On the Apparent Compensation Effect Found for Two Consecutive Reactions

A critical analysis of the use of an overall single rate reaction equation instead of the true rate equation corresponding to a complex process consisting in two consecutive reactions is presented. In accordance with this approximation, often used in the kinetic analysis of the system in which several reactions take place, the overall process is described by the apparent activation parameters (the apparent activation energy, E _ap, and the apparent pre-exponential factor, A _ap) and the apparent conversion function. The theoretical isotherms (α=α(t), where a is the conversion degree and t is the time) have been simulated for a system in which two consecutive reactions occur. In this case, the apparent activation parameters depends on: (a) the considered range of the temperature; (b) the temperature, for a given conversion degree. It is shown that the apparent activation parameters are corrrelated by the compensation effect relationship: lnA _ap=α*+β*E _ap where α* and β* are the parameters of the linear regression. The possibility of using the apparent kinetic parameters to predict the isotherms α=α(t) for temperatures lower than those for which these parameters were evaluated, is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

A kinetic analysis of thermal decomposition of polyaniline/ZrO<Subscript>2</Subscript> composite

Synthesis, characterization and thermal analysis of polyaniline (PANI)/ZrO₂ composite and PANI was reported in our early work. In this present, the kinetic analysis of decomposition process for these two materials was performed under non-isothermal conditions. The activation energies were calculated through Friedman and Ozawa-Flynn-Wall methods, and the possible kinetic model functions have been estimated through the multiple linear regression method. The results show that the kinetic models for the decomposition process of PANI/ZrO₂ composite and PANI are all D₃, and the corresponding function is ƒ(α)=1.5(1−α)^2/3[1−(1-α)^1/3]−1. The correlated kinetic parameters are E _a=112.7±9.2 kJ mol⁻¹, lnA=13.9 and E _a=81.8±5.6 kJ mol⁻¹, lnA=8.8 for PANI/ZrO₂ composite and PANI, respectively.     

Kinetic Analysis of Thermal Decomposition of Ca(OH)2 Formed During Hydration of Commercial Portland Cement by DSC

In this paper, evaluation of kinetic parameters (the activation energy – E,the pre-exponential factor – A and the reaction order – n) with simultaneous determination of the possible reaction mechanism of thermal decomposition of calcium hydroxide (portlandite), Ca(OH)₂ formed during hydration of commercial Portland-slag cement, by means of differential scanning calorimetry (DSC) in non-isothermal conditions with a single heating–rate plot has been studied and discussed. The kinetic parameters and a mechanism function were calculated by fitting the experimental data to the integral, differential and rate equation methods. To determine the most probable mechanism, 30 forms of the solid-state mechanism functions, f(α_c) have been tried. Having used the procedure developed and the appropriate program support, it has been established that the non-isothermal thermal decomposition of calcium hydroxide in the acceleratory period (0.004<α_c<0.554) can be described by the rate equation: d α_c/dT=A/βexp(−E/RT)f(α_c), which is based on the concept of the mechanism reaction:f(α_c)=2(α_c)^1/2. The mechanism functions as well as the values of the kinetic parameters are in good agreement with those given in literature. This revised version was published online in August 2006 with corrections to the Cover Date.     

Kinetics of the exothermic decomposition of 1-nitro-3-(β,β,β-trinitroethyl)-4,5-dinitroiminoimidazolidine-2-one

The kinetic parameters of the exothermic decomposition of the title compound in a temperatureprogrammed mode have been studied by means of DSC. The DSC data obtained are fitted to the integral, differential, and exothermic rate equations by the linear least-squares, iterative, combined dichotomous, and least-squares methods, respectively. After establishing the most probable general expression of differential and integral mechanism functions by the logical choice method, the corresponding values of the apparent activation energy (E _a), preexponential factor (A), and reaction order (n) are obtained by the exothermic rate equation. The results show that the empirical kinetic model function in differential form and the values of E _a and A of this reaction are (1 − α)^−4.08, 149.95 kJ mol⁻¹, and 10^14.06 s⁻¹, respectively. With the help of the heating rate and kinetic parameters obtained, the kinetic equation of the exothermic decomposition of the title compound is proposed. The critical temperature of thermal explosion of the compound is 155.71°C. The above-mentioned kinetic parameters are quite useful for analyzing and evaluating the stability and thermal explosion rule of the title compound. The text was submitted by the authors in English.     

Study of catalase immobilized on a silicate matrix for non-aqueous biocatalysis

Catalytic activity of catalase (CAT) immobilized on a modified silicate matrix to mediate decomposition of meta-chloroperoxibenzoic acid (3-CPBA) in acetonitrile has been investigated by means of quantitative UV-spectrophotometry. Under the selected experimental conditions, the kinetic parameters: the apparent Michaelis constat (K _M ), the apparent maximum rate of enzymatic reaction (V _max ^app ), the first order specific rate constants (k _sp ), the energy of activation (E _a ) and the pre-exponential factor of the Arrhenius equation (Z₀) were calculated. Conclusions regarding the rate-limiting step of the overall catalytic process were drawn from the calculated values of the Gibbs energy of activation ΔG^*, the enthalpy of activation ΔH^*, and the entropy of activation ΔS^*.     

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.     

Synthesis and thermal decomposition kinetics of Th(IV) complex with unsymmetrical Schiff base ligand

Summary A new unsymmetrical Schiff base ligand (H₂LLi) was synthesized using L-lysine, o-vanillin and salicylaladyde. Thorium(IV) complex of this ligand [Th(H₂L)(NO₃)](NO₃)₂^.3H₂O have been prepared and characterized by elemental analyses, IR, UV and molar conductance. The thermal decomposition kinetics of the complex for the second stage was studied under non-isothermal condition by TG and DTG methods. The kinetic equation may be expressed as: dα/dt=A^.e^-E/RT.1/2 (1-α)^.[-ln(1-α)]^-1. The kinetic parameters (E, A), activation entropy ΔS¹and activation free-energy ΔG¹were also calculated.     

Synthesis and kinetic analysis of isothermal and non-isothermal decomposition of ammonium dinitramide prills

Ammonium dinitramide (ADN) prills were prepared by emulsion crystallization and characterized by optical microscopic, thermogravimetric (TG) and differential scanning calorimetric (DSC) techniques. The isothermal and non-isothermal decomposition kinetics of ADN prills were studied by TG. The differential isoconversional method of Friedman (FR) and integral isoconversional method of Vyazovkin were used to investigate the dependence of activation energy (E _a) with conversion (α) and the results were compared with literature data. The dependence of activation energy was also derived from isothermal data. A strong dependence of E _a with α is observed for the ADN prills. All the methods showed an initial increase in E _a up to α=∼0.2 and later decreases over the rest of conversion. The apparent E _a values of FR method are higher than that of Vyazovkin method up to α=∼0.45. The calculated mean E _a values by FR, Vyazovkin and standard isoconversional method for α between 0.05 and 0.95 were 211.0, 203.9 and 156.9 kJ mol⁻¹, respectively.     

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.     

Reactivity of C<Subscript>3</Subscript>-C<Subscript>8</Subscript> alkanes with nitronium ions in sulfuric acid

We have determined the parameters of the Arrhenius equation (E, log A) for reactions between \textNO₂⁺ {\text{NO}}_2^{+} ions and C₃-C₈ alkanes in HNO₃–93 wt.% H₂SO₄ solutions at 277–353 K, and we have also estimated the activation parameters E _j , log A _j for secondary and tertiary C—H bonds of these alkanes. We show that the following compensation relations are satisfied: E = 2.3R βlog A + C with isokinetic temperature β = 360 ± 65 K, and also E _j =2.3Rβ _j log A _j  + C _j , for secondary C—H bonds, β₂ =300 ± 60, and for tertiary C—H bonds, β₃ =310 ± 50.     

Solvatochromic parameters for binary mixtures of an ionic liquid with various protic molecular solvents

Abstract  

Solvatochromic parameters (E _T ^N, normalized polarity parameter; π*, dipolarity/polarizability; β, hydrogen-bond acceptor basicity; α, hydrogen-bond donor acidity) have been determined for binary mixtures of propan-2-ol, propan-1-ol, ethanol, methanol and water with recently synthesized ionic liquid (IL; 2-hydroxyethylammonium formate) at 25 °C. In all solutions except aqueous solution, E _T ^N values of the media increase abruptly with the ILs mole fraction and then increase gradually to the value of pure IL. A synergistic behavior is observed for the α parameter in all solutions. The behavior of π* and β are nearly ideal for all solutions except for solutions of methanol with the IL. The applicability of nearly ideal combined binary solvent/Redlich–Kister equation was proved for the correlation of various solvatochromic parameters with solvent composition. The correlation between the calculated and the experimental values of various parameters was in accordance with this model. Solute–solvent and solvent–solvent interactions were applied to interpret the results.     

Synthesis,crystal structure,and thermal decomposition kinetics of complex [Nd(BA)<Subscript>3</Subscript>bipy]<Subscript>2</Subscript>

The complex of [Nd(BA)₃bipy]₂ (BA = benzoic acid; bipy = 2,2′-bipyridine) has been synthesized and characterized by elemental analysis, IR spectra, single crystal X-ray diffraction, and TG/DTG techniques. The crystal is monoclinic with space group P2(1)/n. The two–eight coordinated Nd³⁺ ions are linked together by four bridged BA ligands and each Nd³⁺ ion is further bonded to one chelated bidentate BA ligand and one 2,2′-bipyridine molecule. The thermal decomposition process of the title complex was discussed by TG/DTG and IR techniques. The non-isothermal kinetics was investigated by using double equal-double step method. The kinetic equation for the first stage can be expressed as dα/dt = A exp(−E/RT)(1 − α). The thermodynamic parameters (ΔH ^≠, ΔG ^≠, and ΔS ^≠) and kinetic parameters (activation energy E and pre-exponential factor A) were also calculated.     

Thermal decomposition behaviors of β-cyclodextrin,its inclusion complexes of alkyl amines,and complexed β-cyclodextrin at different heating rates

The present work revealed there was a conceptual difference in the thermal decomposition behaviors between the complexed β-cyclodextrin (CD) in an inclusion system and the β-CD complex of guest. The thermal decomposition behaviors of the solid inclusion complexes of β-CD with ethylenediamine (Eda), diethylenetriamine (Dta) and triethylamine (Tea) were investigated using nonisothermal thermogravimetry (TG) analysis based on weight loss as a function of temperature. In view of TG profiles, a consecutive mechanism describing the formation and thermal decomposition of the three solid supermolecules of β-CD was presented. Heating rate has very different effects on the thermal decomposition behaviors of these complexes. The faster the heating rate is, the higher the melting-decomposition point of the complexed β-CD in an inclusion system is, and on the whole the bigger the rate constant (k) of the thermal decomposition reaction of the complexed β-CD is. The thermal decomposition process of the complexed β-CD for each inclusion system is determined to be simple first-order reaction using Ozawa method. The apparent activation energies (E _a) and frequency factors (A) of the thermal decomposition reactions of the complexed β-CD molecules have been also calculated. It is found that when the decomposition reaction of the complexed β-CD encountered a large value of E _a, such as that in Dta–β-CD system, an apparent compensation effect of A on E _a can provide enough energy to conquer the reaction barrier in prompting the k value of thermal decomposition reaction of the complexed β-CD according to Arrhenius equation.     

Kinetics of the alkylation of phenol with methanol over catalysts derived from hydrotalcite-like anionic clays

Vapor phase alkylation of phenol with methanol was carried out over catalysts derived from a series of hydrotalcite (HT)-like compounds of the form M(II)Al-HT; where M(II)=Mg, Mn, Co, Ni, Cu and Zn with M(II)/Al atomic ratios of2–5. The kinetic parameters such as rate constant (k), apparent activation energy (E_a) and Arrhenius frequency factor (A_o) for the disappearance of phenol were evaluated employing a power law equation assuming pseudo-first order kinetics. The kinetic parameters were found to be in good agreement with phenol conversion. The existence of the compensation effect between E_a and ln A_o was tested.     

Kinetic of decomposition of some complexes under non-isothermal conditions

Kinetics of thermal decomposition of three structurally similar complexes Co₂Cu(C₂O₄)₃ (R-diam)₂, where R is ethyl, 1,2-propyl or 1,3-propyl, was studied under non-isothermal conditions and nitrogen dynamic atmosphere at heating rates of 5, 7, 10, 12 and 15 K min⁻¹. For data processing the Flynn-Wall-Ozawa and a modified non-parametric kinetic methods were used. By both methods the activation energy are in the range of 97–102 kJ mol⁻¹. The formal kinetic is r=kα(1−α)². Also a compensation effect between lnA and E was evidenced. The kinetic analysis lead to the conclusion of an identic decomposition mechanism by a single step process.     

Synthesis,spectroscopic, thermal and biological aspect of mixed ligand copper(II) complexes

Derivative of 8-hydroxyquinoline i.e. Clioquinol is well known for its antibiotic properties, drug design and coordinating ability towards metal ion such as Copper(II). The structure of mixed ligand complexes has been investigated using spectral, elemental and thermal analysis. In vitro anti microbial activity against four bacterial species were performed i.e. Escherichia coli, Pseudomonas aeruginosa, Serratia marcescens, Bacillus substilis and found that synthesized complexes (15–37 mm) were found to be significant potent compared to standard drugs (clioquinol i.e. 10–26 mm), parental ligands and metal salts employed for complexation. The kinetic parameters such as order of reaction (n = 0.96–1.49), and the energy of activation (E _a = 3.065–142.9 kJ mol⁻¹), have been calculated using Freeman–Carroll method. The range found for the pre-exponential factor (A), the activation entropy (S* = −91.03 to−102.6 JK⁻¹ mol⁻¹), the activation enthalpy (H* = 0.380–135.15 kJ mol⁻¹), and the free energy (G* = 33.52–222.4 kJ mol⁻¹) of activation reveals that the complexes are more stable. Order of stability of complexes were found to be [Cu(A⁴)(CQ)OH] · 4H₂O > [Cu(A³)(CQ)OH] · 5H₂O > [Cu(A¹)(CQ)OH] · H₂O > [Cu(A²)(CQ)OH] · 3H₂O     

Solvatochromic parameters for binary mixtures of an ionic liquid with various protic molecular solvents

Abstract  Solvatochromic parameters (E _T ^N, normalized polarity parameter; π*, dipolarity/polarizability; β, hydrogen-bond acceptor basicity; α, hydrogen-bond donor acidity) have been determined for binary mixtures of propan-2-ol, propan-1-ol, ethanol, methanol and water with recently synthesized ionic liquid (IL; 2-hydroxyethylammonium formate) at 25 °C. In all solutions except aqueous solution, E _T ^N values of the media increase abruptly with the ILs mole fraction and then increase gradually to the value of pure IL. A synergistic behavior is observed for the α parameter in all solutions. The behavior of π* and β are nearly ideal for all solutions except for solutions of methanol with the IL. The applicability of nearly ideal combined binary solvent/Redlich–Kister equation was proved for the correlation of various solvatochromic parameters with solvent composition. The correlation between the calculated and the experimental values of various parameters was in accordance with this model. Solute–solvent and solvent–solvent interactions were applied to interpret the results. Graphical Abstract  Predicted values of solvatochromic parameters (SP) (E _T ^N, normalized polarity parameter; π*, dipolarity/polarizability; β, hydrogen-bond acceptor basicity; α, hydrogen-bond donor acidity) from the correlation equations versus its experimental values for binary mixtures of 2-hydroxyethylammonium formate with water, methanol, ethanol, propan-1-ol and propan-2-ol.      

Comparative method to evaluate reliable kinetic triplets of thermal decomposition reactions

Reliable kinetic information for thermal analysis kinetic triplets can be determined by the comparative method: (1) An iterative procedure or the KAS method had been established to obtain the reliable value of activation energy E _a of a reaction. (2) A combined method including Coats-Redfern integral equation and Achar differential equation was put forward to confirm the most probable mechanism of the reaction and calculate the pre-exponential factor A. By applying the comparative method above, the thermal analysis kinetic triplets of the dehydration of CaC₂O₄·H₂O were determined, which apparent activation energy: 81±3 kJ mol^-1, pre-exponential factor: 4.51·106-1.78·10⁸ s^-1, the most probable mechanism function: f(α)=1 or g(α)=α, which the kinetic equation of dehydration is dα/dt=Ae^-E _a ^/RT. This revised version was published online in August 2006 with corrections to the Cover Date.     

Kinetic characterization of the reduction of silica supported cobalt catalysts

Abstact  The reduction process of silica supported cobalt catalyst was studied by thermal analysis technique. The reduction of the catalyst proceeds in two steps:

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.