title: Self-assembly of like-charged nanoparticles into Voronoi diagrams.
abstract: The self-assembly of nanoscopic building blocks into higher order macroscopic patterns is one possible approach for the bottom-up fabrication of complex functional systems. Macroscopic pattern formation, in general, is determined by the reaction and diffusion of ions and molecules. In some cases macroscopic patterns emerge from diffusion and interactions existing between nanoscopic or microscopic building blocks. In systems where the distribution of the interaction-determining species is influenced by the presence of a diffusion barrier, the evolving macroscopic patterns will be determined by the spatiotemporal evolution of the building blocks. Here we show that a macroscopic pattern can be generated by the spatiotemporally controlled aggregation of like-charged carboxyl-terminated gold nanoparticles in a hydrogel, where clustering is induced by the screening effect of the sodium ions that diffuse in a hydrogel. Diffusion fronts of the sodium ions and the induced nanoparticle aggregation generate Voronoi diagrams, where the Voronoi cells consist of aggregated nanoparticles and their edges are aggregation-free and nanoparticle-free zones. We also developed a simple aggregation-diffusion model to adequately describe the evolution of the experimentally observed Voronoi patterns.
authors.affiliation: Centre for Energy Research, Institute of Technical Physics and Materials Science, Budapest, Hungary.
authors.forename: Dániel
authors.initials: D
authors.lastname: Zámbó
authors.affiliation: Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo, Japan.
authors.forename: Kohta
authors.initials: K
authors.lastname: Suzuno
authors.affiliation: Centre for Energy Research, Institute of Technical Physics and Materials Science, Budapest, Hungary.
authors.forename: Szilárd
authors.initials: S
authors.lastname: Pothorszky
authors.affiliation: Department of Physics, Budapest University of Technology and Economics, 1111, Budafoki út 8, Budapest, Hungary. lagzi@vuk.chem.elte.hu.
authors.forename: Dóra
authors.initials: D
authors.lastname: Bárdfalvy
authors.affiliation: Department of Physics, Budapest University of Technology and Economics, 1111, Budafoki út 8, Budapest, Hungary. lagzi@vuk.chem.elte.hu.
authors.forename: Gábor
authors.initials: G
authors.lastname: Holló
authors.affiliation: Department of Macromolecular Science and Engineering, Graduate School of Science and Technology, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan.
authors.forename: Hideyuki
authors.initials: H
authors.lastname: Nakanishi
authors.affiliation: Lehn Institute of Functional Materials, School of Chemistry and Chemical Engineering, Sun Yat-Sen University, Guangzhou 510275, China.
authors.forename: Dawei
authors.initials: D
authors.lastname: Wang
authors.affiliation: Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo, Japan.
authors.forename: Daishin
authors.initials: D
authors.lastname: Ueyama
authors.affiliation: Centre for Energy Research, Institute of Technical Physics and Materials Science, Budapest, Hungary.
authors.forename: András
authors.initials: A
authors.lastname: Deák
authors.affiliation: Department of Physics, Budapest University of Technology and Economics, 1111, Budafoki út 8, Budapest, Hungary. lagzi@vuk.chem.elte.hu.
authors.forename: István
authors.initials: I
authors.lastname: Lagzi