971 resultados para REACTION-DIFFUSION PROBLEMS


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The stress concentration that occurs when load is diffused from a constant stress member into thin sheet is an important problem in the design of light weight structures. By using solutions in biharmonic polar-trigonometric series, the stress concentration can be effectively isolated so that highly accurate information necessary for design can be obtained. A method of analysis yielding high accuracy with limited effort is presented for rectangular panels with transverse edges free or supported by inextensional end ribs. Numerical data are given for panels with length twice the width.

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The water-gas shift (WGS) reaction was carried out in the presence of Pd and Pt substituted nanocrystalline ceria catalysts synthesized by solution combustion technique. The catalysts were characterized by powder XRD and XPS. The noble metals were found to be present in ionic form substituted for the cerium atoms. The catalysts showed highactivity for the WGS reaction with high conversions below 250 degrees C. The products of reaction were only carbon dioxide and hydrogen, and no hydrocarbons were observed even in trace quantities. The reactions were carried out with different amounts of noble metal ion substitution and 2% Pt substituted ceria was found to be the best catalyst. The various possible mechanisms for the reaction were proposed and tested for their consistency with experimental data. The dual site mechanism best described the kinetics of the reaction and the corresponding rate parameters were obtained.

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The structure of the by-product, obtained in the Diels-Alder condensation of maleic anhydride with β-trans-ocimene followed by distillation of the adduct formed, has been established as 2-isopropylidene-4-methyl-7-carboxy- ,3,3a,6,7,7a-hexahydroindanone (IVa) and the mechanism of its formation from the adduct (II) discussed. Some hitherto unreported reactions of the maleic anhydride adduct (II) and its derivatives are described. These throw light on the stereochemistry of the adduct and derived products.

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A semi-experimental approach to solve two-dimensional problems in elasticity is given. The method has been applied to two problems, (i) a square deep beam, and (ii) a bridge pier with a sloping boundary. For the first problem sufficient analytical results are available and hence the accuracy of the method can be verified. Then the method has been extended to the second problem for which sufficient results are not available.

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The colour reaction between 3-phenyl-2-thiohydantoin and ammonia is studied quantitatively. Determinations of 0.1–0.6 μmoles of 3-phenyl-2-thiohydantoin are possible with a precision close to 2%. In analyses of amino acid mixtures for glycine after conversion to 3-phenyl-2-thiohydantoin, only derivatives of serine and threonine interfere to a slight extent. The specificity of the primary colour reaction with ammonia, and the structural requirements for it are discussed; a structure for the pigment species is proposed.

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The para orientation by the carbonyl groups in the bromination of phenanthrenequinone derivatives has been explained on the basis of an excited state resulting from thermal excitation of the quinone and/or from a n→π* transition of the nonbonding electrons of the oxygen atoms. A general preparative method for the syntheses of 3-bromophenanthrenequinone derivatives has been developed. The structure of 2-nitro-6-bromophenanthrenequinone has been established by degradation. Synthesis of 2-nitro-6-bromofluorenone is described. Direct bromination of phenanthrenequinone to 2-bromo and 2,7-dibromo derivatives has also been described.

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With a view to understanding the mechanism of the formation of 6-methoxy-2,2-(tetrachloro--phenylenedioxy)-naphthalen-1 (2H)-one (IIIa) in the reaction of 6-methoxy-1-tetralone (Ia) with tetrachloro-1,2-benzoquinone (II), the reaction of (II) with various tetralones and naphthols has been studied. Reaction with either α-tetralone or α-naphthol gives 2,2-(tetrachloro-o-phenylenedioxy)naphthalen-1 (2H)-one (IIIb), whereas reaction with either β-tetralone or β-naphthol gives a mixture of (IIIb) and ,1-(tetrachloro-o-phenylenedioxy)-naphthalen-2 (1H)-one (IX), with the former predominating. Further, reactions of (II) with 7-methoxy-3,4-dihydrophenanthren- 1 (2H)-one and m-methoxyphenol gave respectively 7-methoxy- ,2-(tetrachloro-o- phenylenedioxy)phenanthren-1 (2H)-one (VII) and 3-methoxy-6,6-(tetrachloro-o- phenylenedioxy)cyclohexa-2,4-dien-1-one (VIII). Structures of all these compounds have been proved on the basis of i.r. and n.m.r. data. The pathway to the formation of the condensates (III) is discussed.

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Carbon disulfide reacts with azide ion to form the 1,2,3,4-thiatriazolinethionate ion and not the acyclic azido dithiocarbonate ion as previously reported. A series of salts of thiatriazoline have been prepared and none shows evidence for the presence of the azido group. Esters of thiatriazolinethione prepared by the reaction of the sodium salt with alkyl or acyl halides have been found to be either 5-(substituted) mercapto-1,2,3,4-thiatriazoles or 4-substituted 1,2,3,4-thiatriazoline-5-thiones. These structures have been assigned on the basis of degradative and spectroscopic evidence. The chemistry of the so-called azidodithiocarbonates has been reinterpreted in terms of the thiatriazole structure.

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The association parameter in the diffuswn equaiior, dye fo Wiike one Chong has been interpreted in deferminable properties, thus permitting easily the calculation of the same for unknown systems. The proposed eqyotion a!se holds goods for water as soiute in organic solvenfs. The over-all percentage error remains the sarrse as that of the original equation.

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Noble metal substituted ionic catalysts were synthesized by solution combustion technique. The compounds were characterized by X-ray diffraction, FT-Raman spectroscopy, and X-ray photoelectron spectroscopy. Zirconia supported compounds crystallized in tetragonal phase. The solid solutions of ceria with zirconia crystallized in fluorite structure. The noble metals were substituted in ionic form.The water-gas shift reaction was carried out over the catalysts.Negligible conversions were observed with unsubstituted compounds. The substitution of a noble metal ion was found to enhance the reaction rate. Equilibrium conversion was obtained below 250 degrees C in the presence of Pt ion substituted compounds. The formation of Bronsted acid-Bronsted base pairs was proposed to explain the activity of zirconia catalysts. The effect of oxide ion vacancies on the reactions over substituted ceria-zirconia solid solutions was established. (c)2010 Elsevier B.V. All rights reserved.

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The addition reaction of alcohols to substituted phenylisothiocyanates is found to be a second-order reaction. The reaction is catalysed by triethylamine. First-order rate constants of the addition reaction have been determined in excess of ethanol, for a number of substituted phenylisothiocyanates and the rate data give a satisfactory linear correlation with Hammett σ constants of groups. While the energies of activation vary randomly with substitution, the entropies of activation bear a linear relationship to the energies of activation. Infra-red spectra indicate that the thiourethanes which are the products of the addition reaction exist in the thioamide form. The most prominent resonance form which can satisfactorily explain both the kinetic and infrared data, has been suggested.