Arrhenius parameters determination in non-isothermal conditions for the uncatalyzed gasification of carbon by carbon dioxide

Non-isothermal thermogravimetric data were used to evaluate the Arrhenius parameters (activation energy, E, and pre-exponential factor, A) for the uncatalyzed gasification by carbon dioxide of two carbons, select as steam activated carbon (BPL) and SP-1 spectroscopically pure graphite. The paper reports on the application of the model-free isoconversional method (KAS/Vyazovkin linear method) for evaluating the activation energy of the gasification process. Activation energies have been calculated by this method were in good agreement with literature data for similar carbons. On the other hand, by means of the kinetic compensation relation between E and ln A, which was established by the model-dependent Coats–Redfern method, the value of the pre-exponential factor was estimated from the known value of the model-independent activation energy.     

Thermo-oxidation of polypropylene in the presence of PbO

A significant retardation effect by PbO on the formation of volatile products from isotactic polypropylene (IPP) was found at temperatures up to 380°C. The effect is explained by the formation of a surface active form of PbO (possibly Pb₃O₄) which is formed by interaction of PbO with peroxy radicals. Primary and secondary alkyl radicals terminate effectively on the active surface and the kinetic length of the degradation reaction is thus decreased.A compensation effect exists between the Arrhenius parameters ln A and E for both inhibited and uninhibited formation of volatile products.     

The use of the rising temperature technique to establish kinetic parameters for solid-state decompositions using a vacuum microbalance

There are certain experimental aspects concerning the effect of rising temperature on the apparent weight of a substance which have been extensively studied. The theoretical treatment of the kinetics of decomposition under rising temperature conditions rests largely on a combination of equations one of which is the Arrhenius equation. One thus has to combine the kinetic law;

the law describing the temperature coefficient of the rate (usually the Arrhenius equation);

and the equation describing the impose temperature (T in degrees Kelvin) against time (t);

where α is the fraction decomposed, k is the specific rate constant, A is a constant (the pre-exponential term in the Arrhenius equation), T_o is the initial starting temperature in the rising temperature experiment, and β is the heating rate.The combination of these three equations carries certain implications. The Arrhenius equation is almost invariably assumed to hold over the entire temperature range. The assumption may not hold and the most common deviation is the occurrence of two or more linear plots when plotting log k against 1/T. It is held that this would apply when there is a discontinuous alternation in “reaction site distribution” when a common compensation plot of log A against E (the activation energy) should result. Another matter which is essential to the calculation is the correct choice of the specific reaction rate incorporated in the Arrhenius expression. It is concluded that E and A values for solid-state decompositions are environmentally dependent and that values calculated from rising temperature experiments should not necessarily agree with those obtained from the more traditional isothermal experiments.     

A new integral method for the kinetic analysis of thermogravimetric data

Methods for the calculation of activation energies, pre-exponential factors and reaction orders from thermogravimetric data are briefly reviewed. A new integral method is proposed for the determination of these kinetic parameters, using data from pairs of TG curves produced at different heating rates. Employing accurate values of the temperature integral of the Arrhenius equation, tabulated over a range ofE andT, and a simple graphical procedure, the method offers advantages of speed and accuracy over those previously reported. It is suggested that at least one of the kinetic parameters should be allowed to move freely in order to achieve the best possible fit between calculated and experimental traces.     

Some observations regarding the compensation effect observed in the kinetics of non-isothermal transformations

A kinetic equation is analyzed whose application in practice for a number of transformations will demonstrate the linear correlation between activation energy and InA (the preexponential factor in the Arrhenius equation).     

A DSC Study on Cure Kinetics of HTPB-IPDI Urethane Reaction

The kinetics of theurethane-forming cure reaction of hydroxyl terminated polybutadiene (HTPB) with isophorone diisocyanate (IPDI) in presence of ferric tris (acetyl acetonate) (FeAA) catalyst was investigated using differential scanning calorimetry (DSC). The Arrhenius activation parameters, viz., activation energy E and pre-exponential factor A were evaluated using the non-isothermal integral Coats-Redfern equation. The cure reaction was catalysed by ferric acetyl acetonate (FeAA), as revealed from the decrease in reaction temperatures and the increase in rate constants; however, the computed activation energy did not show any correlation to the catalyst concentration. The values of E and A for the uncatalysed reaction at different heating rates showed interdependence through kinetic compensation (KC) effect. Using KC correction, E values were normalised for the value of A for the uncatalysed reaction under identical conditions. The normalised E values decreased exponentially with increase in concentration of FeAA, showing high propensity of the HTPB-IPDI system for catalysis.This revised version was published online in November 2005 with corrections to the Cover Date.     

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.     

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.     

Application of non-isothermal cure kinetics on the interaction of poly(ethylene terephthalate) — Alkyd resin paints

Samples of paint (P), reused PET (PET-R) and paint/PET-R mixtures (PPET-R) were evaluated using DSC to verify their physical-chemical properties and thermal behavior. Films from paints and PPET-R are visually similar. It was possible to establish that the maximum amount of PET-R that can be added to paint without significantly altering its filming properties is 2%. The cure process (80–203°C) was identified through DSC curves. The kinetic parameters, activation energy (E _a) and Arrhenius parameters (A) for the samples containing 0.5 to 1% of PET-R, were calculated using the Flynn-Wall-Ozawa isoconversional method. It was observed that for greater amounts of PET-R added, there is a decrease in the E _a values for the cure process. A Kinetic compensation effect (KCE), represented by the equation InA=−2.70+0.31E _a was observed for all the samples. The most suitable kinetic model to describe this cure process is the autocatalytic Šesták-Berggreen, model applied to heterogeneous systems.     

Kinetic compensation effect in the thermal degradation of polymers

The kinetic study of thermal degradation takes into account the validity of the Arrhenius equation. From TG data, the activation energy,E _a and pre-exponential factor,A, are evaluated. These results are interpreted by using the kinetic compensation effect as basis. A linear correlation between In(A) andE _a is obtained in all cases studied. However, in a plot of the logarithm of the rate constant as a function of reciprocal temperature for the same series of reactions, the thermal oxidative degradations of Nylon-6 and PVC display a point of concurrence and one isokinetic temperature, whereas those of HIPS and PC do not. Therefore, in the thermal oxidative degradations of Nylon-6 and PVC a true compensation effect occurs, which could be related to the bulk properties of metal oxides, such as different valence states, whereas for other polymers it displays only an apparent compensation effect. This means that degradation is largely independent of the bulk properties of oxides, but may be related to the distribution of different kinds of active links in the polymer surface having different activation energies.     

Kinetic compensation effects observed during oxidation of carbon monoxide on γ‐alumina supported palladium,platinum, and rhodium metal catalysts: Toward a mechanistic explanation

The kinetic compensation effect (KCE) is a well‐known behavior pattern wherein a set of related reactions show a linear relationship between the calculated Arrhenius parameters, log₁₀ A and E_a. Although various theoretical explanations have been advanced, none has yet found general acceptance. The present paper reports multiple rate measurements for the heterogeneously catalyzed oxidation of CO on several identically prepared samples of supported noble metal (Pd, Pt, or Rh) catalysts. Distinctive KCEs were observed for all three metals; these are discussed with reference to a new parameter, the degree of compensation (κ), which quantitatively measures deviation from the ideal isokinetic relationship (κ = 1.00 KCE). For carbon monoxide oxidation on each of the three metals, κ was greater than 0.85 KCE, regarded as significant compensation. These KCEs are discussed in the context of published kinetic and mechanistic studies of CO oxidation, from which a theoretical explanation of the observed pattern of rate characteristics is proposed. Overall kinetic control is ascribed to a common dominant, rate‐determining process on each metal, resulting in approximately isokinetic behavior. Temperature‐dependent secondary controls are identified as modifying the kinetics of surface reactions involving adsorbed intermediates, and thus the apparent magnitudes of Arrhenius parameters. Different contributions from secondary controls, between the individual reactions of each set, are attributed to temperature‐determined variations of concentrations, equilibria, and mobilities of adsorbed participants in the (dominant) rate‐controlling process. A modified Arrhenius equation, applicable to KCE reaction sets, is suggested in which the preexponential term varies with temperature. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 38: 689–702, 2006     

Significance of the kinetics of thermal decomposition of NaHCO3 evaluated by thermal analysis

The Arrhenius parameters and kinetic obedience were determined by TG at constant temperatures as well as at linearly increasing temperatures for the thermal decomposition of sodium hydrogencarbonate. Effects of the sample size (0.5–10 mg) and the particle size on the rate behavior were examined. With such a sample size smaller than ca. 5 mg, an effect of the heating rate was not so critical as is the case with the larger sample size. The Arrhenius parameters and kinetic obedience determined by use of the Ozawa method were in excellent agreement with those determined isothermally. The activation energyE determined with ca. 1 mg of sample was nearly constant independently of the fractional reactiona. Any change in the Arrhenius parameters with different experimental conditions was dicussed in connection with the kinetic compensation effect.     

Non-isothermal analysis of the kinetics of the combustion of carbonaceous materials

Non-isothermal thermogravimetric data were used to evaluate the Arrhenius parameters (activation energy and the pre-exponential factor) of the combustion of two carbonaceous materials, selected as diesel soot surrogates. The paper reports on the application of model-free isoconversional methods (Flynn-Wall-Ozawa and Kissinger methods) for evaluating the activation energy of the combustion process. On the other hand, by means of the compensation relation between E and lnA, which was established by the model-dependent Coats-Redfern method, the value of the pre-exponential factor was estimated from the known value of the model-independent activation energy.     

Kinetics and enthalpy change in decomposition of Ni(NCS)2(3-R-pyridine)4 complexes (R=ethyl,Cl, Br,CN, NH2)

Isothermal TG and DSC measurements were used to study the effect of the pyridine substituent (3-R) on the kinetics and enthalpy change in the thermal decomposition of Ni(NCS)₂(3-R-py)₄ complexes.The found activation energies (E) of the interface advance decreased with the increase in volume of the substituent, allowing the assumption of a dissociative activation mechanism in the thermal decomposition reaction.The relations between (E) and H and the occurrence of the kinetic compensation effect InA=f(E) are discussed.Part XX in the series Heterogeneous reactions of solid Ni(II) complexes.     

A device for sample agitation in an accelerating rate calorimeter

A stirring bar type agitation system has been designed and characterized for the accelerating rate calorimeter (ARC). The device allows stirring of the contents of a standard ARC sample container at stirring rates of up to 500 rev. min^?1, depending on sample viscosity. Experiments on a well-characterized thermal decomposition reaction, such as that of di-t-butyl peroxide, indicate that the device does not degrade the measurement of the energy of reaction, ΔE_v, the Arrhenius activation energy, E_a, or the pre-exponential factor, A.The utility of this stirring apparatus is demonstrated by examining the runaway data of a suspension polymerization. The results indicate that a polymerization “kill” agent can be successfully used for that particular reaction.     

Study of the nature of the crystallization water in some magnesium hydrates by thermal methods

The nature of the crystallization water in MgSO₄·7H₂O, Mg(NO₃)₂·6H₂O and MgCl₂·6H₂O has been studied with the nonisothermal methods of thermogravimetry (TG), derived thermogravimetry (DTG) and differential thermal analysis (DTA). Analysis of the characteristic thermogravimetric data (T _M,W _∞) and the kinetic parameters (n, E _a), together with the DTA results, with CuSO₄·5H₂O as control sample, provided evidence of the existence of coordinated water and of the nature of the anions in these hydrates. The results are confirmed by the observation of a real compensation effect. For the compensation effect, the following equation is proposed: InA=0.220E-0.8 Structures explaining the presence of the coordinated water and the nature of the anions in these hydrates are also proposed.     

Influence of heating rate on kinetic quantities of solid phase thermal decomposition

Thermogravimetric analyses of thermal decomposition (pyrolysis, thermal dissociation and combustion) of 9 different samples were carried out in dynamic conditions at different heating rates. The kinetic parameters (E, A and k_m) of thermal decomposition were determined and interrelations between the parameters and heating rate q were analyzed. There were also relations between Arrhenius and Eyring equations analyzed for thermal decomposition of solid phase. It was concluded that Eyring theory is an element, which interconnects used thermokinetic equations containing Arrhenius law and suggests considering kinetic quantities in way relative to 3 kinetic constants (E, A and k_m). Analysis of quantities other than km (i.e. E, A, Δ⁺H, Δ⁺S) in relation to heating rate is an incomplete method and does not lead to unambiguous conclusions. It was ascertained that in ideal case, assuming constant values of kinetic parameters (E and A) towards heating rate and satisfying both Kissinger equations, reaction rate constant k_m should take on values intermediate between constants (k_m)₁ and (k_m)₂ determined from these equations. Whereas behavior of parameters E and A towards q were not subjected to any rule, then plotting relation k_m vs. q in the background of (k_m)₁ and (k_m)₂ made possible classification of differences between thermal decomposition processes taking place in oxidizing and oxygen-free atmosphere.     

Kinetic description of bimolecular reactions with low energy cross sections in dilute gases

The rate ν of bimolecular chemical reaction A+A=B+C is analyzed for simple models of reactive cross sections. Collisions of particles colliding with energy E larger than a relatively low characteristic energy E _Lare either non-reactive (reversed Prigogine-Xhrouet model = rPX) or the ability to react is decreasing for E>E _L(reversed line-of-centres model = rLC). After solution of the Boltzmann equation analytical expressions for the distribution function f and the rate coefficient k have been derived. It is shown that the Arrhenius activation energy E _Ais small and even negative for sufficiently small E _L. The non-equilibrium corrections to ν are small.     

Kinetic parameters of decomposition of some selenites

Studying the kinetics of isothermal decomposition of thirteen selenites at isothermal heating, the values of activation energy E of the process, pre-exponential factor A in Arrhenius equation and changes of entropy for the formation of the activated complex of the reagent were calculated. Direct dependence between the thermal stability of the selenites and their cation radii on their 'hardness' or 'softness' was found. The dependence was interpreted in the terms of the generalized perturbation theory of chemical reactivity. Kinetic compensation effect was observed only for the selenites, which thermally decompose by the same mechanism.