Dimensional Analysis of Percolation Theory: Applications to Polymer Composites

Percolation theory is well known to describe functional phenomena in polymer composites such as electrical conductivity, when combining a conducting particle and insulating matrix. Nanostructured composites can, however, present unique morphologies that are not easily described by the typical one, two, or three-dimensional viewpoint. One example is random mats of polymer/carbon nanotube (or silver nanoparticle) composite nanofibers. With this motivation, Monte Carlo simulations were developed to investigate various effects within such a fibrous geometry, including changes to the critical volume fraction due to the dimensionality: particle aspect ratio, relative size of particle and fiber (or film), sample size, continuous vs. porous structure. From these simulations a model was developed to predict the percolation threshold based on the dimensionality of the system. The results of these simulations and the derived model will be presented.