Next Article in Journal
An Analysis of Deterministic Chaos as an Entropy Source for Random Number Generators
Next Article in Special Issue
Complex Behavior of Nano-Scale Tribo-Ceramic Films in Adaptive PVD Coatings under Extreme Tribological Conditions
Previous Article in Journal
Asymptotic Properties for Methods Combining the Minimum Hellinger Distance Estimate and the Bayesian Nonparametric Density Estimate
Previous Article in Special Issue
Entropy Contribution to the Line Tension: Insights from Polymer Physics, Water String Theory, and the Three-Phase Tension
Open AccessReview

Characterization of Self-Assembled 2D Patterns with Voronoi Entropy

1
Department of Chemical Engineering, Biotechnology and Materials, Engineering Sciences Faculty, Ariel University, Ariel 407000, Israel
2
University of Tyumen, 6 Volodarskogo St., Tyumen 625003, Russia
3
Joint Institute for High Temperatures, 17A Krasnokazarmennaya St., Moscow 111116, Russia
4
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; https://doi.org/10.3390/e20120956
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
Show Figures

Figure 1

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.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop