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     

Water wave radiation by a sphere submerged in water with an ice-cover

Using the multipoles method, we formulate the problems of radiation (both heave and sway) of water waves by a submerged sphere in deep as well as in uniform finite depth water with an ice-cover, with the ice-cover being modelled as an elastic plate of very small thickness. In each case this leads to an infinite system of linear equations which are solved numerically by standard techniques. The added-mass and damping coefficients for a heaving and swaying sphere are obtained and depicted graphically against the wave number for various values of the radius of the submerged sphere and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. When the flexural rigidity is taken to be zero, the numerical results for the added-mass and damping coefficient for water with a free surface are recovered.     

Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

Synthesis of some chiral liquid crystals and study of the effect of intramolecular hydrogen bonding on the phase behaviour

The synthesis of three new series of chiral Schiff's bases containing benzilideneaniline and 2-hydroxybenzilideneaniline moieties as mesogenic cores is presented. Differential scanning calorimetry, optical polarizing microscopy and X-ray diffraction measurements were used to study the phase transition temperatures and behaviour. The results reveal that most of these materials show chiral smectic mesomorphism.     

Synthesis and transition temperatures of liquid crystals incorporating a 1,4-tetrafluorophenylene unit

Two homologous series of mesogenic materials which incorporate a 1,4-tetrafluorophenylene moiety and a terminal cyano- or nitro-substituent have been synthesized by using palladiumcatalysed coupling procedures. The compounds exhibit nematic and/or smectic A phases.     

Synthesis and characterization of poly(arylene ether)s containing 6‐(4‐hydroxyphenyl)pyridazin‐3(2H)‐one or 6‐(4‐hydroxyphenyl)pyridazine moieties

A series of novel soluble pyridazinone‐ or pyridazine‐containing poly(arylene ether)s were prepared by a polycondensation reaction. The pyridazinone monomer, 6‐(4‐hydroxyphenyl)pyridazin‐3(2H)‐one ( 1 ), was synthesized from the corresponding acetophenone and glyoxylic acid in a simple one‐pot reaction. The pyridazinone monomer was successfully copolymerized with bisphenol A (BPA) or 1,2‐dihydro‐4‐(4‐hydroxyphenyl)phthalazin‐1(2H)‐one (DHPZ) and bis(4‐fluorophenyl)sulfone to form high‐molecular‐weight polymers. The copolymers had inherent viscosities of 0.5–0.9 dL/g. The glass‐transition temperatures (T_g's) of the copolymers synthesized with BPA increased with increasing content of the pyridazinone monomer. The T_g's of the copolymers synthesized from DHPZ with different pyridazinone contents were similar to those of the two homopolymers. The homopolymers showed T_g's from 202 to 291 °C by differential scanning calorimetry. The 5% weight loss temperatures in nitrogen measured by thermogravimetric analysis were in the range of 411–500 °C. 4‐(6‐Chloropyridazin‐3‐yl)phenol ( 2 ) was synthesized from 1 via a simple one‐pot reaction. 2 was copolymerized with 4,4′‐isopropylidenediphenol and bis(4‐fluorophenyl)sulfone to form high‐T_g polymers. The copolymers with less than 80 mol % pyridazinone or chloropyridazine monomers were soluble in chlorinated solvents such as chloroform. The copolymers with higher pyridazinone contents and homopolymers were not soluble in chlorinated solvents but were still soluble in dipolar aprotic solvents such as N‐methylpyrrolidinone. The soluble polymers could be cast into flexible films from solution. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3328–3335, 2006     

Synthesis of TiO2–SiO2/polymer core–shell microspheres with a microphase‐inversion method

A novel microphase‐inversion method was proposed for the preparation of TiO₂–SiO₂/poly(methyl methacrylate) core–shell nanocomposite particles. The inorganic–polymer nanocomposites were first synthesized via a free‐radical copolymerization in a tetrahydrofuran solution, and the poor solvent was added slowly to induce the microphase separation of the nanocomposite and result in the formation of nanoparticles. The average particle sizes of the microspheres ranged from 70 to 1000 nm, depending on the reaction conditions. Transmission electron microscopy and scanning electron microscopy indicated a core–shell morphology for the obtained microspheres. Thermogravimetric analysis and X‐ray photoelectron spectroscopy measurements confirmed that the surface of the nanocomposite microspheres was polymer‐rich, and this was consistent with the core–shell morphology. The influence of the synthetic conditions, such as the inorganic composition and the content of the crosslinking monomer, on the particle properties was studied in detail. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3911–3920, 2006     

Preparation and characterization of optically active polystyrene via a chiral nitroxide‐mediated polymerization

2,2,6,6‐Tetramethyl‐4‐[d‐(+)‐10‐camphorsulfonyl]‐1‐piperidinyloxy was synthesized and used as a chiral nitroxide for the bulk polymerizations of styrene initiated with benzoyl peroxide (BPO), tetraethylthiuram disulfide (TETD), and thermal initiation. The results showed that the polymerizations proceeded in a controlled/living way; that is, the kinetics presented approximately first‐order plots, and the number‐average molecular weights of the polymers with narrow molecular weight distributions (weight‐average molecular weight/number‐average molecular weight) increased with the monomer conversion linearly. The molecular weight distributions in the case of thermal initiation were narrower than those in the case of BPO and TETD, whereas the polymerization rate with BPO or TETD as an initiator was obviously faster than that with thermal initiation. In addition, successful chain‐extension reactions were carried out, and the structures of the obtained polymers were characterized by gel permeation chromatography and ¹H NMR. The specific rotations of the polymers were also measured by polarimetric analysis. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1522–1528, 2006