Extension of the chain‐end,free‐volume theory for predicting glass temperature as a function of conversion in hyperbranched polymers obtained through one‐pot approaches

Compared with linear polymers, more factors may affect the glass‐transition temperature (T_g) of a hyperbranched structure, for instance, the contents of end groups, the chemical properties of end groups, branching junctions, and the compactness of a hyperbranched structure. T_g's decrease with increasing content of end‐group free volumes, whereas they increase with increasing polarity of end groups, junction density, or compactness of a hyperbranched structure. However, end‐group free volumes are often a prevailing factor according to the literature. In this work, chain‐end, free‐volume theory was extended for predicting the relations of T_g to conversion (X) and molecular weight (M) in hyperbranched polymers obtained through one‐pot approaches of either polycondensation or self‐condensing vinyl polymerization. The theoretical relations of polymerization degrees to monomer conversions in developing processes of hyperbranched structures reported in the literature were applied in the extended model, and some interesting results were obtained. T_g's of hyperbranched polymers showed a nonlinear relation to reciprocal molecular weight, which differed from the linear relation observed in linear polymers. T_g values decreased with increasing molecular weight in the low‐molecular‐weight range; however, they increased with increasing molecular weight in the high‐molecular‐weight range. T_g values decreased with increasing log M and then turned to a constant value in the high‐molecular‐weight range. The plot of T_g versus 1/M or log M for hyperbranched polymers may exhibit intersecting straight‐line behaviors. The intersection or transition does not result from entanglements that account for such intersections in linear polymers but from a nonlinear feature in hyperbranched polymers according to chain‐end, free‐volume theory. However, the conclusions obtained in this work cannot be extended to dendrimers because after the third generation, the end‐group extents of a dendrimer decrease with molecular weight. Thus, it is very possible for a dendrimer that T_g increases with 1/M before the third generation; however, it decreases with 1/M after the third generation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1235–1242, 2004     

Viscosity,particle size distribution,and structural investigation of tetramethyloxysilane/2‐hydroxyethyl methacrylate sols during the sol–gel process with acid and base catalysts

The tetramethoxysilane (TMOS)/2‐hydroxylethyl methacrylate (HEMA) hybrid gels were synthesized with acid and base catalysts, via the in situ polymerization of HEMA, with and without the cosolvent methanol. With methanol in the TMOS/HEMA sol, the enhanced esterification and depolymerization reactions of the silanols resulted in a slower growth of silica particles. The silica particles that were synthesized with an acid catalyst were less than 40 nm. The thermal resistance of the poly(2‐hydroxyethyl methacrylate) (PHEMA) chains was enhanced by the addition of colloidal silica. The Fourier transform infrared characterizations and the exothermal peaks on the differential scanning calorimetry traces of these hybrid gels indicated chemical hybridization occurring as a result of condensation of the colloid silica and PHEMA at higher temperatures. Hence, the residual weight content of the hybrid gel after its synthesis with the base catalyst was even higher than the content of TMOS in the hybrid sol. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3476–3486, 2004     

Influence of surfactant and lipid chain length on the solubilisation of phosphatidylcholine vesicles by micelles comprised of polyoxyethylene sorbitan monoesters

Photon correlation spectroscopy and freeze-fracture electron microscopy have been used to determine the ability of a range of micelle-forming, polyoxyethylene (20) sorbitan monoesters (Tweens) to solubilise vesicles prepared from phosphatidylcholines of different acyl chain lengths and degrees of saturation with a view to rationalising (in terms of their membrane toxicity) which of the micelle-forming surfactants to use as drug delivery vehicles. The phosphatidylcholines used were dimyristoyl-, dipalmitoyl-, distearoyl- and dioleoylphosphatidylcholine (DMPC, DPPC, DSPC and DOPC, respectively) while the nonionic polyoxyethylene sorbitan monoesters studied were polyoxyethylene (20) sorbitan monolaurate (Tween 20), a 9:1 weight ratio mixture of polyoxyethylene (20) sorbitan monopalmitate and monostearate (Tween 40), a 1:1 weight ratio mixture of polyoxyethylene (20) sorbitan monopalmitate and monostearate (Tween 60), and polyoxyethylene (20) sorbitan monooleate (Tween 80). The ability of the Tween micelles to solubilise phospholipid vesicles was found to depend both upon the length of the surfactant acyl chain and the length of the acyl chains of the phospholipid comprising the vesicle. Vesicles composed of long saturated diacyl chain phospholipids, namely DSPC and DPPC, were the most resistant to solubilisation, while those prepared from the shorter acyl chained DMPC were more readily solubilised. In terms of their solubilisation behaviour, vesicles made from phospholipids containing long, unsaturated acyl chains, namely DOPC behaved more akin to those vesicles prepared from DMPC. None of the Tween surfactants were effective at solubilising vesicles prepared from DPPC or DSPC. In contrast, there were clear differences in the ability of the various surfactants to solubilise vesicles prepared from DMPC and DOPC, in that micelles formed from Tween 20 were the most effective solubilising agent while those formed by Tween 60 were the least effective. As a consequence of these observations it was considered that Tween 60 was the surfactant least likely to cause membrane damage in vivo and, therefore, is the most suitable surfactant for use as a micellar drug delivery vehicle.     

A flexible and generic approach to dynamic modelling of supply chains

In this paper, we present a new modelling approach for realistic supply chain simulation. The model provides an experimental environment for informed comparison between different supply chain policies. A basic simulation model for a generic node, from which a supply chain network can be built, has been developed using an object-oriented approach. This generic model allows the incorporation of the information and physical systems and decision-making policies used by each node. The object-oriented approach gives the flexibility in specifying the supply chain configuration and operation decisions, and policies. Stochastic simulations are achieved by applying Latin Supercube Sampling to the uncertain variables in descending order of importance, which reduces the number of simulations required. We also present a case study to show that the model is applicable to a real-life situation for dynamic stochastic studies.     

On the Essential Self-Adjointness of Wick Powers of Relativistic Fields and of Fields Unitary Equivalent to Random Fields

The essential self-adjointness on a natural domain of the sharp-time Wick powers of the relativistic free field in two space-time dimension is proven. Other results on Wick powers are reviewed and discussed.     

On a class of preconditioners for solving the Helmholtz equation

In 1983, a preconditioner was proposed [J. Comput. Phys. 49 (1983) 443] based on the Laplace operator for solving the discrete Helmholtz equation efficiently with CGNR. The preconditioner is especially effective for low wavenumber cases where the linear system is slightly indefinite. Laird [Preconditioned iterative solution of the 2D Helmholtz equation, First Year's Report, St. Hugh's College, Oxford, 2001] proposed a preconditioner where an extra term is added to the Laplace operator. This term is similar to the zeroth order term in the Helmholtz equation but with reversed sign. In this paper, both approaches are further generalized to a new class of preconditioners, the so-called “shifted Laplace” preconditioners of the form Δφ−k²φ with . Numerical experiments for various wavenumbers indicate the effectiveness of the preconditioner. The preconditioner is evaluated in combination with GMRES, Bi-CGSTAB, and CGNR.     

Three-dimensional structure of Saccharomyces cerevisiae inorganic pyrophosphatase complexed with cobalt and phosphate ions

Crystals of Saccharomyces cerevisiae inorganic pyrophosphatase suitable for X-ray diffraction study were grown by cocrystallization of the enzyme with cobalt chloride and imidodiphosphate. Saccharomyces cerevisiae is a metal-dependent enzyme which catalyzes hydrolysis of inorganic pyrophosphate to orthophosphate. The three-dimensional structure of this enzyme was solved by the molecular-replacement method and refined at 1.8 Å resolution to an R factor of 19.5%. Cobalt and phosphate ions were revealed in the active centers of both identical subunits (A and B) of the pyrophosphatase molecule. In subunit B, a water molecule was found between two cobalt ions. It is believed that this water molecule acts as an attacking nucleophile in the enzymatic cleavage of the pyrophosphate bond. It was demonstrated that cobalt ions and a phosphate group occupy only part of the potential binding sites (two chemically identical and crystallographically independent subunits have different binding sites). The arrangement of ligands and the structure of the nucleophile-binding site are discussed in relation to the mechanism of action of the enzyme and the nature of the metal activator.     

Krylov subspaces and the analytic grade

Typical behaviour of the solution of a linear system of equations obtained iteratively by Krylov methods can be characterized by three stages. Initially the residual diminishes steadily; this is followed by stagnation and finally rapid convergence near the algebraic grade. This study examines this behaviour in terms of the concepts of approximately invariant subspace and what we have called the analytic grade of a Krylov sequence. It is shown how the small Ritz values play a vital role in the convergence and how this knowledge helps in the construction of an effective preconditioner. Copyright © 2004 John Wiley & Sons, Ltd.     

Photoproduction of jets and heavy flavors at future polarized ep-colliders

We study photoproduction of jets and heavy flavors in a polarized collider mode of HERA and in polarized ep collisions at √S ≈ GeV. We examine the sensitivity of the cross sections and their asymmetries to the proton’s polarized gluon distribution and to the completely unknown parton distributions of longitudinally polarized photons.