Circulant Double Coverings of a Circulant Graph of Valency Four

Several isomorphism classes of graph coverings of a graph G have been enumerated by many authors (see [3], [8]–[15]). A covering of G is called circulant if its covering graph is circulant. Recently, the authors [4] enumerated the isomorphism classes of circulant double coverings of a certain kind, called typical, and showed that no double covering of a circulant graph of valency 3 is circulant. In this paper, the isomorphism classes of connected circulant double coverings of a circulant graph of valency 4 are enumerated. As a consequence, it is shown that no double covering of a non-circulant graph G of valency 4 can be circulant if G is vertex-transitive or G has a prime power of vertices. The first author is supported by NSF of China (No. 60473019) and by NKBRPC (2004CB318000), and the second author is supported by Com²MaC-KOSEF (R11-1999-054) in Korea.     

Synthesis and characterization of polyimides from bis(3‐aminophenyl)‐4‐(1‐adamantyl)phenoxyphenyl phosphine oxide

A novel diamine, bis(3‐aminophenyl)‐4‐(1‐adamantyl)phenoxyphenyl phosphine oxide (mDAATPPO), was synthesized via the Williamson ether reaction of 4‐(1‐adamantyl)phenol and bis(3‐nitrophenyl)‐4‐fluorophenyl phosphine oxide, followed by reduction. The phenol group was prepared by the Friedel–Crafts reaction of 1‐bromoadamantane and phenol, whereas the phosphine oxide group was synthesized by the Grignard reaction of 1‐bromo‐4‐fluorobezene and diphenyl phosphinic chloride, followed by nitration. The monomer and its intermediate compounds were characterized with Fourier transform infrared, NMR, and melting‐point apparatus. The monomer was then used to prepare polyimides with 2,2‐bis(3,4‐dicarboxyphenyl)hexafluoropropane dianhydride, 3,3′,4,4′‐benzophenonetetracarboxylic dianhydride, 4,4′‐oxydiphthalic dianhydride, and pyromellitic dianhydride by the conventional two‐step synthesis: the preparation of poly(amic acid) followed by solution imidization. The molecular weights of the polyimides were controlled to 20,000 g/mol by off‐stoichiometry, and the synthesized polyimides were characterized with Fourier transform infrared, NMR, gel permeation chromatography, thermogravimetric analysis, and differential scanning calorimetry. In addition, the solubility, intrinsic viscosity, dielectric constant, and birefringence of the polyimides were evaluated. Novel polyimides with mDAATPPO exhibited good solubility, high glass‐transition temperatures (290–330 °C), excellent thermal stability (>500 °C), low dielectric constants (2.77–3.01), low refractive indices, and low birefringence values (0.0019–0.0030). © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2567–2578, 2006     

Transport properties of heavily AsF5 doped polyacetylene

We report measurements of the temperature dependence of the thermoelectric power and electrical conductivity for polyacetylene heavily doped (more than 10%) with arsenic pentafluoride. The thermopower is small, positive and linear with temperature. The conductivity is very large for a polymeric system, about 1000 (Ω cm)^-1 at room temperature, and as temperature is decreased drops in value by less than a factor of two, becoming essentially temperature independent below 4 K. The samples exhibited ohmic behavior at the current densities used and did not show any frequency dependence up to 1000 Hz. No evidence for superconductivity was found down to 30 mK. The results are interpreted as the first conclusive evidence for the existence of a metallic state at all temperatures in this material.     

Synthesis and microstructural properties of ZnO nanorods on Ti-buffer layers

This study examined the structural properties of ZnO nanorods grown on Ti-buffer layers with different surface roughnesses of 1.5 and 4.0 nm. Vertically aligned ZnO nanorods were synthesized on Al₂O₃ substrates with a Ti-buffer layer by metal-organic chemical vapor deposition. X-ray diffraction revealed the ZnO nanorods grown on a smooth surface to have higher quality and better alignment in the ab-plane than those grown on the rough surface. Field-emission transmission electron microscopy (FE-TEM) measurements revealed a disordered layer at the ZnO/Ti interface. FE-TEM demonstrated that the Ti-buffer layer contained a mixture of ordered and amorphous phases. Energy dispersive spectroscopy (EDS) analysis revealed the Ti-buffer layers to be entirely oxides.     

Ultrafast two-dimensional infrared vibrational echo chemical exchange experiments and theory

Ultrafast two-dimensional (2D) infrared vibrational echo experiments and theory are used to examine chemical exchange between solute-solvent complexes and the free solute for the solute phenol and three solvent complex partners, p-xylene, benzene, and bromobenzene, in mixed solvents of the partner and CCl4. The experiments measure the time evolution of the 2D spectra of the hydroxyl (OD) stretching mode of the phenol. The time-dependent 2D spectra are analyzed using time-dependent diagrammatic perturbation theory with a model that includes the chemical exchange (formation and dissociation of the complexes), spectral diffusion of both the complex and the free phenol, orientational relaxation of the complexes and free phenol, and the vibrational lifetimes. The detailed calculations are able to reproduce the experimental results and demonstrate that a method employed previously that used a kinetic model for the volumes of the peaks is adequate to extract the exchange kinetics. The current analysis also yields the spectral diffusion (time evolution of the dynamic line widths) and shows that the spectral diffusion is significantly different for phenol complexes and free phenol.     

Tunable aggregation-induced emission of diphenyldibenzofulvenes

Nonemissive fulvenes can be induced to luminesce by aggregate formation, with the crystalline aggregates emitting bluer lights more intensely than their amorphous counterparts.     

pH-Dependent rectification in self-assembled monolayers based on electrostatic interactions

Asymmetric electrostatic interactions dependent on pH between the redox molecules and the terminal group on the top of the self-assembled monolayer (SAM) afford control of the electron transfer property of the SAM having the imidazole terminal group.     

Complementary control by additives of the kinetics of amorphous CaCO3 mineralization at an organic interface: in-situ synchrotron x-ray observations

The kinetics of biomimetic mineralization at a fatty acid monolayer interface have been measured in situ by synchrotron x-ray reflectivity. The formation of biologically relevant amorphous calcium carbonate films is affected by soluble macromolecules, supersaturation rate of change, and Mg cations. We find that these solution conditions influence mineral film formation in a complementary fashion. Poly(sodium acrylate) extends the lifetime of metastable amorphous calcium carbonate, solution saturation controls the mineral film growth rate, and Mg cations create a longer induction time. This is the first quantification of potentially competitive biomineralization mechanisms that addresses nucleation and growth of the amorphous mineral phases, which are important in biomineralization.     

Optimal convergence analysis of an immersed interface finite element method

We analyze an immersed interface finite element method based on linear polynomials on noninterface triangular elements and piecewise linear polynomials on interface triangular elements. The flux jump condition is weakly enforced on the smooth interface. Optimal error estimates are derived in the broken H ¹-norm and L ²-norm.