The determination of kinetic parameters for some solid state reactions

The kinetics of many solid state reactions can best be explained in terms of an order of reaction; this is particularly true in the case of polymer degradation. The methods currently available for the determination ofn andk, from isothermal data, are either limited in the range of which can be used or are difference-difference techniques where the data must of necessity be highly accurate. This paper presents a review of these methods and introduces a new approach by whichn andk can be obtained directly, giving results which are unique and objective in that they provide a best fit to the experimental data.

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Zusammenfassung Die Kinetik vieler Reaktionen in fester Phase kann am besten an Hand einer Reaktions-Ordnung erklärt werden; dies besteht besonders bei dem Abbau von Polymeren. Die für die Bestimmung vonn undk aus isothermen Daten zur Verfügung stehenden Methoden sind entweder auf den verwendbaren Bereich von beschränkt oder sind Differenz-Differenz-Methoden, bei welchen es äußerst genauer Angaben bedarf. Die vorliegende Veröffentlichung gibt eine übersicht dieser Methoden und führt eine neue Annäherung ein, durch welchen undk unmittelbar erhalten werden können. Diese Methode ergibt einzigartige und zielgerechte Ergebnisse, indem diese sich den Versuchsdaten am besten anpassen.

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Résumé Pour de nombreuses réactions dans l'état solide l'ordre de réaction constitue un très bon moyen pour exprimer leur cinétique; c'est le cas, en particulier, de la dégradation des polymères. Les différentes méthodes dont on dispose pour déterminern et k à partir des données isothermes sont limitées à l'intervalle d'utilisation de ou opèrent par différences successives ce qui nécessite des données très précises. L'article présente une revue de ces méthodes et introduit une nouvelle approche oùn etk peuvent Être obtenus directement, en donnant des résultats uniques et objectifs qui assurent un meilleur accord avec les données expérimentales.

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; . , n ,k . , « — », . , n k. .

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The calculations presented in this paper were performed on an ICL 4130 computer using the program SOLITER. This program was written in ALGOL 60.     

Energy of activation for the decomposition of the alkaline-earth carbonates from thermogravimetric data

Activation energies for the vacuum thermal decomposition of calcium, strontium and barium carbonates have been determined from thermogravimetric data, using the Coats and Redfern equation. A computer program, written in 4100 Algol, was used to process the data and to obtain the order (n) of the decomposition reactions. In all three cases, a value ofn=2/3 was in closest agreement with the experimental results, suggesting that decomposition occurs at a progressively shrinking spherical interface. The energies of activation obtained were in close agreement with the corresponding values of the enthalpy of decomposition, calculated at the temperature at which half of the sample had decomposed.     

Concentration dependent chemical shifts in the NMR spectrum of 3,5-dimethyl-5-nitro-tetrahydro-1,3-oxazine

The marked concentration dependence of the chemical shifts of the C2, C4 and C6 protons in 3,5-dimethyl-5-nitro-tetrahydro-1,3-oxazine is described.     

Spin-orbit matrix elements in the atomic f shell from automorphisms of SO(8)

A scrutiny of the matrix elements within the f shell of the spin-other-orbit interaction H(soo) has revealed many unexpected proportionalities that go beyond an application of the Wigner-Eckart theorem to Racah's groups G2 and SO(7). An explanation is sought by using the automorphisms of SO(8) by means of which the states of the atomic f shell are generated by two alternative SO(7) bases of the type (1 / 21 / 21 / 2)(4), each augmented by two parity labels. Transformations between the bases can be made by reversing the relative phases of the two angular-momentum states 3 and 0 that comprise any one of the four SO(7) spinors. The method is exemplified by the single-electron spin-orbit interaction H(so), for which a component can be found that is invariant under the phase reversal. The extension from H(so) to H(soo) is described for the component z(6) of H(soo), and several examples drawn from the comparatively inaccessible configurations near the middle of the f shell are presented.     

Trichlorophenol (TCP) sulfonate esters: a selective alternative to pentafluorophenol (PFP) esters and sulfonyl chlorides for the preparation of sulfonamides

2,4,6-Trichlorophenol (TCP) sulfonate esters undergo effective aminolysis under conventional heating and microwave irradiation; the reactivity of these species is such that chemoselective transformations of PFP sulfonate esters can be achieved.     

A photo-optical technique for measuring flow-induced vibrations in cantilevered tube bundles

A photo-optical technique has been developed for monitoring the dynamic displacement of cantilevered tubes in fluid flow. The technique employs an optical fiber to transmit light through the tube and a phototransistor array to measure the motion of the light beam that is projected from the end of the tube. The device is simple, inexpensive, and very sensitive to small displacements. Details are given for the development of the technique, analysis of performance, and static calibration. The device was tested by monitoring the dynamic response of a bundle of cantilevered tubes in both single-phase and two-phase Freon 11 flows. The results are compared with those of a standard strain gauge bridge.     

The Szlenk index and local ℓ<Subscript>1</Subscript>-indices

We introduce two new local ₁-indices of the same type as the Bourgain ₁-index; the ⁺₁-index and the ⁺₁-weakly null index. We show that the ⁺₁-weakly null index of a Banach space X is the same as the Szlenk index of X, provided X does not contain ₁. The ⁺₁-weakly null index has the same form as the Bourgain ₁-index: if it is countable it must take values for some <₁. The different ₁-indices are closely related and so knowing the Szlenk index of a Banach space helps us calculate its ₁-index, via the ⁺₁-weakly null index. We show that I(C(^{))=^1++1}.     

ICP-MS determination of lead isotope ratios in legal and counterfeit cigarette tobacco samples

A method for the determination of Pb isotope ratios (IR) in cigarette tobacco by quadrupole inductively coupled plasma mass spectrometry (Q-ICP-MS) has been developed and applied to tobacco samples from genuine and counterfeit cigarettes obtained in the USA. The IR 2??Pb/2??Pb, (208)Pb/2??Pb, 2??Pb/2??Pb, 2??Pb/2??Pb and 2??Pb/2??Pb were measured using a Q-ICP-MS instrument. Two certified reference materials, grown in the USA and Bulgaria, were also analysed for comparison with the tobacco samples, as were tobacco samples from cigarettes obtained in Pakistan and China. The precision of the results was sufficient to distinguish between the counterfeit and genuine USA cigarettes. All of the genuine cigarettes and both reference materials, grown in different regions, were statistically distinct based on the measured ratios. The counterfeit cigarettes were indistinguishable from the reference material grown in Bulgaria. The technique shows promise as a method for identifying counterfeit cigarettes, possibly determining the source region.     

A guide to using shadowing filters for forecasting and state estimation

Most traditional, and many modern, methods of state estimation have a number a failings when applied to high-dimensional and nonlinear systems. A promising new alternative that avoids many of these failings is a shadowing filter. An additional advantage of shadowing filters is that when combined with indistinguishable states they provide a consistent generalisation to the imperfect model scenario. This paper is a practical guide to implementing shadowing filters in nonlinear systems. It provides a detailed account of various tests and procedures to ensure successful implementation of a shadowing filter using gradient descent of indeterminism.