Two complex cure mechanisms were simulated. Isoconversional kinetic analysis was applied to the resulting data. The study highlighted correlations between the reaction rate, activation energy ...dependency, rate constants for the chemically controlled part of the reaction and the diffusion-controlled part, activation energy and pre-exponential factors of the individual steps and change in rate-limiting steps. It was shown how some parameters computed using Friedman's method can help to identify change in the rate-limiting steps of the overall polymerization mechanism as measured by thermoanalytical techniques. It was concluded that the assumption of the validity of a single-step equation when restricted to a given
value holds for complex reactions. The method is not limited to chemical reactions, but can be applied to any complex chemical or physical transformation.
Several successful examples—where physically sounded kinetic information was obtained from thermoanalytical data in different application fields, such as polymerization of thermosetting resins, ...biobased polymers and nanocomposites, crystallization and glass transition of semi-crystalline polymers and their nanocomposites—are here presented and discussed. It is explained how the kinetic parameters obtained from advanced isoconversional methods can be interpreted in terms of reaction mechanisms or changes in the rate-limiting step of the overall process, in the case of complex chemical reactions or complex physical transitions, and how these parameters can be used to extract model-fitting parameters.
•Recommendations are provided for kinetic analysis of multi-step processes.•Focus is on four most commonly used approaches to multi-step kinetic analysis.•Specific advices are offered for efficient ...usage of each approach.
The present recommendations have been developed by the Kinetics Committee of the International Confederation for Thermal Analysis and Calorimetry (ICTAC). The recommendations provide guidance on kinetic analysis of multi-step processes as measured by thermal analysis methods such as thermogravimetry (TGA) and differential scanning calorimetry (DSC). Ways of detecting the multi-step kinetics are discussed first. Then, four different approaches to evaluation of kinetic parameters (the activation energy, the pre-exponential factor, and the reaction model) for individual steps are considered. The approaches considered include multi-step model-fitting as well as distributed reactivity, isoconversional, and deconvolution analyses. For each approach practical advice is offered on its effective usage. Due attention is also paid to the typical problems encountered and to the ways of resolving them. The objective of these recommendations is to help a non-expert with efficiently performing multi-step kinetic analysis and interpreting its results.
•Recommendations are provided for kinetic analysis of thermal polymerization.•Main focus is on analysis of DSC measurements.•Multi-step nature of polymerization kinetics is emphasized.•Model-fitting, ...isoconversional, and deconvolution analyses are discussed.•Specific advices are offered for efficient usage of each analysis.
The present recommendations have been developed by the Kinetics Committee of the International Confederation for Thermal Analysis and Calorimetry (ICTAC). The recommendations provide guidance on kinetic analysis of thermal polymerization, which incorporates both linear and crosslinking polymerization (curing). The focus is on treating the kinetics as measured by differential scanning calorimetry (DSC). The recommendations discuss basic reaction mechanisms and emphasize the multi-step nature of the polymerization kinetics. An overview of mechanistic and phenomenological models is provided for polymerization controlled by reaction kinetics and diffusion. Three different approaches to evaluation of kinetic parameters (activation energy, preexponential factor, reaction model) for individual steps are considered. These approaches comprise model-fitting, isoconversional, and deconvolution analyses. Practical advices are offered for effective usage of each approach. Attention is paid to the typical problems and to the ways of addressing them. The recommendations are intended to assist with efficiently conducting kinetic analysis and interpreting its results.
Isoconversional kinetic analysis involves evaluating a dependence of the effective activation energy on conversion or temperature and using this dependence for making kinetic predictions and for ...exploring the mechanisms of thermally stimulated processes. The paper discusses major results obtained by the authors in the area of the isoconversional analysis of polymer kinetics over the past decade. It provides a brief introduction to isoconversional methods and surveys the impact made by isoconversional analysis in several application areas that include kinetic predictions, thermal degradation, crosslinking (curing), glass transition, and glass and melt crystallization. It is concluded that isoconversional analysis has been used broadly and fruitfully because it presents a fortunate compromise between the single‐step Arrhenius kinetic treatments and the prevalent occurrence of processes whose kinetics are multi‐step and/or non‐Arrhenius.
An isoconversional method applies the Arrhenius equation to a narrow temperature region, ΔT related to a given extent of conversion.
•Recommendations developed for collecting TG, DSC, and DTA data for successful kinetic analysis.•Focus is on preparing proper samples and selecting adequate experimental conditions.•Specific advice ...is offered for most common types of thermal processes, chemical and physical.
The present recommendations have been developed by the Kinetics Committee of the International Confederation for Thermal Analysis and Calorimetry (ICTAC). The recommendations offer guidance for obtaining kinetic data that are adequate to the actual kinetics of various processes, including thermal decomposition of inorganic solids; thermal and thermo-oxidative degradation of polymers and organics; reactions of solids with gases; polymerization and crosslinking; crystallization of polymers and inorganics; hazardous processes. The recommendations focus on kinetic measurements performed by means of thermal analysis methods such as thermogravimetry (TG) or thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), and differential thermal analysis (DTA). The objective of these recommendations is to assist a non-expert with collecting adequate kinetic data by properly selecting the samples and measurement conditions.
The effective activation energy (Eα) dependency is used to compute the dependence of the pre-exponential factor (Aα) and of the mathematical function that describe the reaction mechanism f(α) in a ...model-free way. The effective rate constant kα(T) depends on both temperature (T) and extent of conversion (α) for multi-step reactions in nonisothermal mode.
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•Three methods to compute the pre-exponential factor in a model-free way are proposed.•Four methods to compute the function that describes the reaction model in a model-free way are proposed.•Accurate results were obtained using the compensation effect in association with Friedman’s or Vyazovkin’s methods.•Accuracies were estimated using a simulated multi-step reaction mechanism.
Four methods to compute the pre-exponential factor and the mathematical function that describe the reaction mechanism in a model-free way are proposed and their accuracies were estimated using a complex (multi-step) reaction mechanism that has been simulated. It is shown that the use of the compensation effect in association with Friedman’s or Vyazovkin’s isoconversional methods gives accurate results. Model-free estimation of these parameters can be an efficient tool for the elucidation of complex reaction mechanisms, in complementarity to the estimation of the effective activation energy dependency with temperature and extent of conversion.
► Kinetics concepts are introduced and advices on collecting data are given. ► Methods based on multiple temperature programs are recommended. ► Evaluation of log
A and
f(
α) or
g(
α) for ...isoconversional methods is described. ► Principles of securing reliability of model-fitting computations are offered. ► Problems of kinetic predictions and approaches to solving them are discussed.
The present recommendations have been developed by the Kinetics Committee of the International Confederation for Thermal Analysis and Calorimetry (ICTAC). The recommendations offer guidance for reliable evaluation of kinetic parameters (the activation energy, the pre-exponential factor, and the reaction model) from the data obtained by means of thermal analysis methods such as thermogravimetry (TGA), differential scanning calorimetry (DSC), and differential thermal analysis (DTA). The recommendations cover the most common kinetic methods, model-free (isoconversional) as well as model-fitting. The focus is on the problems faced by various kinetic methods and on the ways how these problems can be resolved. Recommendations on making reliable kinetic predictions are also provided. The objective of these recommendations is to help a non-expert with efficiently performing analysis and interpreting its results.
Advanced isoconversional methods allow isothermal and nonisothermal predictions to be made in a model-free way, i.e. without the knowledge of the reaction mechanism. Methods to perform these ...predictions are proposed and their accuracies estimated using simulated multi-step reactions.
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•Methods to perform isothermal and nonisothermal predictions in a model-free way are proposed.•The accuracy of each method has been estimated using simulated multi-step mechanisms.•Accurate results were obtained using two methods derived from Friedman’s and Vyazovkin’s equations.•Accurate results were obtained in the case of a multi-step reaction with two steps bearing the same activation energy.
Four complex mechanisms of two parallel independent reactions were simulated under various isothermal and nonisothermal conditions. Equations to perform isothermal predictions and nonisothermal simulations at a different temperature program are presented, based on the isoconversional methods of Vyazovkin and Friedman. Isoconversional kinetic parameters were used to simulate the reaction progress under different isothermal and nonisothermal conditions. It was shown that accurate simulations can be performed in a model-free way, i.e. without knowledge of the reaction mechanism. A higher accuracy was obtained for mechanism involving more separated individual steps. The methods proposed are applicable to both DSC and TG data.
•Two methods are presented for the model-free computation of pre-exponential factors.•Three new methods are proposed to compute the function that describes the reaction mechanism.•These methods give ...accurate results for both single-step and multi-step kinetics.
The study compared the accuracy of several model-fitting methods for the computation of compensation parameters. Two methods were presented for the model-free computation of the pre-exponential factor dependency using kinetic compensation parameters and isoconversional methods. These methods give accurate results for both single and multi-step kinetics. Once the pre-exponential factors have been evaluated in a model-free way, three model-free methods were proposed to compute the values of the mathematical function that describes the reaction mechanism for multi-step kinetics. These methods can be preferred according to the type of data available (i.e. differential or integral). Accurate results were obtained for both single and multi-step kinetics using two sets of simulated data and an experimental example.
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