Geometric curvature of a low-dimensional host material often leads to drastic changes in physical properties of the system living upon it. In this article, I give a bird’s-eye review on the theoretical progresses on the geometry-property relations, i.e., intriguing correlation between geometric curvature and physical property of the material considered. Some differential-geometry-based approaches that are aimed at quantitative description of physical systems confined to curved surfaces are presented.
Well-defined inhomogeneous α-Sb2O4/VSbO4 catalysts were prepared using an electron lithography method to investigate the effects of µm order structures on an atomic scale catalytic reaction. X-ray photoelectron spectroscopy (XPS) and laser microscopy revealed that µm order structures were successfully developed on a Si substrate where an α-Sb2O4 micro line with a controlled width was deposited on VSbO4. We carried out a propene partial oxidation reaction on this surface and found that the acrolein formation rate was significantly influenced by the width and interval of the α-Sb2O4 µm line. The results of this study indicate the possibility of controlling the surface reaction by the inhomogeneity of the surface structure in the µm order.
