Irreversible deformation of macromolecular networks

Based upon a thermodynamical approach, the generalized Onsager type of relaxation of van der Waals networks is presented. By linearly and identically coupling the set hidden variables to the network, the memory function of the system can be related to the equilibrium strain-energy function. The relaxation behavior of real networks on stretching can quantitatively be described by means of a distribution of relaxation times known from small strain experiments. Some new and interesting conclusions are discussed as to how the macroscopically non-linear visco-elastic response might be interpreted.     

Intramolecular meerwein reactions of the anthraquinone system. Synthesis,X-ray structural analysis and spectroscopic properties of anthra[9,1-bc:10,5-b'c']tetrahydrodipyran derivatives

Meerwein reactions of 1,5-anthraquinone bis(diazonium hydrogen sulfate) with sufficiently activated olefins, such as acrylonitrile, acrylic esters, methacrylonitrile and its esters, styrene and α-methylstyrene yielded derivatives of the new heterocyclic system anthra[9,1-bc:10,5-b'c']-2,3,7,8-tetrahydrodipyran. Isolation of derivatives was realized and yields enhanced by using dimethyl methylphosphonate as reaction medium. Compounds 5–18 were isolated as mixtures of diastereomers, some of which were separated by crystallization. Proof of structure and stereochemistry was obtained for some of the compounds by X-ray crystallographic analysis. The ¹H- and ¹³C-nmr data provided further support. Surprisingly large chemical shift differences between some of the proton signals of isomers were observed although the two asymmetric centers are far apart through bonds and through space. The mechanism of formation is explained on the basis of redox modulation of a charge transfer complex in which the aliphatic radical attacks the oxygen atom of the anthraquinone. It is proposed to classify this new type of reaction as an intramolecular Meerwein reaction.     

Adsorption of lignosulphonates on polystyrene latex particles from aqueous solution and flocculation of the dispersions by electrolytes

Summary The adsorption isotherms of lignosulphonates with various degrees of sulphonation (0.5, 1,0, 2.0 and 4.0 moles per 840 unit weight of lignin) were measured on polystyrene latex particles from aqueous solution at 25 °C. The results showed that the lignin with the lowest degree of sulphonation gave the highest adsorption. The lignin with 1.0 and 2.0 degrees of sulphonation gave similar adsorption which was lower than that obtained with the half sulphonated lignin. However, further increase in degree of sulphonation resulted in an increase in the adsorption.Adsorption layer thickness measurements showed that the lignosulphonate with half degree of sulphonation gave thicker layers than that with 2.0 moles sulphonation. Increasing electrolyte (NaCl and CaCl,) concentration resulted in a decrease in the adsorbed layer thickness. Microelectrophoresis at 25 °C, showed only small differences in the zeta potential as a function of degree of sulphonation. Addition of electrolytes (KCl, Na₂SO₄ and CaCl₂) showed a reduction in the zeta potential. Flocculation by salts of various valence types, namely KCl, Na₂SO₄ and CaCl₂ showed that the critical flocculation concentration (C.F.C.) decreases in the order KCl > Na₂SO₄ > CaCl₂. The change in degree of sulphonation had only a marginal effect on the C.F.C.

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Zusammenfassung Die Isothermen der Adsorption von Lignosulfonaten mit verschiedenen Sulfonierungsgraden (S = 0,5, 1,0, 2,0 und 4,0 Mole pro 840 Gewichtseinheit des Lignins) an PolystyrolLatex-Teilchen in wäßriger Lösung wurden bei 25 °C gemessen. Hiernach wird Lignin mit den niedrigsten S-Werten am stärksten adsorbiert. Lignine mitS = 1,0 und 2,0 zeigen ähnliche Adsorption; sie ist aber kleiner als die fürS = 0,5. Mit weiter steigendemS nimmt die Adsorption zu.Aus der Messung der Dicke der Adsorptionsschicht folgt, daß fürS = 0,5 größer als fürS = 2,0 ist. Bei wachsendem Zusatz von NaCl oder CaCl₂ fällt ab. Nach Mikroelektrophorese-Messungen bei 25 °C hängt das -Potential nur wenig vonS ab. fällt durch die Gegenwart von KCl, Na₂SO₄ oder CaCl₂ ab. Mit den gleichen Salzen erfolgt eine Ausflockung, wobei die kritische Flockungskonzentration CFC in der Reihenfolge KCl, Na₂SO₄, CaCl₂ abnimmt; CFC ändert sich nur wenig mitS.

     

Massenspektrometrie isomerer Diazaphenanthrene—I

The mass spectra of five diazaphenanthrenes formed by photochemical cyclodehydrogenation of styryl diazines are investigated. It is shown that fragmentation of these compounds starts almost exclusively at the heterocyclic part of the molecule and proceeds by competitive α-cleavage. From the intensity ratios of the ions [M ? H˙]⁺, [M ? HCN]⁺˙, [M ? N₂]⁺˙ and [M ? 2 HCN]⁺˙ generated in this way, each isomer can unequivocally be identified.     

Exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation

The computation of the energy eigenvalues of the one-dimensional time-independent Schrödinger equation is considered. Exponentially fitted and trigonometrically fitted symplectic integrators are obtained, by modification of the first and second order Yoshida symplectic methods. Numerical results are obtained for the one-dimensional harmonic oscillator and Morse potential.AMS subject classification: 65L15Funding by research project 71239 of Prefecture of Western Macedonia and the E.U. is gratefully acknowledged.     

On the average length of lexicographic paths

A bound is given for the average length of a lexicographic path, a definition that is motivated by degeneracies encountered when using the randomized simplex method.