Evaluating the logistic mixture model on real and simulated TG curves

The aim of this paper is to evaluate and explain the fitting of dynamic TG curves by a mixture of logistic functions. This model assumes that more than one physical process may be involved in each mass loss step and that each physical process may extend along all the experiment. One of the main sources of difficulties in TG is that, very often, different stages of decomposition substantially overlap each other. Several real and simulated TG curves were analysed in this paper. An optimal fitting of the TG curves was obtained by a mixture of logistics. In many cases the optimal fitting reproduces accurately the TG curve. Accordingly, the TG curve can be understood as a sum of parallel reactions, where each single reaction is represented by one or a small number of logistic components. Additionally, making use of the analytical derivative of the fitting, a mixture of Arrhenius reaction order equations was applied to the same curves. In all the cases, the fitting obtained with the mixture of Arrhenius was worse than the obtained with the mixture of logistics. A software was developed to automatically perform these tasks. The physical meaning of the fitting was explained.     

Simulation study for generalized logistic function in thermal data modeling

The principal aim of the present study is to describe, analyze, and compare from a statistical standpoint the generalized logistic model with some well-known models used in the solid-state kinetics: power law, Avrami–Erofeev, and reaction order. For this purpose, synthetic conversion curves that simulate the kinetic processes were generated using the power law, Avrami–Erofeev, and reaction order models, where the Arrhenius equation was assumed in all the cases. This comprehensive simulation study allows to describe the relationship between the parameters belonging to the proposed generalized logistic model and the pointed traditional models’ parameters, and also to validate the performance of the generalized logistic model in a wide variety of cases where other methods can be applied. Performing this analysis has been necessary to employ some new statistical techniques in thermal analysis modeling as the generalized additive models, and to perform global optimization evolutionary algorithms as the differential evolution for solving the non-linear regression problem. In order to implement these techniques, R statistical software routines were developed and applied.     

聚芳醚醚酮的热老化寿命研究

本工作用热重法(TG)研究了聚芳醚醚酮(PEEK)在空气和氮气中的热分解反应过程;确定了PEEK在这两种气氛中的热分解反应模型均符合无规引发断裂模型;在空气中PEEK的热分解显示两个过程,由此计算其在空气中第一阶段的热分解和氮气中的热分解反应活化能分别为214.7kJ/mol和232.2kJ/mol;由热分解反应动力学参数推算出热老化寿命曲线,并讨论了实验条件对结果的影响,进而以失重5%作为材料寿终指标估算出PEEK在氮气和空气中使用10年的最高温度分别为307℃和274℃。     

Genetic algorithms based on wavelet transform for resolving simulated overlapped spectra

Wavelet transform-based genetic algorithms are proposed for resolving simulated overlapped spectra. Wavelet transform as a derivative method is used for de-noising, for deducting background absorption as well as for peak finding in order to get an estimation of parameters of unresolved spectra. Then genetic algorithms, using the estimations of parameters as input values, are employed to resolve unresolved bands. As a consequence, a good optimized solution was achieved since the reliable estimation of initial values can greatly facilitate the convergence of genetic algorithms and the calculation time is shortened accordingly.     

Kinetics of the complex process of thermo-oxidative degradation of poly(vinyl alcohol)

The thermo-oxidative degradation of poly(vinyl alcohol) (PVA) has been investigated by TG+DTG+DTA simultaneous analysis performed in static air atmosphere, at four heating rates, namely 3, 5, 10 and 15 K min⁻¹. TG, DTG and DTA curves showed that, in the temperature range 25–700°C, four successive processes occur. The first process consisting in the loss of physical adsorbed water is followed by three processes of thermal and/or thermo-oxidative degradations. The processing of the non-isothermal data corresponding to the second process (the first process of thermo-oxidation) was performed by using Netzsch Thermokinetics — A Software Module for Kinetic Analysis. The dependence of the activation energy evaluated by Friedman’s isoconversional method on the conversion degree shows that the investigated process is complex one. The mechanism of this process and the corresponding kinetic parameters were determined by Multivariate Non-linear Regression Program and checked for quasi-isothermal experimental data. It was pointed out that the first process of thermo-oxidation of PVA consists in three consecutive steps having Avrami-Erofeev kinetic model. The obtained results can be used for prediction of the thermal lifetime of PVA corresponding to a certain temperature of use and an endpoint criterion.     

Thermal behavior of Cd<Superscript>2+</Superscript> and Co<Superscript>2+</Superscript> phenyl-vinyl-phosphonates under non-isothermal condition

The thermal behavior of Cd²⁺ and Co²⁺ phenyl-vinyl-phosphonates was studied using two different experimental strategies: the coupled TG-EGA (FTIR) technique by decomposition in nitrogen respectively air, and the kinetic analysis of TG data obtained in dynamic air atmosphere at four heating rates. In nitrogen two decomposition steps were observed: the loss of crystallization water, respectively the decomposition of the phenyl-vinyl radical. In air, the same dehydration was observed as the first step, but the second one is a thermooxidation of the organic radical with formation of the pyrophosphoric anion. The kinetic analysis of the TG non-isothermal data was performed by the isoconversional methods suggested by Friedman and Flynn, Wall and Ozawa, as well as by the non-parametric (Sempere-Nomen) method. All processes put in evidence in TG curves exhibit strong changes of the activation energy values with the conversion degree, which mean that these processes are complex ones. Assuming that each of these processes consists in two steps, the application of non-parametric method leads to average values of the activation energy close to the average values of this parameter obtained by isoconversional methods.     

Thermal characterization of ammonium alum

Thermal decomposition of ammonium alum was studied by simultaneous thermogravimetry (TG)-differential scanning calorimetry (DSC) attached to a Fourier transform infrared (FTIR) spectrometer, so that each mass loss was related with the simultaneous endo- or exothermal behavior and to the FTIR absorption produced by the evolved gases. Apart from some clear dehydration and desulfation processes, other overlapping peaks were observed by DSC, TG, and FTIR. Optimal fitting to logistic mixture models was performed to separate the overlapping processes. Deconvolution of overlapping DTG peaks resulted in single constituent peaks, which were related to plots of some specific FTIR bands along time. Thus, a more accurate insight of the chemical processes taking place was obtained.     

Kinetic approach to partially overlapped thermal decomposition processes

Practical usefulness of the kinetic deconvolution for partially overlapped thermal decomposition processes of solids was examined by applying to the co-precipitated basic zinc carbonate and zinc carbonate. Comparing with the experimental deconvolutions by thermoanalytical techniques and mathematical deconvolutions using different statistical fitting functions, performance of the kinetic deconvolution based on an accumulative kinetic equation for the independent processes overlapped partially was evaluated in views of the peak deconvolution and kinetic evaluation. Two-independent kinetic processes of thermal decompositions of basic zinc carbonate and zinc carbonate were successfully deconvoluted by means of the thermoanalytical measurements in flowing CO₂ and by applying sample controlled thermal analysis (SCTA). The deconvolutions by the mathematical curve fittings using different fitting functions and subsequent formal kinetic analysis provide acceptable values of the mass-loss fractions and apparent activation energies of the respective reaction processes, but the estimated kinetic model function changes depending on the fitting functions employed for the peak deconvolution. The mass-loss fractions and apparent kinetic parameters of the respective reaction processes can be optimized simultaneously by the kinetic deconvolution based on the kinetic equation through nonlinear least square analysis, where all the parameters indicated acceptable correspondences to those estimated through the experimental and mathematical deconvolutions. As long as the reaction processes overlapped are independent kinetically, the simple and rapid procedure of kinetic deconvolution is useful as a tool for characterizing the partially overlapped kinetic processes of the thermal decomposition of solids.     

Preparation, crystal structure, and thermolysis of phenylenediammonium diperchlorate salts

Three salts of phenylenediammonium diperchlorate have been prepared and characterized by X-ray crystallography. Their thermal decomposition has been studied by thermogravimetry (TG), differential thermal analysis (DTA), and explosion delay (DE) measurements. The kinetics of thermal decomposition was evaluated by model fitting and isoconversional methods using TG data. The oxidation-reduction reactions near the surface of thermolysing perchlorates may be responsible for the decomposition followed by explosion. The possible pathways of thermolysis have also been proposed.     

Some methodological problems concerning nonisothermal kinetic analysis of heterogeneous solid–gas reactions

Isoconversional methods, those using only one curve α = α(T) (α is the conversion degree and T is the temperature), and invariant kinetic parameter method were applied to estimate the kinetic parameters from the following nonisothermal data: (1) simulated TG curves for a single reaction; (2) TG curves for thermal degradation of PVC; and (3) TG curves for the dehydration of CaC₂O₄·H₂O. The results obtained by applying various methods for the same system are compared and discussed. Finally, a procedure of kinetic analysis is suggested. Its application could lead to kinetic parameter values that can be used to predict either α = α(t) curves for other heating rates or α = α(T) curves for isothermal conditions. © 2001 John Wiley & Sons, Inc. Int J chem Kinet 33: 564–573, 2001     

Enhanced thermal stability of poly(vinyl alcohol) in presence of melanin

A novel method was developed to enhance the thermal stability of PVA by using natural and synthetic melanins from oxidation of dopamine. Thermogravimetric (TG) curves indicated that the synthetic melanin changed the thermal degradation behaviors of PVA and largely improved the decomposed temperature by 80–110 °C in nitrogen when incorporation of synthetic melanin with low content (0.5–2 mass%). The thermal degradation kinetics suggested the activation energies of PVA/synthetic melanin blends were much higher than these of pure PVA. Isothermal TG curves conformed that the PVA/synthetic melanin blends exhibited more thermal stability than pure PVA. Moreover, the chemical structure changes of macromolecular after degradation were characterized by using fourier transform infrared and the results suggested that elimination reaction on the first degradation step did not took place for the PVA/synthetic melanin blends at 270 °C.     

Thermal stability of metronidazole drug and tablets

TG and DSC data were used to determine the thermal parameters of metronidazole drug and tablets. Three tablets A, B and C were analysed. The TG curves of metronidazole drug and tablets A and B displayed five and C four thermal decomposition processes, respectively. Analysis of the DSC data pointed to chemical interactions between metronidazole drug and the excipients of tablets, suggested by alterations in the melting point of metronidazole. The rate constants obtained from the isothermal TG data presents following sequence of the thermal stability: tablet A>tablet C>metronidazole drug>tablet B. This revised version was published online in July 2006 with corrections to the Cover Date.     

聚芳醚醚酮和磺化聚芳醚醚酮的热分解动力学

用热重法(TG)研究了聚芳醚醚酮(PEEK)和磺化改性的聚芳醚醚酮(S-PEEK)的热分解动力学,计算了热分解动力学参数,结果表明PEEK及S-PEEK的热分解符合无规引发裂解模型。进一步考察了磺化对PEEK热分解的影响,结合温度程序裂解色谱-质谱结果,探讨了S-PEEK的TG曲线上呈现二个失重台阶的意义。     

An indirect method of X-ray spectra measurement by simultaneous attenuations of the scattered beam

Direct and indirect methods of X-ray spectra determination present obstacles to their practical use since they must position either the collimator-detector assembly or the attenuators-ionization chamber, respectively, along the X-ray beam direction. These arrangements require considerable space and in many instances the detectors promptly saturate. An indirect procedure, which overcomes the aforementioned problems, is developed. It consists of the scattering of the X-ray beam from a carbon disk, which is detected simultaneously by several detectors placed away from the beam. The X-ray flux reaching each of these detectors is attenuated in metal sheets of different thicknesses, thus obtaining simultaneously the attenuation curve values. A set of analytical equations are derived to calculate attenuation curves by taking into account all the absorption and elastic and inelastic scattering processes that a beam of photons undergoes when going from the X-ray tube to the detector. Users, even those who are not well acquainted with computer programming, can easily obtain the X-ray spectrum by a least square fitting of a measured attenuation curve to a previously derived analytical expression. A simulated Monte Carlo program of photon transport from the X-ray tube to the detector provided simulated attenuation curves data. Analytically calculated and simulated attenuation curves for the same input spectrum wholly overlap and furthermore, reconstructed spectra from both sets of curves for different kilovoltages are also in full agreement. Finally, in addition to the importance of having the detectors out of the beam direction, the proposed arrangement features other main advantages, namely, only one X-ray tube shot is needed to obtain the required data, the physical processes involved are very well known, analytical equations are easily interpreted, and the measuring apparatuses can be comparatively simple to assemble and operate.     

The effect of the hydration degree on the hydrothermal and thermo-oxidative stability of some collageneous matrices

The methods of the thermal analysis (TG, DTG and DTA) were used in order to investigate the effect of the hydration degree on the thermal behaviour of some collageneous matrices. It was pointed out that the degradation of hydrated collagen in the temperature range 20-400°C occurs through two successive processes accompanied by mass losses. The first process, consisting in the collagen dehydration, is endothermic and takes place in the temperature range ≈25 - ≈125°C. The second process is exothermic and consists in the decomposition and/or thermo-oxidation of dry collagen. The thermal parameters of both processes depend on the hydration degree of collagen. The observed dependencies show that the hydrothermal and thermo-oxidative stability of collagen are strongly correlated with its water content. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermogravimetric study of some crosslinked copolymers based on poly(acrylonitrile-co-divinylbenzene)

Copolymer networks based on acrylonitrile (AN)/divinylbenzene (DVB) have been investigated by thermogravimetric analysis (TG) to evaluate their thermal stability in nitrogen atmosphere. Thermal stability was determined from TG-DTG curves to investigate the influence of AN and DVB in the synthesis of copolymers on the copolymer thermal properties. The TG and DTG curves of copolymers clearly show two thermodegradation stages. The solid residues produced after thermodegradation stages were analyzed by FTIR and elemental analysis (CHN). The decomposition temperatures were dependent on amount of AN and DVB used as the crosslinking agent. The degradation temperatures of copolymers were influenced by the diluent system during their synthesis. FTIR analyses indicate that the cyclization of the polymer proceeds before any mass loss.     

Thermal characterization of the poultry fat biodiesel

Chemical composition of oils and fats used in the biodiesel synthesis can influence in processing and storage conditions, due to the presence of unsaturated fatty acids. An important point is the study of the biodiesel thermal stability to evaluate its quality using thermal analysis methods. In this study the thermal stabilities of the poultry fat and of their ethyl (BEF) and methyl (BMF) biodiesels were determined with the use of thermogravimetry (TG/DTG), differential thermal analysis (DTA) and differential scanning calorimetry (DSC), in different atmospheres. The TG/DTG curves of the poultry fat in synthetic air presented three decomposition steps while only one step was observed in nitrogen (N₂) atmosphere. The DSC results indicated four exothermic enthalpic transitions in synthetic air and an endothermic transitions in N₂ atmosphere attributed to the combustion process and to the volatilization and/or decomposition of the fatty acids, respectively. For both biodiesels the TG/DTG curves in air indicated two mass loss steps. In the DSC curves four exothermic transitions were observed in synthetic air besides an endothermic one in N₂ atmosphere.     

Prediction of breakthrough curves for multicomponent adsorption in a fixed-bed column using logistic and Gompertz functions

In order to facilely predict the multicomponent breakthrough curves and avoid the complicated numerical solution, this work proposes two empirical models based on the logistic and Gompertz functions. The S-shaped and bell-like curves correspond to the adsorption and displacement processes respectively. The equilibrium loading of each component can be calculated by integration of the measured breakthrough curves. The effects of the model parameters on the breakthrough curves are investigated. The applicability of the two empirical models is validated by three binary and four ternary adsorption systems, including the gas–solid and liquid–solid adsorption. The residual plot and coefficient of determination (R²) are used to evaluate their fitting quality. The results indicate that the fitting curves agree well with the experimental data and all of the residuals are distributed randomly. The five model parameters (k, τ, k*, τ* and c) are easily obtained by the nonlinear regression. For example, the fitting results are k = 1.37 × 10^?2 min^?1, τ = 292 min, k* = 1.25 × 10^?2 min^?1, τ* = 453 min and c = 85.3 for adsorption of n-butyl acetate and p-xylene on granular activated carbon. On the whole, the Gompertz model is superior to the logistic model in terms of the fitting accuracy. The significance of this work is to provide a simple and practical method for prediction of the multicomponent breakthrough curves.     

Thermal behaviour of binary and ternary copolymers containing acrylonitrile

Three types of acrylonitrile copolymers (acrylonitrile-styrene-butadiene copolymer (ABS¹), acrylonitrile-styrene random copolymer (SAN²) and acrylonitrile-butadiene random copolymer (BAN³) were studied by thermogravimetry (TG/DTG⁴) and by pyrolysis in a semi-batch process at 450 °C in order to find structure–thermal behaviour relationships. The overlapped thermo-oxidative degradation processes were separated and the corresponding kinetic parameters were calculated. The TG/DTG studies have evidenced that the styrene-acrylonitrile interactions stabilize the nitrile groups reacting by chain scission rather than cyclization and destabilize the styrene units. Also, the cyclization of the acrylonitrile units in ABS is favoured by interactions with the styrene and butadiene units. The pyrolysis behaviour evidenced that the styrene-acrylonitrile interactions in SAN and ABS lead to the formation of 4-phenylbutyronitrile as the most important decomposition compound. ABS shows similar composition of the degradation oil with SAN copolymer therefore in the ABS the styrene-butadiene interactions are less important than those between styrene and acrylonitrile units.