Fluorinated,crosslinkable terpolymers based on vinylidene fluoride and bearing sulfonic acid side groups for fuel‐cell membranes

The radical terpolymerization of 8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene with vinylidene fluoride (VDF) and perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride is presented. Changing the feed compositions of these three fluorinated comonomers enabled us to obtain different random‐type poly[vinylidene fluoride‐ter‐perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride‐ter‐8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene] terpolymers containing various sulfonyl fluoride and brominated side groups. Yields higher than 70% were reached in all cases. The hydrolysis of the sulfonyl fluoride group into the ? SO₃Li function in the presence of lithium carbonate was quantitatively achieved without the content of VDF being affected, and so dehydrofluorination of the VDF base unit was avoided. These original terpolymers were then crosslinked via dangling bromine atoms in the presence of a peroxide/triallyl isocyanurate system, which produced films insoluble in organic solvents such as acetone and dimethylformamide (which totally dissolved uncured terpolymers). The acidification of ? SO₃Li into the ? SO₃H function enabled protonic membranes to be obtained. The thermal stabilities of the crosslinked materials were higher than those of the uncured terpolymers, and their electrochemical performances were investigated. According to the contents of the sulfonic acid side functions, the ion‐exchange capacities ranged from 0.6 to 1.5 mequiv of H⁺/g, whereas the water uptake and conductivities ranged from 5–26% (±11%) and from 0.5 to 6.0 mS/cm, respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4566–4578, 2006     

A two-echelon base-stock inventory model with Poisson demand and the sequential processing of orders at the upper echelon

We consider a two-echelon inventory system with a number of non-identical, independent ‘retailers’ at the lower echelon and a single ‘supplier’ at the upper echelon. Each retailer experiences Poisson demand and operates a base stock policy with backorders. The supplier manufactures to order and holds no stock. Orders are produced, in first-come first-served sequence, with a fixed production time. The supplier therefore functions as an M/D/1 queue. We are interested in the performance characteristics (average inventory, average backorder level) at each retailer. By finding the distribution of order lead time and hence the distribution of demand during order lead time, we find the steady state inventory and backorder levels based on the assumption that order lead times are independent of demand during order lead time at a retailer. We also propose two alternative approximation procedures based on assumed forms for the order lead time distribution. Finally we provide a derivation of the steady state inventory and backorder levels which will be exact as long as there is no transportation time on orders between the supplier and retailers. A numerical comparison is made between the exact and approximate measures. We conclude by recommending an approach which is intuitive and computationally straightforward.     

Nitroxide‐mediated radical polymerization of 2‐(dimethylamino)ethyl acrylate and its sequential block copolymerization with styrene and N‐butyl acrylate

Nitroxide‐mediated radical polymerization (NMRP) of 2‐(dimethylamino)ethyl acrylate (DMAEA) was carried out at 100–120 °C, initiated by MONAMS, an alkoxyamine based on N‐tert‐butyl‐N‐(1‐diethyl phosphono‐2,2‐dimethylpropyl)nitroxide, SG1. Controlled polymerization can be achieved by the addition of free SG1 (the initial molar ratio of SG1 to MONAMS ranged from 0.06 to 0.12), giving a linear first‐order kinetic plot up to 55–70% conversion depending on the reaction conditions. The molecular weights show a near linear increase with conversion; however, they deviate to some extent with theoretical values. SG1‐mediated polymerization of DMAEA at 112 °C is also controlled in organic solvents (N,N‐dimethylformide, anisole, xylene). Polymerization rate increases with increasing solvent polarity. Chain transfer to polymer produces ～1 mol % branches in bulk and 1.2–1.9 mol % in organic solvents, typical of those for acrylates. From poly(styrene) (pS) and poly(n‐butyl acrylate) (pBA) macroinitiators, amphiphilic di‐ and triblock copolymers p(S‐b‐DMAEA), p(DMAEA‐b‐S‐b‐DMAEA), p(BA‐b‐DMAEA), and p(DMAEA‐b‐BA‐b‐DMAEA) were synthesized via NMRP at 110 °C. Polymers were characterized by GPC, NMR, surface tension measurements, and DSC. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 414–426, 2006     

Synthesis of poly(ethylene oxide) with pending 2,2,6,6‐tetramethylpiperidine‐1‐oxyl groups and its further initiation of the grafting polymerization of styrene

A new stratagem for the synthesis of amphiphilic graft copolymers of hydrophilic poly(ethylene oxide) as the main chain and hydrophobic polystyrene as the side chains is suggested. A poly(ethylene oxide) with pending 2,2,6,6‐tetramethylpiperidine‐1‐oxyls [poly(4‐glycidyloxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl‐co‐ethylene oxide)] was first prepared by the anionic ring‐opening copolymerization of ethylene oxide and 4‐glycidyloxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl, and then the graft copolymerization of styrene was completed with benzoyl peroxide as the initiator in the presence of poly(4‐glycidyloxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl‐co‐ethylene oxide). The polymerization of styrene was under control, and comblike, amphiphilic poly(ethylene oxide)‐g‐polystyrene was obtained. The copolymer and its intermediates were characterized with size exclusion chromatography, ¹H NMR, and electron spin resonance in detail. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3836–3842, 2006     

Metallocene copolymers of propene and 1‐hexene: The influence of the comonomer content and thermal history on the structure and mechanical properties

The relationships between the structure and properties have been established for copolymers of propylene and 1‐hexene synthesized with an isotactic metallocene catalyst system. The most important factor affecting the structure and properties of these copolymers is the comonomer content. The thermal treatment, that is, the rate of cooling from the melt, is also important. These factors affect the thermal properties, the degree of crystallinity, and therefore the structural parameters and the viscoelastic behavior. A slow cooling from the melt favors the formation of the γ phase instead of the α modification. Regarding the viscoelastic behavior, the β relaxation, associated with the glass‐transition temperature, is shifted to lower temperatures and its intensity is increased as the 1‐hexene content raises. The microhardness values are correlated with those of the storage modulus deduced from dynamic mechanical thermal analysis curves, and good linear relations have been obtained between these parameters. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1253–1267, 2006     

Some refinements of Dade's projective conjecture

In this paper a further refinement of Dade's projective conjecture, due to Boltje, is presented. This new statement includes ideas first published by Isaacs and Navarro as well as the recent contractibility version of Alperin's conjecture introduced by Boltje. Leaning heavily on the work of Robinson, weaker forms of the conjecture are proved in the case of p-solvable groups.     

Disturbing the Dyson conjecture, in a generally GOOD way

Dyson's celebrated constant term conjecture [F.J. Dyson, Statistical theory of the energy levels of complex systems I, J. Math. Phys. 3 (1962) 140-156] states that the constant term in the expansion of _∏1≦i≠j≦naj(1−xi/xj) is the multinomial coefficient (a₁+a₂+?+an)!/(a₁!a₂!?an!). The definitive proof was given by I.J. Good [I.J. Good, Short proof of a conjecture of Dyson, J. Math. Phys. 11 (1970) 1884]. Later, Andrews extended Dyson's conjecture to a q-analog [G.E. Andrews, Problems and prospects for basic hypergeometric functions, in: R. Askey (Ed.), The Theory and Application of Special Functions, Academic Press, New York, 1975, pp. 191-224]. In this paper, closed form expressions are given for the coefficients of several other terms in the Dyson product, and are proved using an extension of Good's idea. Also, conjectures for the corresponding q-analogs are supplied. Finally, perturbed versions of the q-Dixon summation formula are presented.     

Nuclear spin-lattice relaxation mechanisms in kaolinite confirmed by magic-angle spinning

Spin-lattice relaxation mechanisms in kaolinite have been reinvestigated by magic-angle spinning (MAS) of the sample. MAS is useful to distinguish between relaxation mechanisms: the direct relaxation rate caused by the dipole-dipole interaction with electron spins is not affected by spinning while the spin diffusion-assisted relaxation rate is. Spin diffusion plays a dominant role in ¹H relaxation. MAS causes only a slight change in the relaxation behavior, because the dipolar coupling between ¹H spins is strong. ²⁹Si relaxes directly through the dipole-dipole interaction with electron spins under spinning conditions higher than 2 kHz. A spin diffusion effect has been clearly observed in the ²⁹Si relaxation of relatively pure samples under static and slow-spinning conditions. ²⁷Al relaxes through three mechanisms: phonon-coupled quadrupole interaction, spin diffusion and dipole-dipole interaction with electron spins. The first mechanism is dominant, while the last is negligibly small. Spin diffusion between ²⁷Al spins is suppressed completely at a spinning rate of 2.5 kHz. We have analyzed the relaxation behavior theoretically and discussed quantitatively. Concentrations of paramagnetic impurities, electron spin-lattice relaxation times and spin diffusion rates have been estimated.     

Representing workloads in GI/G/1 queues through the preemptive-resume LIFO queue discipline

We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-resume LIFO (last-in-first-out) queue discipline: we study the long-run state behavior of the system by averaging over arrival epochs, departure epochs, as well as time, and obtain relations that express the resulting averages in terms of basic characteristics within busy cycles. These relations, together with the fact that the preemptive-resume LIFO queue discipline is work-conserving, imply new representations for both actual and virtual delays in standard GI/G/1 queues with the FIFO (first-in-first-out) queue discipline. The arguments by which our results are obtained unveil the underlying structural explanations for many classical and somewhat mysterious results relating to queue lengths and/or delays in standard GI/G/1 queues, including the well-known Bene's formula for the delay distribution in M/G/l. We also discuss how to extend our results to settings more general than GI/G/1.     

Fermi and Coulomb correlations in the 21 S state of the helium isoelectronic sequence

The Fermi and Coulomb holes of the 2¹ S state of the helium isoelectronic sequence are investigated. Several interesting differences between the results obtained and those which might be expected on the basis of the corresponding 2³ S state are pointed out and discussed.