A general formalism of deriving the pair potential of polymer chains for arbitrary interaction potentials between isolated chain segments at and close to the theta-point

A formalism has been worked out which allows to transform any non-punctiform segment-segment potential of isolated polymer segments ε of fairly short-ranged character into the pair-potentialU operating between linear polymer chains with a certain reference to the arguments as they have been originally put forward byFlory andKrigbaum. Although no restrictions are made in the derivation as to the repulsive or attractive contribution of the segment-segment potential ε because of some known general deficiencies of theFlory-Krigbaum treatment for exclusively repulsive interaction, the resulting equations are primarily intended to describe the thermodynamic situation at and close to the θ-point where repulsion and attraction—though working at different ranges of segment separation—cancel. As the equation derived is somewhat complicated two different approximate forms have been developed: The first one is based on aTaylor series expansion retaining terms up to the fourth order which allows to characterizeU by the second and the fourth moment of the pair segment-segment distribution function, β and γ (β being the so-called binary cluster integral of segment-segment interaction, which is considered to be zero for θ-conditions). In this caseU may be represented by an expression of the general form $$U/kT = A(1 - BR^2 )\exp \{ - bR^2 \} .$$ The second method is based on a separate integration over the repulsive and attractive ranges of ε giving the repulsive (U ₊) and the attractive (U _?) part ofU finally after some approximations leading to an equation of the general form $$U/kT = (U_ + + U_ - )/kT = A_1 \exp \{ - b_1 R^2 \} - A_2 \exp \{ - b_2 R^2 \} .$$ In both cases the knowledge of the exact form of ε is dispensable, only β and γ—or for the second case their repulsive (β₊ and γ₊) and attractive (β_? and γ_?) parts have to be known. It is shown that the approximations are in excellent accordance with the exact form so that they may be conveniently used to describe pair potentials of polymer chains and to analyze pair potentials of segment-segment interactions under the limitations and conditions indicated.     

Ansamycine, 5. Mitt., Chemie der Metacycloprodigiosine

In order to obtain a better partition of a prodigiosin derivative in biological media, two hydroxy groups were introduced into theansa-part of the molecule. The synthesis of the title compound is described in detail.     

Efficient kinetic resolution of a racemic 7-membered biaryl lactone: enantioselective synthesis of 2,2′-dihydroxymethyl-1,1′-binaphthyl

A novel pathway to enantiomerically pure 2,2′-dihydroxymethyl-1,1′-binaphthyl is described, through kinetic resolution of its racemic 7-membered biaryl lactone precursor. Oxazaborolidine-assisted borane reduction of this lactone proceeds with very high enantioselectivity (k_rel=50). For optimum results on a preparative scale, a ‘three fractions strategy’ is suggested, which combines kinetic resolution and fractional crystallization and leads to both atropisomers in high enantiomeric excess.     

Electrophoretic clean-up of organic acids from coffee for the GC/MS analysis

The clean-up presented here includes a free flow field step electrophoresis followed by ultrafiltration. Thus, organic acids can be separated from non-acidic and high-molecular compounds in roasted and instant coffee. The acids are identified by gas chromatography/mass spectrometry after freeze-drying and trimethylsilylation. With the method presented, 31 acids could be identified in commercial roasted coffee blends and in instant coffee, among them for the first time in coffee: 3-hydroxypropionic, 2-oxobutyric, glyceric, 2,4-dihydroxybutyric, 5-hydroxymethylfuran-2-carboxylic and 2-hydroxyglutaric acid.     

Die Klassengruppen quadratischer und kubischer Zahlkörper und die Selmergruppen gewisser elliptischer Kurven

For k∈?\0 we define the elliptic curve A_k, by the equation: Y²=X³+k. Let C(k) be the class group of \(K_o = Q(\sqrt[6]{k})\) . If k is a square we find a close connection between the elements of order 2 of the Selmer group of A_k and C(k); there is a corresponding connection between the elements of order 3 if k is a cube and satisfies some additional conditions. The main tool to prove the statements is the global and local Galois cohomology of elliptic curves; it seems remarkable that nearly no “explicit” number theory has to be used.     

Two-photon four-level hologram recording in poly-(alkyl-α-cyanoacrylates)

We have investigated the suitability of poly-(alkyl--cyanoacrylates) (p-(alkyl-CAc)) for two-photon four-level holographic recording. It is shown that these materials follow indeed a two-photon four-level mechanism with the second absorption step in the near infrared. Light induces the polymerization of residual monomer in the matrix. The reaction is associated with positive density changes. The sensitivity ofp-(alkyl-CAc) depends strongly on composition and age of the sample. Maximum sensitivities achieved are comparable to the so far best-known two-photon four-level ir-sensitive systems.