Solid-state Reaction Models Research Articles

Multivariate data analysis as a tool to investigate the reaction kinetics of intramolecular cyclization of enalapril maleate studied by isothermal and non-isothermal FT-IR microscopy

In this paper, the use of multivariate data analysis approach to investigate the kinetics of solid-state reaction monitored via FT-IR thermal microscopy is discussed. The solid-state degradation of enalapril maleate was monitored non-isothermally at temperature range from 25 to 200 °C and isothermally at various temperatures (115, 120, 125, 130, and 135 °C) for a few hours. The collected FT-IR spectra were subjected to self-modeling curve resolution (SMCR) in order to elucidate the pure component spectral estimates. Subsequently, the relative contributions from the observed species could be obtained by projecting the pure component spectral estimates onto the collected FT-IR spectra. Accordingly, the conversion factors from enalapril maleate to diketopiperazine were calculated and were fitted to various solid-state reaction models. The activation energy values ( E a) calculated from seven nucleation models were ranging from 176.4 to 193.9 kJ/mol. This multivariate data analysis approach proves to be an effective tool for analyzing the kinetic spectroscopic data having a high degree of overlap between original compound and its degradation product since the information from the whole spectral range is used.

Thermal decomposition kinetics of strontium oxalate

AbstractThe thermal decomposition behavior in air of SrC2O4 · 1.25H2O was studied up to the formation of SrO using DTA-TG-DTG techniques. The decomposition proceeds through four well-defined steps. The first two steps are attributed to the dehydration of the salt, while the third and fourth ones are assigned to the decomposition of the anhydrous strontium oxalate into SrCO3 and the decomposition of SrCO3 to SrO, respectively. The exothermic DTA peak found at around 300°C is ascribed to the recrystallization of the anhydrous strontium oxalate. On the other hand, the endothermic DTA peak observed at 910°C can be attributed to the transition of orthorhombic-hexagonal phase of SrCO3. The kinetics of the thermal decomposition of anhydrous strontium oxalate and strontium carbonate, which are formed as stable intermediates, have been studied using non-isothermal TG technique. Analysis of kinetic data was carried out assuming various solid-state reaction models and applying three different computational methods. The data analysis according to the composite method showed that the anhydrous oxalate decomposition is best described by the two-dimensional diffusion-controlled mechanism (D2), while the decomposition of strontium carbonate is best fitted by means of the three-dimensional phase boundary-controlled mechanism (R3). The values of activation parameters obtained using different methods were compared and discussed.

Investigation of the Multi-Step Dehydration Reaction of Theophylline Monohydrate Using 2-Dimensional Powder X-ray Diffractometry

(i) To study the dehydration kinetics of theophylline monohydrate using 2-dimensional (2D) powder X-ray diffractometry (XRD), and (ii) to investigate the effect of polyvinylpyrrolidone (PVP) on the dehydration pathway and kinetics. Theophylline monohydrate (C(7)H(8)N(4)O(2).H(2)O; M) was recrystallized from aqueous PVP solutions of different concentrations. Dehydration kinetics was studied isothermally, at several temperatures, from 35 to 130 degrees C. The experimental set-up comprised of a high intensity X-ray source (synchrotron radiation or 8 kW rotating anode), a heating chamber, and a 2D area detector. Diffraction patterns were collected continuously, with a time resolution ranging from 40 ms to 30 s, over the angular range of 3 to 27 degrees 2theta. Dehydration of M resulted in either the stable (C(7)H(8)N(4)O(2); A), or the metastable anhydrate (A*), with the latter having a tendency to transform to A. The XRD technique allowed simultaneous quantification of M, A* and A during the dehydration reaction. The rate constants for individual reaction steps (M-->A*; M-->A and A*-->A) were determined by fitting the data to solid-state reaction models. In presence of PVP, there was a decrease in the magnitude of the rate constant associated with the M-->A transition, resulting in an increased build-up of A* in the product. The inhibitory effect of PVP on M-->A transition was more pronounced at lower dehydration temperatures, and was proportional to the concentration of PVP. Two dimensional powder X-ray diffractometry, using a high intensity source, is a powerful technique to study kinetics of rapid solid-state reactions. The inhibitory effect of excipients can have profound effect on phases formed during pharmaceutical processing.

Comparison between dehydration and desolvation kinetics of fluconazole monohydrate and fluconazole ethylacetate solvate using three different methods

It was of interest to study the dehydration and the desolvation of fluconazole monohydrate and ethyl acetate solvate respectively and also to determine the kinetics of dehydration and desolvation using thermogravimetry (TGA). Fluconazole monohydrate and ethyl acetate solvate were prepared by crystallization in water and in ethyl acetate solvent respectively. The dehydration and the desolvation processes were characterized by differential scanning calorimetry, thermogravimetry, powder X-ray diffractometry, and Fourier transform infrared spectroscopy. The weight changes of the fluconazole monohydrate and ethyl acetate solvate samples were monitored by isothermal TGA. Kinetic analyses of isothermal TGA data were done using model dependent and model independent methods. Various heating rates were also employed in different TGA samples, in order to apply the Ozawa method to determine the kinetic parameters. Eighteen solid-state reaction models were used to interpret the isothermal TGA experiments. Based on statistics, the three-dimensional phase boundary reaction model provided the best fit of the monohydrate data while the three-dimensional diffusion model provided the best fit for the ethyl acetate solvate data. The activation energy (Ea) values derived from rate constants of the aforementioned models were 90±11 and 153±11 kJ/mol for fluconazole monohydrate and ethyl acetate solvate respectively. Model independent analysis and the Ozawa method were also applied to the experimental results. Based on the results obtained from the model dependent, model independent and the Ozawa method, the mechanisms of the dehydration and the desolvation were determined.

Kinetic study on the thermal dehydration of CaCO3 · H2O by the master plots method

AbstractThermal dehydration process of calcium oxalate monohydrate, CaC2O4 · H2O, was reinvestigated from a viewpoint of reaction kinetics. On the basis of data of thermogravimetry, kinetic analysis was performed under nonisothermal conditions using an integral composite procedure, which includes a integral isoconversional method and an integral master plots method. The results of the integral isoconversional method of TGA data at various heating rates suggested that dehydration of CaC2O4 · H2O followed a single step with an activation energy of 99.02 ± 2.61 kJ/mol, and from the master plots method, the reaction was described by an Rn model. Finally, it was estimated that the pre‐exponential factor A = (2.82 ± 1.81) ×109 s−1, and the kinetic exponent n = 2.3 ± 0.2. The results of nonisothermal kinetic analysis of the thermal dehydration reactions of CaC2O4 · H2O suggested that the integral composite procedure be very successful in evaluating kinetic parameters and describing kinetic model of solid‐state reactions. © 2006 American Institute of Chemical Engineers AIChE J, 2006

Kinetic analysis of the thermal decomposition of pristine and γ-irradiated zinc uranyl acetate

Thermal decomposition of pristine and γ-irradiated zinc uranyl acetate was investigated in air using isothermal and dynamic thermogravimetric techniques. The decomposition proceeded via one major process with the formation of triuranates ZnU3O10 as solid residues. Kinetic analysis of isothermal data, when compared with various solid-state reaction models, showed that the decomposition reaction is best fitted by the phase-boundary model. Kinetic analysis of the dynamic TG curves was discussed with reference to integral methods of modified Coats and Redfern equations. Kinetic and thermodynamic parameters were calculated and evaluated. IR spectroscopy and X-ray powder diffraction techniques were employed to follow the chemical composition of solid residue at different calcination temperatures. The results display that the triuranate ZnU3O10 starts forming by calcination of zinc uranyl acetate at temperatures > 300 °C and undergoes decomposition at higher temperatures (>600 °C) with the formation of U3O8. The results were evaluated regarding the utilization of zinc uranyl acetate as an important source of diuranates and triuranates.

Predicting polymorphic transformation curves using a logistic equation

The commonly used solid-state reaction models (for example—Prout–Tompkins, Avrami–Erofe’ev) describe the polymorphic transformation data only over a certain range, α from 10% to 90%. Predictions based on a fit to a fraction of the data are inadequate because we ignore the early induction phase of the reaction, which is important for predictive purposes. A four-parameter logistic equation describes the data over the entire curve for polymorphic transformation at high temperatures. We use the parameters of the logistic equation to predict the transformation curves. The predicted curves agree with the experimental data.

γ-irradiation effects on kinetics and mechanism of the thermal decomposition of zinc acetate

The kinetics of the thermal decomposition of un-irradiated (pristine) and pre-γ-irradiated dehydrated zinc acetate was studied in the temperature range (553–573 K) and in air using both isothermal and dynamic thermogravimetric techniques. The data were analyzed using various solid state reaction models. The integral method using the Coats–Redfern equation was applied in the dynamic data analysis. The results showed that the kinetics of isothermal decomposition of dehydrated zinc acetate was governed by a phase-boundary controlled reaction (R 2) while in non-isothermal (dynamic) decomposition the kinetic was controlled by a nucleation process. The activation energies of the main decomposition process for un-irradiated and pre-γ-irradiated samples were calculated and the results of the isothermal and dynamic integral methods were compared and discussed. The changes in texture and crystal structure of the investigated zinc acetate by γ-irradiation were studied using electron microscopy and X-ray diffraction techniques.

Pasted positive plate of lead–acid battery: General analysis of discharge process

A general analysis of the discharge process of pasted positive plates of lead–acid batteries is presented. Two models are explored in order to understand qualitatively the phenomenon: a solid-state reaction model and a dissolution–precipitation reaction model. The two models are presented and related to two important phenomena: the existence, always during the discharge, of a reaction zone going from the surface to the bulk of the plate active material and the possibility, for low H2SO4 concentrations and high rates of discharge, of H2SO4 depletion, producing the reduction of the used active material. The influence of the rate of discharge and sulfuric acid concentration on potential versus charge curves during the discharge, on capacity and on plate resistance during the discharge transient, especially for very low discharge rate conditions are analyzed. Two equivalent plates from two different manufacturing technologies are tested. Both models, sometimes with the introduction of some modifications from traditional formulations, explain the different results found.

Kinetic study of the corrosion of silicon nitride materials in acids

Abstract The leaching behaviour of gas-pressure-sintered silicon nitride materials with different yttria, alumina and silica contents in 1N sulfuric acid at 60–101 °C was studied. The progress of corrosion was investigated in terms of mass loss and thickness of the corroded layer. Dependencies affecting the progression of the corrosive attack, such as the SiO 2 content of the grain boundary phase and the size distribution of the triple junctions, were described. The influence of temperature on the individual stages of the entire process was investigated. First attempts at modelling the complex corrosion behaviour were made. To simplify the mathematical modelling, plates (16 × 16 × 2.5 mm) fulfilling conditions allowing them to be considered as one-dimensional were chosen. Activation energies were calculated for the pure dissolution of the grain boundary phase from mass loss data and from the thickness of the corroded layer. Known solid state reaction models and corrosion models show only a limited ability to describe the investigated system.

A model for mechanochemical transformations: Applications to molecular hardness, instabilities, and shock initiation of reaction

A basic theoretical structure for mechanochemical transformations based on prior models for solid-state reactions and HOMO–LUMO (highest occupied molecular orbital–lowest unoccupied molecular orbital) gap closing produces the concept of distortion-induced molecular electronic degeneracy (DIMED) of the highest occupied and lowest unoccupied molecular orbitals of an energetic molecule. Both intermolecular and intramolecular charge transfer are involved. The resulting distortion-induced local instability, a mechanochemical effect, leads to chemical transformations and can be analyzed by renormalization of the molecular hardness through the molecular deformation energy. Linear combinations of normal modes are shown to be useful for description of the mechanically induced reaction path. Numerical calculations for the RDX (hexahydro-1,3,5-trinitro-1,3,5-triazine) molecule are used to construct a path for initiation of a reaction by shock. They show the breaking of a single N–N bond as the primary step. DIMED is shown to be a kind of “inverse Jahn–Teller effect” leading to the general conclusion that distortion-induced instabilities and mechanically induced reactions require some, but not necessarily complete, HOMO–LUMO gap closure. This indicates that large local strains due to defects or cracks will contribute to DIMED. The DIMED concept, because of its generality, has wide applicability in solid-state chemistry.

Solid-state reaction kinetics of the system CaO-FeO

The solid-state reaction mechanisms of the CaO-FeO system have been studied by a diffusion couple method in the temperature range of 1073 to 1273 K, under controlled oxygen-partial pressures. The interdiffusivities and intrinsic diffusivities of Ca2+ and Fe2+ have been determined in the limited FeO solid-solution range. Based on the obtained results, a solid-state reaction model of the system has been developed, taking account of the formation of the Ca2Fe2O5 phase. According to the model, the diffusivities of Fe3− in the Ca2Fe2O5 phase have been estimated at 1273 K.

Physicochemical stability of cimetidine amorphous forms estimated by isothermal microcalorimetry.

The effect of humidity on the physicochemical properties of amorphous forms of cimetidine was investigated using differential scanning calorimetry, isothermal microcalorimetry, and x-ray diffraction analysis. Amorphous forms were obtained by the melting (amorphous form M [AM]) and the cotton candy (amorphous form C [AC]) methods. Thermal behaviors of AM and AC with or without seed crystals were measured using an isothermal microcalorimeter under various conditions of relative humidity (RH) and temperature, respectively. The crystallization kinetics of amorphous solids was analyzed based on 10 kinds of solid-state reaction models. AM transformed into form A at 11% RH, 50 degrees C but transformed into a mixture of form A and monohydrate at 51% and 75% RH at 25 degrees C. The mean crystallization times (MCTs) of the heat flow curve of AM and AC at 11% RH, 50 degrees C were 47.82 and 32.00 hours, respectively, but at 11% RH, 25 degrees C both were more than 4320 hours. In contrast, AC transformed into form A under all storage conditions. The MCTs of AC at 51% and 75% RH were 29.61 and 11.81 hours, respectively; whereas the MCTs of AM were 46.79 and 15.52 hours, respectively. The crystallization of amorphous solids followed the three-dimensional growth of nuclei (Avrami equation) with an induction period (IP). The IP for AM at 11% RH, 50 degrees C was more than 2 times that for AC, but the difference in the crystal growth rate constant (CR) between AC and AM was within 10%. The IP for AM at 75% RH, 25 degrees C was reduced to only 10% of the IP at 51% RH with increasing humidity, but the CR did not change significantly. In contrast, the IP for AC was slightly reduced at 75% RH compared with 51% RH, but the CR was about 5 times greater. At 75% RH, 25 degrees C, the IP and CR of AM were about one-fourth the values of AC. This result suggests that the crystallization process consists of an initial stage during which the nuclei are formed and a final stage of growth.

Kinetics of the thermal decomposition of γ-irradiated gadolinium acetate

Kinetics of the thermal decomposition of un-irradiated (pristine) and pre-γ-irradiated hydrated gadolinium acetate was studied within the temperature range (603–623K) and in air using isothermal and dynamics thermogravimetric techniques. The data were analyzed using various solid-state reaction models. Integral method using Coat–Redfon equation was applied in dynamic data analysis. The results showed that the kinetic of isothermal and non-isothermal (dynamic) decomposition for acceleratory stage was governed by phase boundary process. The activation energies for pristine and pre-irradiated samples were calculated and the results of the isothermal and dynamic decomposition integral methods were compared and discussed. Thermodynamic values of the main decomposition process were calculated and evaluated.

Effect of γ-irradiation and semiconducting oxide (tio2) on the thermal decomposition of mgc2o4: A comparative study

The simultaneous rising temperature (DTA-TG) technique and the gas evolution method are adopted for studying the thermal decomposition of unirradiated and irradiated MgC2O4 and MgC2O4 + TiO2 mixtures. The data are applied to theories of different solid state reaction models and the best fit is obtained for the Avrami-Erofeev mechanism (n=2) suggesting that both the nucleation and growth processes occur at the reactant product interface in a two dimensional chain branching manner. Low irradiation doses decrease the rate of reaction remarkably whereas the reverse phenomenon takes place at higher doses. The n-type semiconducting oxide, TiO2 (5-40 mol%) enhances the rate of decomposition which increases with increasing concentration of the catalyst. The influence of n -irradiation is explained in the light of defects, dislocations and electron-hole (e−, h+) pairs generated in the lattice, whereas the influence of TiO2 is understood on the basis of electron transfer process involved in the reaction.

Influence of γ-irradiation on the non-isothermal decomposition of calcium-gadolinium oxalate

Thermal decomposition of co-precipitated unirradiated and irradiated Ca-Gd oxalate has been studied by adopting differential thermal analysis (DTA) and thermogravimetric (TG) techniques. The reaction occurs through two stages corresponding to the decomposition of gadolinium oxalate (Gd-Ox) followed by that of calcium oxalate (Ca-Ox). The kinetic parameters for both the stages are calculated by using solid state reaction models and Coats-Redfern's equation. The co-precipitation as well as irradiation alter the DTA peak temperatures and the kinetic parameters of Ca-Ox. The decomposition of Gd-Ox follows the two dimensional Contracting area ( R 2 ) mechanism, while that of Ca-Ox follows the Avrami-Erofeev ( A 2 ) mechanism ( n =2), which are also exhibited by the co-precipitated and irradiated samples. Co-precipitation decreases the energy of activation and the pre-exponential factor of the individual components but the reverse phenomenon takes place upon irradiation of the co-precipitate. The mechanisms underlying the phenomena are explored.

Thermal analysis of La–Ba oxalate and role of γ-irradiation there on

Lanthanum–barium oxalate was prepared and characterised by chemical and thermal analysis, X-ray diffraction and plasma emission spectroscopy. X-ray analysis showed the presence of a uniphase system. The kinetics of decomposition of oxalates of La and Ba as well as coprecipitated La–Ba oxalate have been investigated in air using dynamic thermogravimetry. The decomposition of mixed oxalate occurred with two over-lapping exotherms, corresponding to the decomposition of lanthanum oxalate followed by that of barium. The kinetics of decomposition of the irradiated salt was studied over the same temperature range as that of the unirradiated one in air and activation energies obtained from the slopes of Coat–Redfern’s plot. Kinetic analyses following various theoretical models of solid state reactions showed that the best fit was obtained for a third order reaction and geometrical models. It was evident that though there was increase in the activation energy as well as frequency factor with increasing radiation dose, reverse phenomenon takes place in the case of reaction rate. The effect of γ-irradiation on the process and the mechanism involved therein has been discussed.

Effects of Dehydration Temperatures on Moisture Absorption and Dissolution Behavior of Theophylline.

Anhydrous theophylline was prepared by heating theophylline monohydrate at temperatures between 60 degrees C and 140 degrees C. The effects of dehydration temperatures on the moisture absorption and dissolution behavior of anhydrous theophylline were investigated in this study. The hydration rate of anhydrous theophylline at 95% relative humidity and 25 degrees C decreased with increasing dehydration temperatures. From the fitting analysis of solid-state reaction models, the hydration reaction was found to be governed by the phase boundary reaction model for samples prepared at lower dehydration temperatures (<100 degrees C) but the reaction obeyed the growth of nuclei reaction model when samples were dehydrated at higher temperatures. The dissolution rates of various anhydrous theophylline samples were measured by the rotating disk method. The calculated solubility of anhydrous theophylline prepared by heating was about 2.5 times higher than that of theophylline monohydrate. The phase transformation rate from the anhydrous form to the monohydrate during dissolution tests decreased with higher dehydration temperatures. It was found that the anhydrous theophylline prepared at different dehydration temperatures transformed to the monohydrate by way of different growth of hydrate nuclei mechanism.

Kinetics of the thermal decomposition of γ-irradiated cobaltous acetate

Kinetics of the thermal decomposition of un-irradiated (pristine) and pre-γ-irradiated dehydrated cobaltous acetate was studied within the temperature range (538–563 K) and in air using isothermal and dynamics thermogravimetric techniques. The data were analyzed using various solid state reaction models. Integral method using Coat–Redfon equation was applied in dynamic data analysis. The results showed that the kinetic of isothermal decomposition for acceleratory stage was governed by diffusion-controlled process while in non-isothermal (dynamic) decomposition the kinetic was controlled by phase boundary process. The activation energies for pristine and pre-irradiated samples were calculated and the results of the isothermal and dynamic decomposition integral methods were compared and discussed. The change in texture and crystal structure of the investigated cobaltous acetate by γ-irradiation was studied using scanning electron microscopy and X-ray diffraction technique. Thermodynamic values of the main decomposition process were calculated and evaluated.

Effect of thermal treatment on physicochemical properties of pure and mixed manganese carbonate and basic copper carbonate

A series of pure and mixed Mn and Cu oxides were prepared by calcination of MnCO 3 and CuCO 3·Cu(OH) 2 at different temperatures, (250, 500, 750 and 1000°C) for 4 h in air. Pyrolyses of pure and mixed solid salts were investigated using the thermal analysis (DTA and TG) technique in a flow of air. Also, the calcined samples were analyzed for different species using X-ray diffraction (XRD). A solid-state reaction model accounting for the Mn oxide–Cu oxide interaction in mixed systems is discussed. The catalytic activity of the thermal products of pure and mixed solids was tested in H 2O 2 decomposition as a model reaction.