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.     

Is the original Kissinger equation obsolete today?

The original Kissinger, Friedman, and modified Kissinger–Akahira–Sunose (KAS) methodologies were used to evaluate the apparent activation energy of theoretically simulated complex processes consisting of two overlapping independent JMA-like (Johnson–Mehl–Avrami-like) subprocesses. Three overlay series were studied, each representing one of the basic conceptual types of peak overlap. It was shown that, in the case of complex processes, both the tested isoconversion methods (KAS and Friedman) provide good qualitative information about the activation energies of the involved overlapping signals. However, from the quantitative point of view, the data are not easy to interpret, and deconvolution procedures are necessary for meaningful results to be obtained. On the other hand, in most cases, the apparent activation energy determined by the original Kissinger equation for the overlapped dominant peak corresponded very well to the true values determined for the sole processes. This suggests large robustness of the Kissinger methodology that even nowadays may be considered very advantageous and utilized in kinetic analysis of complex processes.     

Application of wavelet transforms and an approximate deconvolution method for the resolution of noisy overlapped peaks in DNA capillary electrophoresis

A new procedure for resolving noisy overlapped peaks in DNA separations by capillary electrophoresis (CE) is developed. The procedure combines both a wavelet-based denoising method that effectively denoises the signal and a novel approximate deconvolution technique that resolves the fragment peaks and improves the ability to separate highly overlapped peaks early in the electrophoresis process. Different kinds of overlapped peaks with and without noise simulated by computer as well as some DNA experimental electropherograms were submitted to the new procedure. A second order differential operator with variable coefficients is applied to the entire electrophoresis signal at any given time and approximate deconvolutions of the individual Gaussian peaks are performed. The operator incorporates the effect of the superposition and gives exact annihilation in the neighborhood of each peak. Overlapped peaks with a resolution higher than 0.46 can be resolved directly. Also, the method can determine the peak components of signals with a signal to noise ratio higher than 1.4     

Applicability of Fraser–Suzuki function in kinetic analysis of complex crystallization processes

A modified peak-deconvolution procedure for complex crystallization processes was introduced. The method is based on the constrained curve-fitting technique using the Fraser–Suzuki (FS) function, where the FS asymmetry parameter a ₃ correlates with the value of the Johnson–Mehl–Avrami (JMA) kinetic parameter m. The correlation was verified for an extensive number of theoretically simulated JMA curves; in addition, the dependencies of the a ₃ parameter on other kinetic variables (E, A, q ⁺) were quantified. The suggested deconvolution procedure was tested on two glassy systems with different overlay degree of the involved overlapping surface and bulk crystallization processes. In both cases, the kinetic analysis of deconvoluted data provided reasonable, consistent and accurate results. However, certain level of knowledge and experience was needed in order to correctly recognize and consequently account for all deviations from the theoretical behavior caused by thermal gradients or imperfections of the data acquisition process. As the input data for the fitting procedure can be in any form equivalent to the dα/dT temperature dependence, the method seems to be highly universal and may be applied to data obtained by various TA techniques.     

On the equations describing chromatographic peaks and the problem of the deconvolution of overlapped peaks

The problem of the appropriate choice of the function that describes a chromatographic peak is examined in combination with the deconvolution of overlapped peaks by means of the non-linear least-squares method. It is shown that the majority of the functions proposed in the literature to describe chromatographic peaks are not suitable for this purpose. Only the polynomial modified Gaussian function can describe almost every peak but it is mathematically incorrect unless it is redefined properly. Two new functions are proposed and discussed. It is also shown that the deconvolution of an overlapping peak can be done with high accuracy using a non-linear least-squares procedure, like Microsoft Solver, but this target is attained only if we use as fitted parameters the position of the peak maximum and the peak area (or height) of every component in the unresolved chromatographic peak. In case we use as fitted parameters all the parameters that describe each single peak enclosed in the multi-component peak, then Solver leads to better fits, which though do not correspond to the best deconvolution of the peak. Finally, it is found that Solver gives much better results than those of modern methods, like the immune and genetic algorithms.     

应用分布活化能模型分析伊敏褐煤丝炭腐植酸热解及氢气生成动力学

应用开放体系的热重-质谱(TG-MS)联用技术在5、20和50℃·min-1三个升温速率下对伊敏褐煤丝炭腐植酸(F-HA)和脱灰丝炭腐植酸(DF-HA)的热解行为进行了分析,并利用分布活化能模型(DAEM)分别对其热解和氢气生成动力学进行分析,获得了热解过程和氢气生成的活化能分布函数.结果表明:(1)F-HA热解活化能分布函数呈类Gaussian分布,且具有一定的对称性,主峰位与标准Gaussian分布相一致;DF-HA热解活化能分布函数也呈类Gaussian分布形式,主峰位与Gaussian分布相比,偏向低活化能值.根据转化率与温度、活化能的关系,结合腐植酸的热失重特征,将F-HA热解过程划分为四个阶段,DF-HA热解过程划分为五个阶段,并对腐植酸热解过程中各阶段的化学反应进行了详细讨论.(2)F-HA和DF-HA热解氢气生成活化能分布函数均呈类Gaussian分布,热解氢气生成活化能的整体趋势为随着转化率的升高而增加,但也表现出一定的阶段集中分布特征.根据热解氢气生成的动力学特征,将其生成过程划分为五个阶段,反映了其生成的不同化学反应机制.(3)酸洗脱灰对伊敏丝炭提取出的HA的热解行为、热解过程及热解氢气生成动力学产生了影响.     

Computerized separation of chromatographically unresolved peaks

A computerized peak deconvolution software and mass spectra were successfully applied for the deconvolution of overlapped peak cluster in the chromatogram obtained separating the complex mixture of pesticides by retention time locking gas chromatography-mass spectroscopy. The method based on the unique fragment ions in the spectra can be used for deconvolution of peak clusters if mass spectra of overlapped peaks differ. This method allows determining actual retention times of overlapped peaks. Peak areas found by this method however, cannot be used naturally for the quantitative purposes as the abundance of fragment ions used for this deconvolution procedure can dramatically differ. Computer assisted deconvolution of peaks in the peak clusters gives more realistic peak area ratios as at this method it is supposed equal response for all peaks overlapped in a cluster.     

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.     

Determination of thermokinetic parameters and thermodynamic functions from thermoforming of LiMnPO<Subscript>4</Subscript>

This article presents the determination of thermokinetic parameters and thermodynamic functions from the thermoforming of LiMnPO₄. In our previous paper, a couple of thermoreaction processes, e.g., co-elimination and polycondensation of thermokinetics and thermodynamics, were incompletely determined. The co-elimination process is considered as dehydration and a deammoniation process in this paper. Evidently, an alternative technique was applied for calculating the extent of conversion values using the ratio of the peak area of the deconvoluted DTG peak after applying the Fraser–Suzuki deconvolution. An iterative equation of the integral isoconversional technique was used to estimate the reliable activation energy E_α. Each separated peak, including dehydration, deammoniation, and polycondensation, was obviously evaluated as a single kinetic process with its own kinetic parameters. In order to choose reliable mechanisms, the y(α) master plots or the plots between the experiment and the model were compared. The plots thus obtained showed that the dehydration, deammoniation, and polycondensation processes were found to be 3/2-order chemical reaction (F_3/2), 2-order chemical reaction (F₂), and nucleation (P_3/2) mechanisms, respectively. The pre-exponential factor values were obtained from E_α, and the reaction mechanisms were found to be 3.78?×?10¹², 7.05?×?10¹², and 1.96?×?10¹³ s^?1, respectively. The evaluated thermodynamic data of the activated complexes showed that the thermal reaction required thermal energy to complete the reaction.     

Rapid characterization of anthocyanins in red raspberry fruit by high-performance liquid chromatography coupled to single quadrupole mass spectrometry

This paper describes the results of a comparison of four peak functions in describing real chromatographic peaks. They are the empirically transformed Gaussian, polynomial modified Gaussian, generalized exponentially modified Gaussian and hybrid function of Gaussian and truncated exponential functions. Real chromatographic peaks of different shapes (fronting. symmetric, and tailing) are obtained by various separation conditions of reversed-phase liquid chromatography. They are then fitted to the peak functions via the Marquardt-Levenberg algorithm, a nonlinear least-squares curve-fitting procedure, by Microsoft Solver. The qualities of the fits are evaluated by the sum of the squares of the residuals. It is concluded in the study that the empirically transformed Gaussian function offers the highest flexibility (best fits) to all shapes of chromatographic peaks, including extremely asymmetric tailing peaks with a peak asymmetry of up to 8. The flexibility of this function should improve our ability to process chromatographic peaks such as deconvolution of overlapped peaks and smoothing noisy peaks for the determination of statistical moments.     

Monolithic silica columns for high-efficiency chromatographic separations

A deconvolution methodology for overlapped chromatographic signals is proposed. Several single-wavelength chromatograms of binary mixtures, obtained in different runs at diverse concentration ratios of the individual components, were simultaneously processed (multi-batch approach), after being arranged as two-way data. The chromatograms were modelled as linear combinations of forced peak profiles according to a polynomially modified Gaussian equation. The fitting was performed with a previously reported hybrid genetic algorithm with local search, leaving all model parameters free. The approach yielded more accurate solutions than those found when each experimental chromatogram was fitted independently to the peak model (single-batch approach). The improvement was especially significant for those chromatograms where the peaks were severely affected by the tails of the preceding compounds. Peak shifts among chromatograms, which are a usual source of non-bilinearity, were modelled in a continuous domain instead of in a discrete way, which avoided some drawbacks associated with latent variable methods. An experimental design involving simulated chromatograms was applied to check the method performance. Five main factors affecting the deconvolution were examined: concentration pattern, chromatographic resolution, number of batches and replicates, and noise level, which were evaluated using first- and second-order figures of merit. The method was also tested on three real samples containing compounds showing different overlap. Four multi-batch deconvolution methods were considered differing in the nature of the processed information and kind of peak matching among chromatograms. In all cases, the multi-batch deconvolution yielded better performance than the single-batch approach.     

Determination of the interconversion energy barrier of enantiomers by separation methods

Separation methods have become versatile tools for the determination of kinetic activation parameters and energy barriers to interconversion of isomers and enantiomers in the last 20 years. New computer-aided evaluation systems allow the on-line determination of these data after separating minute amount of pure compounds or mixture of isomers or enantiomers, respectively. Both dynamic interconversion during the separation process as well as static stopped-flow techniques have been applied to determine the kinetic activation parameters and interconversion energy barriers by separation methods. The use of (1) combinations of batchwise kinetic studies with enantioselective separations, (2) a continuous flow model, (3) a comparison of real chromatograms with simulated ones, (4) stopped-flow techniques, (5) stochastic methods, (6) approximation functions and (7) deconvolution methods, for the determination of interconversion energy barriers by separation methods is summarized in detail.     

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.     

Application of curve fitting in thin-layer chromatography-flame ionization detection analysis of the carbohydrate fraction in marine mucilage and marine snow samples from Italian seas

This paper presents a thin-layer chromatographic-flame ionization detection (TLC-FID) procedure to characterize the carbohydrate fraction of marine mucilage and marine snow samples from the Italian Seas. The identification of the different carbohydrate subfractions is supported by the application of a deconvolution procedure based on a new mathematical function for describing chromatographic peaks and enhancing their resolution. The joint-approach TLC-FID analysis and deconvolution procedure allows for the characterization of the carbohydrate fraction of the marine samples in a single step without using the different derivatization procedures requested by the most common gas chromatography and high-performance liquid chromatographic methods for carbohydrate analysis. In fact, the results obtained by the TLC-FID procedure show that different neutral, uronic acid, and aminosugar subfractions can be present simultaneously in these samples. Moreover, the results support some hypotheses about the causes of the presence of mucilages in the Italian Seas.     

Kinetic triplet evaluation of a complicated dehydration of Co<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript>·8H<Subscript>2</Subscript>O using the deconvolution and the simplified master plots combined with nonlinear regression

Kinetic triplet of the complex decomposition processes of Co₃Ni₃(PO₄)₂·8H₂O was evaluated for the first time by using the deconvolution method to separate the overlapping DTG curves. After the completion of the deconvolution, five steps of the decomposition were obtained. The activation energy E and the pre-exponential factor A of each step were determined by KAS method. The kinetic compensation effect (KCE) method was applied to identify the individual step of the decomposition. Each master plot was simplified by generating the general equations and combined with the nonlinear regression curve fitting. According to kinetic analysis results obtained from this modified method, it was found that the early four steps of dehydration follow the mechanisms of nucleation and subsequent growth with different n-orders, while the last step occurs in the same mechanism but accompanied by the phase transition (lattice reorientation).     

Kinetic study of the multistep thermal behaviour of barium titanyl oxalate prepared via chemical precipitation method

This study describes the physico-geometrical mechanism and overall kinetics for the multistep thermal dehydration of barium titanyl oxalate tetrahydrate (BTO). The thermal dehydration kinetics of BTO was studied at four different linear heating rates under non-isothermal conditions. The reaction kinetics was performed using differential scanning calorimetry (DSC) and the curves obtained were analysed using different isoconversional model-free equations and the values are found to be compatible with each other. The kinetic deconvolution principle is used for identifying the partially overlapped kinetic processes of the thermal dehydration of BTO, and it occurs in two stages. The overall reaction kinetics parameters calculated via kinetic deconvolution of the sample indicate the multistep nature of the process and the kinetic analysis of the non-isothermal data of this reaction model shows that the reaction is best described by Sestak–Berggren (m, n) empirical kinetic model. The prepared sample was identified and characterized by means of FT-IR, XRD, SEM, and TEM.

     

Ignoring heat inertia impairs accuracy of determination of activation energy in thermal analysis

This paper critically analyzes the traditional method of kinetic determination of activation energy by sectioning the recorded differential thermal analysis peak area. This procedure is incorrect because it misses the impact of thermal inertia, which changes the shape of the peak's base line from straight to s-shape. This effect has been known since the Newton cooling law, but the resulting errors persist to be interwoven into all the kinetic methods based on nonisothermal thermoanalytical measurements. Relating to calorimetry, it is necessary here because heat inertia has become a standard part of heat determination via using the Tian historical equation. The role and impact of heat inertia is discussed and analyzed in detail.     

Thermal degradation of alkyl triphenyl phosphonium intercalated montmorillonites

The decomposition mechanism of intercalated montmorillonites at a particular temperature region and the activation energy involved in it are the two important aspects which determines the thermal stability of intercalated montmorillonites. In this study, montmorillonite was intercalated with alkyl (methyl, ethyl, propyl, and dodecyl) triphenyl phosphonium intercalates. Differential thermogravimetric analysis of each intercalated montmorillonites showed different peaks with associated organic loss at different temperature zone. Intercalated montmorillonites were subjected to isothermal kinetic analysis corresponding to selected temperature zone obtained from DTG peaks. Activation energies of organic decomposition process at selected temperature zones were determined. Mass spectral analysis and FTIR were done to understand the decomposition mechanisms and to relate them with the estimated activation energies.     

差示扫描量热研究水稻线粒体能量释放动力学

线粒体是细胞的一个重要的亚细胞器．它通过呼吸作用为细胞各项活动提供能量，有细胞'动力戒'之称．生物摄取的食物通过代谢分解形成小分子产物之后，被输送至线粒体，经过氧化作用将其中贮存的能量逐步释放出来，并转化为三磷酸腺苦（ATP）以供生命机体各种活动的需要，因而它