Effect of quantum confinement on the dielectric function of PbSe

Monolayers of lead selenide nanocrystals of a few nanometers in height have been made by electrodeposition on a Au(111) substrate. These layers show a thickness-dependent dielectric function, which was determined using spectroscopic ellipsometry. The experimental results are compared with electronic structure calculations of the imaginary part of the dielectric function of PbSe nanocrystals. We demonstrate that the size-dependent variation of the dielectric function is affected by quantum confinement at well-identifiable points in the Brillouin zone, different from the position of the band-gap transition.     

Long-range order of organized oligonucleotide monolayers on Au(111) electrodes

Oligonucleotides modified by a hexamethylene linker group adsorb on gold electrodes via Au-S bond formation. We have obtained novel data for adsorption of thiol-modified (HS) single-strand HS-10A and double-stranded HS-10AT oligonucleotides and for analogous thiol-free 10A (A = adenine) and 10T (T = thymine) nonspecifically adsorbed as reference molecules. Mercaptohexanol has served as a second reference molecule. The data are based on cyclic and differential pulse voltammetry, interfacial capacitance data, and in situ scanning tunneling microscopy (STM) directly in an aqueous buffer solution, with electrochemical potential control of both the sample electrode and the tip. All the data are based on single-crystal, atomically planar Au(111)-electrode surfaces. The high sensitivity of such surfaces provides accurate HS-10A and HS-10AT electrode coverages on the basis of the reductive desorption of the Au-S bond. The coverage is high and in keeping with dense monolayers of adsorbed HS-10A and HS-10AT in an upright or tilted orientation, with the oligonucleotide backbone repelled from the strongly negatively charged electrode surface. Adsorbed thiol-free 10A only gives a Au(111)-reconstruction peak, while 10T shows a subtle pattern involving pronounced voltammetric adsorption peaks indicative of both nonspecific adsorption via single thymine units and potential-dependent structural reorganization in the surface layer. In situ STM supports these findings at the molecular level. In situ STM of HS-10A discloses large, highly ordered domains at strongly negative sample potentials. Reversible domain formation and disordering could, moreover, be controlled by an electrochemical potential variation in the negative and positive directions, respectively. 10A and 10T did not form ordered adsorbate domains, substantiating that domain formation rests on adsorption of thiol-modified oligonucleotide adsorption in an upright or tilted orientation. The comprehensive, high-resolution information reported may hold prospects for single-molecule electronic conduction and molecular-scale mapping of oligonucleotide hybridization.     

Background noise in piezoresistive,electret condenser,and ceramic microphones

Background noise studies have been extended from air condenser microphones to piezoresistive, electret condenser, and ceramic microphones. Theoretical models of the respective noise sources within each microphone are developed and are used to derive analytical expressions for the noise power spectral density for each type. Several additional noise sources for the piezoresistive and electret microphones, beyond what had previously been considered, were applied to the models and were found to contribute significantly to the total noise power spectral density. Experimental background noise measurements were taken using an upgraded acoustic isolation vessel and data acquisition system, and the results were compared to the theoretically obtained expressions. The models were found to yield power spectral densities consistent with the experimental results. The measurements reveal that the 1/f noise coefficient is strongly correlated with the diaphragm damping resistance, irrespective of the detection technology, i.e., air condenser, piezoresistive, etc. This conclusion has profound implications upon the expected 1/f noise component of micromachined (MEMS) microphones.     

Ray helicity: geometric invariant for multidimensional resonant wave conversion

For a multicomponent wave field propagating into a multidimensional conversion region, the rays are shown to be helical, in general. For a ray-based quantity to have a fundamental physical meaning, it must be invariant under the following two groups of transformations, which are used to construct solutions: congruence transformations (which involve linear combinations of components of the multicomponent wave field) and canonical transformations (which act on the ray phase space). It is shown that for conversion between two waves there is a new invariant not previously discussed: the intrinsic helicity of the ray.     

N,N-dichloro-2-nitrobenzenesulfonamide as the electrophilic nitrogen source for direct diamination of enones

N,N-dichloro-o-nitrobenzenesulfonamide (2-NsNCl2) was found to be an effective electrophilic nitrogen source for the direct diamination of alpha,beta-unsaturated ketones without the use of any metal catalysts. The reaction is very convenient to carry out without the protection of inert gases. Molecular sieves (4 A) and temperature were found to play key roles in controlling the formations of 3-trichloromethyl and dichloromethyl imidazoline products (16 examples). The 2-Ns-protection group of the resulting diamine products can be easily cleaved under mild Fukuyama's conditions. A new mechanism hypothesis of [2+3] cyclization and N-chlorination has been proposed to explain the product structures, particularly their regio- and stereochemistry.     

Structure-activity relationship of new octaethylporphyrin-based benzochlorins as photosensitizers for photodynamic therapy

An in vitro and in vivo structure-activity relationship study was carried out on a series of benzochlorins with variable lipophilicity. The structural features evaluated in this study include the length of the alkyl or fluoroalkyl groups attached to the six-member exocyclic ring either by an ether or by a carbon-carbon bond. In preliminary in vitro (radiation-induced fibrosarcoma [RIF] cells) and in vivo screening (C3H mice, bearing RIF tumors), all Zn (II) benzochlorins were found to be effective. However, benzochlorins bearing alkyl groups with carbon-carbon bonds showed enhanced efficacy compared with the related alkyl ether analogs. A comparative intracellular localization study of the newly synthesized benzochlorins with Rhodamine-123 indicated that the effective photosensitizers localize in mitochondria, and a displacement study with PK11195 showed their partial affinity for the peripheral benzodiazepine receptor (PBR). Interestingly, compared with the Zn(II) benzochlorin that was found to be quite effective in vivo, the corresponding free-base analog produced less photosensitizing activity and was found to localize in lysosomes. A comparative study with dansyl-proline confirmed the binding of the effective benzochlorins to Site II of human serum albumin (HSA). However, no direct correlation was observed between the binding constant values (to HSA or to PBR) of benzochlorins and their photosensitizing ability.     

Denominators for the Poincaré series of invariants of matrices with involution

The goal of this paper is to study some Poincaré series associated to the invariants of the symplectic and odd orthogonal groups. These series turn out to be rational functions and our main results will describe the denominators. This work will generalize some known results on the invariants of the general linear groups. In addition to whatever intrinsic interest we hope our results may have, the subject involves an interesting interplay of invariant theory and complex variables. The first author gratefully acknowledges Support from DePaul University Research Council. The second author was supported in part by the Israel Science Foundation, founded by the Israel Academy of Sciences and Humanities, and by an Internal Research Grant from Bar-Ilan University.     

Apollonian circle packings: number theory

Apollonian circle packings arise by repeatedly filling the interstices between mutually tangent circles with further tangent circles. It is possible for every circle in such a packing to have integer radius of curvature, and we call such a packing an integral Apollonian circle packing. This paper studies number-theoretic properties of the set of integer curvatures appearing in such packings. Each Descartes quadruple of four tangent circles in the packing gives an integer solution to the Descartes equation, which relates the radii of curvature of four mutually tangent circles: . Each integral Apollonian circle packing is classified by a certain root quadruple of integers that satisfies the Descartes equation, and that corresponds to a particular quadruple of circles appearing in the packing. We express the number of root quadruples with fixed minimal element −n as a class number, and give an exact formula for it. We study which integers occur in a given integer packing, and determine congruence restrictions which sometimes apply. We present evidence suggesting that the set of integer radii of curvatures that appear in an integral Apollonian circle packing has positive density, and in fact represents all sufficiently large integers not excluded by congruence conditions. Finally, we discuss asymptotic properties of the set of curvatures obtained as the packing is recursively constructed from a root quadruple.     

Optical and photocatalytic properties of nanocrystalline TiO2 synthesised by solid-state chemical reaction

Nanoparticulate TiO₂ is of interest for a variety of technological applications, including optically transparent UV-filters and photocatalysts for the destruction of chemical waste. The successful use of nanoparticulate TiO₂ in such applications requires an understanding of how the synthesis conditions effect the optical and photocatalytic properties. In this study, we have investigated the effect of heat treatment temperature on the properties of nanoparticulate TiO₂ powders that were synthesised by solid-state chemical reaction of anhydrous TiOSO₄ with Na₂CO₃. It was found that the photocatalytic activity increased with the heat treatment temperature up to a maximum at 600 °C and thereafter declined. In contrast, the optical transparency decreased monotonically with the heat treatment temperature. These results indicate that solid-state chemical reaction can be used to prepare powders of nanoparticulate TiO₂ with properties that are optimised for use as either optically transparent UV-filters or photocatalysts.