Preprint Review Version 1 This version is not peer-reviewed

Characterization of Self-Assembled 2D Patterns with Voronoi Entropy

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

A peer-reviewed article of this Preprint also exists.

Bormashenko, E.; Frenkel, M.; Vilk, A.; Legchenkova, I.; Fedorets, A.A.; Aktaev, N.E.; Dombrovsky, L.A.; Nosonovsky, M. Characterization of Self-Assembled 2D Patterns with Voronoi Entropy. Entropy 2018, 20, 956. Bormashenko, E.; Frenkel, M.; Vilk, A.; Legchenkova, I.; Fedorets, A.A.; Aktaev, N.E.; Dombrovsky, L.A.; Nosonovsky, M. Characterization of Self-Assembled 2D Patterns with Voronoi Entropy. Entropy 2018, 20, 956.

Journal reference: Entropy 2018, 20, 956
DOI: 10.3390/e20120956

Abstract

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.

Subject Areas

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

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