Zu dem Borelschen Satz über die asymptotische Verteilung der Ziffern in Dezimalbrüchen

Ohne Zusammenfassung     

Über die Verteilung der quadratischen Reste

Ohne Zusammenfassung     

Wissenschaftliche und technische Sammelreferate

Ohne Zusammenfassung     

Über gewisse trigonometrische Integrale. II

Ohne Zusammenfassung     

Solid‐State NMR investigations of anhydrous proton‐conducting acid–base poly(acrylic acid)– poly(4‐vinyl pyridine) polymer blend system: A study of hydrogen bonding and proton conduction

NMR studies of the structure and dynamics of a system composed of the acidic polymer poly(acrylic acid) (PAA) and the basic polymer poly(4‐vinyl pyridine) (P4VP) are presented. This system aims at the application of anhydrous proton‐conducting membranes that can be used at elevated temperatures at which the proton conduction of hydrated membranes breaks down. The ¹H NMR measurements have been preformed under fast magic angle spinning (MAS) conditions to achieve sufficient resolution and the applied ¹H NMR methods vary from simple ¹H MAS to double‐quantum filtered methods and two‐dimensional ¹H double‐quantum spectroscopy. The dynamic behavior of the systems has been investigated via variable temperature ¹H MAS NMR. ¹³C cross‐polarization MAS NMR provides additional aspects of dynamic and structural features to complete the picture. Different types of acidic protons have been identified in the studied PAA‐P4VP systems that are nonhydrogen‐bonded free acidic protons, hydrogen‐bonded dicarboxylic dimers, and protons forming hydrogen bonds between carboxylic protons and ring nitrogens. The conversion of dimer structures in dried PAA to free carboxylic acid groups is accomplished at temperatures above 380 K. However, the stability of hydrogen‐bonding strongly depends on the hydration level of the polymer systems. The effect of hydration becomes less apparent in the complexes. An inverse proportionality between hydrogen‐bonding strength and proton conduction in the PAA‐P4VP acid–base polymer blend systems was established. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 138–155, 2009