Bicircular projections and characterization of Hilbert spaces

We prove that every JB* triple with rank one bicircular projection is a direct sum of two ideals, one of which is isometrically isomorphic to a Hilbert space.

     

Axiale Korrelationsfunktion gereckter Polyäthylenfilme

Zusammenfassung Für Proben mit zylindrischer Symmetrie wird die Korrelationsfunktion entwickelt und aus dem mit einerKratky-Spaltkamera aufgenommenen Röntgenkleinwinkelstreudiagramm eines gereckten High-Density-Polyäthylenfilms berechnet. Es wurden Proben mit einem Reckungsverhältnis von 8 bis 20 untersucht, an denen die Reckung bei Temperaturen zwischen 24 und 120°C ausgeführt wurde, sowie Proben, die bei 110° getempert wurden. Die Amplitude der periodischen Änderung der Korrelationsfunktion nimmt mit steigender Reckungstemperatur und Dauer der Temperung stark zu und sinkt mit wachsendem Reckungsgrad. Die Anzahl der beobachtbaren Maxima wird hingegen nur sehr wenig beeinflußt, so daß man schließen muß, daß die Schwankung der Periodizität in der Reckrichtung für alle untersuchten Proben annähernd gleich ist. Die Amplitudenänderung ist eher mit der Unregelmäßigkeit des Übergangs zwischen den kristallinen und den amorphen Bereichen verknüpft, die durch höhere Reckungsgrade verstärkt, durch höhere Reckungstemperaturen und durch Temperung hingegen verringert wird.

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Axial correlation function of drawn polyethylene films

The correlation function is developed for a sample with cylindrical symmetry and calculated from the small-angle X-ray scattering pattern of drawn high density polyethylene film obtained with theKratky slit camera. Samples with draw ratio between 8 and 20, draw temperature between 24 and 120°C and annealed at 110°C were investigated. The amplitude of the periodic variation of the correlation function increases drastically with the temperature of drawing and with annealing and decreases with increasing draw ratio. But the number of detectable maxima is very little affected so that one has to conclude that the fluctuation of periodicity in the direction of draw is almost the same for all samples investigated. The change in amplitude is more connected with the irregularity of transition between the crystalline and amorphous domains which is enhanced by higher draw ratio and reduced by higher temperature during drawing or annealing.

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Mit 8 Abbildungen

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Herrn Prof. Dr.O. Kratky zum 70. Geburtstag gewidmet.     

Some aspects of quality assessment of the k0-based method of NAA

Neutron activation analysis is one of the analytical techniques often used for certification of reference materials. The k₀-based method of instrumental neutron activation analysis can also be applied in intercomparison runs in the certification process and therefore it is desirable to know its accuracy in advance. Possible systematic errors related to the application of nuclear data at given neutron flux rate parameters, that can affect the uncertainties of the results obtained by this specific method, are elucidated and error propagation factors calculated for a typical irradiation position in the TRIGA Mark II reactor of the Jozef Stefan Institute. It was found that these uncertainties are at the level of 1–2% on the average.     

Time dependence of viscosity of dilute polyisobutylene solutions

Summary Shearing at constant gradient of polyisobutylene (PIB) solutions in viscous polybutene oils results in time dependent changes of their viscosities. Two PIB fractions (M=8·10⁶ and 3.8·10⁶) have been studied in a variety of solvents, covering the viscosity range from 5 to 0.5·10⁻² poise. The overall phenomenon is similar to that already observed for polymethylmethacrylate, polystyrene, and polyethylene oxide solutions in Aroclor. Results have been discussed in terms of polymer molecular weight and concentration, solvent viscosity and gradient. The systems investigated are free from strong polar interactions and tendency toward molecular aggregation; time dependent changes of viscosity are therefore observable also for true molecularly dispersed solutions.

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Zusammenfassung Scherung mit konstantem Geschwindigkeitsgradienten von Polyisobutylen (PIB)-L?sungen in viskosen Polybuten-?len ergibt zeitabh?ngige ?nderungen ihrer Viskosit?ten. Zwei PIB-Fraktionen (M=8·10⁶ und 3,8·10⁶) wurden in einer Vielzahl von L?sungsmitteln untersucht, die den Viskosit?tsbereich von 5 bis 0,5·10⁻² Poise überdeckten. Das ph?nomenologische Erscheinungsbild ist ?hnlich dem schon beobachteten für Polymethylmethacrylat, Polystyrol und Poly?thylenoxid-L?sungen in Aroclor. Die Ergebnisse wurden hinsichtlich des Polymer-Molekulargewichts und der Konzentration, der L?sungsmittelviskosit?t und des Gradienten diskutiert. Die untersuchten Systeme sind frei von starken polaren Wechselwirkungen und von Tendenzen in Richtung auf molekulare Aggregation. Zeitabh?ngige ?nderungen der Viskosit?t sind deshalb auch für wahre molekulardisperse L?sungen beobachtbar.

     

Influence of the surface morphology on the melting of polymer crystals. I. Loops of random length and adjacent reentry

A polymer crystal with a noncrystalline surface layer formed by chain loops of different lengths is considered. It is assumed that the length of each loop can be changed by longitudinal diffusion of the molecule through the crystal lattice. From the condition that the free energy of the system is minimum, the loop length distribution and the average loop length as function of temperature are calculated. In contrast to the results for loops of equal length, for the present model, a substantial thickness of the noncrystalline surface layer and a broad melting range is obtained also for the case of adjacent reentry. In order to get this result one has to take into account that even an “ideal fold” consists of at least four rigidly arranged CH2 groups in energetically unfavored conformation.     

Status of uncertainty assessment in k 0-NAA measurement: anything still missing?

Several approaches to quantifying measurement uncertainty in k ₀-based neutron activation analysis (k ₀-NAA) are reviewed, comprising the original approach, the spreadsheet approach, the dedicated computer program involving analytical calculations and the two k ₀-NAA programs available on the market. Two imperfectness in the dedicated programs are identified, their impact assessed and possible improvements presented for a concrete experimental situation. The status of uncertainty assessment in k ₀-NAA is discussed and steps for improvement are recommended. It is concluded that the present magnitude of measurement uncertainty should further be improved by making additional efforts in reducing uncertainties of the relevant nuclear constants used.     

Time dependence of mechanical and transport properties of drawn and annealed linear polyethylene

Linear polyethylene both as drawn, or drawn and subsequently annealed with free ends, changes its length, density, crystallinity, elastic modulus, sorption, and diffusivity as the sample stands completely unrestrained at room temperature. Most of these changes occur during the first few hours. But they are important on a molecular scale since they suggest strongly that drawn, and drawn and annealed samples are far from equilibrium. As a consequence of the tendency of each mobile tie molecule in the amorphous conformation to retract and to crystallize, the specimen approaches but does not reach complete equilibrium. The transient seems to be caused by slow crystallization of tie molecules which creates crystalline bridges across the amorphous layers.     

Infrared studies of drawn polyethylene. II. Orientation behavior of highly drawn linear and ethyl-branched polyethylene

Infrared dichroism is employed to study the orientation of chain molecules in linear and ethyl-branched polyethylene in the crystalline and noncrystalline regions during drawing and subsequent annealing. A crystalline (1894 cm^?1) and a noncrystalline (1368 cm^?1) band, as well as the bands at 909 cm^?1 and 1375 cm^?1 resulting from vinyl endgroups and methyl endgroups and sidegroups, are studied. For these bands relative orientation functions are derived and compared as a function of draw ratio and annealing temperature. It is shown that the relative orientation functions as derived from the dichroism of the noncrystalline, vinyl and methyl bands follow the same curve while the orientation function for the crystalline bands does not. These results support a two-phase model for partially crystalline polyethylene and additionally favor segregation of the endgroups and sidegroups in the noncrystalline component during crystallization. It is further shown that shrinkage occurs at the temperature at which the noncrystalline chain molecules start to disorient. From the dichroism of the methyl groups in ethyl-branched polyethylene, a value for the mean orientation of the noncrystalline chain molecules is calculated. We obtain for the orientation function of the noncrystalline regions at highest draw ratios (λ = 15–20), f = 0.35–0.57, while the chain molecules in the crystallites are nearly perfectly oriented (f ≈ 1.0). On the assumption that the noncrystalline component consists of folds, tie molecules, and chain ends, the different contributions of these components to the overall orientation are estimated. From these the relative number of CH₂ groups incorporated into folds, tie molecules, and cilia can be derived. Further, on the basis of a simple structural model, the relative number of chains on the crystal surface contributing to the different noncrystalline components and their average length are estimated.