Structural criterion for the onset of rigidity in a colloidal gel

Identifying the conditions for rigidity onset in gels is challenging. We propose a model that distinguishes attractive bonds from repulsive steric constraints, allowing the systematic variation of the number of bonded and nonbonded neighbors. Using simulations, rheology, and percolation analysis, we find that rigidity coincides with the percolation of particles with three or more bonds, occurring after connectivity percolation. This interplay of bonding and steric interactions, which is not a local but a large-scale effect, provides the mechanism for the rigidity of low-valence colloidal gels.