Solid-state Reaction Models Research Articles

Effects of environmental factors on the dehydration of diclofenac HEP dihydrate and theophylline monohydrate

The effects of temperature and humidity on the kinetics of dehydration of diclofenac N-(2-hydroxyethyl)pyrollidine dihydrate (DHEPH) were examined. Dehydration threshold temperature ( T d) was shown to be unsuitable for such investigations. Nine solid state reaction models were applied to the dehydration data. In the temperature range 34–40°C, a diffusion model gave the best fit to the data, dehydration rate varied significantly and activation energies of dehydration ( E aD) were constant (average 240.7 kJ/mol) with respect to change in relative humidity. In the temperature range 42–48°C, best fit to the data was given by a phase boundary model, dehydration rate did not vary with relative humidity change and activation energies of dehydration were constant (average 140.2 kJ/mol). Choice of solid state reaction model within the diffusion or phase boundary types did not significantly affect the derived activation energy values. Previously reported differences in E aD values for theophylline monohydrate (TH) may be explained in terms of the different experimental temperature ranges used. The use of activation energy of dehydration values in the study of factors affecting dehydration and in comparing hydrate physical stability, requires careful consideration of sample factors, relative humidity and temperature range of experimentation.

Isothermal studies on gamma irradiated oxalates of yttrium and samarium

The influence of γ-irradiation (0.01–1.0 MGy) on the isothermal decomposition of Y 2(C 2O 4) 3 and Sm 2(C 2O 4) 3 has been studied by gas evolution method between the temperature range 603–643 and 623–663 K respectively. The “ α- t” plots of both unirradiated and irradiated salts follow: (i) initial gas evolution, (ii) a short acceleratory period, and (iii) a long decay period. The data on all categories of samples are discussed in the light of various kinetic models for solid state reactions and are found to be well-fitted to Prout-Tompkins and Avrami-Erofeyev mechanisms. Results on unirradiated and irradiated, Y 2(C 2O 4) 3 are also well explained by contracting square relationship. The fractional decomposition, α is enhanced by irradiation, the effect being higher at higher doses in case of both the substances. Irradiation has marginal effect on the energy of activation of the acceleratory and decay periods in the case of Sm 2(C 2O 4) 3 but it reduces the same in the former stage and reverse phenomenon occurs in the latter period in the case of Y 2(C 2O 4) 3.

The Kinetics of Thermal Decomposition of Nickel Formate Dihydrate in Air

Differential thermal analysis-thermogravimetry (DTA-TG), and electron scanning microscopy (ESM) were used to study the decomposition of nickel formate dihydrate in air. The results showed that the decomposition pro- ceeds in two successive TG steps, the first is due to dehydration and the second is due to decomposition of the anhydrous salt and oxidation to form NiO. Ki- netic analysis of the isothermal TG data of the two steps in view of various het- erogeneous solid-state reaction models showed that the dehydration step is hest described by phase boundary models whereas the second step reactions are best described by the branching nucleation model. The changes in morphology that accompany the thermal decomposition of samples as revealed by ESM mi- crographs, were described and the kinetics and mechanism of the thermal de- composition reaction were discussed.

Influence of experimental conditions on the kinetic parameters of gas-solid reactions—parametric sensitivity of thermal analysis

The influence of experimental conditions on the kinetic parameters of gas-solid reactions has been investigated using the reduction of nickel oxide by hydrogen as a model reaction. The experimental parameters studied were heating rate, sample mass, total gas flow and hydrogen concentration. For arbitrarily chosen “standard conditions” the kinetic parameters best describing the course of the reaction were calculated using the global curves analysis method. Experiments were carried out with different heating rates, in the range 1.3–10.6 K min −1. Twenty two kinetic models of solid-state reactions proposed in the literature were tested using numeric integration methods. The confidence space, in which the kinetic parameters, calculated for “standard conditions”, fit the kinetics of NiO reduction properly, was calculated taking into account the influence of all investigated variables. The results illustrate the great influence of the experimental conditions on the measured thermoanalytic curves (“parametric sensitivity”) and demonstrate the limited validity of kinetic data calculated from experiments carried out under arbitrary chosen conditions.

The use of master plots for discriminating the kinetic model of solid state reactions from a single constant-rate thermal analysis (CRTA) experiment

A new method has been outlined that improves the discrimination of the kinetic model fitted by a solid state reaction from a single CRTA experiment, by means of a series of master plots that represent the values of ( T 0.5 T ) 2[( dα dT ) 0.5/( dα dT )] as a function of α. The suffix 0.5 refers to the values of the temperature T and dα dT when the fraction reacted α is 0.5. Kinetic analyses of the thermal decompositions of calcium carbonate and anhydrous nickel nitrate have been used to check this method.

Effect of calcination on the structure of Ni/MgO catalyst: an X-ray diffraction study

The progressive diffusion of Ni2+ ions into the MgO matrix, with the consequent formation of an NixMg(1–x)O solid solution, occurring during the air calcination of a 19% Ni/MgO catalyst in the range 400–1000 °C, has been monitored by X-ray diffraction (XRD) measurements using monochromatized non-doublet synchrotron radiation. A solid-state reaction model accounting for the NiO–MgO interaction in supported and mechanically mixed systems is discussed.

Isothermal kinetic analysis of solid-state reactions using plots of rate against derivative function of the rate equation

Since the advent of digital data capture and the development of quick and accurate numerical methods for data processing, the use of rate measurements ( dα dt ) for kinetic analysis of solid-state reactions has gained in popularity. Rate measurements may readily be obtained through use of isothermal derivative thermogravimetry (DTG), or from isothermal differential scanning calorimetry (DSC) (on the assumption that the evolution or absorption of heat may be used to measure the extent of reaction, α). In this paper, the feasibility and desirability of using plots of experimental dα dt values against the derivative functions for the various models for solid-state reactions is considered critically and discussed quantitatively.

Thermal decomposition of iron(III) oxalate-magnesium oxalate mixtures

The differential thermal analysis-thermogravimetry (DTA-TG) behaviour of chemically coprecipitated iron(III) oxalate-magnesium oxalate (1:1 mole ratio) was investigated. X-ray diffractometry (XRD) of samples calcined at different temperatures showed that magnesium ferrite is formed in samples heated at higher temperatures. Integral composite analyses of dynamic TG data of the decomposition reactions in the coprecipitated mixture were carried out using various solid state reaction model equations, and the results showed that the decomposition reactions are best described by the two- and three-phase boundary, R 2 and R 3 models. Kinetic analyses of dynamic data were also carried out in accordance with the integral methods of Ozawa and Coats-Redfern and the results are discussed in comparison with the integral composite analysis of data.

Formation of Copper-Chromium Sulfide Spinel and Thermal Decomposition Reactions in CuS-Cr2S3 Crystalline Mixtures

Differential thermal analysis-thermogravimetry (DTA-TG), X ray diffraction (XRD), and scanning electron microscopy (SEM) techniques were used to study the formation of CuCr2S4 spinel and the thermal decomposition reactions in crystalline mixtures of copper and chromium sulfides. The copper-chromium sulfide spinel was characterized by XRD and SEM and the kinetics of formation was followed in the temperature range 200-300°C by a titrimetric method. Kinetic analysis in view of various solid-state reaction models showed that the reaction is best described by the diffusion models with an average activation energy 24.6 ± 1.6 kJ/mol.

Diagnostic limits of phenomenological models of heterogeneous reactions and thermal analysis kinetics

Kinetic models of solid-state reactions are often based on a formal description of geometrically well defined bodies treated under strictly isothermal conditions; for real processes these prepositions are evidently incorrect. It can be equally useful to find an empirical function containing the smallest possible number of constants. In such a case the models of heterogeneous kinetics can be assumed as a distorted (fractal) case of the simpler homogeneous kinetics and mathematically treated by multiplying by an “accomodation” function. In addition, the conventional thermoanalytical (TA) studies apply intentionally the experimental conditions with constant heating and/or cooling where the model's validity must again be investigated. The general method of kinetic data evaluation is proposed to include two-step evaluation: first, determining the activation energy, E, from a set of TA curves at different heating rates, and second, using the pre-established E to search for the reaction mechanism by analyzing the entire course of the single TA curve. In this respect the possibility of a simultaneous determination of all kinetic data is discussed. The computer method is recommended to be based on the evaluation of two specific functions available for a direct derivation from experimental data.

The synthesis of beta alumina from aluminium hydroxide and oxyhydroxide precursors

Two aluminium oxyhydroxides, boehmite and pseudoboehmite, and two aluminium hydroxides, bayerite and gibbsite, have been investigated as precursors for the synthesis of the solid electrolyte, beta alumina. Reaction pathways and products have been characterized by thermal analysis and powder X-ray diffraction. A solid state reaction model for the formation of β″-Al 2O 3 is proposed.

Kinetic analysis of thermal decomposition reactions: Part VI. Thermal decomposition of manganese(II) acetate tetrahydrate

The kinetics of the thermal decomposition of manganese(II) acetate tetrahydrate were studied using isothermal and dynamic thermogravimetric techniques. The dehydration of the tetrahydrate proceeds via a two-stage reaction, each stage involving loss of two water molecules, while the thermal decomposition of the anhydrous salt proceeds in one step to MnO. Kinetic analysis of isothermal data of the three decomposition reactions, when compared with the various solid state reaction models, showed that the reactions are best described by the phase boundary and random nucleation models. Kinetic analysis of the dynamic TG curves were discussed with reference to a composite integral method, in comparison with the integral methods due to Coats and Redfern and to Ozawa. The activation parameters were calculated and the results of the isothermal and dynamic integral methods were compared and discussed.

The new method of constant rate thermal analysis (CRTA): Application to discrimination of the kinetic model of solid state reactions and the synthesis of materials

The advantage of CRTA in discriminating the kinetics of solid state reactions by comparison with conventional non-isothermal methods is described. It is also shown that control of the thermal decomposition rate of BaTiO(C 2O 4) 2 · 4.5H 2O by CRTA gives BaTiO 3 with a particle size considerably smaller than that obtained by decomposing the mixed oxalate by conventional methods. The influence of the decomposition method of this compound on the crystalline structure of BaTiO 3 is analysed.

Kinetic analysis of thermal decomposition reactions. VII. Effect of radiation and doping on the thermal decomposition of BaCO3–TiO2 and SrCO3–TiO2 crystalline mixtures

DTA–TG techniques were applied to study the thermal decomposition and reactivity in intimately mixed powders of barium or strontium carbonate and titanium dioxide. The results showed that the temperature for the thermal decomposition of BaCO3–TiO2 mixtures precedes the decomposition of pure BaCO3 by about 250 °C, whereas the decomposition of SrCO3–TiO2 mixtures precedes the decomposition of pure SrCO3 by about 60 °C. Kinetic analysis of the isothermal data in view of various solid-state reaction models showed that the reaction is best described by the phase boundary models. The effects of 60Co γ irradiation and of doping the metal oxide with Li+ or Cu2+ ions on the thermal decomposition reactions were investigated. Keywords: titanates, thermal decomposition, doping, irradiation effects.

Kinetic analysis of thermal decomposition reactions: Part 5. Gamma irradiation effects on the thermal decomposition of potassium nickel oxalate

Differential thermal analysis-thermogravimetry techniques were used to study the thermal decomposition of potassium nickel(II) oxalate hexahydrate crystals and the effects of 60Co gamma irradiation on the kinetics of the decomposition in air of K 2Ni(C 2O 4) 2 to NiO, K 2C 2O 4 and CO 2. The kinetics of the isothermal decomposition were studied over the temperature range 310–350°C, both for irradiated and non-irradiated K 2Ni(C 2O 4) 2·6H 2O crystals. Kinetic analysis of the results according to the various theoretical models of solid state reactions showed that the best fit is obtained for the first-order and the diffusion models. There is a decrease in both the energy of activation and the frequency factor with increasing radiation dose. The mechanism of the thermal decomposition and the effects produced by radiolysis were discussed.

Evaluation of thermal analysis experimental data

The possibilities of the THERMOKIN software package for evaluation of experimental data of solid state thermal decomposition are described. The software package makes it possible to simulate the solid state reactions, to evaluate the results of various thermal analysis methods such as TG/DTG, DSC., evolved gas analysis etc. The software enabled us to choose the adequate model of solid state reactions, to calculate the parameters of reactions and the errors of the parameters. Using this software package the interpretation of the results obtained by various methods of thermal analysis as well as the determination of the optimal experimental conditions for the studied substances can be made.

A comment on mathematical expressions used in solid state reaction kinetics studies by thermal analysis

Computer calculations pertaining to the reaction kinetics analyses of simulated thermoanalytical data, generated under non-isothermal conditions, have been performed. Results obtained by using the two forms of the differential and integral equations descriptive of three different models of rate-controlled solid state reactions: phase boundary movement, nucleation-growth and three-dimensional diffusion, have been examined and compared. Calculations have also been performed to examine the correctness of employing the simple diffusion model equations to analyze data generated by taking into consideration differences in the density of reactant and product. For all models studied and compared, the activation energies are the same, but the pre-exponential factors differ slightly. They can be interconverted by the use of an appropriate multiplicative constant.

Kinetic analysis of thermal decomposition reactions: Part IV: Kinetics of formation of barium titanate in crystalline mixtures of barium carbonate and titanium dioxide

The kinetics of formation of barium titanate from banum carbonate and titanium dioxide have been studied using isothermal and dynamic thermogravimetry techniques. Kinetic analysis of the isothermal data, considered from the point of view of various solid state reaction models, showed that the reaction is best described by the random nucleation Avrami equation Analysis of dynamic TG data, according to the integral methods of Coats and Redfern and of Ozawa, gave results which are not in agreement with each other or with the results obtained under isothermal conditions.

Kinetic analysis of thermal decomposition of praseodymium(III) nitrate hexahydrate

The kinetics of thermal decomposition of praseodymium(III) nitrate hexahydrate was studied by using isothermal and dynamic thermogravimetric techniques. Kinetic analysis of the isothermal data with respect to various solid-state reaction models showed that the reaction is best described by phase boundary-controlled and random nucleation models. Kinetic analysis of the dynamic TG curves was discussed and a critical comparison was made of two integral methods, that of Coats and Redfern and that of Ozawa. The results showed that the Ozawa method gives a better correlation, and the results are in good agreement with those obtained under isothermal thermogravimetric conditions.

On stochastic models of solid-state reactions

The Avrami model of solid-state reactions or transformations has frequently been presented and compared with other stochastic models. The equation often applied is shown to be merely a simplification of the full Avrami model equation (FAME). A convenient procedure for application of the FAME to the kinetics of solid-state reactions is proposed.