Continuity and differentiability for weighted Sobolev spaces

Our aim in this paper is to discuss continuity and differentiability of functions in weighted Sobolev spaces in the limiting case of Sobolev's imbedding theorem.

     

Impedance and frequency characteristics of electrode-separated piezoelectric quartz crystals in liquids

The electrical equivalent circuit parameters of an electrode-separated piezoelectric quartz crystal (PQC), where the gaps between the electrodes and the crystal plate were filled with various liquids, were evaluated from admittance measurements and were compared with those of a normal PQC with Au electrodes adhering to the crystal plate. The resistance parameter in the equivalent circuit of the electrode-separated PQC was more sensitive to the specific conductivity, density and viscosity of liquids than was that of the normal PQC. This parameter, unlike that of the normal PQC, was also affecteded by the permittivity of the liquid. The effect of the liquid properties on the other parameters in the equivalent circuit and the series resonant frequency are also discussed.     

Positioning of cationic silver nanoparticle by using AFM lithography and electrostatic interaction

One-dimensional metal lines of silver nanoparticles with a nano-sized width were generated onto silicon surface by using a nano-level lithography technique, field induced oxidation (FIO) by AFM, on self-assembled monolayer-modified Si wafers. This FIO technique provided SiO₂ lines a width of less than 100 nm. Short-time immersion of partially anodized silicon surface which is covered by a cationic silanol surfactant ((CH₃O)₃SiCH₂CH₂CH₂N(CH₃)₃⁺Cl⁻)-monolayer into quaternary ammonium (HSCH₂CH₂N(CH₃)₃⁺Br⁻)-covered silver nanoparticles readily and reproducibly gave nano-metal lines of silver onto silicon wafers. Hydrophilicity of the whole wafer surface was indispensable for homogeneously wetting the anodized SiO₂ area with a nanodimensional width.     

Detailed structural examinations of covalently immobilized gold nanoparticles onto hydrogen-terminated silicon surfaces

The modification of flat semiconductor surfaces with nanoscale materials has been the subject of considerable interest. This paper provides detailed structural examinations of gold nanoparticles covalently immobilized onto hydrogen-terminated silicon surfaces by a convenient thermal hydrosilylation to form Si-C bonds. Gold nanoparticles stabilized by omega-alkene-1-thiols with different alkyl chain lengths (C3, C6, and C11), with average diameters of 2-3 nm and a narrow size distribution were used. The thermal hydrosilylation reactions of these nanoparticles with hydrogen-terminated Si(111) surfaces were carried out in toluene at various conditions under N2. The obtained modified surfaces were observed by high-resolution scanning electron microscopy (HR-SEM). The obtained images indicate considerable changes in morphology with reaction time, reaction temperature, as well as the length of the stabilizing omega-alkene-1-thiol molecules. These surfaces are stable and can be stored under ambient conditions for several weeks without measurable decomposition. It was also found that the aggregation of immobilized particles on a silicon surface occurred at high temperature (> 100 degrees C). Precise XPS measurements of modified surfaces were carried out by using a Au-S ligand-exchange technique. The spectrum clearly showed the existence of Si-C bonds. Cross-sectional HR-TEM images also directly indicate that the particles were covalently attached to the silicon surface through Si-C bonds.     

Monolayer-derivative functionalization of non-oxidized silicon surfaces

This article describes a variety of monolayers anchored directly onto silicon surfaces without an oxide interlayer, their formation mechanisms, their technological applications, and our personal views on the future prospects for this field. The chemical modification of non-oxidized silicon surfaces utilizing monolayers was first reported in 1993. The basic finding that a non-oxidized silicon surface could be neutralized with alkyl chains through direct covalent linkage, i.e., silicon-carbon, has offered chemical scientists ease of handling even in an ambient environment and, thus, research has been predictably focused on forming anti-stiction coating films for nano- and micro-electromechanical systems (NEMS/MEMS). Such surface reforming has also been achieved by using other monolayers, which form interfacial bonds, e.g., silicon-nitrogen and silicon-oxygen. The resultant monolayer surfaces are useful for silicon-based applications including molecular electron transfer films, monolayer templates, molecular insulators, capsulators, and bioderivatives. Such monolayers are applicable not only for surface modification, but also for manipulating individual nanomaterials. By modifying the terminal groups of monolayers with nanomaterials including nanocrystals and biomolecules, the nanomaterials can remarkably be immobilized directly onto non-oxidized silicon surfaces based on the formation mechanisms of the monolayer. Such immobilizations will revolutionize the analysis of the specific features and capabilities of individual nanomaterials. Furthermore, the path will be opened for the development of more advanced monolayer-derived chip technology. To achieve this goal, it is extremely important to thoroughly understand the functionalization processes on silicon, since the resultant internal structures and properties of monolayer-derivative silicon may strongly depend on their course of formation.     

Partitioning of clay colloids at air-water interfaces

Colloid sorption onto air-water interfaces in a variety of natural environments has been previously recognized, but better quantification and understanding is still needed. Affinities of clay colloids for the air-water interface were measured using a bubble-column method and reported as partition coefficients (K). Four types of dilute clay suspensions were measured in NaCl solutions under varying pH and ionic strength conditions: kaolinite KGa-1, illite IMt-2, montmorillonite SWy-2, and bentonite. The K values of three types of polystyrene latex particles with different surface-charge properties were also measured for comparison. Kaolinite exhibited extremely high affinity to the air-water interface at pH values below 7. Illite has lower affinity to air-water interfaces than kaolinite, but has similar pH dependence. Na-montmorillonite and bentonite clay were found excluded from the air-water interface at any given pH and ionic strength. Positively and negatively charged latex particles exhibited sorption and exclusion, respectively, at the air-water interface. These results show the importance of electrostatic interactions between the air-water interface and colloids, especially the influence of pH-dependent edge charges, and influence of particle shape.     

Single-step synthesis of acetic acid (methyl acetate) from methanol alone by Ru(II)-Sn(II) hetero-bimetallic catalysts

Single-step conversion of methanol into acetic acid (methyl acetate) has been found possible by use of Ru(II)-Sn(II) hetero-bimetallic catalysts. By analyzing the homogeneous solution reactions, reaction paths are elucidated. Applications of lacunary heteropolyanions as model oxide ligands and of Y-type zeolite as a unique support for the gas-phase reaction are presented.     

Plasmon-induced photoelectrochemistry at metal nanoparticles supported on nanoporous TiO2

Nanoporous TiO(2) films loaded with gold and silver nanoparticles exhibit negative potential changes and anodic currents in response to visible light irradiation, so that the films would potentially be applicable to inexpensive photovoltaic cells, photocatalysts and simple plasmon sensors.     

The aromaticity of pyracylene: an experimental and computational study of the energetics of the hydrogenation of acenaphthylene and pyracylene

In this work, the aromaticity of pyracylene (2) was investigated from an energetic point of view. The standard enthalpy of hydrogenation of acenaphthylene (1) to acenaphthene (3) at 298.15 K was determined to be minus sign(114.5 +/- 4.2) kJ x mol(-1) in toluene solution and minus sign(107.9 +/- 4.2) kJ x mol(-1) in the gas phase, by combining results of combustion and reaction-solution calorimetry. A direct calorimetric measurement of the standard enthalpy of hydrogenation of pyracylene (2) to pyracene (4) in toluene at 298.15 K gave -(249.9 plus minus 4.6) kJ x mol(-1). The corresponding enthalpy of hydrogenation in the gas phase, computed from the Delta(f)H(o)m(cr) and DeltaH(o)m(sub) values obtained in this work for 2 and 4, was -(236.0 +/- 7.0) kJ x mol(-1). Molecular mechanics calculations (MM3) led to Delta(hyd)H(o)m(1,g) = -110.9 kJ x mol(-1) and Delta(hyd)H(o)m(2,g) = -249.3 kJ x mol(-1) at 298.15 K. Density functional theory calculations [B3LYP/6-311+G(3d,2p)//B3LYP/6-31G(d)] provided Delta(hyd)H(o)m(2,g) = -(244.6 +/- 8.9) kJ x mol(-1) at 298.15 K. The results are put in perspective with discussions concerning the "aromaticity" of pyracylene. It is concluded that, on energetic grounds, pyracylene is a borderline case in terms of aromaticity/antiaromaticity character.