N identical particles under quantum confinement: a many-body dimensional perturbation theory approach

Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional perturbation theory, a powerful set of tools that uses symmetry to yield simple results for studying such many-body systems. We present a detailed discussion of the dimensional continuation of the N-particle Schrödinger equation, the spatial dimension D→∞ equilibrium (D⁰) structure, and the normal-mode (D⁻¹) structure. We use the FG matrix method to derive general, analytical expressions for the many-body normal-mode vibrational frequencies, and we give specific analytical results for three confined N-body quantum systems: the N-electron atom, N-electron quantum dot, and N-atom inhomogeneous Bose-Einstein condensate with a repulsive hard-core potential.     

Electrochemical Properties of Vanadium Oxide Aerogels and Aerogel Nanocomposites

The electrochemical properties of high surface area transition metal oxide aerogels are extremely interesting because aerogels serve to amplify surface effects. As a result, the electrochemical properties are dominated by surfaces rather than by bulk behavior. In the case of vanadium oxide aerogels this leads to extraordinary electrochemical properties, including an extremely high capacity for lithium and electrochemical responses that are both battery-like and capacitor-like. By exploiting sol-gel synthesis, it is possible to synthesize nanocomposite electrodes in which aerogels are in intimate contact with carbon nanotubes. The resulting nanocomposites exhibit superior electrochemical properties, especially at high discharge.     

Germacreme derivatives from diverse marine soft-corals (octocorallia)

Examinations of the extracts of 8 taxonomically-diverse marine soft-corals (Orders Gorgonaceae, Alcyonaceae and Stolonifera, Subclass Octocorallia, Phylum Cnidaria), have resulted in the isolation of 4 new sesquiterpenoids (1–4) of the germacrene type. Three previously known germacrene derivatives (5–7), and the elemane 8, have also been isolated, and complete ¹H and ¹³C NMR assignments for these compounds are reported.     

The structure of thorikosite,a naturally occurring member of the bismuth oxyhalide group

Thorikosite, (Pb₃Sb_0.6As_0.4)(O₃0H)Cl₂, is a naturally occurring member of the bismuth oxyhalide group isostructural with LiBi₃O₄Cl₂. The space group isI4/mmm witha = 3.919(1)A?,c = 12.854(5)A?, andZ = 1. A crystal structure analysis showed complete solid solution of Pb²⁺, Sb³⁺, and As³⁺ on the single cation site and large atomic temperature factors indicative of pervasive structural disorder. The latter is due to the structural adjustments necessary to accommodate cations of very different sizes in the same site. Thorikosite is closely related to synthetic tetragonal PbSbO₂Cl through the coupled substitution Sb³⁺O^2? ? Pb²⁺(OH)^?.     

Four levels of pattern recognition

Problems of pattern recognition in chemistry and other subjects can be divided conveniently into four different types depending on the level of scope of the problem.(1) Classification into one of a number of defined classes. As an example blood samples taken from persons known to be either controls or welders are considered. The problem is whether trace element concentrations in these samples contain information on whether or not a person is a welder.(2) Level 1 plus the possibility that an object is an outlier, i.e. does not belong to any of the defined classes. As an example, the üse of ¹³C-n.m.r. data to decide whether 2-substituted norbornanes have the exo or endo structure is discussed. (2A) Level 2, asymmetric. This situation occurs when one class does not have a systematic structure, but another class is homogeneous and can be described by a level 2 model. This occurs in the classification of materials or compounds as good or bad, active or inactive, and in binary classifications. As an example the use of trace element data to classify steel samples as having good or poor properties of strength is discussed.(3) Level 2 plus the ability to relate the variables measured to external properties of continuous character. As an example, the classification of a series of chemical compounds as β -receptor blockers, β -receptor stimulants, or neither, on the basis of their structural variables is discussed. In addition, relations between these structural variables and the measured biological activity are sought within each of the two classes.(4) Level 3 with the difference that several external property variables in the objects are measured. It may be desirable to use variables of the objects both for classification and for relations to several property variables: such examples are numerous in analytical chemistry.     

Effect of homologous series of alkyl sulfate surfactants on the emulsion polymerization of styrene. I. Equal total concentrations

There is evidence in the literature that the rates of emulsion polymerization increase by a large factor as the alkyl chain length increases for a homologous series of surfactants. However, the area occupied by a surfactant molecule in a saturated monolayer at the polystryene/water interface is independent of chain length for alkyl sulfates so that, on the basis of Gardon's theory, equal rates of polymerization would be expected when equal concentrations of surfactants are used. There is a large increase in the number of polymer latex particles formed and in the rate of emulsion polymerization as the surfactant concentration is increased through the critical micelle concentration; this accounts for the large increases reported, because the lower members of the homologous series are below their critical micelle concentrations in most of the published studies. When a common concentration is chosen that is above the critical micelle concentration even for the lowest member of the series, only a relatively small increase in latex particle number and rate of emulsion polymerization with alkyl chain length of the surfactant is observed. This is attributable to an increase in the concentration of surfactant micelles. Good agreement with Gardon's theory is obtained when the concentration of micellar surfactant is used instead of the total surfactant concentration.     

Oxygen diffusion in poly(dimethyl siloxane) using fluorescence quenching. I. Measurement technique and analysis

The transport properties of oxygen in poly(dimethyl siloxane) have been measured using the method of quenching of fluorescence. This paper discusses the uniqueness of this method and its use in measuring the diffusion coefficient of oxygen in unfilled PDMS. The results show (1) a large value for the diffusion coefficient of oxygen in pure PDMS at 25°C, D = 3.55 × 10^?5 cm²/s, (2) a low value of the acitivation energy, E_D = 4.77 kcal/mole, which was not temperature dependent in the ranges evaluated, and (3) a large value of the preexponential term, D₀ = 0.115 cm²/s. The diffusion coefficient was found to be independent of both the oxygen concentration and fluorophor concentration in the pressure and temperature ranges used in these experiments. The import of these experiments lies in their application to a unique biomedical oxygen sensor which is fast, sensitive, and does not consume oxygen.     

Evaluation of octadecyl-bonded alumina for separations of proteins and peptides by reversed-phase high-performance liquid chromatography

Summary A recently-developed octadecyl-bonded alumina (ODA) stationary phase was evaluated for the separation of peptides and proteins by reversed phase high performance liquid chromatography. Using standard water-acetonitrile mobile phase gradients containing 0.1 % trifluoroacetic acid, the average peak capacity obtained for the separation of a mixture of ribonuclease a, cytochrome c, lysozyme and carbonic anhydrase on an ODA column are similar to that obtained on a widely used octadecylsilane (ODS) column. However, overall chromatographic resolution of the components of this mixture on ODA is inferior to that obtained on ODS. Cytochrome c peak areas were found to be 50% smaller on the ODA column than on ODS. On the other hand, both peak capacities and resolutions of octapeptide mixtures were found to be generally superior on the ODA column, and peak areas for a representative octapeptide were found to be virtually identical for both ODA and ODS columns. The differences in the results obtained on the ODA and ODS columns for these separations are attributed to the smaller pore size and unique fused-microplatelet shape of the ODA particles. Comparisons of the separations of the tryptic digest of cytochrome c on the ODS and ODA columns demonstrate that the ODA phase is potentially as useful as ODS for peptide mapping applications.     

Dual-label autoradiographic analysis of human skin fibroblast and myoblast proteins by two-dimensional polyacrylamide gel electrophoresis using immobilised pH gradients in the first dimension

Horizontal two-dimensional polyacrylamide gel electrophoresis with immobilised pH gradients in the first dimension has been applied to the analysis of human skin fibroblast and muscle myoblast total cell proteins. Excellent two-dimensional separations of skin fibroblast proteins were obtained using pH 4-10 immobilised pH gradient gels with a long interelectrode distance (16 cm), but resolution was degraded, particularly of the more acidic proteins, by the use of shorter (10 cm) gels. Improved resolution of acidic and basic proteins was obtained using separate pH 4-7 and pH 7-10 immobilised pH gradient gels respectively in the first dimension. Two-dimensional protein maps of skin fibroblast proteins were visualised both by silver staining and by autoradiography of samples labelled synthetically with [35S]methionine. Horizontal two-dimensional electrophoresis, using pH 4-7 and pH 7-10 immobilised pH gradient gels in the first dimension, was applied to the analysis of protein samples from skin fibroblasts and muscle myoblasts dual-labelled synthetically with [35S]methionine and [75Se]selenomethionine in an attempt to identify sets of proteins specific to each cell type. In addition, two-dimensional maps or protein samples derived from normal individuals and patients with Duchenne muscular dystrophy were compared to search for protein changes associated with the disease state. Although sets of qualitative protein spot differences were observed by visual inspection of the two-dimensional gels, more rigorous qualitative and quantitative analysis of the patterns using a computerised analysis system will be required to obtain the maximum amount of information from these data.