Scher and Zallen criterion: Applicability to composite systems

The application of the Scher and Zallen criterion to continuum systems, made of metallic particles of radius RM and insulating particles of radius RI, is examined in view of the many cases of its misuse. It is argued that in the RMRI limit an excluded-volume determination of the percolation threshold should be used. For the RMRI case the Scher and Zallen critical fractional volume is maintained in the continuum only when the particles are spherical and of equal size. In the more common case of RMRI, a hard-core soft-skin particle model provides the best available description of the system.