Abstract
Phase separation often leads to gelation in soft and biomatter. For colloidal suspensions, we have a consensus that gels form by the dynamical arrest of phase separation. In this gelation, percolation of the phase-separated structure occurs before the dynamical arrest, leading to the generation of mechanical stress in the gel network. Here, we find a previously unrecognized type of gelation in dilute colloidal suspensions, in which percolation occurs after the local dynamical arrest, i.e., the formation of mechanically stable, rigid clusters. Thus, topological percolation generates little mechanical stress, and the resulting gel is almost stress-free when formed. We also show that the selection of these two types of gelation (stressed and stress-free) is determined solely by the volume fraction as long as the interaction is short-ranged. This universal classification of gelation of particulate systems may have a substantial impact on material and biological science.