Quasi-elastic light scattering from polymethylmethacrylate in a good and a theta solvent

Summary Translational diffusion coefficients of 9 PMMA samples have been measured by quasi-elastic light scattering in acetone at 20 °C and butylchloride at 34.5 °C (theta solvent). The coil expansion due to excluded volume effects has been characterized by the expansion factor _h of the hydrodynamic radiusR _h . _h has been found to reach avalue well below 1.0 atM _w M _o (the monomer). By means of CowieBywater plots on the other hand the unperturbed chain dimensions are shown being virtually identical in both solvents. Thus, the _h < 1.0 values is the result of differences in the hydrodynamic radii of the segments in the two solvents. The ratioS/R =S ² =^1/2/R _b is found being lower than predicted by theory. Reasons for this behaviour are discussed. The concentration dependence ofD has been evaluated on the basis of a theory by Pyun and Fixman. A reasonably good agreement with the simple models of a hard and a soft sphere in a good and a poor solvent, respectively, is observed.

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Zusammenfassung Die translatorische Diffusionskoeffizienten von 9 verschiedenen PMMA Proben wurden in Aceton bei 20 °C und in Butylchlorid bei 34.5 °C (Thetatemperatur)|durch quasielastische Lichtstreuung bestimmt. Die durch das ausgeschlossene Volumen verursachte Knäuelexpansion wurde durch einen Expansionsfaktor ah des hydrodynamischen RadiusR _h beschrieben. _h erreicht beiM _w M _o (MonomerMolekulargewicht) Werte deutlich unterhalb von 1.0. Aus der Cowie-Bywater Auftragung wurden andererseits keine unterschiedlichen ungestörten Dimensionen in den beiden Lösungsmitteln erhalten. Hieraus wird der Schluß gezogen, daß _h < 1.0 eine Folge unterschiedlicher hydrodynamischer Radien der Segmente ist. Das VerhältnisS/R =S ²> ^1/2/R _h erwies sich nach den Messungen kleiner als die Theorie erwarten ließ. Mögliche Gründe für dieses Verhalten werden diskutiert. Die Konzentrationsabhängigkeit der Diffusionskoeffizienten wurde anhand der Theorie vonPyun undFixman ausgewertet. Es wurde eine zufriedenstellende Übereinstimmung mit den von den Autoren verwendeten einfachen Modellen der harten bzw. weichen Kugel in dem guten bzw. schlechten Lösungsmittel gefunden.

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Dedicated to Professor Dr. G. Rehage on the occasion of his 60th birthday.

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With 8 figures and 4 tables     

Flow birefringence of short-chain molecules: Cellulose tricarbanilates in benzophenone

Measurements of flow birefringence of cellulose tricarbanilates were carried out on nine fractions (0.27 × 10⁵ < M ≤ 12 × 10⁵) in a temperature range of 55–110°C, with benzophenone as a matching solvent (dn/dc = 0). The ratio of Maxwell constant to intrinsic viscosity, which has been found to be independent of molecular weight for the limiting case of Gaussian molecules, is successfully interpreted as a function of molecular weight in terms of the recent theory of Gotlib and Svetlov (based on the wormlike chain model of Kratky and Porod). From the measurements at 55°C a number of 36.6 monomer units per random link is deduced. This is in accord with results of small-angle x-ray scattering. For the extinction angle curves a clear transition is observed from rodlike to statistical molecules when the molecular weight is increased. At high molecular weights the master curves obtained for anionic polystyrenes and cellulose tricarbanilates coincide. Implications of this observation on the kinetic stiffness of the cellulose tricarbanilate chain are discussed. The intrinsic viscosity-molecular weight relationship is considered. From a comparison with the results of the theory of Eizner and Ptitsyn it is concluded that the cellulose tricarbanilate chain must be highly solvated in benzophenone.     

Compactness via symmetrization

Consider two types of translation-invariant functionals and on , and a sequence of functions f_n whose corresponding symmetric rearrangements are convergent. We show that f_n themselves converge up to translations if either or . These compactness results lead to applications in variational problems and stability problems in stellar dynamics.