Connectedness percolation in athermal mixtures of flexible and rigid macromolecules: Analytic theory

A semianalytic theory is developed for calculating percolation thresholds for rod-like nanoparticles dispersed in a flexible polymeric matrix. Methods of macromolecular integral equation theory are combined with the connectedness Ornstein-Zernike equation and an explicitly two-component model in which both the molecules constituting the matrix as well as the filler species are accounted for. The effects on the percolation threshold of explicitly including the matrix species are examined and compared with predictions based on an analogous approach which restricts attention to the rod-rod second virial coefficient. Explicit inclusion of the polymeric matrix does not alter the qualitative dependence of the percolation threshold on rod aspect ratio. However, accounting for the matrix leads to a quantitative reduction of the critical volume fraction by a factor independent of the rod length. Although the present work focuses on the athermal situation (excluded volume interactions alone), the methodology developed in this account can be readily extended to model matrix-filler specific interactions as well. (C) 2003 American Institute of Physics.