Nonlinear Boundary Layers of the Boltzmann Equation: I. Existence

 We study the half-space problem of the nonlinear Boltzmann equation, assigning the Dirichlet data for outgoing particles at the boundary and a Maxwellian as the far field. We will show that the solvability of the problem changes with the Mach number ℳ^∞ of the far Maxwellian. If ℳ^∞<−1, there exists a unique smooth solution connecting the Dirichlet data and the far Maxwellian for any Dirichlet data sufficiently close to the far Maxwellian. Otherwise, such a solution exists only for the Dirichlet data satisfying certain admissible conditions. The set of admissible Dirichlet data forms a smooth manifold of codimension 1 for the case −1<ℳ^∞<0, 4 for 0<ℳ^∞<1 and 5 for ℳ^∞>1, respectively. We also show that the same is true for the linearized problem at the far Maxwellian, and the manifold is, then, a hyperplane. The proof is essentially based on the macro-micro or hydrodynamics-kinetic decomposition of solutions combined with an artificial damping term and a spatially exponential decay weight. Received: 20 April 2002 / Accepted: 4 December 2002 Published online: 21 March 2003 Communicated by H.-T. Yau     

Construction of self-assembled monolayer terminated with N-heterocyclic carbene-rhodium(I) complex moiety

Functionalization of self-assembled monolayer (SAM) of alkanethiolate with metal containing unit is one of the versatile methods to obtain functional surfaces such as heterogeneous catalysts. However, organic molecules that strongly bind to transition metals at SAM terminal are limited. Recently N-heterocyclic carbenes (NHCs) such as cyclic diaminocarbenes have emerged as strongly σ-donating ligands forming a robust bond with broad spectrum of transition metals. In the present study, for the purpose of establishment of a new robust basement for heterogeneous metal catalysts, a SAM of the alkanethiolate terminated with NHC-rhodium(I) complex moiety was prepared by utilizing a newly designed disulfide molecule bearing NHC-metal complex terminals. X-ray photoelectron spectroscopy (XPS) analysis and angle resolved XPS measurement revealed successful formation of the Rh-complex-terminated SAM on a gold substrate. Infrared reflection absorption spectroscopy (IRRAS) analysis suggested that the linker methylene chains connecting the rhodium complex moiety and the gold surface are in a loosely packed structure. This unique chemical species, NHC, would be a promising candidate as a basement for the construction of functional surface.     

Effect of pressure on the solubilities ofo-,m- andp-xylene in water

The solubilities of o-, m- and p-xylene in water were measured at 25.0°C up to 250, 385, and 50 MPa, respectively. The solubility increased with increasing pressure up to 120 MPa (50 MPa for p-xylene) and then decreased. The reaction volumes, V^o accompanying the dissolution at 0.1 MPa were estimated as –3.6±0.5, –3.4±0.5, and –4.1±0.5 cm³-mol^–1 for o-, m-, and p-xylene, respectively, from the pressure dependences of the solubilities. The limiting partial molar volumes, of p- and o-xylene in water under high pressure were estimated from V^o and the molar volume of the xylene. The partial molar volumes decreased with increasing pressure. The reaction volume for the formation of intra-molecular pairwise hydrophobic interaction between the methyl groups, as proposed by Ben-Naim, is discussed for the V^o of p- and o-xylene at 0.1 MPa.     

Thermodynamic Insight into the Origin of a Calix[n]arene-[60]fullerene Interaction and its Application to a Porphyrin-[60]fullerene Energy Transfer System

The calixarene-fullerene interaction,which causes only a slight change in the absorptionspectra, has been substantiated by calorimetricmeasurements: the H° values arecomparable with those obtained from the associationconstants estimated by a spectroscopic method. Furthermore, we determined the association constantbetween homooxacalix[3]arene and [60]fullerenederivatives with a porphyrin moiety by fluorescencespectra.     

First thermally responsive supramolecular polymer based on glycosylated amino acid

In materials science, a dynamic property sensitive to an environmental change (heat, light, electric current, pH, and other chemical or physical changes) is indispensable for intelligent materials. Such organic materials, however, are very limited even in conventional polymers. This paper clearly demonstrates that, regardless of the low molecular weight, a glycosylated amino acid derivative newly screened by a combinatorial method forms a macroscopic supramolecular hydrogel that reversibly swells or shrinks in response to the external temperature. Using the unique thermal response of the present hydrogel, we carried out the controlled release of DNA and the perfect removal of bisphenol A from the polluted water. Recently, advanced supramolecular polymers, in which monomers are noncovalently connected, are expected to be highly advantageous over traditional polymers because of their tunable and recyclable characteristics. The present result newly confers a dynamic feature on the supramolecular polymers, which is desirable for the sophisticated application in many fields.     

Solubility of α-amino acids in water under high pressure: glycine, -alanine, -valine, -leucine, and -isoleucine

The solubility of glycine, -alanine, -valine, -leucine, and -isoleucine in water was measured at 298.15 K and pressures up to 400 MPa. The standard deviation of the logarithm of the solubility is 0.001–0.003, equal to or better than the accuracy of atmospheric pressure measurement in the literature (0.001–0.05). A variety of solubility phenomena were observed. The solubility of glycine decreased with increasing pressure, whereas that of -alanine increased. The -valine and -isoleucine have a solubility maximum at around 100 MPa, and -leucine seems to exhibit a solid-phase phase transition at around 200 MPa. Pressure coefficient of the solubilities at 0.10 MPa is compared with that thermodynamically estimated in reference to aqueous density measurements of glycine and -alanine at 298.15 K and 0.10 MPa, supporting a reliability of our high-pressure measurements.     

Heteroatom-guided torquoselective olefination of alpha-oxy and alpha-amino ketones via ynolates

Ynolates were found to react with alpha-alkoxy-, alpha-siloxy-, and alpha-aryloxyketones at room temperature to afford tetrasubstituted olefins with high Z selectivity. Since the geometrical selectivity was determined in the ring opening of the beta-lactone enolate intermediates, the torquoselectivity was controlled by the ethereal oxygen atoms. From experimental and theoretical studies, the high Z selectivity is induced by orbital and steric interactions rather than by chelation. In a similar manner, alpha-dialkylamino ketones provided olefins with excellent Z selectivity. These products can be easily converted into multisubstituted butenolides and gamma-butyrolactams in good yield.     

Host-guest interactions in the supramolecular incorporation of fullerenes into tailored holes on porphyrin-modified gold nanoparticles in molecular photovoltaics

Novel gold nanoparticles modified with a mixed self-assembled monolayer of porphyrin alkanethiol and short-chain alkanethiol were prepared (first step) to examine the size and shape effects of surface holes (host) on porphyrin-modified gold nanoparticles. The porphyrin-modified gold nanoparticles with a size of about 10 nm incorporated C60 molecules (guest) into the large, bucket-shaped holes, leading to the formation of a supramolecular complex of porphyrin-C60 composites (second step). Large composite clusters with a size of 200-400 nm were grown from the supramolecular complex of porphyrin-C60 composites in mixed solvents (third step) and deposited electrophoretically onto nanostructured SnO2 electrodes (fourth step). Differences in the porphyrin:C60 ratio were found to affect the structures and photoelectrochemical properties of the composite clusters in mixed solvents as well as on the SnO2 electrodes. The photoelectrochemical performance of a photoelectrochemical device consisting of SnO2 electrodes modified with the porphyrin-C60 composites was enhanced relative to a reference system with small, wedged-shaped surface holes on the gold nanoparticle. Time-resolved transient absorption spectroscopy with fluorescence lifetime measurements suggest the occurrence of ultrafast electron transfer from the porphyrin excited singlet states to C60 or the formation of a partial charge-transfer state in the composite clusters of supramolecular complexes formed between porphyrin and C60 leading to efficient photocurrent generation in the system. Elucidation of the relationship between host-guest interactions and photoelectrochemical function in the present system will provide valuable information on the design of molecular devices and machines including molecular photovoltaics.