Algorithms for generating planar networks simulating hierarchical patterns of cracks formed during film drying

Hierarchical crack patterns that arise during the drying of thin films of colloidal dispersions or polymer solutions on a solid substrate are of interest both from a fundamental standpoint and in the context of the creation of transparent electrodes for optoelectronics. This paper analyzes the morphology of such patterns based on image processing of real-world samples. Three approaches are used to generate artificial hierarchical networks: random homogeneous tessellation, recursive Voronoi tessellation, and a crack growth simulation model, each modified to reproduce the hierarchical structure. A comparison was made of the geometric characteristics (distribution of crack angles, edge lengths, cell areas, and circularity coefficient) and topological properties (distribution of the number of cell sides) of real and simulated networks. It was shown that the simulation model best reproduces the key features of real cracks, including the characteristic right angles of their connections.