Sulfonation of polystyrene: Toward the “ideal” polyelectrolyte

Sulfonation of narrow polydispersity polystyrene, PS, standards remains the method of choice for generating polystyrene sulfonate, PSS, samples with defined composition. Although a variety of sulfonation techniques have been described, relatively little is reported on the material obtained, which is used for so many studies on the fundamental behavior of polyelectrolytes. Here, we show that powdered polystyrene treated with concentrated sulfuric acid (96%) at 90 °C without catalyst yields fully sulfonated PSS. Extensive characterization with ¹H and ¹³C NMR as well as size exclusion chromatography coupled with static and dynamic light scattering shows no evidence of sulfone crosslinking or chain degradation under the conditions used. Though mono‐sulfonated as soon as it dissolves in the acid, the PSS contains about 6% meta substitution. Sulfonation kinetics for this heterogeneous reaction depend strongly on particle size, sulfuric acid content and temperature. For preparing perdeuterated PSS from the corresponding PS it is essential to employ D₂SO₄, as about half of the aromatic units undergo H/D exchange during sulfonation. The remaining ortho H/D may be exchanged with extended exposure to the concentrated sulfuric acid, but the meta site is deactivated. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2416–2624     

Nitroxide mediated synthesis of low dispersity random copolymers for low‐loss optical waveguides

Candidate materials for low‐loss optical waveguides based on poly(glycidyl methacrylate‐ran‐pentafluostyrene) [P(GMA‐ran‐PFS)] copolymers were synthesized by nitroxide mediated polymerization (NMP) initiated with BlocBuilder^® [N‐(2‐methylpropyl)‐N‐(1‐diethlphosphono‐2,2‐dimethylpropyl)‐O‐(2‐carboxylprop‐2‐yl) hydroxylamine] bearing a succinimidyl ester group (NHS‐BlocBuilder) at 90 °C in 1,4 dioxane. The copolymerizations yielded copolymers with low dispersity M_w/M_n between 1.2 and 1.4. The core structure of single‐mode channel waveguides was fabricated by direct UV lithographic patterning. The copolymers with low M_w/M_n resulted in line width roughness (LWR) of about 0.16 μm, whereas LWR of copolymers with M_w/M_n=3.5 but similar compositions was about 0.5 μm. The improvement in microstructural control allotted by NMP permitted finer pattern replication for copolymers desired for optical waveguides, as suggested for photoresist polymers. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2970–2978     

ELASTIC CALCULATION OF STRESSES IN RINGS USING AIRY STRESS FUNCTION

Stress calculation formulae for a ring have been obtained by using Airy stress function of the plane strain field with the decomposition of the solutions for normal stresses of Airy biharmonic equation into two parts when it is loaded under two opposite inside forces along a diameter. One part should fulfill a constraint condition about normal stress distribution along the circumference at an energy valley to do the minimum work. Other part is a stress residue constant. In order to verify these formulae and the computed results, the computed contour lines of equi-maximal shear stresses were plotted and quite compared with that of photo-elasticity test results. This constraint condition about normal stress distribution along circumference is confirmed by using Greens’ theorem. An additional compression exists along the circumference of the loaded ring, explaining the divorcement and displacement of singularity points at inner and outer boundaries.     

Modelling losses and locating the tail with the Pareto Positive Stable distribution

This paper focuses on modelling the severity distribution. We directly model the small, moderate and large losses with the Pareto Positive Stable (PPS) distribution and thus it is not necessary to fix a threshold for the tail behaviour. Estimation with the method of moments is straightforward. Properties, graphical tests and expressions for value-at risk and tail value-at-risk are presented. Furthermore, we show that the PPS distribution can be used to construct a statistical test for the Pareto distribution and to determine the threshold for the Pareto shape if required. An application to loss data is presented. We conclude that the PPS distribution can perform better than commonly used distributions when modelling a single loss distribution for moderate and large losses. This approach avoids the pitfalls of cut-off selection and it is very simple to implement for quantitative risk analysis.     

Crossover between tetrahedral and hexagonal structures in liquid water

It is widely accepted that liquid water structure is comprised of two closely interweaved components; i.e. tetrahedral (low density) and hexagonal (high density) structures. The relative amount of these components is temperature and pressure dependent. We propose an order parameter, based on the radial distribution function, that quantifies the relative structural composition at any defined temperature and pressure, thus establishing the crossover point in structural dominance. At 300 K this point lies close to 2 kbar, pressure at which water looses most of its ‘anomalous’ properties.     

A note on the subexponential asymptotics of the stationary distribution of M/G/1 type Markov chains

Masuyama (2011) obtained the subexponential asymptotics of the stationary distribution of an M/G/1 type Markov chain under the assumption related to the periodic structure of G-matrix. In this note, we improve Masuyama’s result by showing that the subexponential asymptotics holds without the assumption related to the periodic structure of G-matrix.     

Univariate Geometric Stable Laws

The paper summarizes recent advances in the theory of geometric stable (GS) distributions. The results presented include parametrizations, characterizations, mixture representations, properties, asymptotic and convergent series expansions of densities and distribution functions, moments and tail behavior, simulation, and estimation.     

A Note on the Difference of Gaussian Measure of Two Balls in Hilbert Spaces

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Dynamics of surface reactions: from “hot” precursors to conventional thermal activation

Heterogeneous catalytic reactions usually contain steps, e.g., adsorption, generating energy-rich (“hot”) precursors for other steps. With increasing the rate of energy relaxation one can observe a transition from the reaction regime dominated by “hot” precursors to conventional thermal activation. To illustrate this transition in detail and to show what may happen in various situations, I present an analytical model based on the Fokker-Planck equation for energy relaxation.