Application of a moments method and of Laplace transforms to heat transfer experiments

We present a mathematical method based on Laplace transform techniques for the analysis of heat capacity and thermal conductivity measurements, for the case of thin film samples on substrates of finite lengths. The method is a further development of the heat pulse technique. This mathematical analysis is capable of separating the heat capacity and thermal conductivity of the sample from those of the substrate, thus eliminating the need for an additional measurement on the substrate alone. This fact substantially reduces the errors and complexity of the experiment and also makes the heat pulse technique the only one capable of obtaining thermal parameters on thin films in a single experiment. The analysis of the experimental data is performed by calculating several moments of the temperature rise in two thermometers as a function of time. Special considerations are taken to adapt the method for on-line computer experiments.

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Zusammenfassung Eine auf Laplace-scher Transformationstechnik beruhende mathematische Methode zur Analyse von Wärmekapazitäts- und Wärmeleitungsmessungen für Dünnschichtproben auf Substraten begrenzter Längen wird vorgestellt. Die Methode ist eine Weiterentwicklung der Wärmepulstechnik. Diese mathematische Analyse vermag die Wärmekapazität und Wärmeleitfähigkeit der Probe von denen des Substrats zu trennen, wodurch sich die zusätzliche Messung des Substrats allein erübrigt. Hierdurch werden Fehler und Komplexität des Versuchs bedeutend reduziert und die Wärmepuls-Methode erweist sich als erstes Verfahren bei dem die thermischen Parameter dünner Filme in einem einzigen Versuch ermittelt werden können. Die Analyse der Versuchsdaten wird durch die Berechnung verschiedener Momente des Temperaturanstiegs in zwei Thermometern als Funktion der Zeit durchgeführt. Besondere Maßnahmen wurden bei der Anpassung der Methode für on-line Computerversuche berücksichtigt.

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Résumé On présente une méthode mathématique reposant sur les techniques de transformation de Laplace, pour l'analyse des mesures de capacité calorifique et de conductivité thermique, dans le cas des échantillons en pellicules minces sur des substrats de longueurs finies. La méthode représente un développement ultérieur de la technique des pulsations de chaleur. Cette analyse mathématique est capable de séparer la capacité calorifique et la conductivité thermique de l'échantillon de celles du substrat, en éliminant ainsi la nécessité d'une mesure suppplémentaire du substrat seul. Ce fait réduit notablement les erreurs et la complexité de l'expérience et rend la technique des pulsations thermiques la seule capable d'obtenir des paramètres thermiques de pellicules minces à partir d'une seule expérience. L'analyse des données expérimentales s'effectue en calculant à divers moments l'augmentation de la température de deux thermomètres, en fonction du temps. Des mesures spéciales ont été prises pour adapter la méthode à des expériences sur ordinateur en ligne.

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, , . . , , , . . . , « ».

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Supported in part by the Karlsruhe Nuclear Research Center.     

Electronic spectral study of the interaction of CoNaX zeolite with C1?C5 hydrocarbons

Interaction of both satured and unsaturated hydrocarbons with tetrahedral Co²⁺ ion complexes lodged in the zeolite skeleton is reported on the basis of diffuse reflectance spectra. While saturated hydrocarbons do not affect the coordination sphere of the Co-complex, the unsaturated hydrocarbons change considerably the distortion of the tetrahedral Co-complex.

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- Co²⁺ - . - Co-, - - Co-.

     

Studies on the Fe2(MoO4)3-V2O5 system

The phase equilibria established in solid state in the whole range of component concentrations in the Fe₂(MoO₄)₃-V₂O₅ system were studied by DTA and X-ray powder diffraction. This system is not a real two-component system.

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Zusammenfassung Im gesamten Konzentrationsbereich der Komponenten des Systems Fe₂(MoO₄)₃-V₂O₅ wurde das im festen Aggregatzustand festgestellte Phasengleichgewicht mittels DTA und Pulverröntgendiffraktionsverfahren untersucht. Dieses System ist kein wirkliches Zweikomponentensystem.

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F₂(₄)₃-V₂O₅ . , .

     

Influence of the entropy factor on the equilibrium and kinetics of chemisorption

A correction to the model of uniform heterogeneous surface has been introduced. This correction extends the limits of application to processes with entropy changes of the adsorbent. On the basis of the model thus corrected a kinetic equation has been deduced, which takes into account the role of the entropy factor. The presence of a compensation effect in chemisorption kinetics is supported theoretically.

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- , , . , . .

     

Mechanism of lateral interactions between molecules adsorbed on oxide surfaces

Comparison of the observed and calculated values for static and dynamic frequency shifts due to lateral interactions between CO molecules adsorbed on oxides indicates that these interactions are indirect and performed through a solid. Mechanism of static interaction includes relaxation, i.e. the displacement of surface atoms due to their adsorption.

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, CO, , . , .. .

     

Microcalorimetric investigation of the recrystallization behaviour of polycrystalline copper deformed at room-temperature

The recrystallization of 5 N copper samples which had been deformed at roomtemperature by torsion to an average shear of by rolling to 65% r.c.s. was investigated by means of a commercial heatflow calorimeter.During recrystallization, which was also studied by hardness tests and optical microscopy, a stored energy release of the order of 0.145 cal/g was observed. Some problems inherent in the use of microsamples are discussed. By kinetic analysis, based on variation of the linear heating rate, a value of 21.9 kcal mole^–1 was determined for the apparent activation energy of the recrystallization process in torsion samples.

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Zusammenfassung Die Rekristallisation von 5 N Kupferproben, die bei Raumtemperatur durch Torsion bzw. durch Walzen (65%) verformt worden waren, wurde mit einem kommerziellen Wärmeströmungskalorimeter untersucht. Bei der Rekristallisation, die ebenfalls mit Härtemessungen und Gefügeuntersuchungen verfolgt wurde, wird eine Energiefreigabe von etwa 0.145 cal/g beobachtet. Einige bei der Verwendung von Microproben auftretende Probleme werden diskutiert. Eine Analyse der Kinetik, die auf der Variation der linearen Aufheizgeschwindigkeit basiert, ergab für die scheinbare Aktivierungsenergie des Rekristallisationprozesses in Torsionsproben einen Wert von 21.9 Kcal Mol^–1.

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Résumé On a étudié à l'aide d'un calorimètre à flux de chaleur commercial la recristallisation d'échantillons de cuivre 5 N, préalablement déformés à température ambiante par torsion ou par laminage (65%).Lors de la recristallisation, également suivie par mesures de dureté et examens de structure, on observe un dégagement d'énergie d'environ 0,145 cal/g. Les problèmes qui surgissent lors de l'utilisation de prélèvements micro sont discutés. L'énergie d'activation apparente du processus de recristallisation après l'écrouissage par torsion s'élève à 21.9 kcal mol^–1.

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5H , , , 65% . . . , , 0.145 /. , . , , , 21.9 ^–1.

     

Modifying action of carbon dioxide in catalytic oxidation of ethylene on silver

Carbon dioxide exerts a strong inhibitory effect on oxygen adsorption and complete oxidation of ethylene on silver but has little effect on the rate of ethylene oxidation to ethylene oxide.

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.

     

Testing the photocatalytic activity of cyanogen-and thiocyanogen-based inorganic polymers

The photocatalytic properties of some cyanogen-and thiocyanogen-based inorganic polymers, such as paracyanogens containing different metals (Hg, Ag, Cu), polythiocyanogens of different iodine contents, polycyanogen and poly (cyanogenthiocyanate), have been tested in two systems. Cu-containing paracyanogen and the iodine-poor polythiocyanogens catalyze the photoreduction of methylviologen under visible light, furthermore the Cu-containing paracyanogen catalyzes the photoreduction of water to hydrogen under UV irradiation.

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, , , , (Hg, Ag, Cu), , (), . , , , , , , -.

     

Changes in iron oxidation state and surface composition of iron-chromium catalyst reduced by hydrogen

X-ray photoelectron spectroscopic studies of the reduction of iron-chromium catalysts have been carried out to determine changes in the relative surface concentrations of iron(II) and (III) oxides and metallic iron and in its surface composition at 100–500°C.

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(II), (III) 100–500°C. .

     

Thermal decomposition kinetics of vanillidene anthranilic acid complexes of cobalt(II), nickel(II), copper(II) and zinc(II)

The thermal decomposition of cobalt(II), nickel(II), copper(II) and zinc(II) complexes of the Schiff base vanillidene anthranilic acid was studied by TG. The chelates show somewhat similar TG plots when heated in an atmosphere of air. Thermoanalytical data (TG and DTG) of these chelates are presented in this communication. Interpretation and mathematical analysis of these data and evaluation of order of reaction, the energy and entropy of activation based on the differential method employing the Freeman-Carroll equation, the integral method using Coats-Redfern equation and the approximation method using the Horowitz-Metzger equation are also given. On the basis of experimental findings in the present course of studies, it is concluded that the relative thermal stability of vanillidene anthranilic acid chelates can be aligned as Co(II)Ni(II)>Zn(II)>Cu(II).

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Zusammenfassung Die thermische Zersetzung von Cobalt(II)-, Nickel(II)-, Kupfer(II)- und Zink(II)-Komplexen der Schiffschen Base Vanillidenanthranilsäure wurde thermogravimetrisch untersucht. Die Chelate zeigen in einer Luftatmosphäre ähnliche TG-Kurven. Thermoanalytische Daten (TG and DTG) dieser Chelate werden mitgeteilt, interpretiert und mathematisch analysiert. Ebenfalls werden die Reaktionsordnung und die Energie und Entropie der Aktivierung nach der von Freeman-Carroll angewandten differentiellen Methode, nach der auf der Coats-Redfern-Gleichung basierenden integralen Methode und nach der die Horowitz-Metzger Gleichung benutzenden Näherungsmethode bestimmt. Aus den Befunden wird geschlossen, dass die thermische Stabilität von Vanillidenanthranilsäure-Chelaten in der Reihenfolge Co(II)Ni(II)>Zn(II)> >Cu(II) abnimmt.

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, , . - . . , , - , , - . , Ni>Zn>u.

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We thank Dr. C. P. Savariar, Professor of Chemistry, University of Calicut for encouragement. We are also grateful to the University Grants Commission for the award of a Senior Research Fellowship to one of us (J. C).     

Kinetics and mechanism of oxidation of quinol by alkaline hexacyanoferrate(III)

The reaction between quinol and alkaline hexacyanoferrate(III) at constant ionic strength gives p-benzoquinone. The rate of the reaction was first order in the concentrations of substrate, oxidant and alkali. The slow step of the reaction involves the formation of the p-benzosemiquinone radical, which was detected by esr spectroscopy as a five-line spectrum with peak intensity ratios of 14641.

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(III) -. , . - , , 14641.

     

Non-equilibrium ion-(polar) molecule reaction rate coefficients

Using the Fokker-Planck version of an approximate Boltzmann equation for the ion (translational) energy distribution function f_I we have calculated the deviation, k, of the non-equilibrium ion-(polar)molecule reaction rate coefficient k (based) on f_I from its equilibrium value k⁽⁰⁾. The _D (dipole moment)-dependence of the reaction cross section applied leads to a corresponding dependence of k on _D.

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- , k - ( f_I) k⁽⁰⁾. k _D.

     

Thermal decomposition kinetics of thorium(IV) chelates of two naphthol dyes

The thermal decomposition of thorium(IV) chelates of 1-(2-fluorenylazo)-2-naphthol ando-carboxyphenylazo-2-naphthol was studied by TG. Thermoanalytical data (TG and DTG) of these chelates are presented in this communication. Interpretation and mathematical analysis of these data and evaluation of order of reaction, the energy and entropy of activation based on the differential method employing the Freeman-Carroll equation, the integral method using Coats-Redfern equation and the approximation method using the Horowitz-Metzger equation are also given. On the basis of experimental findings in the present course of studies the relative thermal stabilities of the thorium chelates can be given as [Th(FAN)₂(NO₃)₂]>[Th(CPAN)₂(H₂O)₂]2H₂O.

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Zusammenfassung Die thermische Zersetzung von Thorium(IV)-Chelaten von 1-(2-Fluorenylazo)-2-naphthol undo-Carboxyphenylazo-2-naphthol wurde thermogravimetrisch untersucht. Thermoanalytische Daten (TG und DTG) dieser Chelate werden angegeben und interpretiert. Reaktionsordnung sowie Aktivierungsenergie und -entropie wurden nach der differentiellen Methode unter Anwendung der Freeman-Carroll-Gleichung, nach der integralen Methode unter Verwendung der Coats-Redfern-Gleichung und nach der Näherungsmethode von Horowitz-Metzger bestimmt. Für die relative thermische Stabilität wird die Reihenfolge [Th(FAN)₂(NO₃)₂]>[Th(CPAN)₂(H₂O)₂]2H₂O angegeben.

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1(2- )-2- 1(2-)-2- --2-, . , . -, , - -. .

     

Analytical investigation of a four-variable model of the BZ reaction

It is proved analytically that the four-variable model reported in the preceding paper [1] has a unique stationary solution for each set of rate constants. An upper and a lower boundary for the stationary concentrations are established.

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, , , . .

     

A new method to determine the distance of electron tunneling transfer and its application to recombination of paramagnetic radiation deffects in CaO

A new method to determine the distance of electron tunneling transfer between paramagnetic reagents based on simultaneous analysis of both kinetic and ESR data is suggested. This method has been used to estimate the tunneling distance and the parameters characterizing the rate of tunneling for finely dispersed CaO.

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, - . CaO , .

     

Effect of vibrational excitation on the reactivity of methyl fluoride with bromine atoms

The influence of non-equilibrium vibrational excitation of CH₃F molecules on the rate of their reaction with bromine atoms has been investigated. A three-fold increace in the reaction rate has been registered at CH₃F and Br₂ pressures of 0.07 Torr and at 100°C. The increase is shown not to be associated with equilibrium thermal heating.

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CH₃F . CH₃F Br₂ 0,07 100°C. , .

     

A method for the treatment of experimental data. Kinetic system comprising two irreversible first order consecutive reactions

A method is proposed for the treatment of data from a kinetic system comprising two irreversible first order consecutive reactions (ABC). It is based on the solving of contrary propositions for an ordinary differential equation.

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(ABC). .

     

Catalytic properties of silica-molybdenum catalysts in propylene oxidation

The activity of silica-molybdenum catalyts in propylene oxidation is shown to be determined by the partially dehydrated silica-molybdenum heteropolyacid stabilized by the SiO₂ surface.

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, , SiO₂.

     

Investigation of propylene oxidation on multicomponent a Bi-and Mo-based oxide catalyst

It has been established that porpylene oxidation to acrolein on a multicomponent oxide catalyst containing Mo, Bi, Fe, Ni, Co, K, P and SiO₂ follows an alternating oxidation-reduction mechanism and involves the participation of lattice oxygen with the bond energy of about 280 kJ/mol.

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, Mo, Bi, Fe, Ni, Co, K, P SiO₂ 280 /.