Poly(styrene-b-2-vinylpyridine-1-oxide) diblock copolymers: 3. Microemulsions in water/propan-2-ol/toluene mixtures

Pseudo-ternary phase diagrams have been constructed for the three-component solvent system (toluene+water+propan-2-ol) containing diblock copolymers of poly(styrene-b-2-vinylpyridine-1-oxide). Microemulsions have been shown to form on the water-rich side of the phase diagram, in the region of the phase boundary without polymer. Dynamic light-scattering experiments have led to droplet size values in the region of 100 nm, with the size depending strongly on the propan-2-ol/water concentration, as well as the amount of solubilised toluene in the core. Viscometry experiments have been carried out to measure polymer aggregation numbers in the microemulsion droplets, and interfacial tension measurements have shown that in the absence of propan-2-ol (effectively a cosurfactant) the limiting value of the oil/water interfacial tension, even an saturation adsorption of the copolymer is 20 mNm^–1. However, addition of propan-2-ol reduces the interfacial tension to the very low values generall commensurate with microemulsion formation.     

Die Strommer-Zykliden des Flaggenraumes

According to H. BRAUNER a flag space is a three-dimensional affine space with an absolute {,f,F}, wheref is a line in the plane of infinity andF a point onf. A cyclide is a surface of order 4 that intersects only atf. A STROMMER-cyclide is a cyclide generated by translation of a circle in an isotropic plane. In this paper we proof that all STROMMER-cyclides can be generated by translation of an isotropic circle along a divergent Newton-parabola or a conic in a full isotropic plane. We give normal-forms and CAD-pictures of these surfaces. Finaly some geometrical results about STROMMER-cyclides are developed.

---

---

Herrn o.Prof. Dr. Gy. Strommer zum 70. Geburtstag gewidmet.     

Density fluctuations in amorphous and semicrystalline polymers

Summary The small-angle scattering of amorphous and semicrystalline polymers contains an intensity component due to density fluctuations within the crystalline and amorphous domains.For amorphous polymers, the density fluctuations aboveT _g correspond to the theoretical value for a fluid system in thermodynamic equilibrium. BelowT _g , a temperature dependence proportional to T is observed over a range of about 50°. At lower temperatures, a linear relationship with a smaller slope has been found which extrapolates to a non-zero value at 0 °K. This value corresponds to the frozen-in disorder, the slope at low temperatures is related to thermal vibrations and can be evaluated in terms of photon-phonon scattering.Semicrystalline polymers show a temperature dependence of the density fluctuation similar to that of the amorphous polymers. At constant temperature the density fluctuations vary linearly with crystallinity.Natural rubber shows an increase of the density fluctuations with increasing cross-linking densities from which information on the density changes in the vicinity of a cross-link and on the statistics of the distribution of cross-linking can be obtained.

---

Zusammenfassung Die Kleinwinkelstreuung amorpher und teilkristalliner Polymere besitzt eine Intensitätskomponente, die von Dichtefluktuationen innerhalb der kristallinen und amorphen Bezirke herrührt. Für amorphe Polymere entspricht die Dichtefluktuation oberhalb vonT _g dem theoretischen Wert für ein fluides System im thermodynamischen Gleichgewicht. UnterhalbT _g wird eine Temperaturabhängigkeit proportional zuT über einen Bereich von etwa 50° beobachtet. Bei tieferen Temperaturen wird eine lineare Beziehung mit einer geringeren Steigung gefunden, welche zu einem endlichen Wert bei 0 °K extrapoliert werden kann. Dieser Wert bezieht sich auf die eingefrorene Fehlordnung, die Steigung bei tiefen Temperaturen ist auf thermische Schwingungen zurückzuführen und kann als Photon-Phonon-Streuung ausgewertet werden.Teilkristalline Polymere zeigen eine Temperaturabhängigkeit der Dichtefluktuation, die der von amorphen Polymeren ähnlich ist. Bei konstanter Temperatur ändert sich die Dichtefluktuation linear mit der Kristallinität.Naturkautschuk zeigt eine mit der Vernetzungsdichte ansteigende Dichtefluktuation, aus der man Information über die Dichteänderung in der Umgebung eines Netzpunktes und die Statistik der Netzpunktverteilung erhalten kann.

     

Absolute infrared intensities of hydrocarbons

Dipole-moment derivatives, calculated by both the CNDO/2 method with different parameterizations and the INDO method, are compared to the experimental values determined from absolute infrared intensity measurements for the IR active modes of methane, ethane, ethylene and acetylene. A parameter refinement procedure is introduced in which the CNDO/2 molecular orbital parameters are adjusted through a damped least-squares treatment to give best agreement with the observed dipole-moment derivatives. It is found that the refinement does not substantially improve the agreement obtained with the original CNDO/2 parameterization. The INDO method gives somewhat poorer agreement than the CNDO/2 calculations. As an example of the applicability of the molecular orbital methods toward reproducing relative infrared intensities, the spectrum of cyclopropane in the gasphase is examined.

---

Zusammenfassung Die Ableitungen des Dipol-Moments, die nach der CNDO/2-Methode mit verschiedenen Parametrisierungen sowie der INDO-Methode berechnet wurden, werden mit den experimentellen Ergebnissen aus Messungen der absoluten Infrarot-Intensitäten für die IR-aktiven Schwingungen von Methan, Äthan, Äthylen und Azetylen verglichen. Die CNDO/2-Parameter werden mit einer Methode der kleinsten Quadrate den beobachteten Dipol-Moment-Ableitungen angepaßt. Die Ergebnisse sind jedoch nicht wesentlich von denen der ursprünglichen CNDO/2-Methode verschieden. Die INDO-Ergebnisse sind nicht so gut wie die CNDO/2-Ergebnisse. Als Beispiel der Anwendbarkeit der MO-Methoden zur Berechnung von relativen IR-Intensitäten wird das Spektrum des Cyclopropans in der Gasphase untersucht.

---

Résumé Les dérivées du moment dipolaire, calculées par la méthode CNDO/2 avec différentes paramétrisations et par la méthode INDO, sont comparées aux valeurs expérimentales déterminées à partir de mesures d'intensité absolue pour les modes actifs dans l'infra-rouge dans le méthane, l'éthane, l'éthylène et l'acétylène. Les paramètres sont ajustés de manière à donner le meilleur accord avec les dérivées du moment dipolaire. Cet ajustement n'améliore pas sensiblement l'accord obtenu avec la paramétrisation CNDO/2 originale. La méthode INDO donne des résultats moins bons que les calculs CNDO/2. Le spectre du cyclopropane en phase gazeuse est étudié comme exemple de l'applicabilité de la méthode des orbitales moléculaires au calcul des intensités relatives infra-rouge.

     

Dipolare (1:1)-Addukte aus der Reaktion von 3-Amino-2H-azirinen mit 1,3,4-Oxadiazol- und 1,3,4-Thiadiazol-2(3H)-onen

Dipolar 1:1 Adducts from the Reaction of 3-Amino-2H-azirines with 1,3,4-Oxadiazol- and 1,3,4-Thiadiazol-2(3H)-ones 3-Amino-2H-azirines 1 react with 5-(trifluoromethyl)-1,3,4-oxadiazol-2(3H)-one ( 2 ) as well as with different 5-substituted 1,3,4-thiadiazol-2(3H)-ones ( 5a–e ) in 2-propanol at room temperature to give dipolar 1:1 adducts of type 3 and 6 , respectively, in reasonable-to-good yields (Schemes 3 and 6, Tab. 1 and 2). The structure of two of these dipolar adducts, 6a and 6e , which are formally donor-acceptor-stabilized azomethin imines, have been elucidated by X-ray crystallography (Figs. 1-4). In the reaction of 2 and sterically crowded 3-amino-2H-azirines 1c–e with a 2-propyl and 2-propenyl substituent, respectively, at C(2), a 4,5-dihydro-1,2,4-triazin-3(2H)-one of type 4 is formed as minor product (Scheme 3 and Table 1). Independent syntheses of these products proved the structure of 4 . Several reaction mechanisms for the formation of compounds 3 and 4 are discussed, the most likely ones are described in Scheme 4: reaction of 2 as an NH-acidic compound leads, via a bicyclic zwitterion of type A , to 3 as well as to 4 . In the latter reaction, a ring-expanded intermediate B is most probable.     

121Sb-Mössbauer-Spektren von Antimon(V)-Verbindungen. II

¹²¹Sb Mössbauer Spectra of Antimony (V) Compounds. II The Mössbauer resonance effect of ¹²¹Sb has been studied at 4.2 K in a series of 11 antimony(V) compounds which are in most cases bridged. Isomer shift and quadrupole splitting variations are considered in the light of results of X-ray and vibrational spectroscopy. Preparation and the vibrational spectra of [NMe₄][SbCl₄(n₃)₂] are described. Within the limitations of available structural data related tin compounds are compared with those of corresponding ¹¹⁹Sn Mössbauer spectra.     

Periodic,multiplicative number-theoretical functions

D. Leitmann andD. Wolke [3] proved that multiplicative functions, which are restrictions of continuous, periodic functionsF: with irrational period, are constant equal to 0 or 1. In this note a simpler proof for this result is given.     

A comparison of two approaches to the optimal positioning of a new product in an attribute space

This paper is concerned with the optimal positioning of a new product in an attribute space. A deterministic optimization model that relies on the axiom of choice is compared with the model byShocker/Srinivasan [1974] that incorporates a probabilistic measure of choice. Investigating the assumptions and the construction of both models, it is shown that the probability function byShocker/Srinivasan is based on a controversial assumption and incorporates a parameter that has not been given an economic explanation. Furthermore, both models are applied to complex configurations. It is demonstrated that the optimal positions for the new product resulting from the model byShocker/Srinivasan depend heavily on the parameter just mentioned and may run contrary to plausible consequences of the axiom of choice.

---

Zusammenfassung Für die optimale Gestaltung neuer Produkte, d.h. ihrer Positionierung in einem Raum von Produkteigenschaften, wird ein Modell angeboten, das auf einer deterministischen Kaufentscheidung beruht, ein anderes, das eine stochastische Kaufentscheidung unterstellt. Es wird gezeigt, daß der zuletzt genannte Modelltyp stark von der Spezifikation eines ökonomisch bisher nicht erklärten Parameters abhängt und z.T. Konsequenzen aufweist, die dem Wahlaxiom zuwider laufen, auf das das erstgenannte Modell aufbaut. Durch einen Vergleich auch komplexer Konfigurationen von Käuferbeurteilungen neuer Produkte wird gezeigt, welche Gestaltungsentscheidungen auf der Grundlage der beiden Modelle zur Optimierung einer Zielfunktion zu treffen sind.

     

On the Fourier transformation on spaces of (p,q)-multipliers

LetG denote a locally compact abelian topological group. The aim of the present paper is to prove an “intermediate” result between two well-known results ofL. Hörmander andG. I. Gaudry concerning the structure of the spaces ?_G?μ?t ^p,q (G).     

Functional Bacterial Amyloids: Understanding Fibrillation,Regulating Biofilm Fibril Formation and Organizing Surface Assemblies

Functional amyloid is produced by many organisms but is particularly well understood in bacteria, where proteins such as CsgA (E. coli) and FapC (Pseudomonas) are assembled as functional bacterial amyloid (FuBA) on the cell surface in a carefully optimized process. Besides a host of helper proteins, FuBA formation is aided by multiple imperfect repeats which stabilize amyloid and streamline the aggregation mechanism to a fast-track assembly dominated by primary nucleation. These repeats, which are found in variable numbers in Pseudomonas, are most likely the structural core of the fibrils, though we still lack experimental data to determine whether the repeats give rise to β-helix structures via stacked β-hairpins (highly likely for CsgA) or more complicated arrangements (possibly the case for FapC). The response of FuBA fibrillation to denaturants suggests that nucleation and elongation involve equal amounts of folding, but protein chaperones preferentially target nucleation for effective inhibition. Smart peptides can be designed based on these imperfect repeats and modified with various flanking sequences to divert aggregation to less stable structures, leading to a reduction in biofilm formation. Small molecules such as EGCG can also divert FuBA to less organized structures, such as partially-folded oligomeric species, with the same detrimental effect on biofilm. Finally, the strong tendency of FuBA to self-assemble can lead to the formation of very regular two-dimensional amyloid films on structured surfaces such as graphite, which strongly implies future use in biosensors or other nanobiomaterials. In summary, the properties of functional amyloid are a much-needed corrective to the unfortunate association of amyloid with neurodegenerative disease and a testimony to nature’s ability to get the best out of a protein fold.