Invariant Kinetic Parameters Method Research Articles

Comprehensive method based on model free method and IKP method for evaluating kinetic parameters of solid state reactions

This article presents, firstly, a short review of methods for evaluating kinetic parameters of solid state reactions and a critical analysis of the isoconversional principle of model free methods. It shows theoretically that the activation energy for complex reactions is not only a function of the reaction degree but also of heating programs, and points out that any method that attempts to extract the dependences of activation energy on conversion degree without considering the dependences of heating programs is problematic. Then an analysis is given of the invariant kinetic parameters (IKP) method and recommends an incremental version of it. Based on the incremental IKP method and model free method, a comprehensive method is proposed that predicts the degree of the dependences of activation energy on heating programs, selects reliable values of activation energy and extracts the values of variable pre-exponential factor. This comprehensive method is tested using both simulation data and experimental data, the results of which show it can not only give reliable values of kinetic parameters but also be helpful in explaining inconsistencies of kinetic results in solid state reactions.

Synthesis, characterization and thermal degradation kinetics of aluminum diisobutylphosphinate

The novel flame retardant aluminum diisobutylphosphinate was synthesized and its structure was identified and studied by elemental analysis, infrared spectroscopy (IR) and X-ray diffraction (XRD). Thermal degradation behaviors of the novel flame retardant in a nitrogen atmosphere were studied using thermogravimetric analysis (TGA) techniques. The kinetic parameters, including the activation energy and frequency factor of the decomposition process for the title compound were calculated through the Friedman and the Kissinger–Akahira–Sunose (KAS) methods and the thermal decomposition mechanism was also studied with the invariant kinetic parameters (IKP) method based on a set of TGA data obtained at different heating rates. It was shown that the activation energies calculated for the decomposition reaction by different methods were found to be consistent and the conversion functions calculated by means of the IKP method depend on a set of kinetic models.

Thermal degradation kinetics and isoconversional analysis of biodegradable poly(3-hydroxybutyrate)/organomodified montmorillonite nanocomposites

Poly(3-hydroxybutyrate) (PHB)/organically modified clay nanocomposites were prepared by the melt mixing method and were characterized using wide-angle X-ray diffraction. Their thermal degradation kinetics was investigated using thermogravimetric analysis at various heating rates. Further kinetic analysis was performed using isoconversional methods and the invariant kinetic parameters method was used to estimate the so-called ‘true’ kinetic parameters, i.e. the pre-exponential factor, A and the activation energy, E, as well as the reaction model. It was found that intercalated structures are formed and the thermal stability of the material is improved by the addition of the nano-filler. From the isoconversional analysis, it was found that the activation energy does not vary significantly with the degree of degradation denoting degradation in one step with similar values for pure PHB and for all nanocomposites. Using the invariant kinetic parameters method, it was found that the model that best describes the experimental data was that of Sestak–Berggren's with f( a) = α n (1 − α) m , where the value of n is always larger than m and is increasing with the amount of the nano-filler. The value of the ‘true’ activation energy was found to be about 100 kJ mol −1 for all nanocomposites and the pre-exponential factor for PHB was estimated equal to 5.35 × 10 9 min −1. Finally, the values of the kinetic rate constant k were found to decrease with the amount of the nano-filler up to 3 wt%, while for amounts larger than 3 wt% k increased reaching a value greater than that of pure PHB for the 10 wt% nanocomposites.

Kinetic analysis of thermal degradation of poly(ethylene glycol) and poly(ethylene oxide)s of different molecular weight

The effect of molecular weight on thermal characteristics and thermal degradation of poly(ethylene glycol) (PEG) and poly(ethylene oxide)s (PEO) was investigated by differential scanning calorimetry, FT-IR spectroscopy and dynamic thermogravimetry. Kinetic analysis of the non-isothermal degradation was performed using isoconversional (Flynn–Wall–Ozawa, Kissinger–Akahira–Sunose and Friedman) and the invariant kinetic parameters method. The empirical kinetic triplets ( E, A, and f( α)) as well as the rate constants have been calculated. The relation between the heating rate, the degradation rate and molecular weight for all investigated samples has been established.

Thermal decomposition kinetics of some aromatic azomonoethers

Thermal analysis of 2-allyl-4-((4-(4-methylb- enzyloxy)phenyl)diazenyl)phenol dye was performed in air flow. The compound thermal behavior was investigated using TG, DTG and DSC techniques, under non-isothermal linear regime. Kinetic parameters of the two decomposition steps were obtained by means of multi-heating rates meth- ods. Isoconversioanl methods (KAS and FWO), Invariant Kinetic Parameters method and Perez-Maqueda et al. criterion (by means of CR and FW equations) were used.

Thermal degradation kinetics of g-HA/PLA composite

Thermal degradation behaviors of a composite constituted by poly( l-lactide) (PLA) and hydroxyapatite nanoparticle that was surface-grafted with l-lactic acid oligomer ( g-HA) in a nitrogen atmosphere were studied using thermogravimetric analysis (TGA) and compared with PLA. The kinetic models and parameters of the thermal degradation of PLA and the g-HA/PLA composite were evaluated by the invariant kinetic parameters (IKP) method and Flynn–Wall–Ozawa (FWO) method based on a set of TGA data obtained at different heating rates. It was shown that the conversion functions calculated by means of the IKP method depend on a set of kinetic models. The g-HA particle slowed down the thermal degradation of PLA polymer matrix.

Kinetic analysis of the non-isothermal degradation of poly(3-hydroxybutyrate) nanocomposites

Poly(3-hydroxybutyrate)/organically modified montmorillonite nanocomposites (PHB/25A) were prepared by the solution-intercalation method. The non-isothermal degradation of pure PHB and PHB/25A nanocomposites was investigated in the temperature range 50–500 °C at four heating rates (2.5, 5, 10 and 20 °C min −1). Kinetic analysis of the non-isothermal degradation of pure PHB and PHB/25A nanocomposites was performed using isoconversional (Flynn-Wall-Ozawa, Kissinger-Akahira-Sunose and Friedman) methods and the invariant kinetic parameters method. The true kinetic triplets ( E, A, and f( α)) were determined.

Thermal Degradation and Kinetics of Poly(3‐hydroxybutyrate)/Organoclay Nanocomposites

AbstractPoly(3‐hydroxybutyrate)/Cloisite30B (PHB/30B) nanocomposites were prepared by solution‐intercalation method. The influence of 30B content on the thermal stability of PHB was investigated. With the addition of 3 wt. % of 30B the highest thermal stability of PHB was achieved. The kinetic analysis of the non‐isothermal degradation was performed using the isoconversional Friedman method and invariant kinetic parameters method.

Thermal Stability Evaluation of PA6/LLDPE/SEBS‐g‐DEM Blends

AbstractSummary: The thermal stability of a polyamide‐6/low linear density polyethylene blend (PA6/LLDPE) was studied using thermal analysis techniques. The thermogravimetric studies carried out showed that when a diethyl maleate grafted styrene‐ ethylene/butadiene‐styrene terpolymer (SEBS‐g‐DEM) is added to the PA6/LLDPE blend there is an actual enhancement of the thermal stability due to the increase in the interfacial area within the blend. The Invariant Kinetic Parameter method (IKP) proved to be a qualitative technique unfolding the type of degradation mechanisms taking place in the material vicinity. Nucleation and phase boundary reactions are the kinetic models of thermal decomposition with the most significant probability of occurring.

The Kissinger law and the IKP method for evaluating the non-isothermal kinetic parameters

The following problems concerning the apparent compensation effect (CE) (lnA=a+bE, where A is the pre-exponential factor, E is the activation energy, a and b are CE parameters) due to the change of the conversion function and on which the invariant kinetic parameters method (IKP method) is based, are discussed: (1) the explanation of this kind of CE; (2) the choice of the set of conversion functions that checks CE relationship; (3) the dependencies of CE parameters on the heating rate and the temperature corresponding to the maximum reaction rate. Using the condition of maximum of the reaction rate suggested by Kissinger (Kissinger law), it is pointed out that, for a certain heating rate, the CE relationship is checked only for reaction order (Fn) and Avrami-Erofeev (An) kinetic models, and not for diffusion kinetic models (Dn). Consequently, IKP method, which is based on the supercorrelation relationship between CE parameters, can be applied only for the set Fn+ An of kinetic models.

Comparative kinetic study of the non-isothermal thermal curing of bis-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)=α0.6(1−α)2.4, E=120.9 kJ mol−1 and lnA=38.28 min−1.

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

AbstractThree 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 (Ea) 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: Ea = 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

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.

The kinetic analysis of non-isothermal nickel oxide reduction in hydrogen atmosphere using the invariant kinetic parameters method

The powder sample of nickel oxide was synthesized by sol–gel procedure. The non-isothermal reduction of nickel oxide using hydrogen, was investigated by temperature-programmed reduction (TPR) at four different heating rates (2.5, 5, 10 and 20 °C min −1). The kinetics parameters ( E a, ln A) were determined using Friedman (FR) isoconversional method and the invariant kinetic parameters method (IKP). The IKP method was applied in the conversion range of 0.20 ≤ α ≤ 0.60. The activation energy value obtained by the IKP method ( E a = 96.4 kJ mol −1) is somewhat higher than the value obtained by Friedman's method ( E a = 90.8 kJ mol −1). The values of invariant kinetic parameters were used for numerical evaluation of conversion function, f( α). The kinetic model of the investigated reduction process was determined, and this model corresponds to the empirical two-parameter Šesták–Berggren equation, which gives a more quantitative description. The kinetic triplet obtained for the investigated process is: E a = 96.4 kJ mol −1; A = 1.04 × 10 8 min −1 and f( α) = α 0.63(1 − α) 1.39. In agreement with the obtained results, the mechanism of nickel oxide reduction by hydrogen was considered.

Thermal decomposition kinetics of some aromatic azomonoethers

Thermal analysis of 2-allyl-4-((4-(4-methylbenzyloxy)phenyl)diazenyl)phenol dye was performed in air flow. The compound thermal behavior was investigated using TG, DTG and DSC techniques, under non-isothermal linear regime. Kinetic parameters of the two decomposition steps were obtained by means of multi-heating rates methods. Isoconversioanl methods (KAS and FWO), Invariant Kinetic Parameters method and Perez-Maqueda et al. criterion (by means of CR and FW equations) were used.

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.

Studies on the Effect of Atmospheric Oxygen Content on the Thermal Resistance of Intumescent, Fire-Retardant Coatings

Studies are conducted to measure the rate of thermal degradation and the thermal resistance of three intumescent fire-retardant coatings under atmospheres of varying oxygen content. The degradation trials are conducted using thermal gravimetric analysis and differential thermal analysis in an atmosphere of nitrogen or air. It has been found that a low oxygen content in the atmosphere significantly affects the rate of degradation of the char material at temperatures greater than 540°C. The global kinetics of the thermal degradation is modeled using three or four first-order parallel reactions. The degradation of char is modeled using the method of invariant kinetic parameters. The derived kinetic parameters are reported. The thermal resistance of the materials coated on steel plates is determined using a cone calorimeter with controlled oxygen content in the atmosphere. It has been found that the thermal resistance of two of the coatings has been strongly influenced by the oxygen content of the atmosphere; hence, this factor may be of importance when predicting the performance of intumescent materials in real fire scenarios.

Determining the temperature to initiate the explosion of a propellant

Gun propellants are per definition instable substances. During their lifetime a slow decomposition process is going-on. During this decomposition process the heat that is generated accelerates the process, which could result to an unsafe situation, or an unexpected explosion of the material. The temperature to initiate the explosion of a propellant is of importance for the storage conditions of such a substance. The method used so far to evaluate this temperature is based on an extrapolation of the Kissinger equation at zero heating rate. A new proposal is the use of the invariant kinetic parameters (IKP) method to determine the iso-kinetic temperature and extrapolating it to zero heating rate as an alternative method. The results are discussed for some examples.

Some methodological problems concerning the kinetic analysis of non-isothermal data for thermal and thermo-oxidative degradation of polymers and polymeric materials

The procedures used in some very recent works for evaluation of the kinetic parameters from non-isothermal data corresponding to thermal and thermo-oxidative degradation of polymers and polymeric materials are critically analysed. It is pointed out that only the use of a set of conversion degree vs. temperature curves recorded at different heating rates can give reliable information on the degradation mechanism and in some suitable cases, can lead to the true kinetic parameters. A general algorithm for evaluation of the kinetic parameters from the non-isothermal data is suggested. The application of this algorithm for a set of simulated non-isothermal data has been shown that when the activation energy is independent of the conversion, the invariant kinetic parameters method associated with the criterion of independence of kinetic parameters on the heating rate is recommended for evaluation of the kinetic triplet (activation energy, pre-exponential factor, conversion function).

The use of the IKP method for evaluating the kinetic parameters and the conversion function of the thermal dehydrochlorination of PVC from non-isothermal data

The isoconversional methods (Friedman and Flynn–Wall–Ozawa) as well as the invariant kinetic parameters method (IKP) were used to discriminate the kinetic models and to determine the kinetic parameters for the thermal degradation of PVC from the simultaneous analysis of a set of TG data obtained at different heating rates ranging from 2 to 10 K min −1 . The activation energy ( E ) value obtained by the IKP method is in good agreement with the values obtained by isoconversional methods. It was also shown that the values of the pre-exponential factor ( A ) and the conversion function ( f ( α ), where α is the conversion) calculated by means of the IKP method depend on the set of kinetic models considered. The ratio of the values of f ( α ), corresponding to two sets of kinetic model, does not depend on the conversion. This proportionality and the differences between f ( α ) values calculated for a certain set of kinetic models and the real values of f ( α ) can be explained by inherent errors in the evaluation of the invariant pre-exponential factor. The kinetic triplet obtained for the investigated process is: E=104.1 kJ mol −1 ; A=1.06×10 8 s −1 and f ( α )= α 0.63 (1− α ) 1.55 ≅(1− α ) 1.81 [−ln(1− α )] 0.62 .