Kinetic analysis of transient permeation curves

The kinetic analysis of transient permeation curves on a systematic basis is suggested as a method for the study of non-ideal membrane—penetrant diffusion systems, analogous and complementary to the method of time-lag analysis which we have previously developed. Experimental data on N₂ or propane permeating through porous graphite pellets of varying non-homogeneity are reported and used for a preliminary application of these ideas. Previous work on early-time permeation kinetics is considerably extended here and late-time permeation kinetics is considered for the first time. The results obtained show that the proposed method promises to play an important role in the study of non-ideal diffusion systems, when an adequate theoretical background has been built up.     

Kinetic applications of thermal analysis

A study was undertaken to compare two computational methods of estimating kinetic parameters from thermoanalytical experiments. Examples illustrating the relationship between reaction complexity and validity of isothermalvs. non-isothermal kinetic analyses will be presented. Thermal decomposition of several compounds was studied both by isothermal and dynamic thermogravimetry (TG). For the isothermal runs, reaction order and activation energy were estimated using established methods. For the dynamic runs, the statistical method of nonlinear least squares was used to estimate all three kinetic parameters of the nth order decomposition reaction and their individual 95% confidence intervals. Both methods assumed Arrhenius temperature dependence.

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Zusammenfassung Es wurde eine Untersuchung zum Vergleich von zwei Methoden zur Berechnung von kinetischen Parametern aus Ergebnissen thermoanalytischer Experimente unternommen. Beispiele werden angegeben, die die Beziehung zwischen isothermer und nichtisothermer kinetischer Analyse in Bezug auf Komplexizität der Reaktion und Gültigkeit illustrieren. Die thermische Zersetzung verschiedener Verbindungen wurde mittels isothermer und dynamischer Thermogravimetrie (TG) untersucht. Aus den isothermen Versuchsergebnissen wurden die Reaktionsordnung und Aktivierungsenergie nach den üblichen Methoden bestimmt. Aus den dynamischen Versuchsdaten wurden alle drei kinetischen Parameter der Reaktion n-ter Ordnung und deren individuelle 95%-Konfidenzintervalle nach der Methode der kleinsten Fehlerquadrate ermittelt. Beide Methoden setzen eine Temperaturabhängigkeit entsprechend der Arrhenius-Gleichung voraus.

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, . , . , . . n- 95% . .

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Presented at the 13th North American Thermal Analysis Society Conference, Philadelphia, PA 23–26 September 1984.     

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.     

Kinetic analysis of thermal decomposition reactions

The effect of⁶⁰C0-gamma radiation on the kinetic parameters of the thermal decomposition of potassium bromate crystals has been investigated. Radiation did not modify the mechanism of thermal decomposition reaction, but resulted in a decrease in activation energy and frequency factor with a rate which is large at small doses and decreases at higher doses. The results showed that the increase in the concentration of decomposition nuclei tends to be more important than the increase in the porous character of the solid.     

Kinetic analysis of thermal decomposition of magnesite

The excess enthalpy of magnesite accumulated by vibration grinding at low specific grinding energy consumption is due predominantly to an increase in specific surface area; at higher energy supply, it is caused by changes in the X-ray amorphous phase content, and when the supplied energy exceeds ca 2000 kJ kg^–1 it is a result of the generation of other kinds of defects. The generated defects are relatively stable below 800 K and are the reason for a broad range of distribution of local molar Gibbs energies. Thus, at low temperatures only the active portion of samples is able to decompose. Defects relax above ca 800 K, with rates comparable with the rate of decomposition itself. Accordingly, the efficiency of mechanical activation is impressive only below this temperature.Dedicated to Dr. Robert Mackenzie on the occasion of his 75th birthday     

Kinetic analysis of reversible thermal decomposition of solids

The isoconversional method was used to elucidate the kinetics of reversible solid-state reactions occurring under nonisothermal linear heating. The characteristic dependencies of the effective activation energy (E) on the extent of conversion (W) were established for two model processes: a reversible first-order reaction and a reversible reaction followed by an irreversible one. For the first process, E is almost independent of W and varies between the activation energy of the direct and inverse reaction. For the second, process with an endothermic reversible step, the dependence of E on W is of decreasing shape. The effective activation energy is limited by the sum of the activation energy of the irreversible reaction and the enthalpy of the reversible reaction, at low conversions, and by the activation energy of the irreversible reaction at high conversions. Analyses of the kinetic data for the dehydration of crystalhydrates, as well as other processes proceeding through a reversible step, show the dependencies of E on W characteristic of a reversible reaction followed by an irreversible one. © 1995 John Wiley & Sons, Inc.     

Kinetic analysis of cis-trans thermal isomerization of polyacetylene

A single broad exothermic peak due to cis-trans isomerization appears near 140°C in the differential scanning calorimetry (DSC) curve of polyacetylene (PA) films, polymerized by a nonsolvent method using a high-temperature-aged catalyst. This exothermic peakis described by a two-state model, in which population probabilities for cis and trans states are assumed to change through the forward and backward reactions. The enthalpy difference between the two states is 1.69 kcal/mol, which was derived from the slope of the plot of heat of isomerization versus cis content. The activation energy was determined experimentally from the heating-rate dependence of the peak temperature. A single activated process with an activation energy of 28 kcal/mol was observed for the PA film. Other parameters such as the preexponential factor were estimated by comparing theoretical and experimental DSC curves.     

Kinetic phenomena in non-crystalline materials studied by thermal analysis

The structural relaxation and viscosity behavior of Ge₃₈S₆₂ glass has been studied by thermomechanical analysis. The relaxation response to any thermal history is well described by the Tool-Naraynaswamy-Moynihan model. The apparent activation energy of structural relaxation is very close to the activation energy of viscous flow (Eη=478±12 kJ mol^-1). However, the activation energy of crystal growth obtained by optical microscopy is about one half of this value. Similar result has been obtained from isothermal DSC measurement (Ea=220±20 kJ mol^-1). The kinetic analysis of these data reveals interface controlled crystal growth with zero nucleation rate. This revised version was published online in July 2006 with corrections to the Cover Date.     

Estimation of activation energies from differential thermal analysis curves

An average activation energy ΔE3 of 31.7 ± 10.0 kcal/mole was calculated from exothermic peaks of urea nitrate differential thermal analysis (DTA) curves using the Murray and White equation and various other reaction rate equations developed by the authors. An average enthalpy of activation, ΔH3 of 30.8 ±9.7 kcal/mole was calculated from the same results. The values of ΔE3 and ΔH3 differed by a fraction of a kcal/mole indicating that ΔE3 <ΔH3 cannot be differentiated experimentally in our study. Application of the Kissinger method of calculating ΔE3 and ΔH3 produced respectively 21.6 ±7.9 and 20.7 ±8.0 kcal/mole, which are quite low. The values of ΔE3 and ΔH3 calculated thermogravimetrically were 28.1, ± 1.1 kcal/mole and 27.6 ± 1.2 kcal/mole which are close to those obtained from the Murray and White approach and the authors' approach to treatment of the DTA data. These results illustrate the pronounced effect of self heating on calculation of activation energies. The Kissinger method of calculating the reaction order developed for endothermic DTA peaks produced good results when applied to the present DTA study.     

Kinetic parameters from thermogravimetric curves

A novel procedure is presented for the evaluation of kinetic parameters, activation energy (E) and reaction order (n), from thermogravimetric (TG) traces. From given values of conversion (α) and corresponding temperatures (T) are calculated values of E corresponding to various arbitrary values of n. Then, the resulting arbitrary E-values may be plotted against respective n-values and the region bounded by intersecting curves used to simultaneously estimate E and n. This procedure was tested against theoretical data, teflon, sodium bicarbonate, and magnesium hydroxide, and was found to be satisfactory. Some advantages of this method are: it is relatively simple to use; it allows the user to readily discern whether the data are homogeneous and, if not, at what conversions the data deviate. A less sensitive ancillary procedure is also described which can dispense with plotting in the estimation of E and n.     

Kinetic parameters of different asphalt binders by thermal analysis

Each year, 100 millions tons of asphalt are manufactured worldwide and 88% of them are designated to act as binder in mineral aggregate producing asphalt mixtures in the paving industry. The present study investigates the kinetics parameters of thermal degradation through thermal analysis behavior of three different asphalt binders’ samples: an asphalt cement C and two asphalt binders modified by polymers: copolymer styrene–butadiene–styrene S and polyphosphoric acid L. By Thermokinetics software a model-free kinetic analysis could be made using two models: Friedman and Ozawa–Flynn–Wall. Kinetic parameters following both models, through Thermogravimetric curves, showed that for the first step, the binder L presented the highest activation energy followed by binder S. Between all simulations, the FnF1 model was the one which best correspond to the experimental data for all samples.     

Kinetic study of heavy crude oils by thermal analysis

The present work investigates the thermal behavior and kinetic of four types of petroleum samples: a medium crude oil—P1, one heavy oil—P2, and two extra heavy oils—P3 and P4 by TG, DTG, and DSC methods. Thus, this study may contribute to the characterization of petroleum with different °API values.     

Determining crystal growth rate-type of curves in glasses by differential thermal analysis

A crystal growth rate vs. temperature (U vs. T)-type of curve for a Li₂O.2SiO₂ glass was determined up to a temperature of 690 °C using a differential thermal analysis (DTA) method. As determined from this (U vs. T)-type of curve, the temperature corresponding to the onset of crystal growth was 570±3 °C which is in excellent agreement with the same value determined by the conventional method. The complete range of temperature where crystal growth can occur and the temperature (T_max) where the crystal growth rate is a maximum for this glass could not be determined. It is concluded that for temperatures <T_max, the DTA method can delineate only a small, initial portion of the (U vs. T)-type of curve, where the crystal growth rate is sufficiently low so that the glass does not totally crystallize after the required (for at least 5 min) isothermal heat treatment at these temperatures. For temperatures >T_max, the curve cannot be determined by the DTA method if the temperature for isothermal heat treatment is approached by heating the glass from room temperature. For determining the curve for temperatures >T_max, the desired temperature (>T_max) for isothermal heat treatment of the glass is suggested to be approached from the melting temperature of the glass.     

Kinetic study of the thermal decomposition of poly(vinyl alcohol)/kraft lignin derivative blends

A kraft lignin derivative (KLD) obtained by reaction with p-aminobenzoic acid/phthalic anhydride, was blended with poly(vinyl alcohol) (PVA) by solution casting from DMSO. PVA and PVA/KLD films were exposed to ultraviolet radiation (Hg lamp, 96 h) and analyzed by thermogravimetry (TG) in inert and oxidative atmosphere. Typical multi-step decomposition profiles were obtained. The apparent activation energy (E_a) of the thermal degradation of the samples was computed by the Vyazovkin method. The KLD degradation presented only small intervals of decomposition degree with constant E_a values. PVA and blends showed intervals of up to 50% in decomposition degree with nearly constant E_a, and smaller intervals in which E_a varies drastically. The influences of samples irradiation and of surrounding gas in TG analysis on E_a are also shown.     

Kinetic analysis of the thermal oxidative degradation of upper peat

Differential thermogravimetric analysis was used to study the thermal oxidative degradation of peat samples from different districts of the Ivanovo Region. The study was performed in nonisothermic conditions. It was found that the thermal oxidative processes involve a few steps. Kinetic characteristics [activation energy (E_a), preexponential factor (ln A), and reaction order (n)] were estimated for each step. It was found that the limiting stage of the entire process is a chemical reaction. The resulting data can be used to develop prognostic models for peatbog combustion.     

Determination of standard enthalpy of vaporization and thermal decomposition reactions from derivative thermogravimetric (DTG) curves

The paper proposes the use of the derivative thermogravimetric (DTG) curve for the acquisition of equilibrium vapor pressure and dissociation pressure for the materials and derivation of their standard enthalpy of formation from single DTG curve recorded under optimum experimental conditions, such as heating rate and the sweep rate of the carrier gas passed over the sample. The vapor pressure and the standard enthalpy of sublimation (Δ_subH ° _298.15) of CdI₂ and the dissociation pressure and the standard enthalpy of formation of CaCO₃ derived from their DTG curves are found to be in good agreement with the best assessed values reported in the literature.     

Kinetic investigation on alcoholysis of triethylaluminium by differential thermal analysis

The alcoholysis of triethylaluminium can be investigated by DTA in the liquid phase. The reaction enthalpy of the alcoholysis with primary alcohols is from –150 to –170 kJ mole^–1 in tetrahydrofuran/toluene as solvent. The reaction rate in pure hydrocarbons is higher than in the presence of Lewis bases. The reaction mechanism is probably ofS _E2 type and the reactivity decreases in the sequence primary, secondary, tertiary alcohol. In the second step of substitution the diethylaluminium alkoxides are less reactive than triethylaluminium because of the stronger association of the alkoxides. For the turnover of two moles of alcohol with one mole of triehylaluminium two DTA peaks appear in accordance with consecutive reactions.

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Zusammenfassung Die Reaktion zwischen einer Lösung von Alumimumtriethyl und einer Reihe von aliphatischen oder aromatischen Alkoholen kann mittels DTA quantitativ verfolgt werden. Die negative Reaktionsenthalpie der Alkoholyse mit primären Alkoholen beträgt 150 bis 170 kJ mol^–1, sofern ein Lösungsmittelgemisch aus Tetrahydrofuran/Toluen eingesetzt wird. Die Reaktionsgeschwindigkeit in unpolaren Kohlenwasserstoffen ist grösser als in Gegenwart von Lewis-Basen. Wahrscheinlich ist der Reaktionsmechanismus vom TypS _E2, wobei die Reaktivität in der Folge primäre, sekundäre, tertiäre Alkohole fällt. Der zweite Schritt der Alkoholyse, ausgehend vom Diethylaluminiumalkoxid, ist wegen der starken Selbstassoziation weniger reaktiv. Bei Umsatz von 2 Mol Alkohol treten entsprechend der Folgereaktion zwei DTA-Peaks auf.

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. –150 –170 ^–1 - . , . , S _E2 , , . , , . -, .