Formation and morphology of closed and porous films grown from grains seeded on substrates: Two-dimensional simulations

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 $\Phi_s$ of the grain surface fraction $\Phi$. 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 $\Phi_p$, the pore over grain ratio, the pore area distribution, and the contribution of pores of certain chosen areas to $\Phi_p$. Pinhole survival is evaluated at the transition when film closure occurs using survival function estimates. The morphology of closed films ($\Phi = 1$) is also characterized and is quantified by measuring grain areas and perimeters. The majority of investigated quantities are found to depend sensitively on $\Phi_s$ and the long-time persistence of pinholes exhibits critical behavior as a function of $\Phi_s$. 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.