Continuum percolation in macromolecular fluids

A heuristic treatment of the connectedness Ornstein-Zernike equation is dev eloped for macromolecular fluids within the framework of the polymer refere nce interaction site model (PRISM). Results are presented for the critical volume fraction at the percolation threshold and for the mean number of int erchain contacts per molecule for athermal rodlike and Gaussian coil-like p articles. The results for rodlike particles are in qualitative agreement wi th prior investigations based on fully numerical solutions of the PRISM equ ations, and with computer simulations of ellipsoids. The method proposed he re leads to the physically reasonable result that the percolation threshold for direct connectivity on the length scale of the molecular dimensions is closely related to the semidilute crossover concentration as usually defin ed, and can be generalized directly to multicomponent systems. (C) 2000 Ame rican Institute of Physics. [S0021-9606(00)50644-8].