Abstract
Two-dimensional simulations are used to explore topological transitions that occur during the formation of films grown from grains that are seeded on substrates. This is done for a relatively large range of the initial value Φs of the grain surface fraction Φ. The morphology of porous films is captured at the transition when grains connect to form a one-component network using newly developed raster-free algorithms that combine computational geometry and network theory. Further insight on the morphology of porous films and their suspended counterparts is obtained by studying the pore surface fraction Φp, the pore over grain ratio, the pore area distribution, and the contribution of pores of certain chosen areas to Φp. Pinhole survival is evaluated at the transition when film closure occurs using survival function estimates. The morphology of closed films (Φ=1) is also characterized and is quantified by measuring grain areas and perimeters. The majority of investigated quantities are found to depend sensitively on Φs and the long-time persistence of pinholes exhibits critical behavior as a function of Φs. In addition to providing guidelines for designing effective processes for manufacturing thin films and suspended porous films with tailored properties, this work may advance the understanding of continuum percolation theory.
Highlights
The percolation threshold in continuum percolation theory [1,2,3] plays a significant role in thin film growth [4], grain boundary engineering [5, 6], and research on porous media [7, 8]
We investigate the formation and the morphology of closed and porous films grown from grains that are seeded on substrates using two-dimensional simulations
Seeding is done with circular grains of radius rs, and as a consequence, grain boundaries correspond to a Voronoi diagram [39,40,41], which often describe the morphology of physical systems [42,43,44], and each grain fills a corresponding Voronoi cell at the instant of film closure
Summary
The percolation threshold in continuum percolation theory [1,2,3] plays a significant role in thin film growth [4], grain boundary engineering [5, 6], and research on porous media [7, 8]. In the formation of a thin film from a random distribution of initially isolated grains on a substrate, we identify the percolation threshold with the instant when the grains form a cluster that connects two opposing edges of the substrate. As a consequence of randomness, these instances differ for a comparable set of samples. We identify the percolation transition with the region spanned by the probability density of these instances. For a comparable set of samples, the probability densities of these respective instances span a connected-grain and a closed-film transition
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