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 $R_M$ and insulating particles of radius $R_I$, is examined in view of the many cases of its misuse. It is argued that in the $R_M$≪$R_I$ limit an excluded-volume determination of the percolation threshold should be used. For the $R_M$≊$R_I$ 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 $R_M$≫$R_I$, a hard-core soft-skin particle model provides the best available description of the system.