proving that the isothermal TG for determination of vapor pressure is eligible and accurate. This work lays the foundation for further study of the reliable trace detection of hazardous low-melting nitrocompounds.