To use solar irradiation or interior lighting efficiently, we sought a photocatalyst with high reactivity under visible light. Films and powders of TiO(2-x)N(x) have revealed an improvement over titanium dioxide (TiO2) under visible light (wavelength < 500 nanometers) in optical absorption and photocatalytic activity such as photodegradations of methylene blue and gaseous acetaldehyde and hydrophilicity of the film surface. Nitrogen doped into substitutional sites of TiO2 has proven to be indispensable for band-gap narrowing and photocatalytic activity, as assessed by first-principles calculations and x-ray photoemission spectroscopy.

TiO2-based powder, including 0.1 at% of N doped in the rutile lattice, has been synthesized by oxidation of TiN. As a result, a significant shift of the absorption edge to a lower energy in the visible-light region has been observed. The substitutional doping of N into the TiO2 lattice is found to be effective; its 2p states contribute to the band-gap narrowing by mixing with O 2p as shown in ab initio electronic structure calculations.

This review describes the theory of mass transport at ultramicroelectrodes that have broken through several experimental limitations of electrochemical measurements. On the basis of the mathematical miniaturization, the ultramicroelectrode can be classified into a point electrode, a line electrode, and a plane electrode. Electrochemical features of these electrodes are described from a viewpoint of the mass transport, especially due to diffusion. Theoretical difficulty in ultramicroelectrodes is mainly due to nonuniform current distribution on the electrode surface. The expression for the time-dependent diffusion-controlled current at any electrode geometry, which predicts the current responding to any potential variation, is presented. Conditions of the steady-state current are specified. The diffusional characteristic functions at a dsk, a cylinder, and a band are presented, from which the theories of various electrochemical techniques can be derived analytically. Voltammetric peak currents at several ultramicroelectrodes are compared in light of the diffusional edge effect. The properties of the steadystate current are described at a disk, a band array, a ring, and a recess electrode. The theory is extended to the current-potential curves complicated by the heterogeneous kinetics at a disk, a cylinder, and a band-array electrode.

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