Kinetic model of poly(3-hydroxybutyrate) thermal degradation from experimental non-isothermal data

The non-isothermal data given by TG curves for poly(3-hydroxybutyrate) (PHB) were studied in order to obtain a consistent kinetic model that better represents the PHB thermal decomposition. Thus, data obtained from the dynamic TG curves were suitably managed in order to obtain the Arrhenius kinetic parameter E according to the isoconversional F-W-O method. Once the E parameters is found, a suitable logA and kinetic model (f(α)) could be calculated. Hence, the kinetic triplet (E±SD, logA±SD and f(α)) obtained for the thermal decomposition of PHB under non-isothermal conditions was E=152±4 kJ mol⁻¹, logA=14.1±0.2 s⁻¹ for the kinetic model, and the autocatalytic model function was: f(α)=α^m(1−α)ⁿ=α^0.42(1−α)^0.56.     

A kinetic analysis of thermal decomposition of polyaniline/ZrO<Subscript>2</Subscript> composite

Synthesis, characterization and thermal analysis of polyaniline (PANI)/ZrO₂ composite and PANI was reported in our early work. In this present, the kinetic analysis of decomposition process for these two materials was performed under non-isothermal conditions. The activation energies were calculated through Friedman and Ozawa-Flynn-Wall methods, and the possible kinetic model functions have been estimated through the multiple linear regression method. The results show that the kinetic models for the decomposition process of PANI/ZrO₂ composite and PANI are all D₃, and the corresponding function is ƒ(α)=1.5(1−α)^2/3[1−(1-α)^1/3]−1. The correlated kinetic parameters are E _a=112.7±9.2 kJ mol⁻¹, lnA=13.9 and E _a=81.8±5.6 kJ mol⁻¹, lnA=8.8 for PANI/ZrO₂ composite and PANI, respectively.     

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.     

Studies on Non-isothermal Kinetics of the Thermal Decomposition of Eu2(BA)6(bipy)2

The thermal decomposition of Eu₂(BA)₆(bipy)₂ (BA=C₂H₅N^– ₂, benzoate; bipy=C₁₀H₈N₂, 2,2'-bipyridine)and its kinetics were studied under the non-isothermal condition by TG-DTG, IR and SEM methods. The kinetic parameters were obtained from analysis of the TG-DTG curves by the Achar method, the Madhusudanan-Krishnan-Ninan (MKN) method, the Ozawa method and the Kissinger method. The most probable mechanism function was suggested by comparing the kinetic parameters. The kinetic equation for the first stage can be expressed as: dα/dt=Aexp(–E/RT)3(1–α)^2/3. This revised version was published online in August 2006 with corrections to the Cover Date.     

Kinetic of decomposition of some complexes under non-isothermal conditions

Kinetics of thermal decomposition of three structurally similar complexes Co₂Cu(C₂O₄)₃ (R-diam)₂, where R is ethyl, 1,2-propyl or 1,3-propyl, was studied under non-isothermal conditions and nitrogen dynamic atmosphere at heating rates of 5, 7, 10, 12 and 15 K min⁻¹. For data processing the Flynn-Wall-Ozawa and a modified non-parametric kinetic methods were used. By both methods the activation energy are in the range of 97–102 kJ mol⁻¹. The formal kinetic is r=kα(1−α)². Also a compensation effect between lnA and E was evidenced. The kinetic analysis lead to the conclusion of an identic decomposition mechanism by a single step process.     

Kinetic Analysis of Single or Multi-Step Decomposition Processes; Limits introduced by statistical analysis

A kinetic study on decomposition processes of some penicillin and some commercial drugs was carried out. As expected by the complex structures of penicillins, several steps with different activation energies occurred in their decomposition processes. Model-fitting and model-free kinetic approach were applied to non-isothermal and isothermal data. 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 penicillins decomposition. The model-free approach represented by isothermal and non-isothermal isoconversional methods, gave dependences of the activation energies on the extent of conversion. The complex nature of the multi-step process of the studied compounds was more easily revealed using a broader temperature range in non-isothermal isoconversional method. The failure in the model fitting method did not allow calculating storage times. Model-fitting and model-free methods, both isothermal and non-isothermal, showed that F1 mechanism is able to describe decomposition processes for drugs (having Phosphomycin salts as active component) for which a single decomposition process occurs. Statistical analysis allowed us to select reliable kinetic parameters related to the decomposition processes for these last compounds. This procedure showed that the values obtained by extrapolation, outside the temperature range where the processes occurred must be used with caution. Indeed half-life and shelf-life values, commonly extrapoled at room temperature, seemed to be unrealistic. This revised version was published online in August 2006 with corrections to the Cover Date.     

Kinetic characterization of the reduction of silica supported cobalt catalysts

Abstact  The reduction process of silica supported cobalt catalyst was studied by thermal analysis technique. The reduction of the catalyst proceeds in two steps:

Non-isothermal kinetics of the thermal decomposition of sodium oxalate Na<Subscript>2</Subscript>C<Subscript>2</Subscript>O<Subscript>4</Subscript>

The thermal transformation of Na₂C₂O₄ was studied in N₂ atmosphere using thermo gravimetric (TG) analysis and differential thermal analysis (DTA). Na₂C₂O₄ and its decomposed product were characterized using a scanning electron microscope (SEM) and the X-ray diffraction technique (XRD). The non-isothermal kinetic of the decomposition was studied by the mean of Ozawa and Kissinger–Akahira–Sunose (KAS) methods. The activation energies (E _α) of Na₂C₂O₄ decomposition were found to be consistent. Decreasing E _α at increased decomposition temperature indicated the multi-step nature of the process. The possible conversion function estimated through the Liqing–Donghua method was ‘cylindrical symmetry (R₂ or F_1/2)’ of the phase boundary mechanism. Thermodynamic functions (ΔH*, ΔG* and ΔS*), calculated by the Activated complex theory and kinetic parameters, indicated that the decomposition step is a high energy pathway and revealed a very hard mechanism.     

Comparative kinetic study of the non-isothermal thermal curing of <Emphasis Type="Italic">bis</Emphasis>-GMA/TEGDMA systems

The thermal polymerization kinetics of dimethacrylate monomers was studied by differential calorimetry using non-isothermal experiments. The kinetic analysis compared the following procedures: isoconversional method (model-free method), reduced master curves, the isokinetic relationship (IKR), the invariant kinetic parameters (IKP) method, the Coats-Redfern method and composite integral method I. Although the study focused on the integral methods, we compared them to differential methods. We saw that even relatively complex processes (in which the variations in the kinetic parameters were only slight) can be described reasonably well using a single kinetic model, so long as the mean value of the activation energy is known (E). It is also shown the usefulness of isoconversional kinetic methods, which provide with reliable kinetic information suitable for adequately choosing the kinetic model which best describes the curing process. For the system studied, we obtained the following kinetic triplet: f(α)=α^0.6(1−α)^2.4, E=120.9 kJ mol⁻¹ and lnA=38.28 min⁻¹.     

Kinetics of thermal decomposition of CeO2 nanocrystalline precursor prepared by precipitation method

The thermal decomposition of CeO₂ nanocrystalline precursor prepared by chemical precipitation method was investigated using thermo-gravimetric/differential scanning calorimetry (TG/DSC) and X-ray powder diffraction (XRD). In particular, the differential thermal analysis curves for the decomposition of CeO₂ nanocrystalline precursor were measured at different heating rates in air by a thermal analyzer (NETZSCH STA 449C, Germany). The kinetic parameters of the thermal decomposition of CeO₂ nanocrystalline precursor were calculated using the Kissinger method and the Coats-Redfern method. Results show that the apparent active energy E of the reaction is 105.51 kJ/mol, the frequency factor lnA is 3.602 and the reaction order n is 2. This thermal decomposition process can be described by the anti-Jander equation and a three-dimensional diffusion mechanism. Tanslated from Journal of Central South University (Science and Technology), 2007, 38(3): 428–432 [译自: 中南大学学报(自然科学版]     

Thermal behavior and thermal safety on 3,3-dinitroazetidinium salt of perchloric acid

3,3-Dinitroazetidinium (DNAZ) salt of perchloric acid (DNAZ·HClO₄) was prepared, it was characterized by the elemental analysis, IR, NMR, and a X-ray diffractometer. The thermal behavior and decomposition reaction kinetics of DNAZ·HClO₄ were investigated under a non-isothermal condition by DSC and TG/DTG techniques. The results show that the thermal decomposition process of DNAZ·HClO₄ has two mass loss stages. The kinetic model function in differential form, the value of apparent activation energy (E _a) and pre-exponential factor (A) of the exothermic decomposition reaction of DNAZ·HClO₄ are f(α) = (1 − α)⁻¹/2, 156.47 kJ mol⁻¹, and 10^15.12 s⁻¹, respectively. The critical temperature of thermal explosion is 188.5 °C. The values of ΔS ^≠, ΔH ^≠, and ΔG ^≠of this reaction are 42.26 J mol⁻¹ K⁻¹, 154.44 kJ mol⁻¹, and 135.42 kJ mol⁻¹, respectively. The specific heat capacity of DNAZ·HClO₄ was determined with a continuous C _p mode of microcalorimeter. Using the relationship between C _p and T and the thermal decomposition parameters, the time of the thermal decomposition from initiation to thermal explosion (adiabatic time-to-explosion) was evaluated as 14.2 s.     

Synthesis,molecular structure,non-isothermal decomposition kinetics and adiabatic time to explosion of 3,3-dinitroazetidinium 3,5-dinitrosalicylate

The title compound 3,3-dinitroazetidinium (DNAZ) 3,5-dinitrosalicylate (3,5-DNSA) was prepared and the crystal structure has been determined by a four-circle X-ray diffractometer. The thermal behavior of the title compound was studied under a non-isothermal condition by DSC and TG/DTG techniques. The kinetic parameters were obtained from analysis of the TG curves by Kissinger method, Ozawa method, the differential method and the integral method. The kinetic model function in differential form and the value of E _a and A of the decomposition reaction of the title compound are f(α)=4α^3/4, 130.83 kJ mol⁻¹ and 10_13.80s⁻¹, respectively. The critical temperature of thermal explosion of the title compound is 147.55 °C. The values of ΔS ^≠, ΔH ^≠ and ΔG ^≠ of this reaction are −1.35 J mol⁻¹ K₋₁, 122.42 and 122.97 kJ mol⁻¹, respectively. The specific heat capacity of the title compound was determined with a continuous C _p mode of mircocalorimeter. Using the relationship between C _p and T and the thermal decomposition parameters, the time of the thermal decomposition from initiation to thermal explosion (adiabatic time-to-explosion) was obtained.     

Comparative method to evaluate reliable kinetic triplets of thermal decomposition reactions

Reliable kinetic information for thermal analysis kinetic triplets can be determined by the comparative method: (1) An iterative procedure or the KAS method had been established to obtain the reliable value of activation energy E _a of a reaction. (2) A combined method including Coats-Redfern integral equation and Achar differential equation was put forward to confirm the most probable mechanism of the reaction and calculate the pre-exponential factor A. By applying the comparative method above, the thermal analysis kinetic triplets of the dehydration of CaC₂O₄·H₂O were determined, which apparent activation energy: 81±3 kJ mol^-1, pre-exponential factor: 4.51·106-1.78·10⁸ s^-1, the most probable mechanism function: f(α)=1 or g(α)=α, which the kinetic equation of dehydration is dα/dt=Ae^-E _a ^/RT. This revised version was published online in August 2006 with corrections to the Cover Date.     

A kinetic study of the thermal degradation of 3-methylaminopropylamine inside AlPO<Subscript>4</Subscript>-21

Kinetics of the thermal decomposition of 3-methylaminopropylamine which was used as a structure-directing agent in the synthesis of AlPO₄-21 has been studied under isothermal and non-isothermal conditions. The decomposition is a single-step reaction occurring in the 573–663 K range. It is a phase-boundary-controlled process, described by the ‘F2/3, R3’ kinetic model. The activation energy values obtained under the non-isothermal and isothermal conditions lie in the 173–151 kJ mol^–1 range.     

Kinetics of the exothermic decomposition of 1-nitro-3-(β,β,β-trinitroethyl)-4,5-dinitroiminoimidazolidine-2-one

The kinetic parameters of the exothermic decomposition of the title compound in a temperatureprogrammed mode have been studied by means of DSC. The DSC data obtained are fitted to the integral, differential, and exothermic rate equations by the linear least-squares, iterative, combined dichotomous, and least-squares methods, respectively. After establishing the most probable general expression of differential and integral mechanism functions by the logical choice method, the corresponding values of the apparent activation energy (E _a), preexponential factor (A), and reaction order (n) are obtained by the exothermic rate equation. The results show that the empirical kinetic model function in differential form and the values of E _a and A of this reaction are (1 − α)^−4.08, 149.95 kJ mol⁻¹, and 10^14.06 s⁻¹, respectively. With the help of the heating rate and kinetic parameters obtained, the kinetic equation of the exothermic decomposition of the title compound is proposed. The critical temperature of thermal explosion of the compound is 155.71°C. The above-mentioned kinetic parameters are quite useful for analyzing and evaluating the stability and thermal explosion rule of the title compound. The text was submitted by the authors in English.     

Synthesis and thermal decomposition kinetics of La(III) complexwith unsymmetrical Schiff base ligand

A new unsymmetrical solid Schiff base (LLi) was synthesized using L-lysine, o-vanillin and 2-hydroxy-l-naphthaldehyde. Solid lanthanum(III) complex of this ligand [LaL(NO₃)]NO₃·2H₂O have been prepared and characterized by elemental analyses, IR, UV and molar conductance. The thermal decomposition kinetics of the complex for the second stage was studied under non-isothermal condition by TG and DTG methods. The kinetic equation may be expressed as: dα/dt=Ae^−E/RT(1−α)². The kinetic parameters (E, A), activation entropy ΔS ^# and activation free-energy ΔG ^# were also gained.     

Thermochemistry of europium and dithiocarbamate complex Eu(C5H8NS2)3(C12H8N2)

A solid complex Eu(C₅H₈NS₂)₃(C₁₂H₈N₂) has been obtained from reaction of hydrous europium chloride with ammonium pyrrolidinedithiocarbamate (APDC) and 1,10-phenanthroline (o-phen⋅H₂O) in absolute ethanol. IR spectrum of the complex indicated that Eu³⁺ in the complex coordinated with sulfur atoms from the APDC and nitrogen atoms from the o-phen. TG-DTG investigation provided the evidence that the title complex was decomposed into EuS. The enthalpy change of the reaction of formation of the complex in ethanol, Δ_r H _m ^θ(l), as –22.214±0.081 kJ mol^–1, and the molar heat capacity of the complex, c _m, as 61.676±0.651 J mol^–1 K^–1, at 298.15 K were determined by an RD-496 III type microcalorimeter. The enthalpy change of the reaction of formation of the complex in solid, Δ_r H _m ^θ(s), was calculated as 54.527±0.314 kJ mol^–1 through a thermochemistry cycle. Based on the thermodynamics and kinetics on the reaction of formation of the complex in ethanol at different temperatures, fundamental parameters, including the activation enthalpy (ΔH _≠ ^θ), the activation entropy (ΔS _≠ ^θ), the activation free energy (ΔG _≠ ^θ), the apparent reaction rate constant (k), the apparent activation energy (E), the pre-exponential constant (A) and the reaction order (n), were obtained. The constant-volume combustion energy of the complex, Δ_c U, was determined as –16937.88±9.79 kJ mol^–1 by an RBC-II type rotating-bomb calorimeter at 298.15 K. Its standard enthalpy of combustion, Δ_c H _m ^θ, and standard enthalpy of formation, Δ_f H _m ^θ, were calculated to be –16953.37±9.79 and –1708.23±10.69 kJ mol^–1, respectively.     

On the Apparent Compensation Effect Found for Two Consecutive Reactions

A critical analysis of the use of an overall single rate reaction equation instead of the true rate equation corresponding to a complex process consisting in two consecutive reactions is presented. In accordance with this approximation, often used in the kinetic analysis of the system in which several reactions take place, the overall process is described by the apparent activation parameters (the apparent activation energy, E _ap, and the apparent pre-exponential factor, A _ap) and the apparent conversion function. The theoretical isotherms (α=α(t), where a is the conversion degree and t is the time) have been simulated for a system in which two consecutive reactions occur. In this case, the apparent activation parameters depends on: (a) the considered range of the temperature; (b) the temperature, for a given conversion degree. It is shown that the apparent activation parameters are corrrelated by the compensation effect relationship: lnA _ap=α*+β*E _ap where α* and β* are the parameters of the linear regression. The possibility of using the apparent kinetic parameters to predict the isotherms α=α(t) for temperatures lower than those for which these parameters were evaluated, is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

The chemiluminescence of dispiro(1,2-dioxetane-diadamantane) sorbed on silipore activated by a phenanthroline complex of Eu(iii)

The thermal decomposition of dispiro(1,2-dioxetane-diadamantane) (1) sorbed on silipore containing EuCl₃ ando-phenanthroline was investigated. The observed chemiluminescence is caused by radiative deactivation of EU^*(iii) formed according to an energy transfer mechanism. Chemiluminescence decay in the course of the decomposition of1 is exponential with the rate constantk. The activation parameters of the decomposition of1 sorbed on silipore were determined from the temperature dependence ofk. These parameters are independent of the Eu(iii) content. A kinetic compensating effect was found: the dependence of logA onE _a as a function of the content of1. The mechanism of the compensating effect is discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 447–451, March, 1995.     

Synthesis and thermal decomposition kinetics of Th(IV) complex with unsymmetrical Schiff base ligand

Summary A new unsymmetrical Schiff base ligand (H₂LLi) was synthesized using L-lysine, o-vanillin and salicylaladyde. Thorium(IV) complex of this ligand [Th(H₂L)(NO₃)](NO₃)₂^.3H₂O have been prepared and characterized by elemental analyses, IR, UV and molar conductance. The thermal decomposition kinetics of the complex for the second stage was studied under non-isothermal condition by TG and DTG methods. The kinetic equation may be expressed as: dα/dt=A^.e^-E/RT.1/2 (1-α)^.[-ln(1-α)]^-1. The kinetic parameters (E, A), activation entropy ΔS¹and activation free-energy ΔG¹were also calculated.