Nicolas Sbirrazzuoli

Learning about epoxy cure mechanisms from isoconversional analysis of DSC data

Model-free isoconversional methods can be effectively applied to isothermal and non-isothermal differential scanning calorimetry (DSC) data on epoxy cures. These methods yield a dependence of the effective activation energy on the extent of cure. Analysis of this dependence allows for untangling complex cure processes that may include different chemical reactions or a chemical reaction complicated by a mass transfer processes such as viscous relaxation and vitrification. The applications are illustrated by simulations as well as by epoxy-anhydride and epoxy-amine cures.

Kinetic methods to study isothermal and nonisothermal epoxy-anhydride cure

The kinetics of epoxy-anhydride cure were studied by differential scanning calorimetry under isothermal and nonisothermal conditions. The data were fitted to single-step and to two-step kinetic models. In both cases the activation energies derived from nonisothermal measurements differ from the values obtained for the isothermal cure data. Unlike the model-fitting methods, a model-free isoconversional method of kinetic analysis yields matching dependencies of the activation energy on the extent of conversion for isothermal and nonisothermal experiments. For both dependencies, the effective activation energy increases from 20 kJ. mol -1 at the beginning of cure to 70 kJ. mol -1 when the process is near completion. The occurrence of the dependence suggests that the cure kinetics is determined by competing reactions. The model-fitting methods have not been capable of reliably detecting the complex character of the cure kinetics.

Simulations for evaluation of kinetic methods in differential scanning calorimetry. Part 3 — Peak maximum evolution methods and isoconversional methods

Abstract Various peak maximum evolution methods and isoconversional methods are compared, and the specific characteristics of each method are shown, from a mathematical viewpoint and by using simulated data. A convenient way of correcting the activation energy of the Ozawa method is proposed. Isoconversional methods should be preferred to peak maximum evolution methods, especially when an interpolation on the power and/or the temperature is performed. In the case of a complex mechanism of two parallel reactions, peak maximum evolution methods give only a mean value of the kinetic parameters, while isoconversional methods are useful in describing this complex mechanism.

Isoconversional Analysis of the Nonisothermal Crystallization of a Polymer Melt

extended the Avramiequation to nonisothermal conditions. While offering asimple way of estimating the Avrami exponent, Ozawa’sanalysis does not suggest a method of determining theactivation energy. However, estimating the activationenergy for nonisothermal crystallization of melts is not asstraightforward as it may seem. The value of k in Equa-tion (3) has the overall nature because the macroscopiccrystallization rate is generally determined by the rates oftwo processes, nucleation and nuclei growth. Since thesetwo processes are likely to have different activation ener-gies, the temperature dependence of the overall rate con-stant can rarely be fit by a single Arrhenius equationk ¼ A exp ERTð4ÞCommunication: The advanced isoconversional methodcan be used to determine effective activation energies ofthe nonisothermal crystallization of polymer melts. Theapplication of this method to differential scanning calori-metric data on the crystallization of poly(ethylene ter-ephthalate) yields an activation energy that increases withthe extent of crystallization from –270 to 20 kJ N mol

ESTIMATING THE ACTIVATION ENERGY FOR NON-ISOTHERMAL CRYSTALLIZATION OF POLYMER MELTS

The advanced isoconversional method can be used to determine the effective activation energy of non-isothermal crystallization of the polymer melts. The method has been applied to DSC data on crystallization of poly(ethylene terephthalate) (PET). The resulting activation energy increases with the extent of crystallization from -270 to 20 kJ mol-1. The variation is interpreted in terms of the Turnbull and Fisher crystallization theory.

Nonisothermal crystallization of polytetrafluoroethylene in a wide range of cooling rates.

Compared to other semicrystalline polymers, PTFE demonstrates a very fast crystallization process on cooling. This study explores for the first time the nonisothermal PTFE ultrafast crystallization under tremendously fast cooling rates (up to 800,000 K·s(-1)) achieved by using fast scanning calorimetry (FSC) and ultra-fast scanning calorimetry (UFSC). Regular DSC was also used to get crystallization at slower rates. The data obtained on a wide range of cooling rates (over 8 orders of magnitudes) help to get new knowledge about crystallization kinetics of PTFE. Both FSC and UFSC data show that it is impossible to bypass the crystallization and thus to reach a metastable glassy state even for the fastest cooling rate employed (800,000 K·s(-1)). The crystals formed under such conditions are slightly less stable than those produced under slower cooling rates, as reflected by a shift of the melting peak to lower temperature. The difference in crystal morphologies was confirmed by SEM observations. The variation of the effective activation energy (Eα) with the relative extent of crystallization reveals that PTFE crystallization follows a transition from regime II to regime III around 315-312 °C. Corroborated temperature dependences of Eα obtained respectively for crystallizations under slow and fast cooling rates were combined and fitted to the theoretical dependence of the growth rate derived from the Hoffman-Lauritzen theory.

Hybrid Nanocomposites: Advanced Nonlinear Method for Calculating Key Kinetic Parameters of Complex Cure Kinetics

Complex cure kinetics involved in the elaboration of organic/inorganic hybrid silicate nanocomposites based on diglycidyl ether of bisphenol A (DGEBA), 1,3-phenylenediamine (m-PDA), and modified montmorillonite (MMTm) clay have been studied. An advanced isoconversional method has been applied to nonisothermal data in order to evaluate cure kinetic parameters. A new method based on nonlinear optimization was proposed to compute nonisothermal kinetic parameters avoiding complex optimization techniques. The objective is to obtain kinetic parameters rather than modeling values in order to give more insight into the elucidation of complex cure mechanisms. Key kinetic parameters of cure have been computed according to this method. It appears that the reaction mechanism changes if MMTm is added to the curing system. The results reveal an increase of the efficiency of collisions in presence of MMTm at the beginning of the cure and an increase of the frequency of diffusion jumps at the later stage of the reaction.

Confidence intervals for the activation energy estimated by few experiments

Abstract Arrhenius parameters are usually estimated by substituting data of 3–5 experiments into a linearized kinetic equation. The use of both small population and linearization invalidates the normal hypothesis. The study focuses on estimating valid confidence intervals for the activation energy computed by the isoconversional method. For this method, a comparison of confidence intervals estimated by using Students distribution and a nonparametric (distribution-free) method has shown that Students estimates tend to be oversized. Realistic 95% confidence intervals can be constructed by using corrected Students percentiles ϑn−2, 0.975 of 4.0, 2.5, and 2.3 for 3, 4, and 5 heating rates experiments, respectively.

Kinetic analysis of isothermal cures performed below the limiting glass transition temperature

The paper addresses the problem of the application of isoconversional kinetic analysis to incomplete cures. Contrary to the expectations, a theoretical analysis suggests that correct estimates of the activation energy can be obtained if one uses the relative extents of cure instead of the absolute values. This conclusion is illustrated by simulated data for a hypothetical process and experimental data for epoxy-novolac cure.

Different kinetic equations analysis

A software is described enabling kinetic analysis under non-isothermal or isothermal conditions from DSC, or from TG data. The program offers thirteen methods of kinetic analysis for DSC, three for isothermal analysis and two for TG, with eight different functions for the choice of the proper mechanism for each of them.ZusammenfassungCu(II)-komplexe von Acenaphthoquinonmono-(4-methyl-quinolinyl)-hydrazon (AMH) der allgemeinen Zusammensetzung [CuLX2] (mitL=AMH;X=Cl, Br, I, OAc oder NO3) -ausgenommen die Sulfato-komplexe, die über die allgemeine Zusammensetzung [CuLSO4]2 verfügen — wurden hergestellt und mittels Elementaranalyse, Messungen des magnetischen Momentes, Leitfähigkeitsmessungen, IR, elektronen- und EPR-spektroskopischen Techniken und durch Thermoanalyse untersucht. Für alle Komplexe wurde eine planare Geometrie gefunden. Die TG-Kurven zeigen, daß die Komplexe in einem Schritt zersetzt werden, wobei am Ende dieses Schrittes CU2O gebildet wird.