The surface-plasmon properties of Au bipyramids are investigated using the finite-difference time-domain method. It is found that both the extinction cross sections and local electric-field enhancements of Au bipyramids are larger than those of Au nanorods that have longitudinal surface plasmon (LSP) wavelengths close to those of Au bipyramids. Following this result the growth of Au bipyramids using cationic surfactants of variously sized headgroups as stabilizing agents is carried out. It is found that the growth using cetyltributylammonium bromide (CTBAB) produces Au bipyramids with tunable LSP wavelengths in high yields. The oxidation behaviour of Au bipyramids using hydrogen peroxide as the oxidizing agent is fully explored and the oxidation is found to occur preferentially at highly curved surface sites. It is further demonstrated that the oxidation rate can be controlled by varying the amounts of hydrogen peroxide and hydrochloric acid. This oxidation approach can be used in conjunction with the seed-mediated growth in CTBAB solutions to produce Au bipyramids, the LSP wavelengths of which are finely tunable from 650 to 1300 nm.

Abstract. Let H be a complex Hilbert space and B(H) the Banach space of all bounded linear operators on H . For any A ∈ B(H) , let w(A) denote the numerical radius of A . Then A is normaloid if w(A) = A . In this note, we show that A is normaloid if there is a sequence of unit vectors (x n ) such that lim n→∞ Ax n = A and lim n→∞ | Ax n ,x n | = w(A) simultaneously. The result is then used to study the Davis-Wielandt radius.Mathematics subject classification (2010): 47A12, 47B20.

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