Thin Cells of Polymer-Modified Liquid Crystals Described by Voronoi Diagrams

We investigated patterns formed during the polymerization process of bifunctional monomers in a liquid crystal for both large polymer concentrations (polymer-dispersed liquid crystals, PDLC) and small concentrations (polymer-stabilized liquid crystals, PSLC). The resulting experimental patterns are reminiscent of Voronoi diagrams, so a reverse Voronoi algorithm was developed that provides the seed locations of cells, thus allowing a computational reproduction of the experimental patterns. Several metrics were developed to quantify the commonality between the faithful experimental patterns and the idealized and generated ones. This led to descriptions of the experimental patterns with accuracies better than 90% and showed that the curvature or concavity of the cell edges was below 2%. Possible reasons for the discrepancies between the original and generated Voronoi diagrams are discussed. The introduced algorithm and quantification of the patterns could be transferred to many other experimental problems, for example, melting of thin polymer films, ultra-thin metal films, or bio-membranes. The discrepancies between the experimental and ideal Voronoi diagrams are quantified, which may be useful in the quality control of privacy windows, reflective displays, or smart glass.