Diffusion and Reaction Rates of the Yttrium Aluminium Garnet Synthesis using Different Techniques

The mathematical model of the yttrium aluminium garnet synthesis presented in this article. The model based on a system of non-stationary diffusion equations containing a non-linear term related to kinetics of reaction. Using computer-simulation tools and known experimental results we estimated the diffusion and reaction rates of the synthesis. Also it was shown that diffusion rate is a limited stage of the synthesis.     

Computational modelling of the YAG synthesis

Mathematical and numerical models of the yttrium aluminium garnet (YAG) synthesis are presented in the article. The models allow the effective computer simulation of the YAG synthesis. The synthesis by sol–gel and solid-state reaction methods is considered in the article. The question concerning the reasons for the observed changes in the preparation temperature by changing synthesis method is answered. The inverse modelling problem is solved: using known experimental data (synthesis time, dimensions of reactants) the unknown input parameters of the model (diffusion and reaction rate coefficients) are calculated.     

Formation of YAG from coprecipitated yttrium aluminium hydroxides

Thermal decomposition of the amorphous coprecipitate of yttrium and aluminium hydroxides forming yttrium aluminium garnet has been investigated employing thermal analyses, X-ray diffraction and IR spectroscopy. On heating, the coprecipitate progressively loses water forming a stable but highly disordered hydroxy garnet which crystallizes at 1180 K and decomposes to YAG at 1290 K. Nucleation of the crystalline phase appears to begin at 800 K.The authors thank Dr. P. V. Ravindran of the Analytical Chemistry and Shri N. K. Kulkarni of the Fuel Chemistry Divisions of BARC for their assistance in the thermoanalytical experiments.     

Computer simulation of the steady state currents at enzyme doped carbon paste electrodes

The plate-gap model of porous enzyme doped electrode has been proposed and analyzed. It was suggested that reaction diffusion conditions in pores of bulk electrode resemble particular conditions in thin gap between parallel conducting plates. The model is based on the diffusion equations containing a nonlinear term related to the Michaelis–Menten kinetic of the enzymatic reaction inside gap. Steady state current was calculated for the wide range of given parameters and substrate concentrations. All dependences of current on substrate concentration were approximated by hyperbolas in order to obtain “apparent” parameters (maximal currents and apparent Michaelis constants) of modelled biosensors. Simple approximate relationships between given and apparent parameters were derived. The applicability of theoretical plate-gap model was tested for the case of carbon paste electrodes which were doped with PQQ – dependent glucose dehydrogenase. It was found, that soluble glucose dehydrogenase based biosensors exhibit characteristic features of the theoretical plate-gap biosensors.     

Analysis of the electrolyte diode. Electro-diffusion and chemical reaction within a hydrogel reactor

A reaction–diffusion system describing the electrolyte diode is investigated. This consists of a chemically crosslinked polyvinylalcohol (PVA) hydrogel cylinder in which a pH gradient is provided by having an acid and a base maintained at constant concentrations in reservoirs at each end of the one-dimensional reactor. A potential difference of a given strength is also applied across the gel cylinder. Previous experimental studies of the current–voltage characteristics (CVC) have shown two distinct cases, depending on whether a positive or negative potential difference was applied. The slopes of the linear current–voltage response curve are substantially different in the two cases, that in the 'forward' case being typically several orders of magnitude greater than that in the 'backward' case. Thus the system behaves like a semiconductor diode. The stationary concentration distribution for the different ions is described by a system of reaction–diffusion equations involving migration caused by the electric field. An approximate solution of these equations, using a simplified model, is presented and compared with results obtained by solving the full system numerically. The concentration profiles obtained from the numerical solution confirm the validity of the simplified model.     

The Impact of Continuous Oxygen Flux in a Thin Film Photopolymerization Reaction with Peroxy‐Mediated Regeneration of Initiator

Eosin, a photosensitizer dye that can exist in multiple oxidation states, has been shown to initiate visible‐light photopolymerizations of acrylates in open air when used in combination with tertiary amines. The exact mechanism behind this reactivity with micromolar concentrations of eosin in aqueous monomer solutions initially containing millimolar concentrations of oxygen has not been conclusively established, although pathways for regeneration of eosin in the presence of oxygen certainly play a role. In this work, a reaction–diffusion model incorporating a peroxy‐mediated eosin‐regeneration mechanism is built to explore the effects of oxygen diffusing into the system as the light‐activated reaction proceeds. An oxygen concentration‐dependent flux boundary condition is used to model the continuous replenishment of oxygen at the surface open to air as it is consumed by reaction. The model predicts the formation of a free radical concentration front that initially forms closer to the open surface and gradually moves toward the closed surface, with polymer film thickness increasing and the time required for polymerization to begin decreasing as the initial eosin concentration is increased. These results suggest that oxygen's dual role as both a free radical inhibitor and a precursor of the oxidizing species required for regeneration of eosin brings about interesting spatial variations when the reaction is carried out in a thin film geometry that is exposed to open air. In this case, an assumption of a well‐mixed system is not appropriate and the kinetics of the reaction and conversion as a function of position are likely to depend on the geometry of the system.

     

The Effect of Diffusion Limitations on the Response of Amperometric Biosensors with Substrate Cyclic Conversion

A mathematical model of amperometric biosensors in which chemical amplification by cyclic substrate conversion takes place in a single enzyme membrane has been developed. The model involves three regions: the enzyme layer where enzyme reaction as well as mass transport by diffusion takes place, a diffusion limiting region where only the diffusion takes place, and a convective region where the analyte concentration is maintained constant. Using computer simulation the influence of the thicknesses of the enzyme layer and the diffusion region on the biosensor response was investigated. This paper deals with conditions when the mass transport in the exterior region may be neglected to simulate the biosensor response in a well-stirred solution. The digital simulation was carried out using the finite difference technique.     

An analysis of the reaction–diffusion mechanism governing the chlorination process of poly(vinyl chloride)

Chlorinated poly(vinyl chloride) (CPVC) obtained through a dry chlorination of PVC films or grains can show a heterogeneous repartition of its chlorine atoms because the reaction process is limited by the mass transfer of the chlorine gas in the material. In order to describe the evolution of such a system, a set of coupled equations is derived where only two dimensionless constants have to be determined: K_S, which depends on the solubility of the chlorine gas in the PVC, and K_T, the ratio between the diffusion and the reaction characteristic times. The kinetics of chlorination obtained for the different regimes matches the available experimental data, and the corresponding concentration profiles for the chlorinated PVC chains are displayed to demonstrate how a heterogeneous chlorination can arise from this dual process. In particular, a sharp interface appears in the diffusion‐limited regime that separates the chlorinated region from an unchlorinated core and is shown to progress deeper into the film with the square root of time. To a larger extent, this analysis shows how heterogeneity of reaction and nonlinear effects can arise from a coupling between a diffusive phenomenon and a reactive phenomenon. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3201–3209, 2000     

On the calculation of the activation energy for solid state reactions

A novel and convenient method for the determination of the activation energy from isothermal kinetic runs has been proposed recently. A significant limitation of this method is discussed and is illustrated with an experimental example. A modification of the proposed method is suggested to circumvent this limitation.     

Shaping Microcrystals of Metal–Organic Frameworks by Reaction–Diffusion

When components of a metal–organic framework (MOF) and a crystal growth modulator diffuse through a gel medium, they can form arrays of regularly‐spaced precipitation bands containing MOF crystals of different morphologies. With time, slow variations in the local concentrations of the growth modulator cause the crystals to change their shapes, ultimately resulting in unusual concave microcrystallites not available via solution‐based methods. The reaction–diffusion and periodic precipitation phenomena 1) extend to various types of MOFs and also MOPs (metal–organic polyhedra), and 2) can be multiplexed to realize within one gel multiple growth conditions, in effect leading to various crystalline phases or polycrystalline formations.     

Kinetics of solid state reactions with a positive feedback between the reaction and fracture

A model describing the steady-state kinetics of thermal decomposition in the solid phase occurring with a decrease in the solid phase volume and accompanied by fracture in the reaction zone is suggested. The model is based on the concept of positive feedback between the reaction and fracture. The rate of the fracture front and the size of the product fragments formed were calculated. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 626–631, April, 1998.     

Aqueous sol-gel synthesis route for the preparation of YAG: Evaluation of sol-gel process by mathematical regression model

Yttrium aluminium garnet (Y₃Al₅O₁₂, YAG) polycrystalline samples have been prepared by a simple aqueous sol-gel methodology. The influence of nineteen sol-gel processing variables on the formation of YAG has been investigated. Effects of different fabrication parameters on the phase purity and morphological properties of the compounds were studied by energy-dispersive spectrometry (EDS), X-ray powder diffraction (XRD) analysis and scanning electron microscopy (SEM). The parameters of the sol-gel processing such as pH of starting solution, concentration and nature of complexing ligand, temperature and duration of gelation, powder rehomogenization during annealing, duration and temperature of the final heat treatment were found to be the most significant. For the evaluation and verification of the experimental results the Brandon's model of a multiple regression was successfully used.     

固相配位化学反应研究 52: 室温固-固相化学反应合成氨基酸铜配合物

本文报道室温固-固相化学反应一步法合成氨基酸铜配合物。trans-Cu(Gly)2.H2O、cis-Cu(GlY)2.H2O、trans-Cu(DL-Ala)2、trans-Cu(DL-Ala)2.H2O、trans-Cu(DL-Val)和trans-Cu(DL-Leu)2, 经元素分析、IR、XRD、DTA测定了配合物的组成及几何构型。并初步讨论了室温固相反应合成机理。     

The sol–gel synthesis of perovskites by an EDTA/citrate complexing method involves nanoscale solid state reactions

Nowadays, sol–gel procedures are well established in the synthesis of complex oxides as they allow to obtain phase pure products and to control precisely their stoichiometry. This quality makes them a tool of choice for the preparation of perovskite-type oxides. To optimize the functional properties of these materials, it is essential to set accurately their possible complex stoichiometries. However, details of the formation of the perovskite crystal remain obscure. Different stages of an ethylene-diamine-tetraacetic acid (EDTA)/citrate-gel based synthesis process for mixed conducting (Ba_0.5Sr_0.5)(Fe_0.8Zn_0.2)O_3−δ of cubic perovskite structure are elucidated. The combination of analytical transmission electron microscopy with X-ray diffraction reveals that the perovskite-type oxide is formed already at moderate temperatures at around 700 °C via nanoscale solid state reactions between finely-dispersed crystalline intermediates identified as a spinel and a carbonate. The reaction scheme, however, is intricate and includes stuffed tridymite structures as transient phases. The ultrafine intermixing of extremely small reactants makes EDTA/citrate-gel based procedures superior to classical solid state routes with respect to applications that demand phase purity and stoichiometry control.     

Ethylene polymerization reactions with Ziegler–Natta catalysts. II. Ethylene polymerization reactions in the presence of deuterium

Ethylene polymerization reactions with many Ziegler–Natta catalysts exhibit several features which differentiate them from polymerization reactions of α-olefins: a relatively low ethylene reactivity, higher polymerization rates in the presence of α-olefins, a high reaction order with respect to ethylene concentration, and strong reversible rate depression in the presence of hydrogen. A detailed kinetic analysis of ethylene polymerization reactions (see ref. 1 ) provided the basis for a new reaction scheme which explains all these features by postulating the equilibrium formation of a Ti C₂H₅ species with the H atom in the methyl group β-agostically coordinated to the Ti atom in an active center. This mechanism predicts that the β-agostically stabilized Ti C₂H₅ groups can decompose in the β-hydride elimination reaction with expulsion of ethylene and the formation of a Ti H bond even in the absence of hydrogen in the reaction medium. If D₂ is used as a chain transfer agent instead of H₂, the mechanism predicts the formation of deuterated ethylene molecules, which copolymerize with protioethylene. To prove this prediction, several ethylene homopolymerization reactions were carried out with a supported Ziegler–Natta titanium-based catalyst in the presence of large amounts of D₂. Analysis of gaseous reaction products and polymers confirmed the formation of several types of deuterated ethylene molecules and protio/deuterioethylene copolymers, respectively. In contrast, a metallocene catalyst, Cp₂ZrCl₂ MAO, does not exhibit these kinetic features. In the presence of deuterium, it produces only DCH₂ CH₂ (CH₂ CH₂)_x CH₂ CH₂D molecules. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 4273–4280, 1999     

Spectroscopic study of solid state photoreaction of di n-propyl ester of dicyano p-phenylenediacrylic acid

Photopolymerization reaction in di n-propyl ester of dicyano p-phenylene diacrylic acid crystal is shown to be mediated by exciton–phonon coupling. Raman phonon spectra suggest that at the initial stage of reaction progress, the reactant and the product form a solid solution. In the later stage, the reactant segregates out and forms its own lattice. The polymer lattice is shown to maintain a good degree of order. Infrared and Raman spectra confirm that the polymerization occurs by cyclobutane ring formation. © 1994 John Wiley & Sons, Inc.     

Hydrogen bonding. Part 77. Molecular orbital study of C–HF hydrogen bonds in tetramethylammonium fluoride; potential effects on solid state structure

The infrared (IR) spectrum of tetramethylammonium fluoride suggests that it contains the strongest C–HF⁻ hydrogen bonds yet observed. Ab initio 3-21G(^*) calculations were used to examine potential solid state arrangements of cation about anion. The favored state is one in which four cations surround each F⁻ in a D_2d arrangement and four F⁻ surround each cation. Each F⁻ acts as acceptor of four hydrogen bonds of −10.8 kcal mol⁻¹, one from each cation. This arrangement, similar to that of tetramethylammon chloride, is consonant with the IR spectrum of the cation in solid tetramethylammonium fluoride. In the preferred form of the monomeric gas phase ion-pair F⁻ lies against one triangular face of the T_d cation with three CHF hydrogen bonds of −11.5 kcal mol⁻¹ each. Constraint of F⁻ in the gas phase ion-pair to interaction with a single cation hydrogen results in a tightly bound molecular complex between HF and trimethylammonium methylide with an interaction energy of −27 kcal mol⁻¹; however, this structure is not seen elsewhere and apparently does not play a role in the solid salt.     

High-temperature thermogravimetric analysis. Influence of gas pressure on kinetics of reactions in the solid state

A magnetic balance apparatus has been set up to follow reactions in the solid state under controlled conditions of pressure and temperature (25–1000°). Magnetic properties are characteristic of solid structures, and thermomagnetic analysis (T. M. A.) can give the variations of the sample susceptibility during the course of a reaction (susceptibilities of the new phases and of initial compounds not yet transformed). By continuous measurement of this susceptibility with the Faraday method, the conversion degree of the synthesis can be obtained.T. M. A. has been used to study the influence of a gas on a solid-solid reaction in which no gas can be evolved or consumed. An example is given for iron tungstate synthesis: Fe₂O₃(s)+WO₃(s) Fe₂WO₆(s). At 800° the reaction kinetics depends on the nature and the pressure of the gas.

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Zusammenfassung Festkörperreaktionen unter kontrollierten Druck- und Temperaturbedingungen (25–1000°) wurden mit einer magnetischen Waage verfolgt. Magnetische Eigenschaften sind charakteristisch für feste Strukturen, und die thermomagnetische Analyse (TMA) kann Veränderungen der Susceptibilität der Probe im Verlaufe der Reaktion (Susceptibilitäten neuer Phasen und noch nicht umgeformter Ausgangsverbindungen) aufzeigen. Durch kontinuierliche Messung dieser Susceptibilität nach der Faraday-Methode kann der Konversionsgrad der Synthese erhalten werden. TMA wurde zur Untersuchung des Einflusses eines Gases auf eine Fest-Fest-Reaktion, bei der kein Gas freiesetzt oder verbraucht werden lann, herangezogen. Als Beispiel wird die Synthese von Eisenwolframat angeführt: Fe₂O₃(s)+WO₃(s) Fe₂WO₆(s). Bei 800° hängt die Kinetik der Reaktion von der Natur und dem Druck des Gases ab.

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(25– 1000°). () , . , . - , . - : Fe₂O₃+WO₃ Fe₂WO₆. , 800°, .

     

Local HSAB rationalization of diels–alder reactions by means of ab initio and ABEEMσπ methods: Stereoselectivity and reaction rate

In this article, four series of Diels–Alder (DA) reactions (totally, 68 reactions) have been investigated, including their transition states, by means of ab initio method at MP2/6‐311+G(d,p) level and atom‐bond electronegativity equalization method (ABEEMσπ) method. The rationalization of stereoselectivities of these DA reactions has been done in the light of the local hard and soft acids and bases (HSAB) criterion. The results show that the finite difference approximation with ab initio method can not always be used to predict the stereoselectivities of these reactions, while ABEEMσπ method can properly be applied to predict the stereoselectivities of these DA reactions. Moreover, we have proposed the generalized Fukui function and local softness which involve the number of the atoms of a molecule. For the first time, we here demonstrate that local HSAB criterion with the generalized local softness can be utilized not only to predict the main products of these DA reactions but also to rationalize the relative magnitudes of the reaction rate constants of these DA reactions. © 2013 Wiley Periodicals, Inc.