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Non-isothermal thermogravimetry of polymer

I. General model involving formal termination of active centres

Journal of Thermal Analysis and Calorimetry
Authors: J. Rychlý and L. Rychlá

A Model of polymer decomposition is proposed which formally involves the termination of active centres. It yields reasonable activation energies for the decompositions of polypropylene, polyethylene, polystyrene and polymethyl methacrylate investigated by non-isothermal thermogravimetry. In the value of a formal reaction orders the model reflects the reaction conditions, such as initial sample weight, atmosphere, ventilation conditions, sample holder nature and shape, etc.

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Abstract  

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.

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The pyrolysis of a suite of brown coal samples and bituminous coal maceral concentrates is investigated by non-isothermal thermogravimetry. The TG data for these coals reveal a two-stage pyrolysis process. The activation energy for the primary pyrolysis stage is considerably higher than that for the secondary pyrolysis stage. It is evident that a particular coal may be characterised by the weighted mean apparent pyrolysis activation energy which correlates with the corresponding specific energy of the coal.

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Abstract  

Dependence of kinetic parameters (activation energy and pre-exponential factor) and procedural factors (sample mass and heating rate) independent of the reversibility and the type of reactions in non-isothermal thermogravimetry have been established. Tris(ethylenediamine)nickel(II) oxalate dihydrate has been selected as a model complex and experiments were carried out at different heating rates and sample masses to study the dependence quantitatively. The kinetic parameters calculated using mechanistic and non-mechanistic equations show a systematic decrease with increase in either sample mass or heating rate for the dehydration and deamination reactions. For the decomposition reaction, the kinetic parameters are not influenced by the procedural factors. Mathematical correlations of high reliability are established between kinetic parameters and heating rate/sample mass using both mechanistic and non-mechanistic equations for dehydration and deamination reactions. The quantification follows an exponential decay of second order relation with respect to heating rate and a sigmoidal relation with regard to sample mass for both the dehydration and deamination reactions. No quantitative correlation is possible for the final decomposition stage. Thus, it is found that independent of the type of reaction (deamination or dehydration) the kinetic parameters have a particular dependence on the procedural variables. The equations for exponential decay and sigmoidal dependence can be represented as
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$y = y_{0} + A_{1} {\text{e}}^{{ - x/t_{1} }} + A_{2} {\text{e}}^{{ - x/t_{2} }}$$ \end{document}
and
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$y = {\frac{{A_{1} - A_{2} }}{{1 + {\text{e}}^{{(x - x_{0} )/{\text{d}}x}} }}} + A_{2}$$ \end{document}
respectively, where y represents kinetic parameters (E or A) and x represents the procedural variables (φ or m). Mechanism of the dehydration reaction is found to be random nucleation with the formation of one nucleus on each particle and the deamination is a phase boundary reaction. It is observed that the mechanism of these reversible reactions is not affected by the variation in sample mass and heating rate.
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Abstract  

Thermal decomposition of BaC2O40.5H2O in air was studied by a combination of stepwise isothermal analysis (SIA) and non-isothermal thermogravimetry. The results from both techniques show that the crystal water is released in one step and that anhydrous barium oxalate is decomposed in one step, while BaCO3 decomposes in three steps to BaO, forming two intermediate compounds with the formulas of BaCO3(BaO)2 and (BaCO3)0.5(BaO)2.5. Reaction mechanism analyses using the data from SIA measurements show that the controlling mechanism for all the five decomposition steps in isothermal conditions is a two-dimensional phase-boundary controlled process. Kinetic parameters are obtained for the five decomposition steps from the non-isothermal thermogravimetric data.

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Abstract  

Dynamic mechanical thermal analysis and isothermal thermogravimetry yield useful information on the temperature dependence of the mechanical properties and thermal stability of silicone rubbers. In the thermal mechanical relaxation spectra, only one characteristic phenomenon may be observed. Isothermal thermogravimetry reveals that the thermal degradation is a first-order reaction. The experimental results provide a possibility for the calculation of overall (apparent) reaction rate constants characteristic of the thermal decomposition process, and for the calculation of half-time values.

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Abstract  

Procedures for measuring sublimation rates of pharmaceutical compounds by isothermal thermogravimetry are discussed. Experimental data was obtained using the Mettler TA4000 thermogravimetric system. The sublimation rate is measured directly from the mean weight loss per unit time in the linear region of the monitored TG profile at a set isothermal temperature. This data when fitted to the Arrhenius equation yields the sublimation enthalpy. For the benzoic acid reference, the enthalpy so calculated is 99% of the value obtained from direct vacuum TG measurements. Thermal degradation in the solid state or pre-melting can effect a departure from the characteristic linear mass loss-time sublimative profile. Data pertaining to several established Merck drugs is discussed. Examples where loss of residual solvent, onset of thermal degradation and pre-melting phenomena affect the measurement, are presented.

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Abstract  

The standard sublimation enthalpies of (2,4,5-trichlorophenoxy)acetonitrile and (2,4,5-trichlorophenoxy)aniline were determined by isothermal thermogravimetry using the Langmuir equation and by non-isothermal differential scanning calorimetry for comparison. The used procedure was previously tested using three reference compounds: benzoic acid, succinic acid and salicylic acid. The results compared to those reported in literature show an excellent agreement for two of the three compounds while the third agrees quite well. For (2,4,5-trichlorophenoxy)acetonitrile and (2,4,5-trichlorophenoxy)aniline, the extrapolation of data at 298.15 K were obtained, respectively: Δsub H(298 K)={(1064) and (1014)} kJ mol–1. From Clausius Clapeyron equation obtained after the determination of the vaporization constant α′, the following standard sublimation entropies for (2,4,5-trichlorophenoxy)acetonitrile and (2,4,5-trichlorophenoxy)aniline equal to Δsub S(298 K)=(251 and 237) J K–1 mol–1, respectively, were derived, with an error of 4 J K–1 mol–1 equal for the studied herbicides.

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Abstract  

Residual carbons from kerogen extracted from two Moroccan oil shales (from Timahdit and Tarfaya) were oxidized in air. The oxidations were studied by isothermal thermogravimetry. Several kinetic models for mechanisms of the reactions were tested to fit the experimental data. Oxidation of the residual carbon derived from Timahdit oil shale followed a two-third order reaction with an activation energy of 58.5 kJ mol–1, whilst that from Tarfaya oil shale was a half order reaction with activation energy of 64.1 kJ mol–1.

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Journal of Thermal Analysis and Calorimetry
Authors: F. S. M. Sinfrônio, J. C. O. Santos, L. G. Pereira, A. G. Souza, M. M. Conceiçăo, V. J. Fernandes Jr., and V. M. Fonseca
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