Gesamtinhaltsverzeichnis der „Semesterberichte“ (1932–2007)

Ohne Zusammenfassung     

Dielectric relaxation analysis of starch oligomers and polymers with respect to their chain length

Starch belongs to the polyglucan group. This type of polysaccharide shows a broad β-relaxation process in dielectric spectra at low temperatures, which has its molecular origin in orientational motions of sugar rings via glucosidic linkages. This chain dynamic was investigated for α(1,4)-linked starch oligomers with well-defined chain lengths of 2, 3, 4, 6, and 7 anhydroglucose units (AGUs) and for α(1,4)-polyglucans with average degrees of polymerization of 5, 10, 56, 70, and so forth (up to 3000; calculated from the mean molecular weight). The activation energy (E_a) of the segmental chain motion was lowest for dimeric maltose (E_a = 49.4 ± 1.3 kJ/mol), and this was followed by passage through a maximum at a degree of polymerization of 6 (E_a = 60.8 ± 1.8 kJ/mol). Subsequently, E_a leveled off at a value of about 52 ± 1.5 kJ/mol for chains containing more than 100 repeating units. The results were compared with the values of cellulose-like oligomers and polymers bearing a β(1,4)-linkage. Interestingly, the shape of the E_a dependency on the chain length of the molecules was qualitatively the same for both systems, whereas quantitatively the starch-like substances generally showed higher E_a values. Additionally, and for comparison, three cyclodextrins were measured by dielectric relaxation spectroscopy. The ringlike molecules, with 6, 7, and 8 α(1,4)-linked AGUs, showed moderately different types of dielectric spectra. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 188–197, 2004     

Rheological and physical properties of aliphatic hyperbranched polyesters

The effects of the size (pseudo‐generation number) and nature of end groups on physical and rheological properties were investigated for a series of hyperbranched polyesters based on an ethoxylated pentaerythritol core and 2,2‐bis‐(hydroxymethyl)propionic acid repeat units. The observed linear dependence of the melt viscosity on the molar mass in the high pseudo‐generation‐number limit indicated that entanglement effects were substantially absent. Moreover, the marked influence of end capping of the end groups on the physical and rheological properties suggested that intermolecular interactions were dominated by contacts between the outer shells of the molecules, in which the end groups were assumed to be concentrated. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1218–1225, 2004     

Lower semicontinuity of quasi-convex integrals in BV

Some boundedness properties for an extension operator are proved and used together with techniques of Maly [24], Meyers [29], Fonseca and Müller [13] and Fonseca and Marcellini [12] to obtain lower semicontinuity results in BV for quasiconvex integrals of super-linear growth. Received January 25, 1997 / Accepted October 3, 1997     

Algebraic representation of the linear problem as a method to construct the Darboux-Bäcklund transformation

An effective algorithm to construct the Darboux matrix based on the dressing method is proposed. Our approach consists in representing the linear problem as a system of algebraic constraints on two matrices. The Darboux matrix is determined from the requirement that the Darboux-Bäcklund transformation preserves these constraints. A non-isospectral deformation of the derivative nonlinear Schrödinger equation is discussed as an example.