Numerical solution of the three‐dimensional parabolic equation with an integral condition

Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040     

A remark on divisibility of definable groups

We show that if G is a definably compact, definably connected definable group defined in an arbitrary o‐minimal structure, then G is divisible. Furthermore, if G is defined in an o‐minimal expansion of a field, k ∈ ? and p_k : G → G is the definable map given by p_k (x ) = x^k for all x ∈ G , then we have |(p_k )^–1(x )| ≥ k^r for all x ∈ G , where r > 0 is the maximal dimension of abelian definable subgroups of G . (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystallographic report: Diiodo[tris(2‐pyridyl)amine]mercury(II), [(C5H4N)3N]HgI2

In mononuclear HgI₂[(C₅H₄N)₃N], mercury is tetrahedrally coordinated by two nitrogen atoms of a tris(2‐pyridyl)amine ligand and two iodides. The coordination moieties are connected by weak intermolecular Hg(II)···I interactions to give a one‐dimensional structure. Copyright © 2003 John Wiley & Sons, Ltd.     

Structure of a poly(2,5‐benzimidazole)/phosphoric acid complex

As‐cast films of poly(2,5‐benzimidazole) exhibit uniplanar orientation in which the planes of the aromatic rings lie parallel to the film surface. Upon doping with phosphoric acid, the original crystalline order is lost, but the doped film can be stretched to produce films with uniaxial orientation. After thermal annealing at 540 °C, nine Bragg reflections are resolved in the fiber diagram, and these are indexed by an orthorhombic unit cell with the dimensions a = 18.1 Å, b = 3.5 Å, and c = 11.4 Å, containing four monomer units of two chains. The absence of odd‐order 00l reflections points to a 2₁ chain conformation, which is probably planar so that the aromatic units can be stacked along the b axis. The water and phosphoric acid contents of the crystalline structure cannot be determined exactly because of the presence of extensive amorphous regions that probably have different solvation. The best agreement between the observed and calculated intensities is for an idealized structure containing two phosphoric acids and two water molecules per unit cell. However, the phosphoric acid is probably present mainly in the form of pyrophosphoric acid and its higher oligomers. In addition, the X‐ray data are consistent with a more disordered structure containing chains with random (up and down) polarity and a lack of c‐axis registry. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2576–2585, 2004     

Non-protein amino acids in peptide design

An overview of the use of non-protein amino acids in the design of conformationally well-defined peptides, based on work from the author’s laboratory, is discussed. The crystal structures of several designed oligopeptides illustrate the useα-aminoisobutyric acid (Aib) in the construction of helices, D-amino acids in the design of helix termination segments and^DPro-Xxx segments for nucleating ofβ-hairpin structures.β- andγ-amino acid residues have been used to expand the range of designed polypeptide structures. Dedicated to Professor C N R Rao on his 70th birthday     

Shape transition from InAs quantum dash to quantum dot on InP(3 1 1)A

We report on the shape transition from InAs quantum dashes to quantum dots (QDs) on lattice-matched GaInAsP on InP(3 1 1)A substrates. InAs quantum dashes develop during chemical-beam epitaxy of 3.2 monolayers InAs, which transform into round InAs QDs by introducing a growth interruption without arsenic flux after InAs deposition. The shape transition is solely attributed to surface properties, i.e., increase of the surface energy and symmetry under arsenic deficient conditions. The round QD shape is maintained during subsequent GaInAsP overgrowth because the reversed shape transition from dot to dash is kinetically hindered by the decreased ad-atom diffusion under arsenic flux.     

Formation of β‐iPP in isotactic polypropylene/ethylene–propylene rubber blends: Effects of preparation method,composition, and thermal condition

The effects of preparation method, composition, and thermal condition on formation of β‐iPP in isotactic polypropylene/ethylene–propylene rubber (iPP/EPR) blends were studied using modulated differential scanning calorimeter (MDSC), wide angle X‐ray diffraction (WAXD), and phase contrast microscopy (PCM). It was found that the α‐iPP and β‐iPP can simultaneity form in the melt‐blended samples, whereas only α‐iPP exists in the solution‐blended samples. The results show that the formation of β‐iPP in the melt‐blended samples is related to the crystallization temperature and the β‐iPP generally diminishes and finally vanishes when the crystallization temperature moves far from 125 °C. The phenomena that the lower critical temperature of β‐iPP in iPP/EPR obviously increases to 114 °C and the upper critical temperature decreases to 134 °C indicate the narrowing of temperature interval, facilitating the formation of β‐iPP in iPP/EPR. Furthermore, it was found that the amount of β‐iPP in melt‐blended iPP/EPR samples is dependent on the composition and the maximum amount of β‐iPP formed when the composition of iPP/EPR blends is 85:15 in weight. The results through examining the effect of annealing for iPP/EPR samples at melt state indicate that this annealing may eliminate the susceptibility to β‐crystallization of iPP. However, only α‐iPP can be observed in solution‐blended samples subjected to annealing for different time. The PCM images demonstrate that an obvious phase‐separation happens in both melt‐blended and solution‐blended iPP/EPR samples, implying that compared with the disperse degree of EPR in iPP, the preparation method plays a dominant role in formation of β‐iPP. It is suggested that the origin of formation of β‐iPP results from the thermomechanical history of the EPR component in iPP/EPR. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1704–1712, 2007     

Self-assembled lipid nanotube hosts: The dimension control for encapsulation of nanometer-scale guest substances

Supramolecular nanotube hosts with precisely controlled inner or outer diameters have been synthesized by self-assembly of unsymmetrical bolaamphiphilic monomers or glucopyranosylamide lipids, respectively. Time-resolved fluorescent measurement using 8-anilinonaphthalene-1-sulfonate (ANS) as a probe revealed that the water confined in a cardanyl-β-D -glucopyranoside lipid nanotube has relatively lower solvent polarity corresponding to that of propanol than bulk water. Extensively developed hydrogen bond networks also characterize the confined water in comparison to the case in bulk water. Encapsulation ability of the glucopyranosylamide lipid nanotube has been examined by filling the lyophilized LNTs with gold or silver nanoparticles, ferritin, or magnetic crystals. Filling the unsymmetrical bolaamphiphile nanotube possessing positively charged inner surfaces with negatively charged polymer beads or ferritin proved to be successful without depending on capillary action. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5137–5152, 2006     

Effect of stoichiometry on liquid crystalline supramolecular polymers formed with complementary nucleobase pair interactions

We report herein studies on the liquid crystalline behavior of a series of supramolecular materials that contain different ratios of two complementary symmetrically-substituted alkoxy-bis(phenylethynyl)benzene AA- and BB-type monomers. One monomer has thymine units placed at either end of the rigid mesogenic core, while the other has N⁶-(4-methoxybenzoyl)-adenine units placed on the ends. Differential scanning calorimetric and polarized optical microscopy studies have been carried out on these systems. These studies show that the material's behavior is strongly dependent on its thermal history. As a result, the materials can exhibit, on heating, either a liquid crystalline phase, a crystalline phase, or the coexistence of crystalline and liquid crystalline regions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5049–5059, 2006     

Some past achievements and future perspectives in main group chemistry

A survey of some recent developments and past achievements in low-valent main group chemistry is presented. Some emerging implications of this area of chemistry in materials science, catalysis and new reagent development are also discussed.