Quantifying order in breath figure patterns through Voronoi entropy

Abstract

In this study, we simulate breath figures that are evolving two-dimensional assemblies of droplets on a substrate. We focus on the Voronoi/Shannon entropy of these figures, which quantifies the order related to the coordination number of droplets. We show that the Voronoi entropy of the complete breath figure pattern converges to a value that is the one of a randomly distributed point system. Conversely, the subset containing exclusively large droplets of the breath figure exhibits significantly lower entropy than that obtained for all droplets. Using molecular dynamics simulations, we show that coalescence events in breath figures induce the same Voronoi entropy as that caused by repulsive interactions in a bidimensional atomic system.