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. The dependencies of a and b parameters on the heating rate and T _m (temperature corresponding to maximum reaction rate) are derived. The theoretical results are discussed and checked for (a) TG simulated data for a single first order reaction; (b) TG data for PVC degradation; (b) the dehydration of CaC₂O₄·H₂O.     

On the evaluation of the nonisothermal kinetic parameters of (GeS2)0.3(Sb2S3)0.7 crystallization using the IKP method

The isoconversional method suggested by Friedman and the invariant kinetic parameters method (IKP) were used in order to examine the kinetics of the nonisothermal crystallization of (GeS₂)_0.3(Sb₂S₃)_0.7. The objective of the paper is to show the usefulness of the IKP method both for determining the activation parameters as well as the model of the investigated process. It was shown that the kinetic triplet [(E, A, f(α), where E is the activation energy, A is the preexponential factor, and f(α) is the differential function of conversion], which results through the application of the IKP method, depends on the set of kinetic models considered. For different sets of kinetic models, proportional values of f(α) are obtained. A criterion for the selection of this set, the use of which lead to the true kinetic triplet corresponding to the analyzed process (E = 163.2 kJ mol^?1; A = 2.47 × 10¹² min^?1 and the Avrami‐Erofeev model, A_m, for m = 2.5–2.6 was suggested. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 309–315, 2004     

An experimental and theoretical mechanistic analysis of thermal degradation of polypropylene/polylactic acid/clay nanocomposites

Polypropylene/polylactic acid (PP/PLA) blends containing 5 wt% of nanoclay in presence and absence of an ethylene‐butylacrylate‐glycidyl methacrylate terpolymer as compatibilizer were prepared by melt‐mixing process. A matrix‐droplet–type morphology confirmed by transmission electron microscope (TEM) and scanning electron microscopy (SEM) studies is formed in presence and absence of the compatibilizer in which the clay platelets were mainly localized in the polylactic acid (PLA) dispersed phase. Degradation studies by means of thermogravimetry analysis (TGA) and analysis of degradation activation energy (E_a), T_max (maximum degradation temperature), and ΔT (difference between initial and final degradation temperatures) parameters for each polymer component of the system revealed that incorporation of less stable PLA phase to polypropylene (PP) decreases E_a and T_max parameters, and hence, reduces the thermal stability of PP phase, while incorporation of clay nanoplatelets to the neat blend further reduces its thermal stability attributed to their lack of localization in PP phase. Compatibilization of the filled system results in migration of clay nanoplatelets toward PP and improves E_a and T_max of PP phase. On the other hand, the E_a and T_max of PLA phase of the blend were increased with incorporation of clay and its localization within that phase, while compatibilization of the filled system slightly reduces thermal stability of PLA phase due to migration of clay toward PP. A correlation was found between E_a and intensity of the thermogravimetry analysis Fourier‐transform infrared spectroscopy (TGA‐FTIR) peaks of the evolved products. Using the Criado method, a detailed analysis on degradation mechanism of each component was performed, and the changes in the degradation mechanism of the developed systems were determined.     

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.     

The influence of grafted cellulose nanofibers and postextrusion annealing treatment on selected properties of poly(lactic acid) filaments for 3D printing

l ‐lactide monomers were grafted onto cellulose nanofibers (CNFs) via ring‐opening polymerization, forming poly(lactic acid) grafted cellulose nanofibers (PLA‐g‐CNFs). PLA‐g‐CNFs and pristine PLA were then blended in chloroform and dried to prepare a master batch. PLA‐g‐CNFs/PLA composite filaments targeted for 3D printing were produced by compounding the master batch in PLA matrix and melt extrusion. The as‐extruded composite filaments were subsequently thermal annealed in a conventional oven, and their morphological, thermal, and mechanical properties were evaluated. PLA was successfully grafted on the surface of CNFs as demonstrated by elemental analysis, and the concentration of grafted PLA was estimated to be 33 wt %. The grafted PLA were highly crystallized, contributing to the growth of crystalline regions of PLA matrix. The incorporation of PLA‐g‐CNFs improved storage modulus of the composite filaments in both low temperature glassy state and high temperature rubbery state. Postextrusion annealing treatment led to 28 and 63% increases for tensile modulus and strength of the filaments, respectively. Simulated Young's moduli from the Halpin‐Tsai and Krenchel models were found comparable with the experimental values. The formed composite filaments are suitable for use in 3D printing. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 847–855     

Thermal Degradation Kinetics of Polyurethane/Organically Modified Montmorillonite Clay Nanocomposites by TGA

Polyurethane (PU) has been prepared by using polyether polyol (jagropol oil) and 1,6- hexamethylene diisocyanate (HMDI) as a cross-linker. The organically modified montmorillonite clay (MMT) is well-dispersed into urethane matrix by an in situ polymerization method. A series of PU/MMT nanocomposites have been prepared by incorporating varying amounts of nanoclay viz., 1, 3, 5 and 6 wt %. Thermogravimetric analysis (TGA) of the PU/MMT nanocomposites has been performed in order to establish the thermal stability and their mode of thermal degradation. The TGA thermograms exhibited the fact that nanocomposites have a higher decomposition temperature in comparison with the pristine PU. It was found that the thermal degradation of all PU nanocomposites takes place in three steps. All the nanocomposites were stable up to 205°C. Degradation kinetic parameters of the composites have been calculated for each step of the thermal degradation processes using three mathematical models namely, Horowitz–Metzger, Coats–Redfern and Broido's methods.     

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     

Biomimetic strengthening polylactide scaffold materials for bone tissue engineering

In this paper, a new polylactide (PLA)-based scaffold composite by biomimetic synthesis was designed. The novel composite mainly consists of nano-hydroxyapatite (n-HA), which is the main inorganic content in natural bone tissue for the PLA. The crystal degree of the n-HA in the composite is low and the crystal size is very small, which is similar to that of natural bone. The compressive strength of the composite is higher than that of the PLA scaffold. Using the osteoblast culture technique, we detected cell behaviors on the biomaterial in vitro by SEM, and the cell affinity of the composite was found to be higher than that of the PLA scaffold. The biomimetic three-dimensional porous composite can serve as a kind of excellent scaffold material for bone tissue engineering because of its microstructure and properties. Translated from Journal of Hunan University (Natural Sciences), 2006, 33(2) (in Chinese)     

Evaluation of the thermal degradation of PC/ABS/montmorillonite nanocomposites

Polycarbonate (PC)/acrylonitrile‐butadiene‐styrene (ABS) polymer alloy/montmorillonite (MMT) nanocomposites were prepared using a direct melt intercalation technique. The pyrolytic degradation and the thermo‐oxidative degradation of the polymer alloy and the nanocomposites were studied by thermogravimetric analysis (TGA). The kinetic evaluations were performed by the model‐free kinetic analysis and the multivariate non‐linear regression. Apparent kinetic parameters for the overall degradation were calculated. The results show that PC/ABS/MMT nanocomposites have high thermal stability and low flammability. Their pyrolytic degradation and the thermo‐oxidative degradation model are different. The pyrolytic degradation reaction of the polymer is a two‐step parallel reaction model: nth‐order reaction model, and ath‐degree autocatalytic reaction with an nth‐order reaction autocatalytic reaction, whereas the thermal oxidative degradation reaction of the polymer is a two‐step following reaction model: A → B → C of nth‐order reaction model, and autocatalytic reaction model. Copyright © 2005 John Wiley & Sons, Ltd.     

Flammability and Thermal Oxidative Degradation Kinetics of Magnesium Hydroxide and Expandable Graphite Flame Retarded Polypropylene Composites

The flammability and the thermal oxidative degradation kinetics of expandable graphite (EG) with magnesium hydroxide (MH) in flame‐retardant polypropylene (PP) composites were studied by limiting oxygen index (LOI), UL‐94 test, and thermogravimetric analysis (TGA). The results show that EG is a good synergist for improving the flame retardancy of PP/MH composite and the effect is enhanced with decreasing EG particle size. The Kissinger method and Flynn‐Wall‐Ozawa method were used to determine the apparent activation energy (E) for degradation of PP and flame retarded PP composites. The data obtained from the TGA curve indicate that EG markedly increases the thermal degradation temperature of PP/MH composites and improves the thermal stability of the composites. The kinetic results show that the values of E for degradation of flame retarded PP composites is much higher than that of neat PP, especially PP/MH composites with suitable amount of EG, which indicates that the flame retardants used in this work have a great effect on the mechanisms of pyrolysis and combustion of PP.     

Thermal degradation and their kinetics of biodegradable poly(butylene succinate-co-butylene terephthate)s under nitrogen and air atmospheres

In this study, thermal degradation and their related kinetics have been investigated mainly by means of thermal gravimetrical analyzer (TGA) under the dynamic nitrogen and air atmospheres for the chemically prepared biodegradable aliphatic-aromatic copolyesters of poly(butylene succinate-co-butylene terephthalate) (PBST). To further shed new lights on the comonomer molar composition and experimental condition dependences of thermal degradation kinetics, the as-known Friedman model was at first applied to quantitatively evaluate the kinetic parameters in terms of activation energy (E), degradation reaction order (n) and the frequency factor (Z). The results clearly demonstrated that thermal stabilities of these PBST copolyesters were substantially enhanced with the incorporation of more rigid butylene terephthalate comonomer, and tended to be much better in nitrogen than in air. Furthermore, the Friedman, Freeman-Carroll and Chang models were concurrently employed to quantitatively evaluate the thermal degradation kinetic parameters of the PBST copolyesters in nitrogen at different heating rates of 1, 2 and 5 K/min. It was found that the thermal degradation kinetic parameters for the PBST copolyesters were strongly dependent on the heating rate and calculating models. In addition, life-time parameters of the biodegradable PBST copolyesters were first calculated to predict the maximum usable temperatures, and this would be useful for practical application of these new bio-based green plastics.     

Equilibrium Structure of Beryllium Dibromide from Combined Gas Electron Diffraction and Vibrational Spectroscopy Analysis

The molecular structure of BeBr₂ has been investigated by gas-phase electron diffraction at the temperature 800(10) K. The conventional analysis yielded the following values: r _g(Be–Br) = 1.944(6)Å, l(Be–Br) = 0.068(4)Å, r _g(Br–Br) = 3.848(8)Å, l(Br–Br) = 0.109(3)Å, k(Be–Br) = 1.1(1.1) × 10^–5 ų, (Br–Br) = 2.1(1.0) × 10^–5 ų. Three models of nuclear dynamics were used to simulate the conventional analysis values—infinitesimal vibrations and two models, which take into account the kinematic and dynamic anharmonicity of the bending vibration. All models give similar values of bond angle, amplitudes, and shrinkage, excluding the harmonic model, which yields too low value l(Br–Br). The equilibrium bond distance r _e(Be–Br) = 1.932(11) Å was estimated, taking into account the anharmonicity corrections for stretching and bending vibrations and centrifugal distortion.     

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.     

Continuous and gradual photo-activation methods: influence on degree of conversion and crosslink density of composite resins

Thermal properties and degree of conversion (DC%) of two composite resins (microhybrid and nanocomposite) and two photo-activation methods (continuous and gradual) displayed by the light-emitting diode (LED) light-curing units (LCUs) were investigated in this study. Differential scanning calorimetry (DSC) thermal analysis technique was used to investigate the glass transition temperature (T _g) and degradation temperature. The DC% was determined by Fourier transform infrared spectroscopy (FT-IR). The results showed that the microhybrid composite resin presented the highest T _g and degradation temperature values, i.e., the best thermal stability. Gradual photo-activation methods showed higher or similar T _g and degradation temperature values when compared to continuous method. The Elipar Freelight 2^TM LCU showed the lowest T _g values. With respect to the DC%, the photo-activation method did not influence the final conversion of composite resins. However, Elipar Freelight 2^TM LCU and microhybrid resin showed the lowest DC% values. Thus, the presented results suggest that gradual method photo-activation with LED LCUs provides adequate degree of conversion without promoting changes in the polymer chain of composite resins. However, the thermal properties and final conversion of composite resins can be influenced by the kind of composite resin and LCU.     

Synthesis,Characterization, and Hydrolytic Degradation of Polylactide/Poly(ethylene glycol)/Nano-silica Composite Films

Poly(lactic acid) (PLA)/PEG/nano-silica composite degradable films have been prepared by solvent casting method. IR measurements showed that vibration of C–O–C group was confined by silica network. SEM results showed that nano-silica particles were dispersed uniformly in the PLA/PEG matrix. TGA results indicated that the thermal decomposition temperature rose with the increase of nano-silica content. The tensile strength of composite film increased by the addition of nano-silica particles into PLA/PEG matrix. The degradation rate of PLA/PEG/nano-silica composites increased with the acidic medium of degradation. On the other hand, the slower degradation was obtained in the neutral buffer solution. PLA/PEG/nano-silica composites were found to exhibit almost similar degradation behavior as that of PLA/PEG films.     

Synthesis and Characterization of a New Energetic Plasticizer: Acyl-Terminated GAP

A new energetic plasticizer, acyl-terminated glycidyl azide polymer (GAP), was synthesized through the reaction between 2,4,6-trinitrobenzoyl (TNB) chloride and GAP. The TNB-GAP structure was confirmed by FT-IR, UV-vis, ¹H NMR, and ¹³C NMR. The glass transition temperature (T _g ) of TNB-GAP was evaluated by differential scanning calorimetry (DSC), and the thermal stability of TNB-GAP was tested by thermogravimetric analysis (TGA). DSC traces showed that TNB-GAP had a T _g of ?46.01°C. TGA curves showed that the thermo-oxidative degradation of TNB-GAP in air was a two-step reaction, and the percentage of degraded TNB-GAP nearly reached 100% at 650°C. Exothermic decomposition reaction kinetic parameters of TNB-GAP were also studied using the non-isothermal DSC method. Results indicated that the values of apparent activation energy of TNB-GAP were 80.16 and 162.92 kJ/mol, and the values of the pre-exponential constant were 1.75 × 10¹⁰ and 1.22 × 10¹⁶.     

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

Summary: 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.     

Synthesis,characterization, and thermal stability of poly (lactic acid)/zinc oxide pillared organic saponite nanocomposites via ring‐opening polymerization of d,l‐lactide

Poly (lactic acid) (PLA) was synthesized using d , l ‐lactide monomer and zinc oxide (ZnO) pillared organic saponite as the green catalyst, through ring‐opening polymerization. The effects of stoichiometry of catalyst and polymerization conditions on molecular weight of PLA were evaluated by orthogonal experiment. The optimum polymerization parameters were: 0.5 wt% ZnO pillared organic saponite and reaction conditions of 170°C for 20 hr. Fourier transform infrared spectroscopy and ¹H nuclear magnetic resonance spectroscopy confirmed the PLA structure. Gel permeation chromatography showed that the average molecular weight of PLA was 48,442 g/mol, and its polydispersity index was 1.875. Differential scanning calorimetry, X‐ray diffraction, and polarized optical microscopy showed that ZnO pillared organic saponite improved the crystallinity of PLA. Thermal gravimetric analysis showed improved thermal stability of PLA because of ZnO pillared organic saponite. Thermal decomposition kinetics of PLA/ZnO pillared organic saponite nanocomposites was also studied. The activation energies (E_a) for thermal degradation of PLA and PLA/ZnO pillared organic saponite nanocomposites were evaluated by the Kissinger and Ozawa methods, which demonstrated that ZnO pillared organic saponite enhanced E_a of thermal degradation of PLA and significantly improved its thermal stability. Copyright © 2015 John Wiley & Sons, Ltd.     

Thermal degradation behavior of radiation synthesized polydiallyldimethylammonium chloride

Thermogravimetric analysis (TGA) and differential scanning calorimetric (DSC) studies were carried out on gamma radiation synthesized polydiallyldimethylammonium chloride (PDADMAC). The polymer was found to undergo thermal degradation in two stages. The first stage showed a weight loss of 33% and the second stage showed a weight loss of 67%. The DSC thermogram shows two endothermic peaks corresponding to the two stages in the TG thermogram and the experimental enthalpy change associated with the first and second stages were 650 J g⁻¹ and 129.5 J g⁻¹, respectively. The nth-order kinetic parameters (order of the reaction, activation energy and the pre-exponential factor) were determined from a single dynamic DSC or thermogravimetric (TG) thermogram by the method of least square. Theoretical TG/differential thermogravimetric (DTG) and DSC thermograms derived from the calculated kinetic parameters were in good agreement with the experimental ones at the heating rate employed. However, the kinetic parameters determined using TG and DSC were different. This leads to the conclusion that the degradation mechanism could be complicated and may consists of a number of parallel or consecutive reactions. The glass transition temperature (T_g) of the polymer was found to be around 150 °C depending on the test method employed.     

Improvement of thermal and mechanical properties of poly(L‐lactic acid) with 4,4‐methylene diphenyl diisocyanate

In this study, the thermal and mechanical properties of biodegradable poly(L ‐lactic acid) (PLA) were improved by reacting with 4,4‐methylene diphenyl diisocyanate (MDI). The resulting PLA samples were characterized with Fourier transformation infrared spectrometer (FT‐IR). The glass transition (T_g) and decomposing (T_d) temperature of the resulting products were measured using differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA), respectively. The tensile properties were also measured with a tensile tester. The results show that when the molar ratio of ? NCO to ? OH was 2:1, the T_g value can be increased to 64°C from the original 55°C, and the tensile strength increased from 4.9 to 5.8 MPa. This demonstrated that by reacting PLA with MDI at an appropriate portion, both the thermal and mechanical performance of PLA can be increased. Copyright © 2006 John Wiley & Sons, Ltd.