Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides

The eigenfield distribution and the band structure of a photonic crystal waveguide have been measured with a phase-sensitive near-field scanning optical microscope. Bloch modes, which consist of more than one spatial frequency, are visualized in the waveguide. In the band structure, multiple Brillouin zones due to zone folding are observed, in which positive and negative dispersion is seen. The negative slopes are shown to correspond to a negative phase velocity but a positive group velocity. The lateral mode profile for modes separated by one reciprocal lattice vector is found to be different.     

On a variational principle of Hashin and Shtrikman

In this paper a simple derivation of a new version of the variational principle of Hashin and Shtrikman is given. It appears possible to dispense with some subsidiary conditions which in the original principle had to be imposed on the class of functions considered in the variational process. However, through the use of the new principle the possibility of obtaining a pair of two sided bounds is lost and this has to be compensated by invoking one of the complementary principles which are formulated in the sequel.     

A molecular-beam investigation of the reaction H2 + 12O2 → H2O on Pd(111)

Using molecular-beam relaxation techniques and isotopic exchange experiments, the water-formation reaction on Pd(111) has been shown to proceed via a Langmuir-Hinshelwood mechanism. The reaction product H₂O is emitted from the surface with a cosine distribution. The rate-determining step is the formation of OH_ad in the reaction O_ad + H_ad → OH_ad. The activation energy for this step is 7 kcal/mole with a pre-exponential factor, v, of 4 × 10^?8 cm² atom^?1 sec^?1. This value for v lies well below that observed for simple second-order desorption of dissociatively adsorbed diatomic gases, but is roughly of the order of that obtained for the oxidation of CO on Pd(111). The formation of H₂O proceeds differently under conditions of excess O₂ or H₂. In an excess of H₂, the kinetics is dominated by the transport of atomic hydrogen between the bulk and the surface as was found for the H?D exchange reaction on Pd(111). In an excess of O₂, diffusion of hydrogen into the bulk is blocked by adsorbed oxygen and the hydrogen reservoir available for reaction at the surface is decreased by several orders of magnitude. This results in a drastic reduction of the reaction rate which can be reversed by increasing the partial pressure of H₂.     

A molecular beam study of the adsorption and desorption of oxygen from a Pt(111) surface

The adsorption and desorption of O₂ on a Pt(111) surface have been studied using molecular beam/surface scattering techniques, in combination with AES and LEED for surface characterization. Dissociative adsorption occurs with an initial sticking probability which decreases from 0.06 at 300 K to 0.025 at 600 K. These results indicate that adsorption occurs through a weakly-held state, which is also supported by a diffuse fraction seen in the angular distribution of scattered O₂ flux. Predominately specular scattering, however, indicates that failure to stick is largely related to failure to accommodate in the molecular adsorption state. Thermal desorption results can be fit by a desorption rate constant with pre-exponential ν_d = 2.4 × 10^?2 cm² s^?1 and activation energy E_D which decreases from 51 to 42 kcal/mole^?1 with increasing coverage. A forward peaking of the angular distribution of desorbing O₂ flux suggests that part of the adsorbed oxygen atoms combine and are ejected from the surface without fully accomodating in the molecular adsorption state. A slight dependance of the dissociative sticking probability upon the angle of beam incidence further supports this contention.     

On the core of information graph games

This paper considers a subclass of minimum cost spanning tree games, called information graph games. It is proved that the core of these games can be described by a set of at most 2n — 1 linear constraints, wheren is the number of players. Furthermore, it is proved that each information graph game has an associated concave information graph game, which has the same core as the original game. Consequently, the set of extreme core allocations of an information graph game is characterized as the set of marginal allocation vectors of its associated concave game. Finally, it is proved that all extreme core allocations of an information graph game are marginal allocation vectors of the game itself, though not all marginal allocation vectors need to be core allocations.     

Spontaneous formation of micrometer-size inorganic peapods

We show that polyoxometalate (ammonium phosphomolybdate) Keggin in aqueous dispersions upon sonication spontaneously transforms into micrometer-sized, peapod-shaped structures. The formation of these peapods is preceded by the generation of spherical aggregates. The particles have been characterized experimentally by time-resolved dynamic light scattering (DLS), transmission electron microscopy (TEM), and scanning TEM with a high-angle annular dark field detector (STEM-HAADF) for energy-dispersive X-ray (STEM/EDX) elemental analyses. A pathway for the phenomenon is proposed.     

Glycerol etherification over highly active CaO-based materials: new mechanistic aspects and related colloidal particle formation

Glycerol is an attractive renewable building block for the synthesis of di- and triglycerols, which have numerous applications in the cosmetic and pharmaceutical industries. In this work, the selective etherification of glycerol to di- and triglycerol was studied in the presence of alkaline earth metal oxides and the data are compared with those obtained with Na2CO3 as a homogeneous catalyst. It was found that glycerol conversion increased with increasing catalyst basicity; that is, the conversion increases in the order: MgO90 % at 60 % conversion) are obtained over CaO, SrO, and BaO. For these catalysts no substantial acrolein formation was observed. Furthermore, at the start of the reaction mainly linear diglycerol was produced, whereas at higher conversion degrees branched diglycerol started to form. In another series of experiments different types of CaO materials were prepared. It was found that these CaO-based materials not only differed in their surface area and number of basic sites, but also in their Lewis acid strength. Within this series the CaO material possessing the strongest Lewis acid sites had the highest catalytic activity, comparable to that of BaO, pointing towards the important role of Lewis acidity for this etherification reaction. Based on these observations a plausible alternative reaction scheme for glycerol etherification is presented, which considers the facilitation of the hydroxyl leaving process. Finally, the stability of the catalytic solids under study was investigated and it was found that colloidal CaO particles of about 50-100 nm can be spontaneously generated during reaction. Catalytic testing of these CaO colloids, after isolation from the reaction medium, revealed a very high etherification activity. Understanding the nature of these Ca-based colloids opens new opportunities for investigating supported colloidal particle catalysts to take advantage of both their hetero- and homogeneous nature.