The adsorption of small silica particles onto large sterically stabilized poly(2-vinylpyridine) [P2VP] latex particles in aqueous solution is assessed as a potential route to nanocomposite particles with a "core-shell" morphology. Geometric considerations allow the packing efficiency, P, to be related to the number of adsorbed silica particles per latex particle, N. Making no assumptions about the packing structure, this approach leads to a theoretical estimate for P of 86 +/- 4%. Experimentally, dynamic light scattering is used to obtain a plot of hydrodynamic diameter against N, which indicates the conditions required for monolayer coverage of the latex by the silica particles. Transmission electron microscopy confirmed that, at approximately monolayer coverage, calcination of these nanocomposite particles led to the formation of well-defined hollow silica shells. This is interpreted as strong evidence for a contiguous monolayer of silica particles surrounding the latex cores. On this basis, an experimental value for P of 69 +/- 4% was estimated for nanocomposite particles prepared by the heteroflocculation of a 20 nm silica sol with near-monodisperse P2VP latexes of either 463 or 616 nm diameter at approximately pH 10. X-ray photoelectron spectroscopy was used to quantify the extent of latex surface coverage by the silica particles. This technique gave good agreement with the silica packing efficiencies estimated from calcination studies.

How must n equal non-overlapping circles be packed on a sphere so that the angular diameter of the circles will be as great as possible? In the paper, the conjectured solutions of this problem for n = 18, 27, 34, 35, 40 are improved on the basis of an idea of Danzer. Using the theory of bar structures it is ascertained that, in these cases, the edge-length of the graphs of the circle-packings can be increased till, in the graphs, additional edges appear which prevent further motions apart from rigid motions. The cases of n = 17 and 32 are also dealt with and there are references to the possibilities of further applications of the method applied in this paper (n = 59,80,110,122).

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Zeeman has drawn attention to the sequences in which catastrophes, or modes of instability, can be linked, and it is a common observation that sequences of catastrophes of low order are always found in the environment of catastrophes of higher order. In this paper, a simple buckling model is presented that generates in an elegant manner a complete sequence of the umbilic catastrophes as represented by the semi-symmetric branching points. The scan of a single fundamental parameter of this model is shown to trace a route through all regimes of the umbilic bracelet, giving in turn the hyperbolic, symbolic, elliptic, parabolic and hyperbolic umbilic catastrophes.