Application of model-fitting and model-free kinetics to the study of non-isothermal dehydration of equilibrium swollen poly (acrylic acid) hydrogel: Thermogravimetric analysis

The dehydration kinetics of equilibrium swollen poly (acrylic acid) hydrogel is analyzed by both model-fitting and model-free approaches. The conventional model-fitting approach assuming a fixed mechanism throughout the reaction and extract a single values of the apparent activation energy (E_a) and pre-exponential factor (A) and was found to be too simplistic. The values of Arrhenius parameters obtained in such a way are in fact an average that does not reflect changes in the reaction mechanism and kinetics with the extent of conversion. The model-free approach allows for a change of mechanism and activation energy, E_a, during the course of a reaction and is therefore more realistic. The complexity of the dehydration of poly (acrylic acid) hydrogel is illustrated by the dependence of E_a and A on the extent of conversion, α (0.05 ≤ α ≤ 0.98). Under non-isothermal conditions, E_a decreases with α for 0 ≤ α ≤ 0.50, followed by an approximately constant value of E_a during further dehydration. For 0 ≤ α ≤ 0.50, dehydration is complex, which probably involving a combination of several processes. In the constant-E_a region, non-isothermal dehydration follows the three-dimensional phase boundary model (R3). The complex hydrogen-bond pattern in poly (acrylic acid) hydrogel is probably responsible for the observed dehydration behavior. An existence of compensation effect is accepted and explanation of compensation effect appearance during the hydrogel dehydration is suggested.     

Kinetics of thermal degradation applied to starches from different botanical origins by non-isothermal procedures

Amylose content, crystallinity, morphology and the kinetic of thermal degradation to starches from different botanical origins are described based on XRD, SEM, DSC and TG/DTG curves. Applying the non-isothermal isoconversional Wall-Flynn-Ozawa method on the TG/DTG curves average activation energy (0.10 ≤ α ≤ 0.70) E = 144.1 ± 9.8, 171.6 ± 14.6, 158.3 ± 7.4 and 159.4 ± 15 kJ mol⁻¹ could be obtained for thermal degradation of corn, rice, potato and cassava starches, respectively. From E values and the generalized time θ, the Sesták-Berggren (SB) in which f(α) = α^m(1 − α)ⁿ seems to be most suitable kinetic model in describing physicogeometrically the thermal degradation for the samples regardless of its botanical origins. The determination of the kinetic exponents m and n allows to obtain the pre-exponential factor (0.2 ≤ α ≤ 0.8) ln A = 8.8, 10.4, 9.2 and 8.9 min⁻¹ for corn, rice, potato and cassava starches, respectively. There were not significant differences between values of the kinetic triplet of the starches, indicating that, despite structural differences, these had little influence on the thermal degradation process of the starches.     

Isothermal and polythermal kinetics of depolymerization of C60 polymers

Isothermal depolymerization of the two polymers of C₆₀, i.e. of 1D orthorhombic phase (O) and of “dimer state” (DS) have been studied by means of Infra-red spectroscopy in the temperature ranges 383-423 and 453-503 K, respectively. Differential Scanning Calorimetry (DSC) has been used to obtained depolymerization polytherms for O-phase and DS. Standard set of reaction models have been applied to describe depolymerization behavior of O-phase and DS. The choice of the reaction models was based primarily on the isotherms. Several models however demonstrated almost equal goodness of fit and were statistically indistinguishable. In this case we looked for simpler/more realistic mechanistic model of the reaction. For DS the first-order expression (Mampel equation) with the activation energy E_a = 134 ± 7 kJ mol⁻¹ and preexponential factor ln(A/s⁻¹) = 30.6 ± 2.1, fitted the isothermal data. This activation energy was nearly the same as the activation energy of the solid-state reaction of dimerization of C₆₀ reported in the literature. This made the enthalpy of depolymerization close to zero in accord with the DSC data on depolymerization of DS. Mampel equation gave the best fit to the polythermal data with E_a = 153 kJ mol⁻¹ and preexponential factor ln(A/s⁻¹) = 35.8. For O-phase two reasonable reaction models, i.e. Mampel equation and “contracting spheres” model equally fitted to the isothermal data with E_a = 196 ± 2 and 194 ± 8 kJ mol⁻¹, respectively and ln(A/s⁻¹) = 39.1 ± 0.5 and 37.4 ± 0.2, respectively and to polythermal data with E_a = 163 and 170 kJ mol⁻¹, respectively and ln(A/s⁻¹) = 32.5 and 29.5, respectively.     

Thermodegradation kinetics of a hybrid inorganic-organic epoxy system

Lifetime of the epoxy system formed by diglycidyl ether of bisphenol A, DGEBA/4,4′-diaminediphenylmethane, DDM, modified with the silsesquioxane, glycidylisobutyl-POSS, was calculated from thermogravimetric analysis. The activation energy of the decomposition of this system was evaluated by the integral method developed by Flynn-Wall-Ozawa (E = 88.9 ± 2.1 kJ mol⁻¹) and by Coats and Redfern method (E = 85.2 ± 1.5 kJ mol⁻¹). The kinetic parameters have been used to estimate the lifetime of the system POSS/DGEBA/DDM. The obtained results by two different ways are similar.     

Energetics of cobalt phosphate frameworks: α, β, and red NaCoPO4

Thermal behavior, relative stability, and enthalpy of formation of α (pink phase), β (blue phase), and red NaCoPO₄ are studied by differential scanning calorimetry, X-ray diffraction, and high-temperature oxide melt drop solution calorimetry. Red NaCoPO₄ with cobalt in trigonal bipyramidal coordination is metastable, irreversibly changing to α NaCoPO₄ at 827 K with an enthalpy of phase transition of −17.4±6.9 kJ mol⁻¹. α NaCoPO₄ with cobalt in octahedral coordination is the most stable phase at room temperature. It undergoes a reversible phase transition to the β phase (cobalt in tetrahedra) at 1006 K with an enthalpy of phase transition of 17.6±1.3 kJ mol⁻¹. Enthalpy of formation from oxides of α, β, and red NaCoPO₄ are −349.7±2.3, −332.1±2.5, and −332.3±7.2 kJ mol⁻¹; standard enthalpy of formation of α, β, and red NaCoPO₄ are −1547.5±2.7, −1529.9±2.8, and −1530.0±7.3 kJ mol⁻¹, respectively. The more exothermic enthalpy of formation from oxides of β NaCoPO₄ compared to a structurally related aluminosilicate, NaAlSiO₄ nepheline, results from the stronger acid-base interaction of oxides in β NaCoPO₄ (Na₂O, CoO, P₂O₅) than in NaAlSiO₄ nepheline (Na₂O, Al₂O₃, SiO₂).     

Calorimetric determination of enthalpy changes for proton ionization of N-[2-hydroxyethyl]piperazine-N′-[2-ethane sulfonic acid] (HEPES) and N-[2-hydroxyethyl]piperazine-N′-[2-hydroxypropane sulfonic acid] (HEPPSO) in water-methanol mixtures

Enthalpies for the two proton ionizations of the biochemical buffers N-[2-hydroxyethyl]piperazine-N′-[2-ethane sulfonic acid] (HEPES) and N-[2-hydroxyethyl]piperazine-N′-[2-hydroxypropane sulfonic acid] (HEPPSO) were obtained in water-methanol mixtures with methanol mole fraction (X_m) from 0 to 0.360. With increasing methanol, the ionization enthalpy for the first proton (ΔH₁) of HEPES increased steadily from 8.4 to 15.3 kJ mol⁻¹ whereas that for HEPPSO rose to a maximum of 21.0 kJ mol⁻¹ at X_m = 0.123 before dropping to 18.4 kJ mol⁻¹ at X_m = 0.360. The ionization enthalpy for the second proton (ΔH₂) of HEPES varied from 20.8 kJ mol⁻¹ in water to 13.6 kJ mol⁻¹ at X_m = 0.360 with a maximum of 24.8 kJ mol⁻¹ at X_m = 0.194. For HEPPSO, ΔH₂ increased steadily from 23.4 to 29.2 kJ mol⁻¹. The solvent composition was selected so as to include the region of maximum structure enhancement of water by methanol. The results were interpreted in terms of solvent-solvent and solvent-solute interactions.     

Carbon black and propylene oxidation over Ru/CoxMgyAl2Oz catalysts

The effects of Co_xMg_yAl₂O_z mixed oxides composition and ruthenium addition on the oxidation of propylene and carbon black (CB) were investigated. Different reactive cobalt and ruthenium oxide species were formed following calcination at 600 °C. The addition of ruthenium was beneficial for the CB oxidation under “loose contact” conditions and for propylene oxidation when the cobalt content was intermediate to low. The calculated activation energy for CB oxidation was decreased from 151 kJ mol⁻¹ for the uncatalyzed reaction to 111 kJ mol⁻¹ over the best catalyst.     

Model-free kinetics analysis of ZSM-5 catalyzed pyrolysis of waste LDPE

Both thermal and catalytic decomposition of waste LDPE sample is studied to understand the effect of catalyst (ZSM-5) on the decomposition behaviour. The nonlinear Vyazovkin model-free technique is applied to evaluate the quantitative information on variation of E_α with α for waste LDPE sample under both catalytic and noncatalytic nonisothermal conditions. The literature reported data on such variation under noncatalytic condition and effects of different catalysts on the LDPE sample are compared with the results of the present study.Results show that the optimum catalyst composition is around 20 wt.%, where the reduction in maximum decomposition temperature is around 70 °C. Presence of ZSM-5 shows similar reduction in maximum decomposition temperature as reported for Al-MCM-41 and MCM-41. Similar trend to literature reported data is observed for variation of E_α with α for LDPE under nonisothermal noncatalytic condition. ZSM-5 catalyzed decomposition of the LDPE sample in the present study indicates that E_α is strong and increasing function of α and consists of four steps. Cracking of large polymer fragments on the external surface of the catalyst, oligomerization, cyclization, and hydrogen transfer reactions inside the catalyst pores might be the possible reaction mechanisms involved during catalytic decomposition.     

Partial molar volume of paracetamol in water, 0.1 M HCl and 0.154 M NaCl at T = (298.15, 303.15, 308.15 and 310.65) K and at 101.325 kPa

The apparent molar volume of paracetamol (4-acetamidophenol) in water, 0.1 M HCl and 0.154 M NaCl as solvents at (298.15, 303.15, 308.15 and 310.65) K temperatures and at a pressure of 101.325 kPa were determined from the density data obtained with the help of a vibrating-tube Anton Paar DMA-48 densimeter. The partial molar volume, V_m, of paracetamol in these solvents at different temperatures was evaluated by extrapolating the apparent molar volume versus molality plots to m = 0. In addition, the partial molar expansivity, E^°, the isobaric coefficient of thermal expansion, α_p, and the interaction coefficient, S_v, have also been computed. The expansivity data show dependence of E^° values on the structure of the solute molecules.     

The decomposition kinetics of [Et4N]2[M(dmit)2] (M = Ni, Pd) in a nitrogen atmosphere using thermogravimetry

Thermal properties and thermal decompositions of [NEt₄]₂[M(dmit)₂] (M = Ni(II), Pd(II), dmit = 1,3-dithiole-2-thione-4,5-dithiolate) have been studied by thermogravimetry (TG). The TG analysis has shown that the complexes are thermally stable up to 460 K and the decomposition of the complexes occurs in three consecutive stages up to 873 K. A thermal stability scale for [M(dmit)₂]ⁿ⁻ anions was based on the thermal properties. Kinetics parameters, such as activation energy, E_a, and kinetic apparent pre-exponential factor, ln A_app, have been calculated from the thermogravimetric data at heating rates of 10, 15, 20 and 25 K/min involving differential (Friedman's equation) and integral (Flynn-Wall-Ozawa's equation) methods.     

Kinetics of reduction of iron oxides by H2: Part I: Low temperature reduction of hematite

This study deals with the reduction of Fe₂O₃ by H₂ in the temperature range of 220-680 °C. It aims to examine the rate controlling processes of Fe₂O₃ reduction by H₂ in the widest and lowest possible temperature range. This is to be related with efforts to decrease the emission of CO₂ in the atmosphere thus decreasing its green house effect.Reduction of hematite to magnetite with H₂ is characterized by an apparent activation energy ‘E_a’ of 76 kJ/mol. E_a of the reduction of magnetite to iron is 88 and 39 kJ/mol for temperatures lower and higher than 420 °C, respectively. Mathematical modeling of experimental data suggests that the reaction rate is controlled by two- and three-dimensional growth of nuclei and by phase boundary reaction at temperatures lower and higher than 420 °C, respectively.Morphological study confirms the formation of compact iron layer generated during the reduction of Fe₂O₃ by H₂ at temperatures higher than 420 °C. It also shows the absence of such layer in case of using CO. It seems that the annealing of magnetite's defects around 420 °C is responsible for the decrease of E_a.The rate of reduction of iron oxide with hydrogen is systematically higher than that obtained by CO.     

Substitution kinetics of W(CO)5(η-bis(trimethylsilyl)ethyne) with triphenylbismuthine

The labile complex W(CO)₅(η²-btmse) undergoes replacement of bis(trimethylsilyl)ethyne, btmse, by triphenylbismuthine in cyclohexane solution at an observable rate in the temperature range of 35-50 °C yielding almost solely W(CO)₅(BiPh₃) as the final product. The kinetics of this substitution reaction was studied in cyclohexane solution by quantitative FT-IR spectroscopy. The substitution reaction obeys a pseudo-first-order kinetics with respect to the concentration of the starting complex. The observed rate constant, k_obs, was determined at four different temperatures and three different concentrations of the entering ligand BiPh₃ in the range 16.8-65.4 mM. From the evaluation of kinetic data a possible reaction mechanism was proposed in which the rate determining step is the cleavage of metal-alkyne bond in the complex W(CO)₅(η²-btmse). A rate law was derived from the proposed mechanism. From the dependence of k_obs on the entering ligand concentration, the rate constant k₁ for the rate determining step was estimated at all temperatures. The activation enthalpy (106 ± 2 kJ mol⁻¹) and the activation entropy (111 ± 6 J K⁻¹ mol⁻¹) were determined for this rate determining step from the evaluation of k₁ values at different temperatures. The large positive value of the activation entropy is consistent with the dissociative nature of reaction. The large value of the activation enthalpy, close to the calculated tungsten-alkyne bond dissociation energy, also supports this dissociative rate-determining step of the substitution reaction.     

Study of oxidation properties and decomposition kinetics of three-dimensional (3-D) braided carbon fiber

The XRD, SEM, isothermal oxidation-weight loss and non-isothermal thermogravimetry (TG)-differential thermogravimetry (DTG) were used to study the oxidation properties and oxidation decomposition kinetics of three-dimensional (3-D) braided carbon fiber (abbreviated as fiber). The results showed that the non-isothermal oxidation process of fiber exhibited self-catalytic characteristic. The kinetic parameters and oxidation mechanism of fiber were studied through analyzing the TG and DTG data by differential and integral methods. The oxidation mechanism was random nucleation, the kinetic parameters were: lg A=10.299 min⁻¹; E_a=156.29 kJ mol⁻¹.     

Determination of the enthalpy of fusion of K3TaF8 and K3TaOF6

The areas of the fusion and crystallization peaks of K₃TaF₈ and K₃TaOF₆ have been measured using the DSC mode of the high-temperature calorimeter (SETARAM 1800 K). On the basis of these quantities and the temperature dependence of the used calorimetric method sensitivity, the values of the enthalpy of fusion of K₃TaF₈ at temperature of fusion 1039 K: Δ_fusH_m(K₃TaF₈; 1039 K) = (52 ± 2) kJ mol⁻¹ and of K₃TaOF₆ at temperature of fusion 1055 K: Δ_fusH_m(K₃TaOF₆; 1055 K) = (62 ± 3) kJ mol⁻¹ have been determined.     

Effects of temperature on the weathering of engineering thermoplastics

We have determined the activation energies (E_a) of yellowing and gloss loss for a large number of engineering thermoplastics and blends under accelerated weathering conditions. The E_a often depend on the property measured and exposure conditions, although they vary over a fairly small range. Under the CIRA/sodalime-filtered xenon arc conditions most likely to be representative of outdoor exposure, the E_a for gloss loss was ≤5 kcal/mol for all samples tested. The E_a for yellowing was also ≤5 kcal/mol except for SAN and ABS. Evidently the color bodies formed from photo-oxidation of SAN are more sensitive to temperature. A reaction with an E_a of 5 kcal/mol will increase its rate by about 33% for each 10 °C increase in temperature near room temperature. Temperature is an important, but not overwhelming, variable in the weathering of most engineering thermoplastics.     

Solubility of HFCs in lower alcohols

This work is inserted in a research program that consists mainly in the experimental and theoretical study of the effect of association between solute and solvent molecules in the solubility of gases in liquids.The solubilities of hydrofluorocarbons, HFCs, (CH₃F, CH₂F₂, CHF₃) in lower alcohols (methanol, ethanol, 1-propanol, 1-butanol) have been determined in the temperature range [284, 313] K, at atmospheric pressure. An automated apparatus based on Ben-Naim-Baer and Tominaga et al. designs was used, which provides an accuracy of 0.6%. A precision of the same order of magnitude was achieved.To represent the temperature dependence of the mole fraction solubilities, the equation R ln x₂ = A + B/T + C ln T was used. From this equation, the experimental Gibbs energies, enthalpies and entropies of solution at 298 K and 1 atm partial pressure of the gas, were calculated.A semiempirical correlation has been developed between the solubilities of HFCs in alcohols at 298 K and the Gutmann acceptor number of solvents, AN, and reduced dipole moment of the gases, μ*.     

Enhanced thermal stability of poly(1,4-dioxan-2-one) in melt by adding a chelator

Thermal stability of poly(p-dioxanone) (PPDO) was investigated isothermally and non-isothermally under air atmosphere using thermogravimetry (TG). The addition of 4-benzoyl-3-methyl-1-phenyl-2-pyrazolin-5-one (PMBP) could enhance successfully the thermal stability of PPDO compared with those of as-prepared and purified PPDO at temperature below about 230 °C. The activation energies for thermal degradation (ΔE_td) were evaluated at different weight loss values from TG data using the procedure recommended by MacCallum et al. The ΔE_td values of as-prepared PPDO, purified PPDO and PPDO containing 1.0 wt% PMBP were in the ranges of 20-50, 35-60, and 56-88 kJ mol⁻¹, respectively, when they were evaluated at weight loss values of 10-80%. The remaining weights increase with the amounts of PMBP added up to 1.5 wt%. The mechanism for the enhanced thermal stability of PPDO was discussed.     

A DSC study on the kinetics of disproportionation reaction of (hfac)Cu(COD)

The kinetics of disproportionation reaction of hexafluoroacetylacetonate-copper(I)-cycloocta-1,5-diene [(hfac)Cu^I(COD)] was investigated by the use of differential scanning calorimetry (DSC) with different heating rates in dynamic nitrogen atmosphere. First, the activation energies (E_as) of the disproportionation reaction were estimated with model-free isoconversional methods, respectively. The E_as were found to fall within the range between 17.6 and 18.7 kJ mol⁻¹, with no temperature and heating rate effects observed. Then, when the E_a was ascertained, the model-fitting methods with least square fitting procedure were adopted to determine the kinetic model for the disproportionation reaction. As a result, the disproportionation reaction follows second-order reaction kinetics.