Characterization of Self-Assembled 2D Patterns with Voronoi Entropy

Edward Bormashenko; Mark Frenkel; Alla Vilk; Alexander A. Fedorets; Nurken E. Aktaev; Leonid A. Dombrovsky; Michael Nosonovsky

doi:10.20944/preprints201811.0535.v1

Preprint Review Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 19 November 2018 / Approved: 22 November 2018 / Online: 22 November 2018 (04:49:13 CET)

The Voronoi entropy is a mathematical tool for quantitative characterization of the orderliness of points distributed on a surface. The tool is useful to study various surface self-assembly processes. We provide the historical background, from Kepler and Descartes to our days, and discuss topological properties of the Voronoi tessellation, upon which the entropy concept is based, and its scaling properties, known as the Lewis and Aboav-Weaire laws. The Voronoi entropy has been successfully applied to recently discovered self-assembled structures, such as patterned micro-porous polymer surfaces obtained by the breath figure method and levitating ordered water micro-droplet clusters.

Voronoi entropy; surface patterns; Lewis law; Aboav law; droplet cluster; self-assembly

Physical Sciences, Condensed Matter Physics

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Characterization of Self-Assembled 2D Patterns with Voronoi Entropy

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