Equilibrium polymerization in a solvent: Solution on the Bethe lattice

The lattice model for equilibrium polymerization in a solvent proposed by Wheeler and Pfeuty is solved exactly on a Bethe lattice (core of a Caylay tree) with general coordination numberq. Earlier mean-field results are reobtained in the limitq, but the phase diagrams show deviations from them for finiteq. Whenq=2, our results turn into the solution of the one-dimensional problem. Although the model is solved directly, without the use of the correspondence between the equilibrium polymerization model and the diluten0 model, we verified that the latter model may also be solved on the Bethe lattice, its solution being identical to the direct solution in all parameter space. As observed in earlier studies of the puren0 vector model, the free energy is not always convex. We obtain the region of negative susceptibility for our solution and compare this result with mean field and renormalization group (-expansion) calculations.     

Fields as Kolmogzrov flows

It is widely recognized that for highly unstable dynamical systems there exists a fundamental limitation on predictability and determinism. An important class of such highly unstable systems is the class of K-flow, which is further characterized by the existence of time-asymmetric objects in the form of K-partition. Our recent approach to the problem of irreversibility has shown that when the implications of the limitation on determinism arising from strong form of instability and those of the existence of K-partition are consistently taken into account, one is naturally led from the physically unrealizable deterministic evolution of phase points to an entropy-increasing stochastic Markovian evolution. Furthermore, this transition is not the result of extraneously imposed coarse graining and/or approximation schemes, but can be brought about by an invertible transformation whose existence and construction are determined by the nature of the instability of the dynamical system itself. After a brief review of this theory which also contains some relatively new remarks, we prove that classical Klein-Gordon field (both massive and massless) possess the structure of K-flow. This seems to provide the first examples of relativistic systems that are K-flows. Some of the implications of this result are briefly discussed. From a mathematical point of view, this seems to be a first step toward an ergodic theory of partial differential equations. In the process, we also provide an independant group-theoretic proof of the existence of incoming and outgoing subspaces of the scattering theory of Lax and Phillips for the wave equation.     

Characterization of SiO2-P2O5-ZrO2 Sol-Gel/NAFION™ Composite Membranes

Composite membranes were prepared by (a) infiltrating NAFION with SiO₂-P₂O₅-ZrO₂ sol, and (b) recasting a film using NAFION solution containing SiO₂-P₂O₅-ZrO₂ sol. The membranes were characterized by Differential Thermal Analysis and ac-impedance spectroscopy as a function of relative humidity. The influences of the heat treatment (80°C–150°C) and cleaning on the electrical properties were investigated. The incorporation of SiO₂-P₂O₅-ZrO₂ gels into NAFION lead to improvements in its thermal stability and proton conductivity.     

Synthesis and Characterization of Tetraosmium Carbonyl Complexes Containing a Bridging CO2 Ligand

Treatment of (thd)H (thd=2,2,6,6-tetramethyl-3,5-heptandionate) with excess Os₃(CO)₁₂ in an autoclave at 180°C gives the formation of a brown metal chain complex [Os₂(CO)₅(thd)₂]₂ (1) and a yellow CO₂ cluster complex [Os₄(-H)(-CO₂)(thd)(CO)₁₃] (2) in low yields. Complex 2 was fully identified by a combination of spectroscopic methods and X-ray diffraction study, showing a unique CO₂ ligand bridging a triosmium metal fragment, Os₃(-H)(CO)₁₀ and a monometallic osmium fragment, Os(CO)₃(thd). Upon treatment of 1 with Me₃NO at an elevated temperature, oxidation of the CO ligand occurred at the position trans to the unique CO₂ ligand on the Os(CO)₃(thd) fragment, giving the formation of a second CO₂ cluster [Os₄(-H)(-CO₂)(thd)(CO)₁₂(NCMe)] (3), which is stabilized by a weakly coordinated acetonitrile molecule.     

Nitrido-Sodalithe. II. Synthese,Struktur und Eigenschaften von M(6+(y/2)–x)H2x[P12N24]Zy mit M = Fe,Co, Ni,Mn; Z = Cl,Br, I; 0 ≤ x ≤ 4; y ≤ 2

Nitrido-Sodalites. II. Synthesis, Crystal Structure, and Properties of M_{(6+(y/2)–x)}H_2x[P₁₂N₂₄]Z_y with M = Fe, Co, Ni, Mn; Z = Cl, Br, I; 0 ≤ x ≤ 4; y ≤ 2 The nitrido sodalites M_{(6+(y/2)–x)}H_2x[P₁₂N₂₄]Z_y with M = Fe, Co, Ni, Mn; Z = Cl, Br, I; 0 ≤ x ≤ 4; y ≤ 2 are obtained by the reaction of HPN₂ or [PN(NH₂)₂]₃ with the metal halogenide MZ₂ (T = 700°C). The compounds are isotypic to Zn_(7–x)H_2x[P₁₂N₂₄]Cl₂. An increase of the ionic radii of the cations or anions results in an expansion of the lattice which is caused by an increase of the P? N? P angle. The influence of the cation is more dominant than that of the anion. By reacting [PN(NH₂)₂]₃ with metal halogenide (MZ₂) hydrogen free, X-ray amorphous products are obtained. The formation of the chloride-containing P? N-sodalite in this reaction begins at temperatures below 450°C.     

Remarks on the sample preparation of oxidic materials for X-ray analysis

Summary The universal method which is established in practice and has the best reproducibility is indicated in a critical comparison of different techniques for producing melting fusion tablets for the X-ray analysis. By studying fusion tablets with methods of local analysis, users of the tablet technique shall be made critical. The different objectives of analytical problems with the analysis of oxides are discussed.

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Bemerkungen zur Probenvorbereitung oxidischer Materialien für die Röntgenfluorescenzanalyse

Zusammenfassung Ausgehend von einem kritischen Vergleich verschiedener Techniken zur Herstellung von Schmelzaufschluß-Tabletten für die RFA wird auf die in der Praxis bewährte Universalmethode mit der besten Reproduzierbarkeit hingewiesen. Durch die Untersuchung von Schmelztabletten mit Hilfe lokalanalytischer Methoden sollen Anwender der Tablettentechnik zur Kritik angeregt werden. Die unterschiedlichen Zielsetzungen analytischer Aufgaben bei der Untersuchung von Oxiden werden diskutiert.

     

Borchelate und Bormetallchelate, 4. Mitt.

The i.r., u. v.,¹H n.m.r.,¹³C n.m.r., and¹¹B n.m.r. spectra of several substituted diphenylboron chelates derived from salicylaldehyde azomethines were compared with respect to the influence of the amine substituentR. O–B–N-6-ring constitution of the chelates29–32 [R=OH, NH₂, NHC₆H₅, N(CH₃)₂] can be deduced from the spectra.

Als 3. Mitt. gilt:F. Umland undE. Hohaus mit Beiträgen vonW. Riepe, K. Brodte, C. Schleyerbach undD. Szonn. Untersuchungen über borhaltige Ringsysteme vom Chelattyp. Forschungsbericht des Landes Nordrhein-Westfalen Nr. 2538. Opladen: Westdeutscher Verlag. 1976.     

Parametric study of the flow and temperature fields in an inductively coupled r.f. plasma torch

A theoretical investigation of the effect of different parameters on the flow and the temperature fields in a radiofrequency inductively coupled plasma is carried out. The parameters studied are: central injection gas flow rate, total gas flow rate, input power, and the type of plasma gas. The results obtained for argon and nitrogen plasmas at atmospheric pressure indicate that the flow and the temperature fields in the coil region, as well as the heat flux to the wall of the plasma confinement tube, are considerably altered by the changes in the torch operating conditions.     

Chelate mit Diimin- und Thiol-Struktur: Analytische Anwendung der Di-(4-substituierten)-thiosemicarbazone von 1,2- und 1,3-Diketonen

Zusammenfassung In der Gruppe der vierzähnigen Liganden mit Diimin- und Thiolstruktur bilden die Bisthiosemicarbazone von 1,2- und 1,3-Diketonen mit 4-substituierten Thiosemicarbaziden intensiv gefärbte Metallchelate, die für extraktionsphotometrische Bestimmungen in der Spurenanalyse verwendet werden können. Die molaren Extinktionskoeffizienten liegen im Bereich 5000–16000. Die leichte Zugänglichkeit von 4-substituierten Thiosemicarbaziden über die Reaktion von Isothiocyanaten mit Hydrazin bietet eine große Auswahl von Reagentien, besonders für die Flüssig-Chromatographie zur Trennung von komplexen Chelatgemischen.Die Arbeit wurde aus den Mitteln der Deutschen Forschungsgemeinschaft Bonn-Bad Godesberg gefördert.     

Darstellung,Eigenschaften und Kristallstruktur von Bis(phthalocyaninato)cer(IV)

Preparation, Properties and Crystal Structure of Bis(phthalocyaninato)cerium(IV) The anodic or chemical oxidation with dibenzoylperoxide of solutions of bis(phthalocyaninato)cerate(III) in dichloromethane yields selectively sparely soluble bis(phthalocyaninato)cerium(IV), [Ce(Pc(2-)) 2 ]. Green, monoclinic needles cristallize with a = 18.783(12) Å b = 18.739(16) Å c= 15.618(10) Å ß114.30(7)°; Z = 4; space group C2/c. [Ce(Pc(2–)) 2 ] is a sandwich complex in which the cerium Atom is eightfold coordinated by the isoindole nitrogens of the two staggered convex Pc-rings. The u.v.-vis., m.i.r., f.i.r. and resonance Raman spectra are consistent with the structure.