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Characterization of Self-Assembled 2D Patterns with Voronoi Entropy

Department of Chemical Engineering, Biotechnology and Materials, Engineering Sciences Faculty, Ariel University, Ariel 407000, Israel
University of Tyumen, 6 Volodarskogo St., Tyumen 625003, Russia
Joint Institute for High Temperatures, 17A Krasnokazarmennaya St., Moscow 111116, Russia
Mechanical Engineering, University of Wisconsin—Milwaukee, 3200 North Cramer St., Milwaukee, WI 53211, USA
Author to whom correspondence should be addressed.
Entropy 2018, 20(12), 956;
Received: 19 November 2018 / Revised: 5 December 2018 / Accepted: 10 December 2018 / Published: 11 December 2018
(This article belongs to the Special Issue Entropic Methods in Surface Science)
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 microporous polymer surfaces obtained by the breath figure method and levitating ordered water microdroplet clusters. View Full-Text
Keywords: Voronoi entropy; surface patterns; Lewis law; Aboav law; droplet cluster; self-assembly Voronoi entropy; surface patterns; Lewis law; Aboav law; droplet cluster; self-assembly
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MDPI and ACS Style

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.

AMA Style

Bormashenko E, Frenkel M, Vilk A, Legchenkova I, Fedorets AA, Aktaev NE, Dombrovsky LA, Nosonovsky M. Characterization of Self-Assembled 2D Patterns with Voronoi Entropy. Entropy. 2018; 20(12):956.

Chicago/Turabian Style

Bormashenko, Edward, Mark Frenkel, Alla Vilk, Irina Legchenkova, Alexander A. Fedorets, Nurken E. Aktaev, Leonid A. Dombrovsky, and Michael Nosonovsky. 2018. "Characterization of Self-Assembled 2D Patterns with Voronoi Entropy" Entropy 20, no. 12: 956.

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