Nanostructures in Physical Materials Chemistry: An Exploratory Laboratory

The blend of nanotechnology and material science is often beyond the scope of undergraduate laboratories. Through undergraduate research, graphite-intercalated compounds have been incorporated in the production of carbon-based nanostructures. Based on this work a series of exploratory exercises were designed for the undergraduate physical chemistry laboratory emphasizing nanostructure material science. This rapidly expanding area of science and technology can be introduced at an undergraduate level using a high temperature oven to produce nanostructure samples that are analyzed by Raman spectroscopy, scanning electron microscopy, and transmission electron microscopy at research university laboratories, infrared spectroscopy, and a bomb calorimeter. In these experiments we use samples of pure graphite, fluorinated graphite, and lanthanum oxide to induce the formation of nanostructures. An overview of fullerenes, nanotubes, boron nitride and Si nanostructures, other carbon forms, graphite-intercalated compounds, and the storage of hydrogen in nanotubes are provided in an appendix. Several extensions of the laboratory are proposed.     

A characterisation of virtually free groups

We prove that a finitely generated group G is virtually free if and only if there exists a generating set for G and k > 0 such that all k-locally geodesic words with respect to that generating set are geodesic. Received: 30 October 2006     

Array gain for a cylindrical array with baffle scatter effects

Cylindrical arrays used in sonar for passive underwater surveillance often have sensors surrounding a cylindrical metal baffle. In some operational sonars, the phones in each stave (i.e., each line of phones aligned with the cylinder axis) are hardwired together so that the array is equivalent to a baffled circular array of directional elements, where each element corresponds to a line array of omnidirectional phones steered to broadside. In this paper a model is introduced for computing the array gain of such an array at high frequencies, which incorporates baffle scatter using infinite, rigid cylinder scattering theory, and with ambient noise described by an angular spectral density function. In practice the phones are often offset from the baffle surface, and the acoustic field sampled by the staves is distorted at high frequencies due to interference between the incident and scattered fields. Examples are given to illustrate the resulting array gain degradation, using three noise distributions that are frequently used in sonar performance modeling: three-dimensional isotropic, two-dimensional isotropic, and surface dipole noise.     

Charge renormalization for effective interactions of colloids at water interfaces

We analyze theoretically the electrostatic interaction of surface-charged colloids at water interfaces with special attention to the experimentally relevant case of large charge densities on the colloid-water interface. Whereas linear theory predicts an effective dipole potential, the strength of which is proportional to the square of the product of charge density and screening length, nonlinear charge renormalization effects change this dependence to a weakly logarithmic one. These results appear to be particularly relevant for structure formation at fluid interfaces with arbitrarily shaped colloids.     

Unexpected four- and eight-membered organo P-Se heterocycles

Reaction of [PhP(Se)(micro-Se)](2) (Woollins' reagent, WR) with symmetrically disubstituted diynes: five-membered P(Se)Se(2)C(2) heterocycles and bis-heterocycles with two five-membered P(Se)Se(2)C(2) rings connected through a C-C single bond; (t)Bu-C[triple bond, length as m-dash]C-C[triple bond, length as m-dash]C-(t)Bu reacts differently to afford an unprecedented four-membered P(Se)SeC(2) heterocycle with one unreacted triple bond and a fused bis-heterocycle containing two five-membered P(Se)SeC(3) rings fused at the middle two carbons of the diyne to give a heterocyclic analogue of pentalene, [3.3.0]octa-1-6-diene.