Real analytic curves in Fréchet spaces and their duals

The following results are presented: 1) a characterization through the Liouville property of those Stein manifoldsU such that every germ of holomorphic functions on xU can be developed locally as a vector-valued Taylor series in the first variable with values inH(U); 2) ifT is a surjective convolution operator on the space of scalar-valued real analytic functions, one can find a solutionu of the equationT u=f which depends holomorphically on the parameterz wheneverf depends in the same manner. These results are obtained as an application of a thorough study of vector-valued real analytic maps by means of the modern functional analytic tools. In particular, we give a tensor product representation and a characterization of those Fréchet spaces or LB-spacesE for whichE-valued real analytic functions defined via composition with functionals and via suitably convergent Taylor series are the same.     

Electrochemistry of Prussian Blue in silica sol-gel electrolytes doped with polyamidoamine dendrimers

The inclusion of a generation-4 polyamidoamine (G4-PAMAM) dendrimer in a silica sol-gel yielded a solid electrolyte that was used to encapsulate Prussian Blue (PB), iron(III) hexacyanoferrate(II), and cobalt hexacyanoferrate. The PB was synthesized in the doped silica by sequential immersion of a monolith in 0.1 M K₄Fe(CN)₆, water, and 0.1 M FeCl₃. Inclusion of G4-PAMAM resulted in a nanoporous anion-exchange material with a capacity of 10.1 mmol g^–1, which is about four times greater than the capacity of silica alone. Relative to its G0 counterpart, the G4-PAMAM doped silica increased the rate of formation of PB by a factor of ca. 20. The solid state voltammetry of PB in the doped silica had the usual features for this compound. At 0.1 V vs. a Ag quasi-reference electrode, a reversible reduction was seen; the relationship between current and scan rate was that for a surface-confined redox couple. The quasi-reversible oxidation of PB was observed at 0.85 V. Inclusion of G4-PAMAM increased the lifetime of silica as a solid electrolyte from a few days to at least three months. Raman microprobe mapping analysis demonstrated that PB was homogeneously distributed across the entire width (ca. 1 mm) of the G4-doped monolith with 20-h immersions. Electronic Publication     

Norbornanes. Part 18. Inductive Charge Dispersal in the Solvolyses of 4- and 5-Substituted 2-Norbornyl p-Toluenesulfonates

The solvolysis rates and products of 4- and 5-exo-substituted 2-exo- and 2-endo-norbornyl tosylates 9 and 10 , respectively, are reported. The logarithms of the rate constants (log k) correlate linearly with the inductive constants σ for the substituents. A comparison of the reaction constants p₁ for the 4-, 5-, 6-, and 7-substituted 2-exo- and 2-endo-tosylates 9 , 10 , 1 , and 2 respectively, indicates that inductivity is higher for 2-exo-ionization than for 2-endo-ionization in all series. This observation is attributed to the more favorable alignment of neighbouring C-atoms for dorsal participation in exo-ionization, especially, in the case of C(6).     

Molecular dynamics simulations of polymer transport in nanocomposites

Molecular dynamics simulations on the Kremer-Grest bead-spring model of polymer melts are used to study the effect of spherical nanoparticles on chain diffusion. We find that chain diffusivity is enhanced relative to its bulk value when polymer-particle interactions are repulsive and is reduced when polymer-particle interactions are strongly attractive. In both cases chain diffusivity assumes its bulk value when the chain center of mass is about one radius of gyration R(g) away from the particle surface. This behavior echoes the behavior of polymer melts confined between two flat surfaces, except in the limit of severe confinement where the surface influence on polymer mobility is more pronounced for flat surfaces. A particularly interesting fact is that, even though chain motion is strongly speeded up in the presence of repulsive boundaries, this effect can be reversed by pinning one isolated monomer onto the surface. This result strongly stresses the importance of properly specifying boundary conditions when the near surface dynamics of chains are studied.     

Polyolefins - poly(ethylene oxide) blends: Structure and properties

Structure and properties of polyolefins-poly(ethylene oxide) (PEO) blends were studied by combination of thermal analysis, light microscopy and fluorescence probe technique. Mixing and preparation conditions influence the calorimetric behavior, changing heat and temperature of melting and crystallinity degree of blended polymers. Values of the static mechanical parameters as well as flow characteristic parameters of the blends are lower for the higher PEO fraction in the samples. Fluorescence investigation of pyrene (changes in the vibrational fine structure) showed a nonhomogeneous distribution of the probe molecules between polyolefin and PEO environment. From these data the partition coefficient between polyolefin and PEO phase can be calculated and correlated with the crystallinity changes of the mixture composition.     

Reliability of Deterioration System

Mathematical models of the reliability assessment of a structure treated as the time to the first passage of the capacity which is degrading in the time are presented. Two stochastic models of the structure degradation caused by different factors and two stochastic models of loading are considered. The relationships for calculating the probability of failure for presented models of the structure load and the capacity degradation, are given. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Helical conformations of isotactic polyacetaldehyde and other isotactic polytrihaloacetaldehydes

Minimum potential energy helical conformations for a family of four isotactic polyacetaldehydes have been determined. Our results indicate that all of the polymers form irrational helices. Comparisons have been made with the reported structures for two of these stereoregular polymers based on earlier X-ray diffraction data. c-Axis values associated with the pitch of the helix for polyacetaldehyde and for polytrichloroacetaldehyde (polychloral) were experimentally measured to be 0.48 and 0.51 nm, respectively. Our calculated conformations afforded values for a helix pitch of 0.47 and 0.52 nm, respectively, which derive from a 3.9/1 helix for polyacetaldehyde and a 3.7/1 helix for polychloral. The structure for polytribromoacetaldehyde (polybromal) was predicted to be similar to that for polychloral. For polytrifluoroacetaldehyde (polyfluoral) and polyacetaldehyde, a number of helical conformations with similar energies were found. All of these conformations could be related to the polychloral helical structure. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 1855–1860, 1998     

Multifunctional Mediating System Composed of a Conducting Polymer Matrix,Redox Mediator and Functionalized Carbon Nanotubes: Integration with an Enzyme for Effective Bioelectrocatalytic Oxidation of Glucose

A multifunctional mediating system for bioelectrocatalytic oxidation of glucose is described. It comprises a conducting polymer, poly(3,4‐ethylenodioxythiophene), carbon nanotubes modified with 4‐(pyrrole‐1‐yl) benzoic acid that provide carboxyl groups that aid immobilization of glucose oxidase in a conductive three‐dimensional network, tetrathiafulvalene that mediates electron exchange with the enzyme. This composite produces a system that is capable of effective oxidation of glucose to gluconic acid at pH 7. The current is concentration dependent to at least 60 mM and maintains 77 % of initial response for 35 days. Data supporting the utility of this system for electrochemical sensing and biofuel cell technology are presented.