Polyelectrolyte complex formation between poly(diallyldimethyl-ammonium chloride) and copolymers of acrylamide and sodium-acrylate

 The interaction between oppositely charged polyelectrolytes, in this study poly(diallyldimethylammonium chloride) (PDADMAC) and copolymers of acrylamide and sodium-acrylate differing in their chain length and charge density parameter (ξ) was investigated in relation to the molar charge ratio of anionic to cationic charges (n ₋/n ₊). The molecular weights of the polyelectrolytes used were 2.9·10⁵g/mol for PDADMAC and for the polyacrylamide copolymers 14 ·10⁶g/mol as well as 5·10⁵g/mol obtained by ultrasonic degradation of the high molecular weight copolymers. The charge density parameters of the polyanions used (ξ ^PR ) varied between 0.14 and 0.64. Complexation between PDADMAC and high molecular weight polyanions leads mainly to macroscopic phase separation whereas the degraded polyanions and PDADMAC formed soluble complexes as well as stable dispersions, if charge excess was available. Precipitates and dispersions were characterized by several methods such as element analysis, thermogravimetry, pyrolysis-GC/MS, PEL titration, ζ-potential measurements, determination of turbidity, particle size measurements and determination of carbon content (TOC).  All precipitated complexes include about 20% water and are of 1:1 stoichiometry concerning ionic binding. Investigations of dispersions confirm 1:1 stoichiometry of complex particles stabilized by excess polyelectrolyte and soluble complexes. It was also found that the particle size can be varied via the charge density parameter of the polyanions used in the range of negative charge excess. Received: 21 June 2001 Accepted: 9 October 2001     

Pushing the envelope of the test functions in the Szegö and Avram–Parter theorems

The Szegö and Avram–Parter theorems give the limit of the arithmetic mean of the values of certain test functions at the eigenvalues of Hermitian Toeplitz matrices and the singular values of arbitrary Toeplitz matrices, respectively, as the matrix dimension goes to infinity. The question on whether these theorems are true whenever they make sense is essentially the question on whether they are valid for all continuous, nonnegative, and monotonously increasing test functions. We show that, surprisingly, the answer to this question is negative. On the other hand, we prove the two theorems in a general form which includes all versions known so far.     

An organocatalytic approach to 2-hydroxyalkyl- and 2-aminoalkyl furanes

The first enantioselective methodology for the synthesis of electron-poor 2-hydroxyalkyl- and 2-aminoalkyl furanes is demonstrated in this study. It utilizes a highly stereoselective organocatalytic one-pot reaction cascade: epoxidation or aziridination of α,β-unsaturated aldehydes followed by Feist-Be?nary reaction of various 1,3-dicarbonyl compounds to give the target furanes. This efficient multibond forming reaction cascade benefits from low catalyst loadings and readily available starting materials. Furthermore, the possibility to interrupt the reaction sequence at the stage of the corresponding optically active 2-hydroxyalkyl- and 2-aminoalkyl 2,3-dihydrofuranes with three stereogenic centers is also presented. Finally, models which account for the formation of the optically active 2,3-dihydrofuranes are proposed.     

Duality respecting representations and compatible complexity measures for gammoids

We show that every gammoid has special digraph representations, such that a representation of the dual of the gammoid may be easily obtained by reversing all arcs. In an informal sense, the duality notion of a poset applied to the digraph of a special representation of a gammoid commutes with the operation of forming the dual of that gammoid. We use these special representations in order to define a complexity measure for gammoids, such that the classes of gammoids with bounded complexity are closed under duality, minors, and direct sums.