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     

On Genuine Bernstein–Durrmeyer Operators

We continue the studies on the so–called genuine Bernstein–Durrmeyer operators U _n by establishing a recurrence formula for the moments and by investigating the semigroup T(t) approximated by U _n . Moreover, for sufficiently smooth functions the degree of this convergence is estimated. We also determine the eigenstructure of U _n , compute the moments of T(t) and establish asymptotic formulas. Received: January 26, 2007.     

Raman spectroscopic investigations of the structure and phase transitions of liquid crystalline lead(II) alkanoates

Lead(II) alkanoates with even chain lengths from octanoate to octadecanoate have been investigated by Raman spectroscopy. In the low frequency region, transverse and longitudinal acoustical modes (TAM, LAM) have been assigned. It was shown that LAM-1 is the vibration of the double chain with the node of the vibration in the Pb²⁺ layer. A fully extended conformation of the chains in the low temperature phase was confirmed. The frequencies and intensities of the LAMs as compared with those of the alkanes and the fatty acids led to an estimate of the force constant and polarizability of the Pb²⁺ -COO^- bond relative to the C-C bond. The defects at the chain ends were investigated in the ρ(CH₃) and v(CC) region. For the intermediate (CM) phase, both the Pb²⁺ layer distance reduction and the chain length independent enthalpy contributions can be attributed mainly to defects at the chain ends.     

R-Matrices for Leibniz Algebras

Leibniz agebras are a generalization of Lie algebras, where no symmetry properties of the bracket are required. In this Letter we introduce a notion of R-matrices for this structure and the related Yang–Baxter equations, and discuss some of their basic properties.     

Characterisation of adsorbed layers on sulphide minerals by photoelectron spectroscopy

The systems galena/2-mercaptobenzothiazole (MBT) and pyrite/MBT have been studied using synchrotron radiation excited photoelectron spectroscopy (SRXPS). The chemisorption of MBT and the multilayer formation of 2,2′-dithiobis(benzothiazole) (BBTD) are evidenced by additional structures, observed beside the substrate signals, in the S2p-spectra of cleaved mineral surfaces after adsorption of MBT. The amount of the complex remains constant at concentrations as high as 10^–5 mol/L whereas the amount of BBTD increases. From the dependence of the adsorbate intensities on the excitation energy the conclusion can be drawn that an overlayer of BBTD on a chemisorbed layer of MBT is formed. The very weak adsorption of MBT on pyrite in alkaline solutions may explain the selective flotation of galena from pyrite in alkaline media.     

Electron screening in backward elastic scattering

Abstact: The elastic scattering cross sections, σ (E,θ), for the systems He+Ta and He+W have been measured at θ_lab=165° and E _lab=76.1 keV to 3.988 MeV using targets with a thickness of a few atomic layers. The results are smaller than the results given by the Rutherford scattering law, σ_R(E,θ), due to the effects of electron screening and can be described by σ(E,θ)/σ_R(E,θ)=(1+U_e/E)⁻¹, where U _e is an atomic screening potential energy. The deduced average value, U _e=28 ± 3 keV, is consistent with the Moliére- and Lenz-Jensen-models as well as electron binding energies. Received: 25 May 1998