#6 Gelation with fewer bonds?

Gelation is a hallmark of a wide variety of soft matter and biological systems. Very often the aggregation of particles (colloids, polymers, nanoparticles, biomolecules, etc.) leads to the formation of an infinite cluster (a gel) and to dramatic change in several properties of these systems. The simplest theoretical explanation for gelation is the following: for a system of particles that may bond to at most f other particles, gelation (or percolation) will occur when the probability p of forming a bond between two particles is p>=1/(f-1). As a consequence f>2,  is a necessary condition for percolation. However, in many experimental systems the valence  of the particles is not fixed but follows some probability distribution. In this work, the influence of polydispersed valence on gelation will be investigated. Special attention will be given to the case where the mean valence is less than 2, i.e. to the possibility that percolation is induced by polydispersity in the valence.