Axisymmetric frictionless contact of functionally graded materials

The main interest of this study is a new method to solve the axisymmetric frictionless contact problem of functionally graded materials (FGMs). Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into a series of sub-layers with shear modulus varying linearly in each sub-layer and continuous at the sub-interfaces. With this model, the axisymmetric frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. An erratum to this article can be found at     

The completely positive and doubly nonnegative completion problems

We prove the following. Let G be an undirected graph. Every partially specified symmetric matrix, the graph of whose specified entries is G and each of whose fully specified submatrices is completely positive (equal to BB^T for some entrywise nonnegative matrix B), may be completed to a completely positive matrix if and only if G is a block-clique graph (a chordal graph in which distinct maximal cliques overlap in at most one vertex). The same result holds for matrices that are doubly nonnegative (entrywise nonnegative and positive semidefinite).     

Synthesis and nuclear magnetic resonance analysis of starch‐g‐poly(1,4‐dioxan‐2‐one) copolymers

A new biodegradable starch graft copolymer, starch‐g‐poly(1,4‐dioxan‐2‐one), was synthesized through the ring‐opening graft polymerization of 1,4‐dioxan‐2‐one onto a starch backbone. The grafting reactions were conducted with various 1,4‐dioxan‐2‐one/starch feed ratios to obtain starch‐g‐poly(1,4‐dioxan‐2‐one) copolymers with various poly(1,4‐dioxan‐2‐one) graft structures. The microstructure of starch‐g‐poly(1,4‐dioxan‐2‐one) was characterized in detail with one‐ and two‐dimensional NMR spectroscopy. The effect of the feed composition on the resulting microstructure of starch‐g‐poly(1,4‐dioxan‐2‐one) was investigated. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3417–3422, 2004     

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     

Literal‐paraconsistent and literal‐paracomplete matrices

We introduce a family of matrices that define logics in which paraconsistency and/or paracompleteness occurs only at the level of literals, that is, formulas that are propositional letters or their iterated negations. We give a sound and complete axiomatization for the logic defined by the class of all these matrices, we give conditions for the maximality of these logics and we study in detail several relevant examples. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis and characterization of model 3‐miktoarm star copolymers of poly(dimethylsiloxane) and poly(2‐vinylpyridine)

3‐Miktoarm star copolymers, 3μ‐D₂V, with two poly(dimethylsiloxane) (PDMS) and one poly(2‐vinylpyridine) (P2VP) arm, were synthesized by using anionic polymerization–high vacuum techniques and (chloromethylphenylethyl)methyl dichlorosilane, heterofunctional linking agent, with two SiCl groups and one CH₂Cl group. The synthetic strategy involves the selective reaction of the two ? SiCl groups with PDMSOLi living chains, followed by reaction of the remaining chloromethyl group with P2VPLi. Combined molecular characterization results (size exclusion chromatography, membrane osmometry, and ¹H NMR spectroscopy) revealed a high degree of structural and compositional homogeneity. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 614–619, 2006     

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     

Glycopolymeric inhibitors of β‐glucuronidase. III. Configurational effects of hydroxy groups in pendant glyco‐units in polymers upon inhibition of β‐glucuronidase

Two kinds of new glycopolymers, (P(VB‐1‐GlcaH‐co‐AAm), 9 ) and (P(VB‐1‐Glco‐co‐AAm), 10 ), were synthesized through the radical copolymerization of styrene derivatives bearing pendant D ‐glucaric and D ‐gluconic moieties, N‐(p‐vinylbenzyl)‐1‐D ‐glucaramide (VB‐1‐GlcaH, 7 ), and N‐(p‐vinylbenzyl)‐D ‐gluconamide (VB‐1‐Glco, 8 ), with acrylamide (AAm). Glycopolymer 9 bearing the pendant glucaric moiety at the first position inhibited the hydrolysis of a model compound for xenobiotics‐β‐glucuronide conjugates, p‐nitrophenyl β‐D ‐glucuronide, uncompetitively, in contrast to the competitive inhibition in the presence of the corresponding isomeric glycopolymer bearing the pendant D ‐glucaric unit at the sixth position (P(VB‐6‐GlcaH‐co‐AAm), 3 ) reported in our previous article. On the other hand, another copolymer 10 bearing the gluconic moiety was found not to inhibit the hydrolysis as well as the corresponding copolymer bearing pendant gulonic unit (P(VB‐6‐Glco‐co‐AAm), 4 ). These results indicate that the hydrolysis is influenced not only by existence of pendant carboxyl units but also by the direction on the linkage of the glyco‐units to the polymer frame. Therefore the configurational position of hydroxy groups in pendant glyco‐units in macromolecular inhibitors may be essential for the interaction with β‐glucuronidase. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4895–4903, 2006