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.
引用
收藏
页数：13
相关论文
共 66 条
  • [61] SELF-ORGANIZED HONEYCOMB MORPHOLOGY OF STAR-POLYMER POLYSTYRENE FILMS
    WIDAWSKI, G
    RAWISO, M
    FRANCOIS, B
    [J]. NATURE, 1994, 369 (6479) : 387 - 389
  • [62] On the constitution of metallic sodium
    Wigner, E
    Seitz, F
    [J]. PHYSICAL REVIEW, 1933, 43 (10): : 0804 - 0810
  • [63] Block copolymer self-assembly in chemically patterned squares
    Xu, Ji
    Russell, Thomas P.
    Ocko, Benjamin M.
    Checco, Antonio
    [J]. SOFT MATTER, 2011, 7 (08) : 3915 - 3919
  • [64] Highly ordered arrays of nanoparticles in large areas from diblock copolymer micelles in hexagonal self-assembly
    Yun, Sang-Hyun
    Yoo, Seong
    Jung, Jin Chul
    Zin, Wang-Cheol
    Sohn, Byeong-Hyeok
    [J]. CHEMISTRY OF MATERIALS, 2006, 18 (24) : 5646 - 5648
  • [65] Self-assembly of like-charged nanoparticles into Voronoi diagrams
    Zambo, Daniel
    Suzuno, Kohta
    Pothorszky, Szilard
    Bardfalvy, Dora
    Hollo, Gabor
    Nakanishi, Hideyuki
    Wang, Dawei
    Ueyama, Daishin
    Deak, Andras
    Lagzi, Istvan
    [J]. PHYSICAL CHEMISTRY CHEMICAL PHYSICS, 2016, 18 (36) : 25735 - 25740
  • [66] The geometrical properties of irregular two-dimensional Voronoi tessellations
    Zhu, HX
    Thorpe, SM
    Windle, AH
    [J]. PHILOSOPHICAL MAGAZINE A-PHYSICS OF CONDENSED MATTER STRUCTURE DEFECTS AND MECHANICAL PROPERTIES, 2001, 81 (12): : 2765 - 2783
1234567