Characterization of Self-Assembled 2D Patterns with Voronoi Entropy

被引：41
作者：
Bormashenko, Edward [1 ]
Frenkel, Mark [1 ]
Vilk, Alla [1 ]
Legchenkova, Irina [1 ]
Fedorets, Alexander A. [2 ]
Aktaev, Nurken E. [2 ]
Dombrovsky, Leonid A. [2 ,3 ]
Nosonovsky, Michael [2 ,4 ]
机构：
[1] Ariel Univ, Engn Sci Fac, Dept Chem Engn Biotechnol & Mat, IL-407000 Ariel, Israel
[2] Univ Tyumen, 6 Volodarskogo St, Tyumen 625003, Russia
[3] Joint Inst High Temperatures, 17A Krasnokazarmennaya St, Moscow 111116, Russia
[4] Univ Wisconsin, Mech Engn, 3200 North Cramer St, Milwaukee, WI 53211 USA
来源：
ENTROPY | 2018年 / 20卷 / 12期
关键词：
Voronoi entropy; surface patterns; Lewis law; Aboav law; droplet cluster; self-assembly; EVAPORATED POLYMER-SOLUTIONS; CELL-DIVISION; HONEYCOMB PATTERNS; DROPLET CLUSTERS; GROWTH; NANOPARTICLES; MORPHOLOGY; MECHANISM; SURFACE; SHAPES;
D O I：
10.3390/e20120956
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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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页数：13
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