Existence for the Cahn-Hilliard phase separation model with a nondifferentiable energy

Summary The Cahn-Hilliard model for phase separation in a binary alloy leads to the equations (I) u_t=w, (II) w= (u)– u with an associated energy functional F(u)=f [(u)+ +¦u¦²/2] dx. In this paper we discuss the existence theory for initial bounday value problems arising from modifications to the Cahn-Hilliard model due to the addition of the non-differentiable term ¦u¦dx to the energy F(u).     

Formation of the surface charge on silica in mixed solvents

At sufficiently high concentrations of methanol and of alkali salts in aqueous silica dispersions, the negative -potentials of the particles are decreased. This effect is more pronounced with lithium than with other alkali cations, and it is independent on the anion. The NMR spectra indicate lithium adsorption on silica from mixed solvents, but not in the absence of alcohol.Supported by a contract with the XMX Corporation, Burlington, Massachusetts, USA     

Study of radioactive labelled chromium (III) ion adsorption on stearic acid monomolecular layer

A study of chromium(III) ion adsorption on a stearic acid monomolecular layer (MML), spread on the surface of a⁵¹CrCl₃ aqueous solution, is presented. From the analysis of the experimental results it can be concluded that MML saturation is achieved at CrCl₃ concentrations above 10^?6M. When the maximum adsorption pH value of Cr(III) ions on MML is 6.7, MML is completely ionized and chromium ion is bonded as Cr(OH) ₂ ⁺ . The kinetics of Cr(III) ion adsorption on MML could be expressed as A^S=A _∞ ^S (1?e^{?k t}).     

The separation of some Bi- and tervalent cations on zirconium phosphate columns

Summary On small columns filled with the inorganic cation-exchanger zirconium phosphate, Zn²⁺-Cd²⁺ were quantitatively and Ni²⁺-Co²⁺ partly separated. The exchanger was in the NH₄+ form, and 0.5–4N NH₄Cl served as eluent. With the exchanger in the H+ form, U0₂ ²⁺ was separated from bivalent cations and ferric iron by stepwise elution with 0.1, 0.5 and 4N HCl solutions.

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Zusammenfassung An kleinen Säulen des anorganischen Kationenaustauschers Zirkoniumphosphat wurden Zn²⁺ und Cd²⁺ quantitativ, Ni²⁺ und Co²⁺ teilweise getrennt. Der Austauscher lag in der NH₄+-Form vor, 0,5-bis 4-n Ammoniumchlorid diente als Eluent. Mit der H+-Form des Austauschers wurde UO₂ ²⁺ von zweiwertigen Kationen und von Fe³⁺ durch schrittweise Elution mit 0,1-, 0,5- und 4-n Salzsäure getrennt.

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Résumé On a séparé Zn²⁺-Cd²⁺ quantitativement et Ni²⁺-Co²⁺ partiellement sur de petites colonnes remplies de phosphate de zirconium comme échangeur minéral cationique. L'échangeur se trouvait sous forme NH₄+ et l'on a pris NH₄Cl 0,5-4N comme éluant. Avec l'échangeur sous forme H⁺, on a séparé UO₂ ²⁺ des cations bivalents et de l'ion ferrique par élution graduelle avec des solutions chlorhydriques 0,1, 0,5 et 4N.

     

On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Threshold electron impact excitation of Cl2

A high resolution electron impact threshold spectroscopy technique was used to examine the excitation of Cl₂ in the 2–14 eV region. This study complements previous photon absorption and emission measurements, because it is capable of detecting transitions which are optically forbidden. In the region up to 7.5 eV, broad dissociative structures are correlated with optically active valence states, although relative intensities in the threshold spectrum differ considerably and indicate a substantial contribution from the optically forbidden transitions. At 7.46 eV a series of 5 equidistant sharp peaks is detected and interpreted as arising from the² π _g Feshbach resonance, which differs from the ground state positive ion Cl ₂ ⁺ by a pair of Rydberg electrons: (4sσ)². The decay channels responsible for the appearance of the resonance in a threshold spectrum are discussed and it is suggested that they include several valence states of the (2431) and (2341) configurations, whose potential energy curves cross the Cl ₂ ^? ,²π_g curve in the region of energy at which the resonance state is formed. At higher incident electron energies and up to ionisation, Rydberg states predominate, starting with (2430) 4s^3,1 π _g states detected for the first time. The absence of broad peaks above 8 eV and the irregular appearance of Rydberg bands is consistent with the strong Rydberg-valence configuration mixing proposed by Peyerimhoff and Buenker. Where our resolution permits comparison, good general agreement is found with recent synchrotron radiation absorption measurements of optically allowed transitions.     

Analytische Bestimmung von Niob,Tantal, Phosphor,Chlorid und 2,2-Dipyridyl in einigen Komplexverbindungen

Zusammenfassung Die analytische Bestimmung der Metalle, des Dipyridyls und der Chloride in Oxo-chloro-alkoxo-dipyridyl-Komplexverbindungen des Niobs und Tantals wurde beschrieben. Eine modifizierte Methode der Dipyridylanalyse, wie auch der Chloridbestimmung in Gegenwart von Dipyridyl wurde angegeben. Die radiometrische Metallbestimmung in Extraktionsverbindungen von Niob und Tantal mit Di-oktyl-methylenbis-phosphonsäure wurde dargelegt.

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Summary The analytical determination of metals, dipyridyl and chlorides in oxochloro-alkoxo-dipyridyl complex compounds of niobium and tantalum is described. A modified procedure of the dipyridyl analysis and also of the determination of chloride in the presence of dipyridyl is given. The radiometric determination of the metals in extraction compounds of niobium and tantalum with di-octyl-methylene-bis-phosphonic acid is discussed.

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Résumé On décrit le dosage des métaux, du dipyridyle et des chlorures dans les composés complexes oxo, chloro, alcoxo, dipyridyle, du niobium et du tantale. On indique une méthode modifiée pour le dosage de dipyridyle ainsi que pour la détermination des chlorures, en présence de dipyridyle. On décrit le dosage radiométrique des métaux dans les produits d'extraction du niobium et du tantale par l'acide di-octyl-méthylène-bis-phosphonique.

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Vorgetragen beim Symposium für analytische Chemie in Graz, 29. September bis 1. Oktober 1965.     

Kinetic determination of ultramicro amounts of copper

A new catalytic reaction is proposed and a kinetic method developed for the determination of ultramicro amounts of Cu(II) on the basis of its catalytic activity in oxidation of the 2-thiosemicarbazone of sodium 1,2-naphthoquinone-4-sulphonate by hydrogen peroxide in the presence of ascorbic acid. Under optimal conditions the sensitivity of the method is 0.25 ng/ml. The relative error is 4.8-18.2% for the concentration range 5-0.8 ng/ml. Most foreign ions do not change the rate of the catalysed reaction. Co(2+) and I(-) catalyse the reaction, Ni(2+) extensively inhibits it, and in the presence of EDTA only the uncatalysed reaction takes place.