Chemical Analogs of Voronoi Diagrams

A Voronoi diagram is a mathematical tool for nesting as set of points on a 2D area, according to a specific mathematical rule. The outcome is a tiling of the whole surface, with the boundaries of every tile (or cell), being based on the distance to the points around it. Each point p(k) has its own corresponding cell R-k. In Chemistry, and in material science, Voronoi diagrams offer aid in crystal growth mechanisms, notably in relation to their topological distribution. A simple application of constructing such topographical maps resides in diffusion-precipitation dynamics. When the precipitation originates from different sources with random spatial distribution, void, precipitate free gaps delineate the various domains, just like the cell boundaries in a mathematical Voronoi diagram. We construct such tessellated sheets, using a variety of precipitate systems including cobalt hydroxide, cobalt phosphate, copper chromate, lead chromate; and precipitates involving the Prussian blue reagents, such as: silver ferrocyanide, silver ferricyanide, cobalt ferrocyanide and cobalt ferricyanide. Besides holes of equal concentration in the diffusing electrolyte (the traditional method), experiments were conducted while varying the concentrations and the hole sizes. Distance and angle measurements allowed a classification of the tessellation parameters from the viewpoint of kinetic laws, chaotic dynamics, and notably entropy calculations.