Polygonal Networks Resulting from Dewetting

The occurence of polygonal structures is widespread in nature [1]. Extensive investigations on the statistics of two-dimensional networks have been performed for biological tissues [2, 3], clusters of metal grains [4, 5], systems of soap bubbles [6, 7, 8], emulsion lattices [9], gas bubbles in Langmuir monolayers [10], magnetic froth [11] or convective patterns in hydrodynamics [12, 13, 14]. The strong similarity between structure and evolution of two-dimensional soap froth and grain boundary networks has become a subject of growing interest [15, 16, 17, 6]. These similarities make it difficult to differentiate the networks occuring in different experimental systems. Additionally, one faces a problem if the system is two-dimensional because it is a planar cut of a three-dimensional systems (grain boundary network) or through putting the three-dimensional structure between two narrowly spaced glass plates (soap froth, emulsion lattice, magnetic froth). Here, we will introduce two new experimental systems representing dewetting processes of a thin liquid films on a solid substrates. The oc-curing polygonal networks are intrinsically two-dimensional. After a short introduction of the concepts of wetting and dewetting, the dewetting experiments of polystyrene on silicon and of collagen solution on highly oriented polygraphite are explained. The different stages of the dewetting process will be discussed at these examples. Main features of the resulting structures are analysed by means of stochastic geometry of polygonal networks. The resulting distributions are compared with distributions obtained for two-dimensional soap froth. Typical differences between dewetting patterns and soap froth and between the two dewetting patterns are explained by distinct driving forces behind structure formation.