Application of isoconversional calculation procedure to non-isothermal kinetics study

The kinetics of thermal decomposition of NH₄CuPO₄·H₂O was studied using isoconversional calculation procedure. The iterative isoconversional procedure was applied to estimate the apparent activation energy E _a; the values of apparent activation energies associated with the first stage (dehydration), the second stage (deamination), and the third stage(condensation) for the thermal decomposition of NH₄CuPO₄·H₂O were determined to be 117.7 ± 7.7, 167.9 ± 8.4, and 217.6 ± 45.5 kJ mol^?1, respectively, which demonstrate that the third stage is a kinetically complex process, and the first and second stages are single-step kinetic processes and can be described by a unique kinetic triplet [E _a, A, g(α)]. A new modified method of the multiple rate iso-temperature was used to define the most probable mechanism g(α) of the two stages; and reliability of the used method for the determination of the kinetic mechanism were tested by the comparison between experimental plot and model results for every heating rate. The results show that the mechanism functions of the two stages are reliable. The pre-exponential factor A of the two stages was obtained on the basis of E _a and g(α). Besides, the thermodynamic parameters (ΔS ^≠, ΔH ^≠, and ΔG ^≠) of the two stages were also calculated.     

Nonisothermal kinetics study with advanced isoconversional procedure and DAEM

The precursor of LiNiPO₄ was synthesized by solid-state reaction at low-heating temperature using LiOH·H₂O and NH₄NiPO₄·H₂O as raw materials. LiNiPO₄ was obtained by calcining the precursor. Based on the advanced isoconversional procedure and the distributed activation energy model (DAEM), the activation energies calculated indicated that the thermal process involved two stages which stage II was a kinetically complex process, but stage I was single-step process. The most probable mechanism for the stage I is random nucleation and subsequent growth. DAEM and nonlinear model-fitting method were applied to study the stage II of decomposition process of the precursor. The distributions of activation energy, f(E _a) and values of preexponential factor A of the stage II of the thermal decomposition of precursor were obtained on the basis of DAEM. The results of nonlinear model-fitting method showed the most probable mechanisms of the parallel reactions for stage II are chemical reaction and nucleation.     

Using ordinary differential equations system to solve isoconversional problems in non-isothermal kinetic analysis

The mathematical evaluation of the activation energy, E, of non-isothermal degradation reactions is usually made using the Ozawa/Flynn–Wall isoconversion principle and involves the numerical resolution of a set of integrals without closed form solution, which are solved by polynomial approximation or by numeric integration. In the present work, the isoconversion principle, originally described and maintained until now as an algebraic problem, was written as a set of ordinary differential equations (ODEs). The individual ODEs obtained are integrated by numeric methods and are used to estimate the activation energy of simulated examples. A least square error (LSE) objective function using the introduced ODEs was written to deal with multiple heating rate CaCO₃ thermal decomposition TG experiments.     

Critical study of the isoconversional methods of kinetic analysis

A critical study of the use of isoconversional methods for the kinetic analysis of non-isothermal data corresponding to processes with either a real or an apparent variation of the activation energy, E, with the reacted fraction, α, has been carried out using for the first time simulated curves. It has been shown that the activation energies obtained from model-free methods are independent of the heating rate. However, the activation energy shows a very strong dependence of the range of heating rates used for simulating the curves if the apparent change of E with α is caused by overlapping processes with different individual activation energies. This criterion perhaps could be used for determining if a real dependence between E and α is really occurring.     

Iso-conversional kinetic study of non-isothermal crystallization in glassy Se98Ag2 alloy

The crystallization kinetics of glassy Se₉₈Ag₂ alloy is studied at different heating rates (5, 10, 15, and 20?K?min^?1) using differential scanning calorimetric technique. Endothermic and exothermic peaks are obtained at glass transition (T _g) and crystallization temperature (T _c). Four iso-conversional methods (Kissinger?CAkahira?CSunose (KAS), Flynn?CWall?COzawa (FWO), Tang and Straink) were used to determine the various kinetic parameters (crystallization temperature T _?? , activation energy of crystallization E _??, order parameter n) in non-isothermal mode.     

Thermal degradation and isoconversional kinetic analysis of light-cured dimethacrylate copolymers

Thermal degradation kinetics of copolymers based on bis-phenol A ethoxylated dimethacrylate (Bis-EMA) with triethylene glycol dimethacrylate (TEGDMA), and urethane dimethacrylate (UDMA) with TEGDMA in wt/wt ratios 30/70, 50/50, or 70/30 were investigated using thermogravimetric analysis as a means to provide specific information regarding the internal structures of these resins. Thermogravimetric scans were taken at four different heating rates to perform an isoconversional analysis to determine the change of the effective activation energy as a function of conversion. A two-step degradation mechanism was found to occur in almost all copolymer compositions attributed to the existence of inhomogeneities in the macromolecular structure and the formation of weak links inside the polymeric network.     

A non-isothermal kinetic study of the thermal decomposition of magnesium alkoxides and amides

The thermal decomposition of alkoxides and amides of magnesium have been studied by vacuum TGA under both isothermal and non-isothermal conditions. These compounds were found to follow a unimolecular decay law, which in integrated form is ln(1  α)  kt, where α is the fraction of material reacted, and k is the Arrhenius rate constant. The rate-controlling process is random nucleation, one nucleus on each particle. Energies of activation calculated by isothermal and non-isothermal methods agree to within ±20%.     

New incremental isoconversional method for kinetic analysis of solid thermal decomposition

A simple and precise incremental isoconversional integral method based on Li-Tang (LT) method is proposed for kinetic analysis of solid thermal decomposition, in order to evaluate the activation energy as a function of conversion degree. The new method overcomes the limitation of LT method in which the calculated activation energy is influenced by the lower limit of integration. By applying the new method to kinetic analysis of both the simulated nonisothermal case and experimental case of strontium carbonate thermal decomposition, it is shown that the dependence of activation energy on conversion degree evaluated by the new method is consistent with those obtained by Friedman (FR) method and the modified Vyazovkin method. As the new method is free from approximating the temperature integral and not sensitive to the noise of the kinetic data, it is believed to be more convenient in nonisothermal kinetic analysis of solid decompositions.     

Comparative kinetic study of decomposition of some diazepine derivatives under isothermal and non-isothermal conditions

Thermal analysis is one of the most widely used methods for studying the solid state of pharmaceutical substances. TG/DTG and DSC curves provide important information regarding the physical properties of the pharmaceutical compounds (stability, compatibility, polymorphism, kinetic analysis, phase transitions etc.). The purpose of a kinetic investigation is to calculate the kinetic parameters and the kinetic model for the studied process. The results are further used to predict the system’s behaviour in various circumstances. A kinetic study regarding the diazepam, nitrazepam and oxazepam thermal decomposition was performed, under non-isothermal and isothermal conditions and in a nitrogen atmosphere, for the temperature steps: 483, 498, 523, 538 and 553 K. The TG/DTG data were processed by three methods: isothermal model-fitting, Friedman’s isothermal-isoconversional and Nomen-Sempere non-parametric kinetics. In the model-fitting methods the kinetic triplets (f(α), A and E _a) that defines a single reaction step resulted in being at variance with the multi-step nature of diazepines decomposition. The model-free approach represented by isothermal and non-isothermal isoconversional methods, gave dependences of the activation energies on the extent of conversion. It is very difficult to obtain an accord with the similar data which resulted under non-isothermal conditions from a previous work. The careful treatment of the kinetic parameters obtained in different thermal conditions was confirmed to be necessary, as well as a different strategy of experimental data processing.     

A statistical comparison of non-isothermal methods of kinetic investigation

A statistical analysis of some non-isothermal kinetic techniques is given. Comparison of the kinetic parameter values obtained by different techniques has shown them to be statistically non-equivalent. Hypotheses of significance or non-significance of discrepancies in the kinetic parameter values should therefore be tested using two-dimensional normal distributions. Comparisons of the results obtained by various techniques using activation energy values only lead to erroneous conclusions.     

Crystallization kinetic of fluoro- zirconate glasses by non-isothermal analysis

Fluoride glasses have been extensively studied due to their high transparency in the infrared wavelength. The crystallization kinetics of these systems has been studied using DTA and DSC techniques. Most of the experimental data is frequently investigated in terms of the Johnson-Mehl-Avrami (JMA) model in order to obtain kinetic parameters. In this work, DSC technique has been used to study the crystallization of fluorozirconate glass under non-isothermal conditions. It was found that JMA model was not fit to be applied directly to these systems, therefore, the method proposed by Málek has been applied and the Šesták-Berggren (SB) model seems to be adequate to describe the crystallization process. This revised version was published online in July 2006 with corrections to the Cover Date.     

Some problems concerning the evaluation of non-isothermal kinetic parameters

The validity of isoconversional methods used to evaluate the activation energy is discussed. The authors have shown that the Flynn-Wall-Ozawa and Friedman methods give results that agree with each other only if the activation energy does not change with the degree of conversion. A criterion for the reaction mechanism as expressed by the differential conversion function is suggested too.     

Synthesis and non-isothermal kinetic study of the thermal decomposition of gadolinium(III) complexes

Summary Pyrrolidinedithiocarbamate (Pyr), piperidinedithiocarbamate (Pip), morpholinedithiocarbamate (Mor) and diethanolaminedithiocarbamate (DEDC) ammonium salts; pyrrolidinedithiocarbamic acid-pyrrolidineammonium salt (HPyrPyr), piperidinedithiocarbamic acid-piperidineammonium salt (HPipPip), morpholinedithiocarbamic acid-morpholineammonium salt (HMorMor), hexamethylenedithiocarbamic acid-hexamethyleneammonium salt (HHexHex), diethanolaminedithiocarbamic acid-diethanolamineammonium salt (HDEADEDC) were synthesized, characterized by IR and elemental analysis and their thermal behaviours were investigated using thermogravimetry (TG) and differential scanning calorimetry (DSC).     

On the dependence of kinetic parameters and functions in non-isothermal kinetics

The approaches to overcoming local ambiguity due to the dependence of the kinetic equation parameters are considered. The application of the mathematical apparatus of the Jacobi matrices enables one to determine the number of both independent kinetic parameters and kinetic functions used to describe a process. No more than five parameters in the Šestak-Berggren equation and only some kinetic functions are found to possess independence.     

Isothermal and non-isothermal kinetic study of the PbGeO3 solid-solid phase transition

A kinetics study on PbGeO₃ solid-solid phase transition was realised by means of differential scanning calorimetry and time-resolved X-ray powder diffraction. Isothermal and non-isothermal Johnson-Mehl-Avrami equations were applied to obtain both the activation energy E_a and the Avrami coefficient n. The latter parameter has been related to morphological evidences collected by scanning electron microscopy. The limits of the applied theory, i.e., the Arrhenian behaviour of the growth rate and a steady-state nucleation rate, are finally discussed in terms of recent theoretical developments.     

TG,EGA and kinetic study by non-isothermal decomposition of a polyaniline with different dispersion degree

Polyaniline was obtained by oxidizing aniline in hydrochloric acid media with ammonium peroxidisulfate as oxidizing agent. Molar ratio aniline/oxidant was 1 and aniline/acid ratio: ½, at ?5 and 400 °C, respectively, 800 mL water. The both compounds were studied using two different experimental strategies: the coupled TG-EGA (FTIR) technique by decomposition in dynamic air atmosphere and the kinetic analysis of TG data obtained at four heating rates (5, 7, 10 and 15 K min^?1). The kinetic analysis of the TG non-isothermal data was performed with the Flynn–Wall–Ozawa, Friedman’s, and modified non-parametric kinetic (NPK) methods. By means of the coupled techniques spectroscopic arguments on the reaction mechanism were obtained, i.e. the oxidative degradation of the quinoine ring as the first step. The values of the activation energy by the three used methods are in good agreements. According to the NPK method, the termodegradation process consist in physical (diffusion) and chemical steps.