The solid state dehydration of d lithium potassium tartrate monohydrate is complete in two rate processes I. The deceleratory diffusion-controlled first reaction

1994 ◽  
Vol 347 (1682) ◽  
pp. 139-156 ◽  
Keyword(s):  
Activation Energy ◽  
Vacancy Concentration ◽  
Nucleation And Growth ◽  
Crystalline Hydrate ◽  
Rate Equations ◽  
Mechanistic Study ◽  
Crystal Thickness ◽  
Potassium Tartrate ◽  
Diffusion Controlled ◽  
Rate Processes

A kinetic and mechanistic study of the dehydration of d lithium potassium tartrate monohydrate has been undertaken. Water evolution is completed through two separate rate processes. The first reaction is the deceleratory, diffusion-controlled release of water from the superficial zones of the reactant crystals. The yield of this process corresponds to the dehydration of a superficial layer of crystal, thickness 10 µm. About 4% of the constituent water was evolved from the single crystals studied, rising to 50% from crushed powder reactants. The second reaction, reported in Part II, is a nucleation and growth process yielding the crystalline anhydrous salt. Gravimetric measurements for the first reaction identified three distinct dehydration processes. The first step was the rapid release of loosely bonded superficial water. The subsequent two deceleratory stages are characterized as diffusive loss of H 2 O molecules from a crystal zone that is at first ordered but later becomes disordered as the water-site vacancy concentration increases. Rate measurements based on water evolution measured the activation energy of this third step as 153 + 4 kJ mol -1 . Irreproducibility of rate data is ascribed to variations in numbers and distributions of imperfections between individual crystals. The extent and rate of the first reaction increased when initiated in small pressures of water vapour. Electron microscope observations identified a structural discontinuity ca. 1 µm below reacted crystal faces, evidence of superficial retexturing of the reactant. Rates of powder dehydrations were more reproducible than those of crystals but the kinetic behaviour was similar. The same rate equations were obeyed and the activation energy was unaltered. Water loss during the first reaction of this crystalline hydrate gives a comprehensive layer of extensively dehydrated material across all surfaces. Subsequently, in or under this water depleted layer, salt is recrystallized and dehydration continues as a nucleation and growth reaction (part II, following paper).

The solid state dehydration of d lithium potassium tartrate monohydrate is complete in two rate processes II. The nucleation and growth second reaction and dehydration mechanism

1994 ◽  
Vol 347 (1682) ◽  
pp. 157-184 ◽  
Keyword(s):  
Water Loss ◽  
Vacancy Concentration ◽  
Preceding Paper ◽  
Nucleation And Growth ◽  
Mechanistic Study ◽  
Water Losses ◽  
Water Release ◽  
Kinetic Measurements ◽  
Potassium Tartrate ◽  
Rate Processes

A kinetic and mechanistic study has been undertaken of the nucleation and growth reaction that is the second of the two consecutive rate processes that occur during the dehydration of d lithium potassium tartrate monohydrate. Electron microscopic examinations of the cleaved surfaces of partly reacted crystals show the development of three-dimensional nuclei that are composed of small crystals of the anhydrous product and above 450 K there is evidence of intranuclear melting. Consistent with this model, the second reaction obeys the Avrami-Erofe’ev equation {[ — ln (1 — α)] 1/2 = kt }. Overall rates of the dehydrations of single crystals and of crushed powder samples were closely similar. The activation energy for dehydration was 150-160 kJ mol -1 for both first (reported in part I, preceding paper) and second reactions and for both single crystal and crushed powder reactants. The addition of product crystallites to the reactant reduced sharply, or eliminated, the induction period to the nucleation and growth process. From consideration of the kinetic characteristics, together with the textural changes observed microscopically, we conclude that the following mechanism very satisfactorily accounts for our results. The first reaction proceeds to the dehydration of all crystal surfaces, representing water losses from a layer ca . 10 µm thickness. This deceleratory process occurs initially in a structure resembling that of the reactant but later the increasing water site vacancy concentration results in increasing reactant disorder and possibly includes fusion of the outer layer. When the first reaction water evolution has slowed, recrystallization to the structure of the anhydrous product occurs at a limited number of sites to generate germ nuclei that effectively act as seed crystals for nucleus growth. During the second reaction the reactant—product contact interface is identified as a zone of diffusive water loss, similar to that described for the first reaction. Here, however, the product crystallites promote reorganization of dehydrated material, thereby opening channels for water escape and continually exposing new hydrate surfaces at which dehydration continues. This product recrystallization enables advance of the nucleus interface to be maintained, so that rates of both first and second reactions are subject to control by diffusive loss of water from an active boundary of the reactant. Product reorganization removes the inhibiting character of accumulated product layer by introducing escape channels for water loss so that interface advance continues and, although spasmodic, this migrates forward at a constant average linear rate. The work is of interest because kinetic measurements have been obtained for both of the consecutive rate processes that contribute to the overall reaction. The controls of both are shown to be closely similar. The reaction model proposed here provides insight into the structure of the dehydration interface and the mechanism of water release.

scholarly journals Study on indium leaching from mechanically activated hard zinc residue

2011 ◽  
Vol 47 (1) ◽  
pp. 63-72 ◽  
Author(s):  
J.H. Yao ◽  
X.H. Li ◽  
Y.W. Li
Keyword(s):  
Activation Energy ◽  
Particle Size ◽  
Planetary Mill ◽  
Leaching Rate ◽  
Obvious Effect ◽  
Diffusion Controlled ◽  
Leaching Reaction ◽  
Kinetics Of ◽  
Positive Effect ◽  
Solution Kinetics

In this study, changes in physicochemical properties and leachability of indium from mechanically activated hard zinc residue by planetary mill were investigated. The results showed that mechanical activation increased specific surface area, reaction activity of hard zinc residue, and decreased its particle size, which had a positive effect on indium extraction from hard zinc residue in hydrochloric acid solution. Kinetics of indium leaching from unmilled and activated hard zinc residue were also investigated, respectively. It was found that temperature had an obvious effect on indium leaching rate. Two different kinetic models corresponding to reactions which are diffusion controlled, [1-(1- x)1/3]2=kt and (1-2x/3)-(1-x)2/3=kt were used to describe the kinetics of indium leaching from unmilled sample and activated sample, respectively. Their activation energies were determined to be 17.89 kJ/mol (umilled) and 11.65 kJ/mol (activated) within the temperature range of 30?C to 90?C, which is characteristic for a diffusion controlled process. The values of activation energy demonstrated that the leaching reaction of indium became less sensitive to temperature after hard zinc residue mechanically activated by planetary mill.

scholarly journals Advanced Isoconversional Kinetic Analysis for the Elucidation of Complex Reaction Mechanisms: A New Method for the Identification of Rate-Limiting Steps

Molecules ◽  
2019 ◽  
Vol 24 (9) ◽  
pp. 1683 ◽  
Author(s):  
Nicolas Sbirrazzuoli
Keyword(s):  
Activation Energy ◽  
Kinetic Analysis ◽  
Single Step ◽  
Thermoanalytical Techniques ◽  
Diffusion Controlled ◽  
Physical Transformation ◽  
Exponential Factors ◽  
Isoconversional Kinetic Analysis ◽  
The Individual ◽  
Rate Limiting

Two complex cure mechanisms were simulated. Isoconversional kinetic analysis was applied to the resulting data. The study highlighted correlations between the reaction rate, activation energy dependency, rate constants for the chemically controlled part of the reaction and the diffusion-controlled part, activation energy and pre-exponential factors of the individual steps and change in rate-limiting steps. It was shown how some parameters computed using Friedman’s method can help to identify change in the rate-limiting steps of the overall polymerization mechanism as measured by thermoanalytical techniques. It was concluded that the assumption of the validity of a single-step equation when restricted to a given α value holds for complex reactions. The method is not limited to chemical reactions, but can be applied to any complex chemical or physical transformation.

Kinetic Studies on the Synthesis of Hydroxyapatite Nanowires by Solvothermal Methods

2007 ◽  
Vol 60 (2) ◽  
pp. 99 ◽  
Author(s):  
Shiying Zhang ◽  
Chen Lai ◽  
Kun Wei ◽  
Yingjun Wang
Keyword(s):  
Activation Energy ◽  
Reaction Rate ◽  
Kinetic Studies ◽  
Axial Ratio ◽  
Reaction Rate Constant ◽  
Rate Equations ◽  
Solvothermal Reaction ◽  
Growth Order ◽  
Constant Diffusion ◽  
Solvothermal Methods

Hydroxyapatite nanowires with a high axial ratio have been synthesized in reverse micelle solutions that consist of cetyltrimethylammonium bromide (CTAB), n-pentanol, cyclohexane, and the reactant solution by solvothermal methods. This paper focusses on the kinetic studies of the solvothermal reaction and the linear growth of hydroxyapatite nanowires. When the reaction was carried out at low temperatures (65°C), the experimental results showed that the reaction rate was of zero order since the whole reaction was diffusion controlled with constant diffusion coefficients. In the middle to high temperature range (130–200°C), the kinetics were characterized by second order reaction kinetics. Since the controlling factor was activation energy and the apparent activation energy was large, the reaction rate was more sensitive to the temperature. Therefore, the exponent of the reaction rate constant increased by two when the temperature was increased from 130 to 200°C. By calculating the yields of products and the specific surface areas at different times, the linear and overall growth rate equations of the hydroxyapatite nanowires could be obtained. The experimental effective growth order of the crystals was 11. The larger growth order indicated that the crystal could grow more effectively in one direction because of the induction of the surfactant in the experiment system.

Study on the Melting Mechanism of Maleic Anhydride

2020 ◽  
Vol 10 (1) ◽  
pp. 65-78
Author(s):  
Bratati Das ◽  
Ashis Bhattacharjee
Keyword(s):  
Phase Transition ◽  
Activation Energy ◽  
Maleic Anhydride ◽  
Temperature Dependence ◽  
Growth Models ◽  
Melting Process ◽  
Nucleation And Growth ◽  
Crystalline Solid ◽  
Scanning Calorimetry ◽  
Melting Mechanism

Background: Melting of a pure crystalline material is generally treated thermodynamically which disregards the dynamic aspects of the melting process. According to the kinetic phenomenon, any process should be characterized by activation energy and preexponential factor where these kinetic parameters are derivable from the temperature dependence of the process rate. Study on such dependence in case of melting of a pure crystalline solid gives rise to a challenge as such melting occurs at a particular temperature only. The temperature region of melting of pure crystalline solid cannot be extended beyond this temperature making it difficult to explore the temperature dependence of the melting rate and consequently the derivation of the related kinetic parameters. Objective: The present study aims to explore the mechanism of the melting process of maleic anhydride in the framework of phase transition models. Taking this process as just another first-order phase transition, occurring through the formation of nuclei of new phase and their growth, particular focus is on the nucleation and growth models. Methods: Non-isothermal thermogravimetry, as well as differential scanning calorimetry studies, has been performed. Using isoconversional kinetic analysis, temperature dependence of the activation energy of melting has been obtained. Nucleation and growth models have been utilized to obtain the theoretical temperature dependencies for the activation energy of melting and these dependencies are then compared with the experimentally estimated ones. Conclusion: The thermogravimetry study indicates that melting is followed by concomitant evaporation, whereas the differential scanning calorimetry study shows that the two processes appear in two different temperature regions, and these differences observed may be due to the applied experimental conditions. From the statistical analysis, the growth model seems more suitable than the nucleation model for the interpretation of the melting mechanism of the maleic anhydride crystals.

scholarly journals Computational mechanistic study of the unimolecular dissociation of ethyl hydroperoxide and its bimolecular reactions with atmospheric species

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Mansour H. Almatarneh ◽  
Asmaa Alnajajrah ◽  
Mohammednoor Altarawneh ◽  
Yuming Zhao ◽  
Mohammad A. Halim
Keyword(s):  
Activation Energy ◽  
Density Functional ◽  
Computational Study ◽  
Basis Sets ◽  
Mechanistic Study ◽  
Intrinsic Reaction Coordinate ◽  
Unimolecular Dissociation ◽  
Phase Reaction ◽  
Atmospheric Species ◽  
Solvation Models

Abstract A detailed computational study of the atmospheric reaction of the simplest Criegee intermediate CH2OO with methane has been performed using the density functional theory (DFT) method and high-level calculations. Solvation models were utilized to address the effect of water molecules on prominent reaction steps and their associated energies. The structures of all proposed mechanisms were optimized using B3LYP functional with several basis sets: 6-31G(d), 6-31G (2df,p), 6-311++G(3df,3pd) and at M06-2X/6-31G(d) and APFD/6-31G(d) levels of theory. Furthermore, all structures were optimized at the B3LYP/6-311++G(3df,3pd) level of theory. The intrinsic reaction coordinate (IRC) analysis was performed for characterizing the transition states on the potential energy surfaces. Fifteen different mechanistic pathways were studied for the reaction of Criegee intermediate with methane. Both thermodynamic functions (ΔH and ΔG), and activation parameters (activation energies Ea, enthalpies of activation ΔHǂ, and Gibbs energies of activation ΔGǂ) were calculated for all pathways investigated. The individual mechanisms for pathways A1, A2, B1, and B2, comprise two key steps: (i) the formation of ethyl hydroperoxide (EHP) accompanying with the hydrogen transfer from the alkanes to the terminal oxygen atom of CIs, and (ii) a following unimolecular dissociation of EHP. Pathways from C1 → H1 involve the bimolecular reaction of EHP with different atmospheric species. The photochemical reaction of methane with EHP (pathway E1) was found to be the most plausible reaction mechanism, exhibiting an overall activation energy of 7 kJ mol−1, which was estimated in vacuum at the B3LYP/6-311++G(3df,3pd) level of theory. All of the reactions were found to be strongly exothermic, expect the case of the sulfur dioxide-involved pathway that is predicted to be endothermic. The solvent effect plays an important role in the reaction of EHP with ammonia (pathway F1). Compared with the gas phase reaction, the overall activation energy for the solution phase reaction is decreased by 162 and 140 kJ mol−1 according to calculations done with the SMD and PCM solvation models, respectively.

scholarly journals Phase Transformation Kinetics of a FCC Al0.25CoCrFeNi High-Entropy Alloy during Isochronal Heating

Metals ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 1015
Author(s):  
Jun Wang ◽  
Chen Wei ◽  
Haoxue Yang ◽  
Tong Guo ◽  
Tingting Xu ◽  
...  
Keyword(s):  
Phase Transition ◽  
Activation Energy ◽  
Phase Transformation ◽  
High Entropy Alloy ◽  
Transformation Kinetics ◽  
High Entropy ◽  
Phase Transformation Kinetics ◽  
Diffusion Controlled ◽  
Thermal Dilation ◽  
Kinetics Of

The phase transformation kinetics of a face-centered-cubic (FCC) Al0.25CoCrFeNi high-entropy alloy during isochronal heating is investigated by thermal dilation experiment. The phase transformed volume fraction is determined from the thermal expansion curve, and results show that the phase transition is controlled by diffusion controlled nucleation-growth mechanism. The kinetic parameters, activation energy and kinetic exponent are determined based on Kissinger–Akahira–Sunose (KAS) and Johnson–Mehl–Avrami (JMA) method, respectively. The activation energy and kinetic exponent determined are almost constant, indicating a stable and slow speed of phase transition in the FCC Al0.25CoCrFeNi high-entropy alloy. During the main transformation process, the kinetic exponent shows that the phase transition is diffusion controlled process without nucleation during the transformation.

Electrical, Optical, Structural, and Analytical Properties of Very Pure GaN

2002 ◽  
Vol 743 ◽  
Author(s):  
D. C. Look ◽  
J. R. Sizelove ◽  
J. Jasinski ◽  
Z. Liliental-Weber ◽  
K. Saarinen ◽  
...  
Keyword(s):  
Activation Energy ◽  
Hall Effect ◽  
Excited States ◽  
Vacancy Concentration ◽  
Strong Line ◽  
Threading Dislocation ◽  
Charge Balance ◽  
Acceptor Concentration ◽  
Flat Surfaces ◽  
The Difference

ABSTRACTPresent hydride vapor phase epitaxial growth of GaN on Al2O3 can produce material of very high quality, especially in regions of the crystal far from the substrate/epilayer interface. In the present study, we characterize a 248-μm-thick epilayer, which had been separated from its Al2O3 substrate and etched on top and bottom to produce flat surfaces. Temperature-dependent Hall-effect data have been fitted to give the following parameters: mobility μ(300) = 1320 cm2/V-s; μ(peak) = 12,000 cm2/V-s; carrier concentration n(300) = 6.27 × 1015 cm−3; donor concentration ND = 7.8 × 1015 cm−3; acceptor concentration NA = 1.3 × 1015 cm−3; and effective donor activation energy ED = 28.1 meV. These mobilities are the highest ever reported in GaN, and the acceptor concentration, the lowest. Positron annihilation measurements give a Ga vacancy concentration very close to NA, showing that the dominant acceptors are likely native defects. Secondary ion mass spectroscopic measurements show that ND is probably composed of the common donors O and Si, with [O] > [S1]. Transmission electron microscopy measurements yield threading dislocation densities of about 1 × 107 cm−2 on the bottom (N) face, and < 5 × 105 cm−2 on the top (Ga) face. Photoluminescence (PL) spectra show a strong donor-bound exciton (D°X) line at 3.47225 eV, and a weaker one at 3.47305 eV; each has a linewidth of about 0.4 meV. In the two-electron satellite region, a strong line appears at 3.44686 eV, and a weaker one at 3.44792 eV. If the two strong lines represent the same donor, then ED,n=1 – ED,n=2 = 25.4 meV for that donor, and the ground-state activation energy (EC – ED,n=1) is (4/3)25.4 = 33.9 meV in a hydrogenic model, and 32.7 meV in a somewhat modified model. The measured Hall-effect donor energy, 28.1 meV, is smaller than the PL donor energy, as is nearly always found in semiconductors. We show that the difference in the Hall and PL donor energies can be explained by donor-band conduction via overlapping donor excited states, and the effects of non-overlapping excited states which should be included in the n vs. T data analysis (charge balance equation).

scholarly journals Study on the Phase Transformation Kinetics of Sol-Gel DrivedTiO2Nanoparticles

2010 ◽  
Vol 2010 ◽  
pp. 1-5 ◽  
Author(s):  
H. Mehranpour ◽  
M. Askari ◽  
M. Sasani Ghamsari ◽  
H. Farzalibeik
Keyword(s):  
Activation Energy ◽  
Phase Transformation ◽  
Sol Gel ◽  
Rutile Phase ◽  
Transformation Kinetics ◽  
X Ray ◽  
Prepared Nanoparticles ◽  
Phase Transformation Kinetics ◽  
Diffusion Controlled ◽  
Kinetics Of

Titanium dioxide nanopowders were synthesized by the diffusion controlled sol-gel process (LaMer model) and characterized by DTA-TG, XRD, and SEM. The preparedTiO2nanoparticles have uniform size and morphology, and the phase transformation kinetics of obtained material was studied by interpretation of the X-ray diffraction patterns peaks on the base of Avrami equation. The stating point of anatase-rutile phase transformation temperature in the prepared nanoparticles was found between 100 and200°C. A decreasing trend on the intensity of X-ray peaks of anatase phase was observed up to600°Cwhen the presence of the rutile phase became predominant. Results indicated that the transition kinetics of the diffusion controlled prepared nanoparticles was begun at low temperature, and it can be concluded that the nucleation and growth sites in these particles were more than other. However, it has been found that the nucleation activation energy of rutile phase was 20 kj/mol, and it is the lowest reported activation energy.

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