End effects for pre-stressed and pre-polarized piezoelectric solids in anti-plane shear

This paper is concerned with investigation of the influence of pre-stress and pre-polarization on the decay of Saint-Venant end effects in piezoelectric solids. This issue is examined within the framework of incremental anti-plane shear states for prestressed and prepolarized solids. Attention is confined to a specific class of materials, namely those of hexagonal 6mm or 4mm symmetry. It is shown that the mechanical and electrical fields uncouple in this case, and the governing system of coupled second-order linear partial differential equations uncouple to a single homogeneous second-order equation with constant coefficients for the displacement and a Poisson equation for the electric potential. The exact decay rate for mechanical and electrical end effects is determined and the influence of pre-stress and pre-polarization is assessed. Motivation for this work arises from the current rapid developments in smart materials technology.     

Reaction of N-phenyl maleimide with aminosilane monolayers

Reaction of N-phenyl maleimide (NPM) with silica surfaces modified with a self-assembled monolayer of (aminopropyl)triethoxysilane (APTES) was investigated using infrared spectroscopy (FTIR), elemental analysis, and titration assays. This reaction is of interest as a test case for using amine-maleimide coupling for immobilization of biomolecules. Addition of NPM to surface APTES residues was consistently sub-stoichiometric, with typical yields of about 75% on monolayers with a coverage of 1.15 APTES residues/nm2. Titration analysis found negligible presence of imide alkene C=C bonds in modified supports, indicating that addition of NPM to APTES proceeded via amine attack at the imide olefinic bond. FTIR measurements also revealed presence of amide bands which intensified over periods of 10 h. These observations were attributed to a slower secondary process in which APTES amines attack imide carbonyls to produce amide linkages. Stability of NPM-modified surfaces was examined under room temperature storage in pH 7 buffer up to 72 h and for 2 h exposure to buffer at temperatures up to 90 degrees C. It was found that stability was determined by robustness of APTES-silica attachment, with about 30% loss under the harshest conditions investigated.     

Polystyrene nanoparticles based on poly(butyl methacrylate-g-methoxypoly(ethylene glycol)) and poly(methyl methacrylate-g-methoxypoly(ethylene glycol)) graft copolymers

The solubilization of styrene by poly(butyl methacrylate-g-methoxypoly(ethylene glycol)) and poly(methyl methacrylate-g-methoxypoly(ethylene glycol)) graft copolymers has been examined. From turbidity measurements the solubility limit of the monomer in the micelles was obtained and the distribution coefficients were evaluated. Dynamic light scattering revealed that below the solubility limit, solubilization leads to a slight increase in micelle size, while above the solubility limit, there is a dramatic increase in particle size and turbidity as oil-in-water emulsions are formed through coalescence of monomer-swollen micelles. Polymerizations carried out below the solubility limit using the graft copolymer micelles as templates resembled microemulsion polymerizations in nature and led to very fine sterically stabilized polystyrene latex particles. Through careful control of the monomer concentration and the polymerization temperature it was possible to obtain spherical nanosize latex particles with similar size to those of the micelle precursors (10 nm) up to 11% monomer by weight. Polymerizations above the solubility limit, on the other hand, showed similarities with emulsion polymerizations and resulted in larger particles with higher polydispersity.     

Poly(butyl methacrylate-g-methoxypoly(ethylene glycol)) and poly(methyl methacrylate-g-methoxypoly(ethylene glycol)) graft copolymers: preparation and aqueous solution properties

A series of water-soluble, amphiphilic graft copolymers has been prepared by free-radical copolymerization of methoxypoly(ethylene glycol) macromonomers, with either methyl methacrylate or butyl methacrylate as the comonomers, in water/ethanol solvent mixtures. Lower molecular weight copolymers were obtained by increasing the concentration of the initiator, azobisisobutyronitrile (AIBN), used in the polymerization reaction. However, the route used also led to the formation of significant quantities of tetramethylsuccinodinitrile, a toxic byproduct resulting from the cage reaction of AIBN. Static fluorescence measurements using pyrene as a probe, along with 1H NMR experiments, showed that the graft copolymers form aggregates in water at very low concentrations (approximately 0.01 g l(-1)) with the pendant hydrophilic graft chains forming a stabilizing shell around the hydrophobic backbone. An increase in the hydrophile-lipophile balance of the graft copolymers was found to lead to smaller aggregates with lower aggregation numbers and highly swollen hydrophilic shells, as revealed by small angle neutron scattering (SANS).     

Divergence of the Bethe-Salpeter wave function at the origin

We point out an error in the proof of Nishijima et al. that the Bethe-Salpeter wave function for composite particles, lying on Regge trajectories, is finite. We describe a simple counter-example drawn from non-relativistic quantum mechanics and cite others from field theory.     

Finite anti-plane shear of an infinite slab with a traction-free elliptical cavity: Bounds on the stress concentration factor

This paper provides an analytical approach for obtaining bounds on elastic stress concentration factors in the theory of finite anti-plane shear of homogeneous, isotropic, incompressible materials. The problem of an infinite slab with traction-free elliptical cavity subject to a state of finite simple shear deformation is considered. Explicit estimates are obtained for the maximum shear stress in terms of the cavity geometry, applied stress at infinity and constitutive parameters. The analysis is based on application of maximum principles for second-order quasilinear uniformly elliptic equations.     

Upper and lower bounds for the shear stress in the Saint-Venant theory of flexure

Upper and lower bounds are derived for the shear stress as it is determined by Saint-Venant's theory of flexure, and used to establish the asymptotic character of the classical Strength of Materials formula in the limit of vanishing thickness.

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Résumé On dérive des limites supérieures et inférieures des contraintes tangentielles suivant la théorie de la flexion de Saint-Venant, que l'on utilise aux fins d'établir le caractère asymptotique de la formule de la Résistance des Matériaux dans le cas limite d'une épaisseur extrêmement petite.