Application of model-free and multivariate non-linear regression methods for evaluation of the thermo-oxidative endurance of a recent manufactured parchment

The thermo-oxidative degradation of a parchment recent manufactured from a goat skin has been investigated by TG/DTG, DSC simultaneous analysis performed in static air atmosphere, at six heating rates in the range 3–15 K min⁻¹. At the progressive heating in air atmosphere, the investigated material exhibits three main successive processes occurring with formation of volatile products, namely the dehydration followed by two thermo-oxidative processes. The processing of the non-isothermal data corresponding to the first process of thermo-oxidation was performed by using Netzsch Thermokinetics—a Software Module for Kinetic Analysis. The dependence of activation energy, evaluated by isoconversional methods suggested by Friedman, and Ozawa, Flynn and Wall, on the conversion degree and the relative high standard deviations of this quantity show that the investigated process is a complex one. The mechanism and the corresponding kinetic parameters were determined by Multivariate Non-linear Regression program. Three mechanisms, one consisting in four successive steps and two others in five successive steps, exhibit the best F-test Fit Quality for TG curves. It was also used the previously suggested criterion, according to which the most probable process mechanism correspond to the best agreement between E _FR  = E _FR (α) (E _FR is the activation energy evaluated by isoconversional method suggested by Friedman; α is the conversion degree) obtained from non-isothermal experimental data and activation energy values, E _iso , obtained by applying the differential method to isothermal data simulated using non-isothermal kinetic parameters. According to this last criterion, the most probable mechanism of parchment oxidation consists in four successive steps. The contribution of the thermo-oxidation process in the parchment damage by natural aging is discussed.     

Thermal investigation of strontium acetate hemihydrate in nitrogen gas

The thermal decomposition of strontium acetate hemihydrate has been studied by TG-DTA/DSC and TG coupled with Fourier transform infrared spectroscopy (FTIR) under non-isothermal conditions in nitrogen gas from ambient temperature to 600°C. The TG-DTA/DSC experiments indicate the decomposition goes mainly through two steps: the dehydration and the subsequent decomposition of anhydrous strontium acetate into strontium carbonate. TG-FTIR analysis of the evolved products from the non-oxidative thermal degradation indicates mainly the release of water, acetone and carbon dioxide. The model-free isoconversional methods are employed to calculate the E _a of both steps at different conversion α from 0.1 to 0.9 with increment of 0.05. The relative constant apparent E _a values during dehydration (0.5<α<0.9) of strontium acetate hemihydrate and decomposition of anhydrous strontium acetate (0.5<α<0.9) suggest that the simplex reactions involved in the corresponding thermal events. The most probable kinetic models during dehydration and decomposition have been estimated by means of the master plots method.     

Comparative kinetic study of decomposition of some diazepine derivatives under isothermal and non-isothermal conditions

Thermal analysis is one of the most widely used methods for studying the solid state of pharmaceutical substances. TG/DTG and DSC curves provide important information regarding the physical properties of the pharmaceutical compounds (stability, compatibility, polymorphism, kinetic analysis, phase transitions etc.). The purpose of a kinetic investigation is to calculate the kinetic parameters and the kinetic model for the studied process. The results are further used to predict the system’s behaviour in various circumstances. A kinetic study regarding the diazepam, nitrazepam and oxazepam thermal decomposition was performed, under non-isothermal and isothermal conditions and in a nitrogen atmosphere, for the temperature steps: 483, 498, 523, 538 and 553 K. The TG/DTG data were processed by three methods: isothermal model-fitting, Friedman’s isothermal-isoconversional and Nomen-Sempere non-parametric kinetics. In the model-fitting methods the kinetic triplets (f(α), A and E _a) that defines a single reaction step resulted in being at variance with the multi-step nature of diazepines decomposition. The model-free approach represented by isothermal and non-isothermal isoconversional methods, gave dependences of the activation energies on the extent of conversion. It is very difficult to obtain an accord with the similar data which resulted under non-isothermal conditions from a previous work. The careful treatment of the kinetic parameters obtained in different thermal conditions was confirmed to be necessary, as well as a different strategy of experimental data processing.     

Advanced isoconversional and master plot analyses on solid-state degradation kinetics of a novel nanocomposite

The decomposition kinetics of glycerol diglycidyl ether (GDE)/3,3-dimethylglutaric anhydride/nanoalumina composite have been investigated by thermogravimetry analysis under nonisothermal mode. The activation energy, E _a, of the solid-state decomposition process was evaluated using the advanced isoconversional method. From the experimental data, the dependence of conversion on temperature and activation energy was constructed allowing calculating the master plots. Our results showed that the decomposition mechanism at temperatures below 400 °C could be fitted by R2 kinetic model with E _a = 143 kJ mol^?1. The information about the kinetic parameters based only on thermal degradation data has been used for quick lifetime estimation at different temperatures. The Vyazovkin method was also employed to predict the times to reach α = 0.5 at isothermal mode using the activation energy calculated by the advanced isoconversional approaches. Scanning electron microscopy (SEM) analysis was carried out to investigate the fracture surface morphology. It was revealed from the SEM images that the presence of nanoalumina results in reinforcement of GDE matrix.     

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.     

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.     

Kinetic analysis of thermal decomposition of some Co-complexes of three unsymmetrical <Emphasis Type="Italic">vic</Emphasis>-dioximes ligands

The thermal decomposition of three new reagent cyclohexylamine-p-tolylglyoxime (L₁H₂), tertiarybutyl amine-p-tolylglyoxime (L₂H₂) and secondary butylamine-p-tolylglyoxime (L₃H₂ and their Co-complexes were studied by both isothermal and nonisothermal methods. As expected, the complex structure of Co-complexes, different steps with different activation energies were realized in decomposition process. Model-fitting and model-free kinetic approaches were applied to nonisothermal and isothermal data. The kinetic triplet (f(α), A and E) related to nonisothermal model-fitting method can not be meaningfully compared with values obtained from isothermal method. The complex nature of the multi-step process of the studied compounds was more easily revealed using a wider temperature range in nonisothermal isoconversional method.     

Thermal cure kinetics of epoxidized linseed oil with anhydride hardener

The thermal cure kinetics of an epoxidized linseed oil with methyl nadic anhydride as curing agent and 1-methyl imidazole as catalyst was studied by differential scanning calorimetry (DSC). The curing process was evaluated by non-isothermal DSC measurements; three iso-conversional methods for kinetic analysis of the original thermo-chemical data were applied to calculate the changes in apparent activation energy in dependence of conversion during the cross-linking reaction. All three iso-conversional methods provided consistent activation energy versus time profiles for the complex curing process. The accuracy and predictive power of the kinetic methods were evaluated by isothermal DSC measurements performed at temperatures above the glass transition temperature of the completely cured mixture (T _g∞ ). It was found that the predictions obtained from the iso-conversional method by Vyazovkin yielded the best agreement with the experimental values. The corresponding activation energy (E _a) regime showed an increase in E _a at the beginning of the curing which was followed by a continuous decrease as the cross-linking proceeded. This decrease in E _a is explained by a diffusion controlled reaction kinetics which is caused by two phenomena, gelation and vitrification. Gelation during curing of the epoxidized linseed/methyl nadic anhydride system was characterized by rheological measurements using a plate/plate rheometer and vitrification of the system was confirmed experimentally by detecting a significant decrease in complex heat capacity using alternating differential scanning calorimetry (ADSC) measurements.     

Kinetic parameters for thermal decomposition of microcrystalline,vegetal, and bacterial cellulose

Cellulose can be obtained from innumerable sources such as cotton, trees, sugar cane bagasse, wood, bacteria, and others. The bacterial cellulose (BC) produced by the Gram-negative acetic-acid bacterium Acetobacter xylinum has several unique properties. This BC is produced as highly hydrated membranes free of lignin and hemicelluloses and has a higher molecular weight and higher crystallinity. Here, the thermal behavior of BC, was compared with those of microcrystalline (MMC) and vegetal cellulose (VC). The kinetic parameters for the thermal decomposition step of the celluloses were determined by the Capela-Ribeiro non-linear isoconversional method. From data for the TG curves in nitrogen atmosphere and at heating rates of 5, 10, and 20 °C/min, the E _α and B _α terms could be determined and consequently the pre-exponential factor A _α as well as the kinetic model g(α). The pyrolysis of celluloses followed kinetic model g(a) = [ - ln(1 - a)]^{1 \mathord}

Model-fitting and model-free analysis of thermal decomposition of palladium acetylacetonate [Pd(acac)2]

The non-isothermal decomposition process of the powder sample of palladium acetylacetonate [Pd(acac)₂] was investigated by thermogravimetric (TG) and the X-ray diffraction (XRD) techniques. Model-free isoconversional method of Tang, applied to the investigated decomposition process, yield practically constant apparent activation energy in the range of 0.05≤α≤0.95. It was established, that the Coats-Redfern (CR) method gives several statistically equivalent reaction models, but only for the phase-boundary reaction models (R2 and R3), the calculated value of the apparent activation energy (E) is nearest to the values of E obtained by the Tang’s and Kissinger’s methods. The apparent activation energy value obtained by the IKP method (132.4 kJ mol⁻¹) displays a good agreement with the value of E obtained using the model-free analysis (130.3 kJ mol⁻¹). The artificial isokinetic relationship (aIKR) was used for the numerical reconstruction of the experimental integral model function, g(α). It was established that the numerically reconstructed experimental function follows R3 reaction model in the range of α, taken from model-free analysis. Generally, decomposition process of Pd(acac)₂ starts with initial nucleation which was characterized by rapid onset of an acceleratory reaction without presence of induction period.     

Kinetic Analysis of Single or Multi-Step Decomposition Processes; Limits introduced by statistical analysis

A kinetic study on decomposition processes of some penicillin and some commercial drugs was carried out. As expected by the complex structures of penicillins, several steps with different activation energies occurred in their decomposition processes. Model-fitting and model-free kinetic approach were applied to non-isothermal and isothermal data. In the model-fitting methods the kinetic triplets (f(α), A and E _a) that defines a single reaction step resulted in being at variance with the multi-step nature of penicillins decomposition. The model-free approach represented by isothermal and non-isothermal isoconversional methods, gave dependences of the activation energies on the extent of conversion. The complex nature of the multi-step process of the studied compounds was more easily revealed using a broader temperature range in non-isothermal isoconversional method. The failure in the model fitting method did not allow calculating storage times. Model-fitting and model-free methods, both isothermal and non-isothermal, showed that F1 mechanism is able to describe decomposition processes for drugs (having Phosphomycin salts as active component) for which a single decomposition process occurs. Statistical analysis allowed us to select reliable kinetic parameters related to the decomposition processes for these last compounds. This procedure showed that the values obtained by extrapolation, outside the temperature range where the processes occurred must be used with caution. Indeed half-life and shelf-life values, commonly extrapoled at room temperature, seemed to be unrealistic. This revised version was published online in August 2006 with corrections to the Cover Date.     

Kinetics of non-isothermal crystallization of some glass-ceramics based on basalt

The crystallization kinetics of some glass-ceramics obtained from Romanian (Şanoviţa) basalt has been studied in non-isothermal conditions using DTA technique. The activation energies of the crystallization processes were calculated using the isoconversional methods Kissinger-Akahira-Sunose and Ozawa-Flynn-Wall. The results obtained show a dependence of the activation energy (E _α) on the crystallized fraction (α) that proves the complex mechanism of the glass-ceramics crystallization process. It has been proved that the Johnson-Mehl-Avrami model cannot be applied for the studied glass-ceramics crystallization process. The effect of 2% TiO₂ as nucleating agent upon the crystallization kinetics and upon the microstructure of the studied glass-ceramics was analyzed.     

Critical study of the isoconversional methods of kinetic analysis

A critical study of the use of isoconversional methods for the kinetic analysis of non-isothermal data corresponding to processes with either a real or an apparent variation of the activation energy, E, with the reacted fraction, α, has been carried out using for the first time simulated curves. It has been shown that the activation energies obtained from model-free methods are independent of the heating rate. However, the activation energy shows a very strong dependence of the range of heating rates used for simulating the curves if the apparent change of E with α is caused by overlapping processes with different individual activation energies. This criterion perhaps could be used for determining if a real dependence between E and α is really occurring.     

Non-isothermal oxidation kinetics of single- and multi-walled carbon nanotubes up to 1273 K in ambient

Non-isothermal oxidation kinetics of single- and multi-walled carbon nanotubes (CNTs) have been studied using thermogravimetry up to 1273 K in ambient using multiple heating rates. One single heating rate based model-fitting technique and four multiple heating rates based model-free isoconversional methods were used for this purpose. Depending on nanotube structure and impurity content, average activation energy (E _a), pre-exponential factor (A), reaction order (n), and degradation mechanism changed considerably. For multi-walled CNTs, E _a and A evaluated using model-fitting technique were ranged from 142.31 to 178.19 kJ mol⁻¹, respectively, and from 1.71 × 10⁵ to 5.81 × 10⁷ s⁻¹, respectively, whereas, E _a for single-walled CNTs ranged from 83.84 to 148.68 kJ mol⁻¹ and A from 2.55 × 10² to 1.18 × 10⁷ s⁻¹. Although, irrespective of CNT type, the model-fitting method resulted in a single kinetic triplet i.e., E _a, A, and reaction mechanism, model-free isoconversional methods suggested that thermal oxidation of these nanotubes could be either a simple single-step mechanism with almost constant activation energy throughout the reaction span or a complex process involving multiple mechanisms that offered varying E _a with extent of conversion. Criado method was employed to predict degradation mechanism(s) of these CNTs.     

Kinetic study of the thermal decomposition of poly(vinyl alcohol)/kraft lignin derivative blends

A kraft lignin derivative (KLD) obtained by reaction with p-aminobenzoic acid/phthalic anhydride, was blended with poly(vinyl alcohol) (PVA) by solution casting from DMSO. PVA and PVA/KLD films were exposed to ultraviolet radiation (Hg lamp, 96 h) and analyzed by thermogravimetry (TG) in inert and oxidative atmosphere. Typical multi-step decomposition profiles were obtained. The apparent activation energy (E_a) of the thermal degradation of the samples was computed by the Vyazovkin method. The KLD degradation presented only small intervals of decomposition degree with constant E_a values. PVA and blends showed intervals of up to 50% in decomposition degree with nearly constant E_a, and smaller intervals in which E_a varies drastically. The influences of samples irradiation and of surrounding gas in TG analysis on E_a are also shown.     

Application of Constant Reaction Rate TG to the Determination of Kinetic Parameters by Hi-Res TG

A simple operation mode to determine the apparent activation energy E _a is introduced. E _a can be determined with a double-curve method by using a constant reaction rate (CRR) approach of Hi-Res TG. The most appropriate mechanism function f(α) and frequency factor A are determined by a single-curve method when the activation energies provided by the two methods are in good agreement with each other. The deacetylation of EVA copolymer has been used for illustration. Advantages of the CRR are discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Electrophoresis of colloidal α-alumina

Measurements of the electrophoretic mobility (u _E) of particles of colloidal α-alumina were made as a function of pH, electrolyte concentration and electrolyte type (NaCl, NaNO₃ and KCl) using two similar instrumental techniques. Significant differences (50% or less) in the values of u _E of particles in NaCl were obtained from the two instruments; however, the isoelectric points (IEPs) (the pH at which u _E=0), estimated from the two sets of measurements, occurred at 7.5 ± 0.3 and 7.8 ± 0.05 and were not significantly different. The latter estimate corresponds with those for particles in KCl and NaNO₃ of 8.05 ± 0.11 and 7.95 ± 0.18, respectively, made using the same instrument and indicate that the IEP was a weak function of electrolyte type. When cations acted as counterions (pH > IEP), the absolute magnitudes and the ranges of u _E with electrolyte concentration were found to be significantly less than when anions acted as counterions (IEP > pH). Estimates of the zeta potential (ζ), made using various procedures, showed variations of up to 25% at low ratios of electrical-double-layer thickness (κ ⁻¹) to particle radius (a) (κa∼10) and were of a similar scale to differences in u _E, but no significant variations (95% confidence) in ζ were obtained at high values (κa∼200). Received: 12 July 2000 Accepted: 17 October 2000     

Determination of the Thermal Degradation Kinetic Parameters of Carbon Fibre Reinforced Epoxy Using TG

In this work, a kinetic study on the thermal degradation of carbon fibre reinforced epoxy is presented. The degradation is investigated by means of dynamic thermogravimetric analysis (TG) in air and inert atmosphere at heating rates from 0.5 to 20°C min⁻¹ . Curves obtained by TG in air are quite different from those obtained in nitrogen. A three-step loss is observed during dynamic TG in air while mass loss proceeded as a two step process in nitrogen at fast heating rate. To elucidate this difference, a kinetic analysis is carried on. A kinetic model described by the Kissinger method or by the Ozawa method gives the kinetic parameters of the composite decomposition. Apparent activation energy calculated by Kissinger method in oxidative atmosphere for each step is between 40–50 kJ mol⁻¹ upper than E _a calculated in inert atmosphere. The thermo-oxidative degradation illustrated by Ozawa method shows a stable apparent activation energy (E _a ≈130 kJ mol⁻¹ ) even though the thermal degradation in nitrogen flow presents a maximum E _a for 15% mass loss (E _a ≈60 kJ mol⁻¹ ). This revised version was published online in July 2006 with corrections to the Cover Date.     

Kinetics of thermal decomposition of some nitrophosphate fertilizers with micronutrients in isothermal conditions

The thermal behavior under isothermal conditions of some ammonia nitrate, ammonia phosphates and calcium phosphates mixtures with added micronutrients was studied. In order to establish the variation of activation energy (E) vs. conversion (α), the TG data were interpolated with spline functions, followed by numeric derivation. Using the so determined reaction rate the Friedman differential-isoconversional method was applied. A dependence of the activation energy vs. conversion was observed, meaning a many-step reaction. Therefore a procedure based on the compensation effect (and suggested by Budrugeac and Segal) was applied.     

Curing reaction of <Emphasis Type="Italic">o</Emphasis>-cresol-formaldehyde epoxy/LC epoxy(<Emphasis Type="Italic">p</Emphasis>-PEPB)/anhydride(MeTHPA)

The curing kinetics of a bi-component system about o-cresol-formaldehyde epoxy resin (o-CFER) modified by liquid crystalline p-phenylene di[4-(2,3-epoxypropyl) benzoate] (p-PEPB), with 3-methyl-tetrahydrophthalic anhydride (MeTHPA) as a curing agent, were studied by non-isothermal differential scanning calorimetry (DSC) method. The relationship between apparent activation energy E _a and the conversion α was obtained by the isoconversional method of Ozawa. The reaction molecular mechanism was proposed. The results show that the values of E _a in the initial stage are higher than other time, and E _a tend to decrease slightly with the reaction processing. There is a phase separation in the cure process with LC phase formation. These curing reactions can be described by the Šesták–Berggren (S–B) equation, the kinetic equation of cure reaction as follows: \frac\textda\textdt = Aexp( - \fracE_\texta RT )a^m ( 1 - a )ⁿ {\frac{{{\text{d}}\alpha }}{{{\text{d}}t}}} = A\exp \left( { - {\frac{{E_{\text{a}} }}{RT}}} \right)\alpha^{m} \left( {1 - a} \right)^{n} .