Characterization of self-assembled 2D patterns with voronoi entropy

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

doi:10.3390/e20120956

Characterization of self-assembled 2D patterns with voronoi entropy

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

Department of Chemical Engineering

Research output: Contribution to journal › Review article › peer-review

57 Scopus citations

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 microporous polymer surfaces obtained by the breath figure method and levitating ordered water microdroplet clusters.

Original language	English
Article number	956
Journal	Entropy
Volume	20
Issue number	12
DOIs	https://doi.org/10.3390/e20120956
State	Published - 1 Dec 2018

Keywords

Aboav law
Droplet cluster
Lewis law
Self-assembly
Surface patterns
Voronoi entropy

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10.3390/e20120956

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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 microporous polymer surfaces obtained by the breath figure method and levitating ordered water microdroplet clusters.",

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AU - Bormashenko, Edward

AU - Frenkel, Mark

AU - Vilk, Alla

AU - Legchenkova, Irina

AU - Fedorets, Alexander A.

AU - Aktaev, Nurken E.

AU - Dombrovsky, Leonid A.

AU - Nosonovsky, Michael

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AB - 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.

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KW - Droplet cluster

KW - Lewis law

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KW - Surface patterns

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Characterization of self-assembled 2D patterns with voronoi entropy

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Keywords

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