The use of the IKP method for evaluating the kinetic parameters and the conversion function of the thermal decomposition of NaHCO3 from nonisothermal thermogravimetric data

Three linear isoconversional methods (Friedman, Flynn–Wall–Ozawa, and Kissinger–Akahira–Sunose) and the invariant kinetic parameters (IKP) method were used in order to examine the kinetics of the nonisothermal decomposition of a sodium bicarbonate (NaHCO₃). The objective of the paper is to show the usefulness of the IKP method to determine both the kinetic parameters and the kinetic model of the investigated process. The activation energy (E_a) value obtained by the IKP method is in good agreement with the values obtained by isoconversional methods. The IKP method associated with the criterion of coincidence of kinetic parameters for all heating rates led us to the following kinetic triplet: E_a = 95.5 kJ mol^?1, A = 2.65 × 10¹⁰ min^?1, and conversion function f(α) = (1 ? α) (first‐order reaction model, F1). © 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39: 462–471, 2007     

Kinetic parameters determination in non-isothermal conditions for the crystallisation of a silica-soda-lead glass

Two integral isoconversional methods (Flynn–Wall–Ozawa and Kissinger–Akahira–Sunose) and the invariant kinetic parameters method (IKP) were used in order to examine the kinetics of the non-isothermal crystallisation of a silica-soda-lead glass. The objective of the paper is to show the usefulness of the IKP method to determine both the activation parameters and the kinetic model of the investigated process. Thismethod associated with the criterion of coincidence of kinetic parameters for all heating rates and some procedures of the evaluation of the parameter from Johnson–Mehl–Avrami–Erofeev–Kolmogorov (JMAEK) equation led us to the following kinetic triplet: activation energy, E=170.5±2.5 kJ mol^–1 , pre-exponential factor, A=1.178±0.350·10 10 min^–1 and JMAEK model (A _m) m=1.5.     

Non-isothermal kinetic study on the decomposition of Zn acetate-based sol-gel precursor

The paper presents a non-isothermal kinetic study of the decomposition of Zn acetate-based gel precursors for ZnO thin films, based on the thermogravimetric (TG) data. The evaluation of the dependence of the activation energy (E) on the mass loss (Δm) using the isoconversional methods (Friedman (FR), Flynn-Wall-Ozawa (FWO) and Kissinger-Akahira-Sunose (KAS)) has been presented in a previous paper. It was obtained that the sample dried at 125°C for 8 h exhibits the activation energy independent on the heating rate for the second decomposition step. In this paper the invariant kinetic parameter (IKP) method is used for evaluating the invariant activation parameters, which were used for numerically evaluation of the function of conversion. The value of the invariant activation energy is in a good agreement with those determined by isoconversional methods. In order to determine the kinetic model, IKP method was associated with the criterion of coincidence of the kinetic parameters for all heating rates. Finally, the following kinetic triplet was obtained: E=91.7 (±0.1) kJ mol⁻¹, lnA(s⁻¹)=16.174 (±0.020) and F1 kinetic model.     

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.     

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.     

Application of iso-temperature method of multiple rate to kinetic analysis

A new method of the multiple rate iso-temperature was used to define the most probable mechanism g(α) of a reaction; the iterative iso-conversional procedure has been employed to estimate apparent activation energy E _a, the pre-exponential factor A was obtained on the basis of E _a and g(α). In this new method, the thermal analysis kinetics triplet of dehydration of calcium oxalate monohydrate is determined, which apparent activation energy E _a is 82.83 kJ mol^-1, pre-exponential factor A is 1.142·10⁵-1.235·10⁵ s^-1, the most probable mechanism belongs to phase boundary reaction R_n with integral form g(α)=1-(1-α)ⁿ and differential form f(α)=n(1-α)^1-(1/n), where accommodation factor n=2.40-1.40.     

草酸镁二水合物的非等温热分解动力学

The thermal decomposition of the magnesium oxalate dihydrate in a static air atmosphere was investigated by TG-DTG techniques. The intermediate and residue of each decomposition were identified from their TG curve. The kinetic triplet, the activation energy E, the pre-exponential factor A and the mechanism functionsf（a） were obtained from analysis of the TG-DTG curves of thermal decomposition of the first stage and the second stage by the Popesou method and the Flynn-Wall-Ozawa method.     

铀(Ⅵ)与不对称希夫碱配合物的合成和热分解反应动力学

邻苯二胺与5－氯－2－羟基二苯酮、邻香草醛作用合成了一种不对称希夫碱配体C₂₇H₂₁N₂O₃Cl（H₂L）。在正丁醇和甲醇体系中硝酸铀酰与该配体反应合成了一种固体希夫碱配合物[UO₂(HL)(NO₃)(H₂O)]·H₂O。通过元素分析、IR、UV、¹H NMR、TG-DTG及摩尔电导率分析等手段对合成的配合物进行了表征,用非等温热重法研究了铀(Ⅵ)配合物的热分解反应动力学,推断出第三步热分解的动力学方程为：d α /d t = A · e^{- E/RT} ·3/2[(1- α )^-1/3-1]^-1,得到了动力学参数E和A。并计算出了活化熵△S^¹和活化吉布斯自由能△G^¹。     

Comparative non-isothermal kinetic analysis of thermal degradation of poly(vinyl chloride) prepared by living and conventional free radical polymerization methods

Non-isothermal kinetics of the thermal degradation of poly(vinyl chloride) (PVC) prepared by a living radical polymerization (LRP) method was performed and compared with the results obtained from PVC prepared by the conventional free-radical process (FRP). Both differential and integral isoconversional methods were applied for determining the apparent activation energy of the dehydrochlorination stage. This study made clear noticeable differences in the thermal degradation of the PVC samples under analysis. The newly synthesized LRP-PVC material has a better thermal stability and presents substantial differences in the macroscopic kinetics of the dehydrochlorination process compared with conventional FRP-PVC. These differences were assessed in quantitative terms on the basis of the kinetic triplet [E_a,A,f(α)].     

1，1－二氨基2，2－二硝基乙烯（DADE）的热化学性质、热行为和热分解机理

The constant-volume combustion energy, △cU （DADE, s, 298.15 K）, the thermal behavior, and kinetics and mechanism of the exothermic decomposition reaction of 1,1-diamino-2,2-dinitroethylene （DADE） have been investigated by a precise rotating bomb calorimeter, TG-DTG, DSC, rapid-scan fourier transform infrared （RSFT-IR） spectroscopy and T-jump/FTIR, respectively. The value of △cHm （DADE, s, 298.15 K） was determined as （-8518.09±4.59） j·g^-1. Its standard enthalpy of combustion, △cU （DADE, s, 298.15 K）, and standard enthalpy of formation, △fHm （DADE, s, 298.15 K） were calculated to be （-1254.00±0.68） and （- 103.98±0.73） kJ·mol^-1, respectively The kinetic parameters （the apparent activation energy Ea and pre-exponential factor A） of the first exothermic decomposition reaction in a temperature-programmed mode obtained by Kissinger＇s method and Ozawa＇s method, were Ek=344.35 kJ·mol^-1, AR= 1034.50 S^-1 and Eo=335.32 kJ·mol^-1, respectively. The critical temperatures of thermal explosion of DADE were 206.98 and 207.08 ℃ by different methods. Information was obtained on its thermolysis detected by RSFT-IR and T-jump/FTIR.     

Correlation Between Polarographic Half-Wave Potentials and Electronic Spectra of Cis-Trans Complexes of Chromium (III) and Rhodium (III)

A linear correlation between half-wave potential (E^1/2) for the process M(III)→M(II) and the first d-d transition band (v) of the types cis and trans-[M(en)₂X₂]ⁿ⁺ (M=Cr(III) and Rh(III), X=ONO^?, NCS^?, F^?, Cl^?, Br^?, I^?, H₂O, DMF, DMSO, n=1, 3) was found. The plots of the difference in half-wave potential (ΔE_1/2) against the difference in the first d-d transition hand (Δv) for the cis and trans isomer are straight lines. The equations, E_1/2=β/nαF+K₁ and ΔE_1/2=(β/NαF)Δ were derived, and used to describe the linear correlations between polarographic behavior and electronic spectrum.     

Researches on Thermal Decomposition Kinetics of Composite Modified Double-base Propellants

The thermal decomposition kinetics of composite modified double‐base (CMDB) propellants with a series of contents of hexogeon (RDX) was investigated by using parameters of T_eo, T_i, T_p, T_f, T_b, T_a, E, lg A and ΔH, which were obtained from using a CDR‐4P differential scanning calorimeter (DSC) and Perkin‐Elmer Pyris 1 thermogravimetric analyzer (TG) analyses with heating rates of 5, 10, 15 and 20 K/min. Reliable activation energy was calculated using Flynn‐Wall‐Ozawa method before analyzing the thermal decomposition mechanism. TG‐DTG curves were treated with Malek method in order to obtain the reaction mechanisms. The obtained results show that the thermal decomposition mechanisms with the conversion from 0.2 to 0.4 was f(α)?1/2α, and with the conversion from 0.5 to 0.7 was f(α)?(1/4)(1?α)[?ln(1?α)]^?3.     

Synthesis and thermal decomposition kinetics of Er(III) complex with unsymmetrical Schiff-base ligand

A new unsymmetrical, solid, Schiff base (H₂LLi) was synthesized using L-lysine, o-vanillin and salicylaldehyde. An Er(III) complex of this ligand [Er(H₂L)(NO₃)](NO₃)?·?2H₂O was prepared and characterized by elemental analysis, IR, UV and molar conductance. The thermal decomposition kinetics of the complex for the second stage was studied under non-isothermal conditions 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 S ^≠ and activation free-energy G ^≠ were also determined.     

Kinetic Analysis of Nonisothermal Decomposition of Acetyl Ferrocene

The work deals with thermal decomposition of acetyl ferrocene in nitrogen atmosphere based on nonisothermal thermogravimetry. It presents a mathematical analysis of nonisothermal thermogravimetric data using multiheating rates to estimate reaction kinetic parameters. Model free (integral isoconversional) methods are employed to analyze the thermogravimetric data. The decomposition is a multistep process. The activation energy E_α of decomposition is conversion (α) dependent. The average values of activation energy are E_α = 49.87, 106.28, and 183.35 kJ mol⁻¹ for three major steps of decomposition. The most probable reaction mechanism function, g(α), for thermal reactions has been identified by the master plot method, and the stepwise reaction mechanisms are found to be different for different steps. The estimated values of the activation energy E_α and g(α) have been utilized in the determination of the reaction rate A_α of thermal decomposition. The α‐dependent reaction rate values are determined and are found to lie in the range of 5.2 × 10⁵ to 3.2 × 10⁴ min⁻¹, 1.7 × 10¹⁵ to 7.8 × 10⁶ min⁻¹, and 3.8 × 10⁸ to 1.4 × 10⁷ min⁻¹ for three different steps. Based on the values of E_α, g(α), and A_α, the thermodynamic triplets (ΔS, ΔH, ΔG) associated with the decomposition reactions have been estimated. Estimated kinetic parameters have been used to construct the conversion curves, and those have been successfully compared with the experimentally observed ones.     

鬼臼毒素及其衍生物热分解反应的动力学研究

The thermal behavior and thermal decomposition kinetic parameters of podophyllotoxin （1） and 4 derivatives, picropodophyllin （2）, deoxypodophyllotoxin （3）, fl-apopicropodophyllin （4）, podophyllotoxone （5） in a temperature-programmed mode have been investigated by means of DSC and TG-DTG. The kinetic model functions in differential and integral forms of the thermal decomposition reactions mentioned above for first stage were established. The kinetic parameters of the apparent activation energy Ea and per-exponential factor A were obtained from analy- sis of the TG-DTG curves by integral and differential methods. The most probable kinetic model function of the decomposition reaction in differential form was （1- a）^2 for compounds 1-3,2/3·a^-1/2 for compound 4 and 1/2（1-a）·[-In（1-a）]^-1 for compound 5. The values of Ea indicated that the reactivity of compounds 1-5was increased in the order： 5〈4〈2〈1〈3. The values of the entropy of activation △S^≠, enthalpy of activation △H^≠ and free energy of activation △G^≠ of the reactions were estimated. The values of △G^≠ indicated that the thermal stability of compounds 1-3 with the samef（a） was increased in the order： 2〈3〈1.     

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.     

Synthesis and Properties of [Cd(HTRTR)2(H2O)4](HTNR)2 as an Energetic Complex

The energetic complex, [Cd(HTRTR)₂(H₂O)₄](HTNR)₂ {HTRTR = 4‐[3‐(1,2,4‐triazol‐yl)‐1,2,4‐triaozle; HTNR^– = styphnic acid anion) was synthesized and characterized by FT‐IR spectroscopy, elemental analysis, and single‐crystal X‐ray diffraction. It crystallizes triclinic in space group P$\bar{1}$ [a = 8.156(2) Å, b = 8.374(2) Å, c = 13.267(4) Å, α = 84.925(11)°, β = 87.016(11)°, γ = 63.683(5)°, V = 808.9(4) ų, ρ = 1.940 g · cm^–3]. The Cd^II ion is six‐coordinate with two HTRTRs and four water molecules. The thermal stabilities were investigated by differential scanning calorimetry (DSC). Non‐isothermal reaction kinetic parameters were calculated by Kissinger's and Ozawa‐Doyle's methods to obtain E_K = 144.0 kJ · mol^–1, lgA_K = 14.22, and E_O = 144.3 kJ · mol^–1. The values of thermodynamic parameters, the peak temperature while β→0 (T_p0), free energy of activation (ΔG^≠), entropy of activation (ΔS^≠), and enthalpy of activation (ΔH^≠) were obtained. Additionally, the enthalpy of formation was calculated by Hess's law on the basis of the experimental constant‐volume heat of combustion measured by bomb calorimetry, obtaining Δ_fH°₂₉₈ = 4985.5 kJ · mol^–1. Finally, the sensitivities toward impact and friction were assessed according to relevant methods. The result indicates it as an insensitive energetic material.     

Kinetic Analysis of Thermal Decomposition of Ca(OH)2 Formed During Hydration of Commercial Portland Cement by DSC

In this paper, evaluation of kinetic parameters (the activation energy – E,the pre-exponential factor – A and the reaction order – n) with simultaneous determination of the possible reaction mechanism of thermal decomposition of calcium hydroxide (portlandite), Ca(OH)₂ formed during hydration of commercial Portland-slag cement, by means of differential scanning calorimetry (DSC) in non-isothermal conditions with a single heating–rate plot has been studied and discussed. The kinetic parameters and a mechanism function were calculated by fitting the experimental data to the integral, differential and rate equation methods. To determine the most probable mechanism, 30 forms of the solid-state mechanism functions, f(α_c) have been tried. Having used the procedure developed and the appropriate program support, it has been established that the non-isothermal thermal decomposition of calcium hydroxide in the acceleratory period (0.004<α_c<0.554) can be described by the rate equation: d α_c/dT=A/βexp(−E/RT)f(α_c), which is based on the concept of the mechanism reaction:f(α_c)=2(α_c)^1/2. The mechanism functions as well as the values of the kinetic parameters are in good agreement with those given in literature. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermally induced incomplete high-spin (5T2) ⇌ low-spin (1A1) transition in solid bis[2-(2-pyridylamino)-4-(2-pyridyl) thiazolato]iron (II)

The ⁵⁷Fe Mössbauer effect in two samples (A and B) of [Fe(papt)₂] and in its solvates with CHCl₃ and C₆H₆ has been studied between 4.2 and 343 K and clearly indicates a temperature induced high-spin (⁵T₂) ? low-spin (¹A₁) transition in these compounds [paptH = 2-(2-pyridylamino)-4-(2-pyridyl) thiazole]. At 343 K, sample B shows a doublet with ΔE_Q = 2.03 mm s^?1 and δIS = +0.87 mm s^?1, characteristic of a ⁵T₂ ground state. At 257 K, a second doublet, typical for a ¹A₁ ground state, is observed and its intensity increases as the transition progresses but levels off below ～ 100 K. At 4.2 K, 83% of the intensity is due to the ¹A₁ state, and ΔE_Q(¹A₁) = 1.56 mm s^?1 and δ^IS(¹A₁ = +0.32 mm s^?1. In an applied magnetic field, V_zz(¹A₁) < 0 and η ≈ 0.7 have been determined, whereas for the ^sT₂ ground state, V_zz(^sT₂) > 0, η ≈ 0.75, and an internal hyperfine field H_n ≈ ?13 kG have been observed. Similar results have been obtained with the other samples.Debye-Waller factors f5_T2 and f1_A1 were determined from the saturation corrected areas in the Mössbauer spectra, assuming Curie-Weiss dependence of the magnetic susceptibility for the ⁵T₂ and constant υ_cff for the ¹A₁ ground state. The temperature dependence of ?In f1_A1 closely follows the Debye model with Θ1_A1 = 165 K, whereas the same applies to ?ln f5_T2 only above ～ 210 K and Θ5_T2 = 134 K. The nature of the observed transition is discussed and the data presented are shown to be incompatible with a model based on a Boltzmann distribution between the two states.