Variable Activation Energy Research Articles

Kinetic parameters of CaCO3 decomposition in vacuum, air and CO2 calculated theoretically by means of the thermochemical approach

Fundamental advantages of the thermochemical approach compared with the activation approach were supported in this work by the results of theoretical calculations of the A and E kinetic parameters of CaCO3 decomposition in vacuum, air and CO2 and their comparison with experimental data. The temperature of the reaction in CO2 increases from 800 K (in vacuum) up to 1,200 K at equal rates of decomposition. This effect (unexplained in the framework of the activation approach) is of tremendous importance for estimating the thermal stability and lifetime of materials. It has been shown that the pre-exponential factor A in the Arrhenius equation is related to the entropy change of decomposition reaction and, in the isobaric mode, additionally, to the pressure of the external gaseous product. The mysterious effect of “variable activation energy” observed in many non-isothermal studies of solid decompositions, in particular, for CaCO3, was explained by the change of the reaction regime from the isobaric mode at low temperature (and decomposition degree) to the equimolar mode at higher temperatures (and higher decomposition degrees). This effect manifests itself for reactions related to the evolution of O2, H2O and CO2 gaseous products, which can be present in the reactor media as impurities.

An innovative reaction model determination methodology in solid state kinetics based on variable activation energy

• A new reaction model(s) determination methodology has been proposed. • This methodology follows variable activation energy concept. • It may not only kinetically model single step but also multi-step reactions. • It is effectively applicable in isothermal as well as non-isothermal kinetics. • This methodology will provide basis for a number of new reaction models. Determination of appropriate reaction model(s) in solid state reactions has been confronting with serious discrepancies over the decades. The dilemma in the choice of reaction models originates from the use of facile methods to handle the complicated multi-step kinetics. In order to minimize these discrepancies, an advanced reaction model determination methodology is put forward which deals with variable energy of activation concept. This methodology is expected to fairly simulate single step as well as multi-step reaction kinetics. The fresh expressions for the well known reaction models under this methodology are derived and their validity conditions are discussed. The methods for determining pre-exponential factor(s) in single step and multi-step processes are also reviewed. The proposed methodology is experimentally verified by taking an experimental example of non-isothermal curing kinetics of the polyepoxy formation (by the reaction between DGEBA and an aliphatic diamine) under constant as well as variable energies of activation. The obtained results are compared and effectively interpreted. The precautions while using the said methodology and its prospective applications are also discussed.

Thermal behaviour of polyethylene‐block‐poly(methyl methacrylate) block copolymer: effect of multiple heating and cooling rates versus mathematical artefact

The melting and crystallization behaviours of a polyethylene‐block‐poly(methyl methacrylate) (PE‐b‐PMMA) diblock copolymer and a PE homopolymer were investigated using multiple heating and cooling rate differential scanning calorimetry (DSC) experiments, and modelling of the crystallization kinetics and lamellar thickness distribution. This new model was first validated applying literature and experimental data. The model‐predicted morphology (n = 3.2) closely matched the spherulitic morphology (n = 3), which was determined using polarized optical microscopy. For each experimental cooling rate, the model predicted diblock copolymer crystallinity that well matched the entire DSC crystallinity curve, notably for an Avrami–Erofeev index of n = 2; and apparent crystallization activation energy that hardly varied with the cooling rates used, relative crystallinity (α), and crystallization temperature or time. This disfavours the concept of variable activation energy. The use of the right crystallization model and parameter estimation algorithm is important for addressing the mathematical artefact. Under non‐isothermal cooling, the PE‐b‐PMMA diblock copolymer, as per the model prediction, crystallized without confinement (n ≠ 1), preserving the cylindrical structure. From the characteristic shapes of the crystallization function f(α(T)) versus 1/T and crystallization rate versus α plots, the resulting Tcmax and narrow αmax range can guide the search for an appropriate crystallization model. The overall treatment illustrated in this study is not restricted to a PE homopolymer and a PE‐b‐isotactic PMMA block copolymer. It can be generally applied to crystalline homopolymers and copolymers (alternating, random and block), as well as their blends. The block copolymers and blends can be crystalline–amorphous as well as crystalline–crystalline. © 2014 Society of Chemical Industry

Ordering and structural changes at the glass–liquid transition

Ordering types of amorphous solids and structural changes which occur at glass–liquid transition are discussed focusing on configuron percolation theory (CPT) of glass transition. The glass transition temperature can be calculated using bond thermodynamic parameters e.g. enthalpy Hd and entropy of formation Sd. Explicit equations have been derived to assess Hd and Sd from available data on viscosity of amorphous materials using the CPT viscosity equation. A universal equation for the variable activation energy of viscous flow Q(T) has been found. The glass–liquid transition is accompanied by formation of a percolation macroscopic cluster made up of broken bonds – configurons – which are dynamic in nature. The characteristic linear size of dynamic clusters formed is given by correlation length which universally depends on formation Gibbs free energy of configurons Gd=Hd−TSd and becomes macroscopic at glass transition. Fractal-type medium range order (MRO) is revealed at correlation length sizes and homogeneous and isotropic disordered state (DS) characteristic for macroscopic sizes larger than the correlation length. The reduction of topological signature (Hausdorff dimensionality) of disordered bonding lattice from 3 for glass to fractal Df=2.4−2.8 for melt is the main signature change to explain the drastic changes of material behaviour at glass transition.

The mathematical incorrectness of the integral isoconversional methods in case of variable activation energy and the consequences

Kinetic parameters resulting from the application of isoconversional methods mostly depend on the degree of conversion. This paper shows that the integral isoconversional methods are mathematically incorrect if the activation energy depends on conversion. In this case, the incorrectness resides in improper separation of variables in the general rate equation. As a consequence, non-sensical snake-like shape of the conversion versus time curves is observed when the kinetic results are extrapolated to lower temperatures.

On non-isothermal kinetics of two Cu-based bulk metallic glasses

In this paper, two Cu-based bulk metallic glasses, Cu55Zr37Ti8 and Cu61Zr34Ti5, have been evaluated in thermodynamics and kinetics. The activation energies with the constant values were generalized by different theoretical models. The Ex of Cu55Zr37Ti8 and Cu61Zr34Ti5 are 319 ± 12 and 359 ± 12 kJ mol−1, respectively, implying that the as-cast alloys have a good stability in thermodynamics. On the other hand, variable activation energies were also determined using Kissinger–Akahira–Sunose method, Ozawa–Flynn–Wall method, and Friedman’s method. The results showed that the Ea(x) at the beginning of the crystallization are higher than that at the end of the crystallization in the first exothermic peak. By introducing the local Avrami exponent, n(x), the growth and nucleation mechanisms were discussed. Furthermore, the effects of different activation energies on local Avrami exponent were also given a discussion.

Evaluation of Kinetic Parameter Calculation Methods for Non-Isothermal Experiments in Case of Varying Activation Energy in Solid-State Transformations / Neizotermisko Eksperimentu Kinētisko Parametru Noteikšanas Metožu Izvērtēšana Mainīgas Aktivācijas Enerģijas Gadījumā Cietfāžu Pārvērtībām

Simulations of solid-state transformation kinetics were carried out calculating temperature and conversion degree for non-isothermal experiments with different heating rates. Simulations were divided in two parts: with constant and with variable activation energy. Simulations were analyzed with widely used model-based and model-free activation energy determination methods, frequency factor and kinetic model determination methods. Much of the attention was devoted to the calculation of kinetic models and frequency factors, as a more difficult and less developed step. For simulations where activation energy did not change all activation energy determination methods were found to give correct results. However, much attention should be devoted to frequency factor determination, because incorrect results would lead to problems in determination of kinetic models. For simulations where activation energy changes, correct activation energy can be determined only by differential methods or integral methods using numerical integration over small intervals. Isokinetic relationship coefficients b and c were more accurately determined with the average linear integral method. Correct kinetic model determination was possible only when coefficients b and c were accurate, and only by analyzing results of all available methods.

Concept of Variable Activation Energy and Its Validity in Nonisothermal Kinetics

The concept of variable activation energy in solid-state kinetics under nonisothermal conditions has been suffering from doubt and controversy. Rate equations of nonisothermal kinetics of solid decomposition, which involve the factors of thermodynamics conditions, pressure of gaseous product, structure parameters of solid, and/or extent of conversion, are derived from the models of the interface reaction, the diffusion of gaseous product, and the nuclei growth of the solid product, respectively. The definition of the validity function in the rate equations represents the influence of the factors on the reaction rate. A function of variable activation energy depending on the validity function is also developed. The changing trend and degree of activation energy are extrapolated from the function of variable activation energy and based on the data of nonisothermal thermal decomposition of calcium carbonate. It is shown that the concept of variable activation energy is meaningfully applicable to solid-state reactions under nonisothermal conditions.

Oil shale pyrolysis kinetics and variable activation energy principle

A modified first order kinetic equation with variable activation energy is employed to model the total weight loss of Ellajjun oil shale samples. Fixed bed retort with 400 g of oil shale sample size is used in this study in 350–550 °C temperature range. Variable heating rate, h, in the range 2.6–5 °C min −1 are tested. Activation energy was allowed to vary as a function of oil shale conversion. The value of the activation energy increased from 98 to 120 kJ mol −1 while the corresponding frequency factor changed from 9.51 × 10 5 to 1.16 × 10 6. Fischer Assay analysis of the studied samples indicated 12.2 wt.% oil content. The oil shale decomposition ranged from 3.2% to 28.0%. The obtained kinetic data are modeled using variable heating rate, pyrolysis temperature and variable activation energy principle in a nitrogen sweeping medium. Good fit to the obtained experimental data is achieved.

Advanced isoconversional kinetics of nanocrystallization in Fe 73.5Si 13.5B 9Nb 3Cu 1 alloy

Nanocrystallization kinetics of amorphous Finemet alloy was studied using Vyazovkin advanced isoconversional method under non-isothermal condition. Well known Kissinger model-fitting method and four isoconversional methods of Kissinger–Akahira–Sunose (KSA), Flynn–Wall–Ozawa (FWO), Tang, and Starink were also used for the determination of activation energy. Differential scanning calorimetry (DSC) and X-ray diffraction (XRD) patterns were used for thermal and structural analyses, respectively. According to Vyazovkin and other isoconversional methods, the mean value of variable activation energy, as a function of conversion, was obtained as 350 kJ mol −1. While, according to Kissinger method, the constant value of activation energy was obtained as 270 ± 10 kJ mol −1 for the same experiments, which shows inaccuracy of this method. The mean value of kinetic exponent 〈 n〉 was 1.44 ± 0.05 by considering instantaneous nucleation condition ( n = m), which is consistent with one-dimensional growth mechanism. Kinetics and mechanistic predictions were also performed using numerical reconstruction of the experimental kinetic function. Comparison of the numerically reconstructed model with theoretical ones showed that no single model could perfectly fit the numerical values of kinetic function and the mechanism of transformation changes with conversion progress. Nevertheless it could be seen that nanocrystallization almost follows the one-dimensional diffusion mechanism.

Development of a Variable Activation Energy Model for Biomass Devolatilization

A thermogravimetric balance is used in this work to characterize different classes of biomass fuels: residues (rice husks, olive cake, cacao shells), woods (poplar, beech, pellets), and grasses (mi...

Curing characteristics of an epoxy resin in the presence of ball-milled graphite particles

The effects of simply-made graphite particles (GPs, 1 wt%) on curing kinetics of an epoxy resin were investigated by means of differential scanning calorimetry (DSC). Two approaches based on constant and variable activation energy were applied to analyze the DSC curves. Results from the constant energy method showed that addition of the GPs increased the activation energy Ec and the overall order of reaction m + n. With the variable energy method, the activation energy varied with curing conversion substantially in the GP/epoxy system; in contrast, the variation in the pure epoxy was very limited. The GPs also decreased the heat of reaction (ΔH) and increased the glass transition temperature (Tg) for the epoxy. Comprehensive analyses indicated that the GPs did not significantly impede the curing reaction, which can enable improvement of the composite functionalities without creating processing penalties. The information obtained from this study provides an understanding of multiple factors involved in the complex relationship of structure and properties of the composites.

Effect of the heating rate on the devolatilization of biomass residues

The devolatilization is the basic step of thermochemical processes and requires a fundamental characterization. Three biomass residues (rice husks, olive cake, cacao shells) are studied here in a thermogravimetric (TG) balance. The effect of the heating rate (HR) is evaluated in the range 5–100 K/min providing significant parameters for the fingerprinting of the fuels. Kinetics are obtained by applying traditional isoconversional methods. The activation energy as function of the conversion reveals the multi-step nature of the biomass devolatilization. Although average values allow the reactivity of different fuels to be compared, a first order reaction model can hardly predict the biomass devolatilization. A VEB (Variable activation Energy model for Biomass devolatilization) model is developed, basing on the results of the kinetic analysis. A good agreement is obtained for the biomass residues in all HR runs in the entire range of temperatures. Similarities in the optimized E VEB curves for the three fuels of this work suggest to pursue a generalization in the approach, enlarging the number and variety of fuels studied.

Oxidation investigation of nickel nanoparticles

This work reported an experimental investigation of complete oxidation of nickel nanoparticles using simultaneous thermogravimetry analysis (TGA) and differential scanning calorimetry (DSC). Nickel nanoparticles and their elemental compositions were characterized by Brunauer-Emmett-Teller (BET) analysis, transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy (EDS). The oxidation experiments were performed under isoconversion conditions for seven heating rates, varying from 2 to 20 K min(-1), with temperatures up to 1000 degrees C. The experiments revealed unique oxidation behaviour of nickel at the nanometre scale, such as early oxidation and melting phenomena, variable activation energies and different oxidation kinetics between low and high conversion ratios. Unlike its bulk counterpart where the activation energy is a constant, the activation energy of nickel nanoparticles depended on the conversion ratio, ranging between 1.4 and 1.8 eV. The oxidation kinetics of nickel nanoparticles changed from the classical diffusion controlled mechanism to a pseudo-homogeneous reaction as conversion ratios were over 50%. The oxidation mechanisms of nickel nanoparticles were further discussed and future studies to enhance understanding were identified.

A simulation of the mass-transfer effects on the kinetics of solid–gas reactions

A theoretical analysis of the influence of mass-transfer effect on the kinetic of solid–gas reactions has been carried out by assuming that the partial pressures of the gases generated in the reaction are proportional to the reaction rate. The influence of mass-transfer phenomena on the apparent activation energy, calculated by the isoconversional methods of Friedman, and on the reaction model is discussed. In the present study, simulated nonisotherm, isotherm, and controlled rate thermal analysis (CRTA) data have been used. Master plots based on the differential forms of the kinetic equations describing solid-state reactions have been employed by using the concept of the generalized time (θ), introduced by Ozawa; this permits the application of these master plots to the kinetic analysis of reactions whatever the type of temperature program used for recording the experimental data. It has been shown that when the simulated mass-transfer effect is present the variable effective activation energy E remains nearly constant while the reaction model approaches zero order. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 217–222, 2008

Effect of strontium and barium doping on the magnetic state and electrical conductivity of GdCoO3

A coordinated investigation of the magnetic and electrical properties of polycrystalline cobalt oxide compounds CdCoO3, Gd0.9Ba0.1CoO3, and Gd0.9Sr0.1CoO3 is carried out. Undoped GdCoO3 reveals a low conductivity; a magnetic moment of 7.4 μB per molecule, which is less than the theoretical value for the Gd3+ ion; and an asymptotic Curie temperature of −6 K. Doping GdCoO3 with barium and strontium to substitution of 10 at. % Gd brings about an increase in the conductivity and magnetic transitions at T = 300 K for Gd0.9Ba0.1CoO3 and T = 170 K for Gd0.9Sr0.1CoO3. The magnetization anomalies imply the formation of magnetic clusters. The behavior of the electrical conductivity at high temperatures suggests a variable activation energy. At low temperatures, Mott hopping conduction sets in.

Comparative study on the curing kinetics and mechanism of a lignin-based-epoxy/anhydride resin system

Curing kinetics and mechanism of liquid lignin based epoxy resin (LEPL)–maleic anhydride (MA) system accelerated with benzyldimethylamine (BDMA) were studied by Fourier transform infrared (FTIR) spectroscopy and differential scanning calorimetry (DSC). In order to investigate the difference in the curing process, heating FTIR was used to study the change of the functional group. Complete consumption of the epoxides has been observed after the heating temperature was higher than 110°C. E constant method and E variable method, to study the dynamic DSC curves, were deduced by assuming a constant and a variable activation energy, respectively. With E constant method, the cure reaction activation energy E, the frequency factor A and overall order of reaction n+m are calculated to be 59.68kJmol−1, e20.6 and 1.462, respectively. With E variable method, E is proved to decrease initially, and then increases as the cure reaction proceeds. The value of E spans from 60.16 to 87.80kJmol−1. With the E constant method, E variable method and heating FTIR spectra used together, we can have a comprehensive and profound understanding of the cure reactions of the LEPL–MA system.

Kinetics of crystallization in amorphous Se 73.2Te 21.1Sb 5.7 under isochronal conditions: Effect of heating rate on the activation energy

The kinetics of crystallization in a-Se 73.2Te 21.1Sb 5.7 were determined at different heating rates (2–99 K/min) using differential scanning calorimetric (DSC) technique. It is evident from this study that the effective activation energy associated with crystallization, E c in a-Se 73.2Te 21.1Sb 5.7 is not constant but heating rate dependent. Attempt is made to explain this variation in terms of recent theoretical models based on the concept of variable effective activation energy. Using isoconversional method, the temperature dependence of E c was determined. It is shown here that the apparent variation of E c with the heating rate is a result of this temperature dependence. It is also shown that the JMA-based models (Kissinger model etc.) which assume constant effective activation energy show clear deviation from linearity giving at least two values of effective activation energy.

Role of isoconversional methods in varying activation energies of solid-state kinetics: II. Nonisothermal kinetic studies

The concept of variable activation energy in solid-state reaction kinetics has caused considerable debate. Activation energy variation has been detected by isoconversional or “model-free” calculation methods, which generate activation energy as a function of reaction progress. The relationship between calculation methods and artifactual variation in activation energy was investigated in this work by employing model-fitting and isoconversional methods to analyze both simulated and experimental nonisothermal data. The experimental data was for nonisothermal sulfameter-dioxolane solvate desolvation by TGA. We show that variable activation energy in simple reactions could be an artifact resulting from the incorrect application of isoconversional methods.

Characterization of FeS 2-pyrite thin films synthesized by sulphuration of amorphous iron oxide films pre-deposited by spray pyrolysis

FeS 2-thin films with good crystallinity were synthesized by a simple method which consists of sulphuration, under vacuum, of amorphous iron oxide thin films pre-deposited by spray pyrolysis of FeCl 3·6H 2O (0.03 M)-based aqueous solution onto glass substrates heated at 350 °C. At optimum sulphuration temperature (450 °C) and duration (6 h), black green layers having granular structure and high absorption coefficient (∼5.10 4 cm −1) were obtained. The study of the electrical properties of the as-prepared films vs. the temperature variations showed three temperature domain dependence of the conductivity behaviour. The first one corresponds to the high temperature range (330 K–550 K) for which an Arrhenius plot type was obtained. The activation energy value was estimated at about 61.47 meV. The second domain corresponding to the intermediate temperature range (80 K–330 K) showed a variable activation energy between the grain boundaries. The barrier height, qϕ¯, was estimated to 27±0.5 meV, and the standard deviation, qσ ϕ , was evaluated at about 14±0.5 meV. We found that at lower temperatures (20 K–80 K), the conductivity is governed by two conduction types. The density of localised states, was about 2.45×10 20 eV −1 cm −3.