Modeling percolation in high-aspect-ratio fiber systems. II. The effect of waviness on the percolation onset.

摘要: The onset of electrical percolation in nanotube-reinforced composites is often modeled by considering the geometric a system penetrable, straight, rigid, capped cylinders, or spherocylinders, despite fact that embedded nanotubes are not straight and do penetrate one another. In Part I this work we investigated applicability soft-core model to present problem, concluded hard-core approach more appropriate for modeling other high-aspect-ratio fiber systems. II, investigate effect waviness on onset. Previously, studied extensively joint morphology two-dimensional nanotube networks. work, results Monte Carlo simulations studying threshold randomly oriented fibers three dimensions. excluded volumes were found numerically, relationships between these thresholds two different morphologies found. We build I, extend our soft-core, wavy develop an analytical solution using relevant model. Our show high- aspect-ratio fibers, generally accepted inverse proportionality volume holds, independent waviness. This suggests that, given expression volume, can be derived identify including composites. Further, high aspect ratios, networks directly proportional constant function only. Thus adequately applying factor based geometry solution.