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Quantifying order in breath figure patterns through Voronoi entropy.

David Paulovics1, Edward Bormashenko2, Christophe Raufaste1,3

  • 1<a href="https://ror.org/019tgvf94">Université Côte d'Azur</a>, CNRS, <a href="https://ror.org/042cesy50">Institut de Physique de Nice</a>, 06200 Nice, France.

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Summary
This summary is machine-generated.

This study simulates droplet patterns, finding that large droplets in breath figures have lower entropy than random systems. Coalescence events in these patterns mirror atomic systems

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Breath figures, or evolving 2D droplet assemblies on substrates, are complex systems.
  • Understanding the spatial distribution and ordering of these droplets is crucial for various applications.
  • Quantifying the order in these patterns requires advanced analytical tools.

Purpose of the Study:

  • To simulate and analyze the statistical properties of evolving two-dimensional droplet assemblies (breath figures).
  • To investigate the role of droplet size and coalescence in determining the overall order of the pattern.
  • To compare the entropy of breath figures with that of other disordered systems.

Main Methods:

  • Utilized molecular dynamics simulations to model breath figure formation and evolution.
  • Applied Voronoi/Shannon entropy analysis to quantify the order based on droplet coordination numbers.
  • Examined the entropy of the complete pattern and subsets of large droplets.

Main Results:

  • The Voronoi entropy of complete breath figure patterns approaches that of randomly distributed point systems.
  • Subsets of exclusively large droplets exhibit significantly lower entropy compared to the overall pattern.
  • Molecular dynamics simulations reveal that droplet coalescence in breath figures leads to the same Voronoi entropy as repulsive interactions in atomic systems.

Conclusions:

  • Droplet coalescence plays a significant role in the ordering of breath figures.
  • The statistical properties of breath figures, particularly concerning large droplets, differ from random distributions.
  • The findings provide insights into the self-organization mechanisms in 2D droplet systems and their relation to atomic systems.