Effects of surface nonlinear interactions on the local critical behavior

The energy spectrum and the wave functions of quantum wells in strong magnetic fields parallel to the potential walls are calculated analytically by means of a new, graph supported method. This Arrow Train Method allows to solve the recurrence relations which originate in the evaluation of eigenvalue determinants of infinite order. The energy eigenvalues for infinite barrier height are computed as a power series in the magnetic fieldB and the center of orbit coordinatez ₀. The power series is evaluated up to the 18th order inB ² for the first four levels and for cyclotron radii comparable to or considerable less than the well width. The corresponding wave functions and the field dependent center of mass shifts are obtained.Work supported in part by the Deutsche Forschungsgemeinschaft     

On the diffusion field in the neighborhood of two identical spheres

Summary Under steady state conditions the reduction in the diffusive flux into a sphere due the presence of a neighboring, identical sphere is calculated. Taking the flux into a sphere as 1 when the particles are at infinite separation, the flux decreases to a minimum value of 0.693 when the spheres are touching.

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Zusammenfassung Unter stationären Bedingungen wird die Abnahme des Diffusionsflusses in eine Kugel, bedingt durch eine benachbarte identische Kugel, berechnet.Wird der Diffusionsfluß in eine Kugel gleich 1 gesetzt, wenn die Partikel unendlich weit voneinander entfernt sind, so nimmt der Diffusionsfluß auf einen Minimalwert von 0,693 ab, wenn sich die Kugeln berühren.

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With 2 figures     

Optical frequency doubling of a single-mode dye laser in an external ring resonator

Optical frequency doubling of a single-mode cw Rhodamin 6G ring dye laser is performed with a thin angle-tuned LiIO₃ Brewster cut crystal in a stabilized passive ring resonator. A conversion efficiency of =5 mW uv/320 mW fundamental input power was achieved at =603 nm.     

Umsetzung von hydrobromiertem 1,4-Polybutadien mit lithiumorganischen Verbindungen

Ohne ZusammenfassungMit 1 Abbildung und 1 Tabelle     

Eine semiempirische Gleichung zur Beschreibung des Lösungsmitteleinflusses auf Statik und Kinetik chemischer Reaktionen. Teil I

A model has been developed for calculating the enthalpy, entropy and free energy change associated with the creation of cavities in a liquid the size of which corresponds to the volume occupied by a solvent molecule. The molar enthalpy change H _cav equals the molar enthalpy of vaporization of the liquid, the free energy change G _cav is given by G _cav=–RT ln (V _m ·p _eq /RT) (V _m =molar volume,p _eq =equilibrium vapor pressure) and is related to the standard free energy of vaporization. This relationship provides an estimate of the free energy of cavity formation required to accomodate a substrate in the liquid. It has been shown, that the free energy of solvation of a substrate can be dissected into different contributions accounting for (1) the concentration dependence of partial molar free energy quantities, (2) the formation of holes in the solvent, (3) the existence of specific, short range solute-solvent interactions and (4) the dielectric polarization of the medium. Application of this concept leads to an equation of the general form G ^S –G ^R =a(DN ^S –DN ^R )+b(AN ^S –AN ^R )+c(G _vp ^oS –G _vp ^oR ), where G represents the free energy of reaction or activation,DN the donor number,AN the acceptor number and G _vp ^o the standard free energy of vaporization of a solventS and a reference solventR, resp.

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Odd/even effect in the chain length on the enthalpy of micellization of gemini surfactants in aqueous solution

The micellization properties of cationic symmetric gemini surfactants, [CmH(2m+1)(CH3)2N(CH2)6N(CH3)2CmH(2m+1)]Br2 (designated as CmC6CmBr2, with m = 7, 8, 9, 10, 11, 12, and 16), has been investigated by isothermal titration microcalorimetry. The critical micelle concentration (CMC) and enthalpy of micellization (DeltaHmic) were determined from calorimetric titration curves. The linear decreasing of log CMC with increasing the length of the hydrophobic chain is consistent with an increase in the hydrophobicity of the alkyl chain. Interestingly, with increasing the length of the alkyl chain, the DeltaHmic values of the surfactants with even numbered alkyl chains vary from endothermic to exothermic, whereas the DeltaHmic values of the surfactants with odd numbered alkyl chains are all endothermic and tend to become more endothermic. The pronounced even/odd effect in DeltaHmic is discussed with respect to the "donor-acceptor" interaction.     

Untersuchung der Temperaturabhängigkeit derg ik -Tensoren von Polyäthyleneinkristallen

Zusammenfassung Es wurden die Kristallitgröße und die Änderungen der parakristallinen Gitterstörungen aus den Linienbreiten des Röntgenweitwinkeldiagramms von lösungskristallisiertem linearem Polyäthylen bei den Temperaturen 15°K, 73°K, 173°K und Zimmertemperatur bestimmt. Es wurde eine Zunahme der Gitterstörungen mit fallender Temperatur gefunden.

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Summary The crystallite size and the paracrystalline distortions in polyethylene single crystals were evaluated by the measurement of the linewidth in the X-ray wide angle diagram at four different temperatures (15°K, 73°K, 173°K and 297°K). An increase of the lattice distortions with decreasing temperature was found.

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Vorgetragen auf der Arbeitssitzung des Fachausschusses Physik der Hochpolymeren in der Frühjahrstagung 1970 des Regionalverbandes Hessen-Mittelrhein-Saar der Deutschen Physikalischen Gesellschaft in Darmstadt, 10.–13. März 1970.     

Die Schmelzdiagramme der Systeme CsN3/Zn(N3)2 und KN3/Zn(N3)2

The phase diagrams of the systems CsN₃/Zn(N₃)₂ and KN₃/Zn(N₃)₂ have been obtained employing the microscopic technique ofL. Kofler andA. Kofler. Within the system CsN₃/Zn(N₃)₂ three eutectics at 148°C, 142°C, and 210°C were found. Besides Cs₂Zn(N₃)₄, melting incongruently in the interval 153°C to 170°C, there exist two further compounds of the most probable composition Cs₃Zn₂(N₃)₇ and CsZn₂(N₃)₅, melting congruently at 170°C and 210°C, resp. In the system KN₃/Zn(N₃)₂ there exist two eutectics at 203°C and 172°C and two compounds, one of them, i.e. K₂Zn(N₃)₄, melting congruently at 206°C, the other one, with composition KZn₃(N₃)₇ or KZn₄(N₃)₉, melting incongruently at 210°C.

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Herrn Professor Dr.Heribert Grubitsch zum 70. Geburtstag gewidmet.     

Über einige Eigenschaften von Zinkphosphiten mit Berücksichtigung ihrer Wasserstoffbrückenbindung

Zinc phosphites ZnPHO₃·2.5 H₂O, Zn₂H₂P₃H₃O₉·H₂O, Zn₃H₄P₅H₅O₁₅·1.5 H₂O, ZnH₂H₂P₂H₂O₆ have been studied at higher temperatures and by X-rays and molecular spectroscopy. Hydrates ZnPHO₃·2.5 H₂O and Zn₂H₂P₃H₃O₉·H₂O, when heated, yield an anhydrous salt. Thermal decomposition of dihydrogen triorthophosphite and tetrahydrogen pentaorthophosphite leads, before oxidation of the anion, to a mixture of zinc phosphite ZnPHO₃ and dihydrogen diorthophosphite ZnH₂P₂H₂O₆ and then after loss of water of constitution dihydrogen diorthophosphite converts to zinc diphosphite ZnP₂H₂O₅. The results of the thermal decomposition study were confirmed by X-ray investigation. Anhydrous zinc dihydrogen triorthophosphite Zn₂H₂P₃H₃O₉ and zinc diphosphite ZnP₂H₂O₅ were hitherto unknown. Infrared spectra confirmed the existence of hydrogen bonding in all the phosphites studied and in the case of zinc phosphite ZnPHO₃·2.5 H₂O exhibited a symmetry decrease of the anion PHO₃ ^2– from the point group C_3v to C_s. In the crystal lattice of ZnPHO₃·2.5 H₂O hydrogen bonding by water molecules participates, with polyorthophosphites hydrogen bonding shares in the production of anions and in the case of their hydrates there is in addition hydrogen bonding by water molecules.

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Hydroxybromierung und Methoxybromierung von (Z)-Cycloocten

In addition totrans-2-bromocyclooctanol andtrans-1,2-dibromocyclooctane,cis-4-bromocyclooctanol,cis-1,4-dibromocyclooctane,trans-1,4-dibromocyclooctane, and (Z)-5-bromocyclooctene are obtained, when (Z)-cyclooctene is treated with N-bromosuccinimide in the presence of water. Similarly the methoxybromination of (Z)-cyclooctene gives transanular products.