Polymeric positive-temperature-coefficient materials: dynamic curing effect

The object of this work was to prepare high-density polyethylene (HDPE)/ethylene–propylene–diene terpolymer (EPDM)/conductive carbon black (CB) composites by dynamic curing and to characterize the positive-temperature-coefficient (PTC) performances of the composites.EPDM and dicumyl peroxide were preblended in a research mill. The roll-milled strands were blended with HDPE and CB in a Haake mixer. The sheet resistivity and morphology of the HDPE/EPDM/CB composites with or without the dynamic curing process were investigated. It was concluded that the dynamically cured blends exhibit better PTC performance than the simple blends without dynamic curing. The effects of shear intensity and dicumyl peroxide content during the dynamic curing process were discussed for the PTC characteristics of the HDPE/EPDM/CB composites.     

A CNDO-MO calculation of VCl4

The electronic structure of the tetrahedral molecule VCL₄ is investigated within the CNDO-MO approximations. The metal and ligand valence orbitals, 3d, 4s, 4p; and 3s, 3p; respectively, have been systematically varied in an attempt to minimize the total energy; “optimum” V 4s(χ₄ = 1.10) and 4p(d ³ p ²) orbitals have been established, but V 3d(d ⁿ ) and Cl(-δ) valence orbitals are only seen to favor lower energy for expanded orbitals. Since determining the one-electron molecular orbital level which is occupied by the vanadium lone electron is a major aspect of this investigation, all calculations have been performed in triplicate: calculations assuming the unpaired electron occupies the 3a ₁, 2 _e and 4t ₂ molecular orbital (ground state electronic configurations² A ₁,² E, and² T ₂, respectively). The Hartree-Fock equations have been solved by Roothaan's SCF method for open shells, but off-diagonal multipliers between filled and partly filled molecular orbitals of the same symmetry have been neglected. As a qualitative estimate of the error introduced by this simplification, the pertinent overlap integrals between the eigenfunctions from calculations for the three possible configurations,² A ₁,² E, and² T ₂, are investigated as functions of the component 3d(d ⁿ ) and Cl(-δ) valence orbitals. The overlap integrals from the relevant² A ₁ and² T ₂ calculations are reasonably small, but the neglect of off-diagonal multipliers in calculations on the² E state is found to be a poor approximation. An ordering of the non-filled molecular orbitals in VCl₄ of 4t ₂ < 3a ₁ < 2e < 5t ₂ seems most consistent with the numerous calculations. This suggested ground state electronic configuration of² T ₂ introduces new aspects to the consideration of a (dynamic) Jahn-Teller effect in VCl₄. Experimental data pertinent to the electronic structure of VCl₄ has been briefly summarized, but unfortunately it is inadequate to confirm or deny the present calculations.     

Fluorescence of tryptophan-containing peptides on paper or silica gel after treatment with formaldehyde, formaldehyde-ozone or formaldehyde-hydrochloric acid.

Sensitive and specific procedures for the chromatographic detection of tryptophan and tryptophan-containing peptides are described. Formaldehyde gas induces strong and characteristic fluorescence from tryptophan and peptides with NH2-terminal tryptophan residues on silica gel. On filter-paper, the detection of small amounts of these compounds requires the additional use of an oxidant, such as ozone. Treatment with formaldehyde-hydrochloric acid was used as a method for inducing fluorescence from tryptophan-containing peptides regardless of the position of the tryptophan residue in the peptide molecule. This reaction is useful for the chromatographic demonstration of small amounts of such peptides on both paper and silica gel. The spectral properties of the fluorophores of such tryptophan-containing peptides are distinctive and serve to distinguish them from all other known biogenic compounds that are capable of giving fluorescence with formaldehyde.     

On the lattice stability of metals

The success of perturbation calculations of second order for the NFE (“Nearly Free Electron”) metals and that of the two-parameter model of Pettifor for the transition elements show that the lattice-stability of the metals has simple physical reasons. Using the results of Harrison, Heine and Weaire, Deegan, and Pettifor, a model is developed which allows to explain the stability of the three metal lattices in terms of differences in the potentials. Only those potential differences are considered which are caused by the different packing of the lattices. With the aid of the virial theorem the band structure energy is connected with the potential bandstructure energy. The sequence of stability is predicted to be body centered cubic (bcc), hexagonal close packed (hcp), face centered cubic (fcc) with increasing valence electron concentration. The ranges of stability can be expressed in simple numbers. This simple model holds in principle for NFE as well as for transition metals because it contains no assumptions restricted to only one of these metal types. Deviations of the observed lattice stability from the model can be understood from the approximations involved.     

High precision measurements of the hyperfine structure of seven metastable atomic states of57Fe by laser-Rf double-resonance

The hyperfine structure of the metastable atomic states (3d ⁷4s)⁵ F _2,3,4,5 and (3d ⁷ 4s)³ F _2,3,4 of⁵⁷Fe has been measured using theABMR- LIRF method (atomic beam magnetic resonance detected by laser induced resonance fluorescence). From these measurements the following hfs constantsA of the magnetic dipole interaction have been obtained (corrected for second order effects):A(⁵ F ₂)=55.994(7) MHzA(⁵ F ₃)=69.632(5) MHzA(⁵ F ₄)=78.435(4) MHzA(⁵ F ₅)=87.246(3) MHzA(³ F ₂)=143.328(4) MHzA(³ F ₃)=50.602(10) MHzA(³ F ₄)=13.456(5) MHz     

Gleichverteilung und Quadratwurzelschnecke

A new proof of a theorem of W. Neiss is given that the rays of the Quadratwurzelschnecke are uniformly distributed mod 2 . The exact order of the discrepancy of the sequence is determined. Multidimensional generalizations of this sequence are also considered. It is shown that the Quadratwurzelschnecke is something like a roulette.

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Mit 2 Abbildungen

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Herrn Prof. R. M. Redheffer in Freundschaft zum 60. Geburtstag gewidmet     

Eine Topologie auf der Menge der endlichdimensionalen nichtassoziativen Algebren über einem lokalen Körper

Motivated by an investigation ofKuz'min [2], in this note we introduce a topology on the set of nonassociative algebras of a fixed dimensionr< over a local fieldF. We obtain a space, which is notT ₁. If the trivial algebra is removed, the remaining subspace is quasicompact. The space is homeomoprhic to the group of square classes ofF ^*; forr3 the space is notT ₁. The set of division algebras is open in.     

Maße für gerichtete Geraden und nicht-symmetrische Pseudometriken in der Ebene II

We continue our investigations started in a paper with the same title. The -length of a curve defined in this paper can be written as an integral along the curve. Furthermore, we determine necessary and sufficient conditions for the existence of a measure of orientated lines which generates a given non-symmetric pseudo-metric.

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Herrn Prof. Dr. H.-J. Kanold zum 65. Geburtstag gewidmet     

Eine Erweiterung des Riemann-Lebesgue-Lemmas

It is proved that iff∈L ₁(?),f'∈L ₁(?) and ∫∣x∣ ⁱ ∣f(x)∣dx<∞ fori=1, ...,k?1 and ifA=(a _ij ) is a (k×k)-matrix with non-vanishing determinant, for $$\tilde f_A (\zeta ): = \smallint \exp (i\zeta _1 \sum\limits_{j = 1}^k {a_{1j} x^j } + ... + i\zeta _k \sum\limits_{j = 1}^k {a_{kj} x^j } )f(x)dx$$ the following relation holds: $$\tilde f_A (\zeta ) = O(\left\| \zeta \right\|)^{ - b_k } with b_k : = (\sum\limits_{j = 1}^k {j!)^{ - 1} } for k \in \mathbb{N}$$ .     

Ein asymptotischer Ausdruck für eine zahlentheoretische Funktion

Arithmetic formulae and an asymptotic expression for the order of magnitude of the arithmetic function ged (s, n) and of a generalisation of it are derived.