Random Trajectory Modeling of Limited-Volume Percolation in a Microporous Structure

Percolation transition of siloxane domain in partially phenylated organic/inorganic hybrid glass

“…Although there have been many previous works related to the percolation transition, the attempt to estimate the percolation threshold from the measurable evidences will be useful. This is because most earlier works are highly conceptual [15][16][17][18]. Thus, we attempt to propose experimental methods for estimating or finding the percolation transition in the present work.…”

“…Therefore, from the viewpoint of the materials design, the occurrence of percolation of the phenyl/siloxane parts will be useful. Nevertheless, methods for monitoring the percolation transition in hybrid glass have not been established [15][16][17][18].…”

Evaluation of Permeability of Microporous Media, Using the Modified Random-Trajectory Approach

“…Whereas the finite-cluster approach lets us conclude about the absence of a percolation threshold (11), the random trajectory solution has a formal percolation threshold, the probability of which is very low (1). However, such a situation is very rare in practice and can be neglected.…”

“…The model is based on the random-trajectory approach developed in (1) for modeling of percolation and evaluation of the percolation threshold. This model is modified, accounting the complexity of the permeability problem.…”