On the path to gelation, attractive colloids develop network connectivity, mechanical rigidity, and slow dynamics. Herein, we employ molecular dynamics simulations to quantitatively characterize these processes using a coarse-grained model of patchy colloidal particles that form equilibrium networks through linker-mediated, reversible binding interactions. We find that linker-mediated gelation proceeds through a cascade of coupled but distinct structural, mechanical, and dynamical changes. Ordinary connectivity percolation first produces a system-spanning network, while rigidity percolation is associated with the formation of a percolating backbone characterized by an average colloid coordination number of approximately 2.4 and a percolating subset of colloids with a coordination number of 3 or more. The rheologically defined gel point occurs at larger bond strengths and higher global coordination, where linker-mediated colloid-colloid connections persist over the deformation timescale. This separation between rigidity percolation and rheological gelation is accompanied by a pronounced increase in the bond persistence time as gelation is approached, indicating that persistent effective network connections are required for a macroscopic gel-like response. Together, these results show that connectivity is central to equilibrium, linker-mediated colloidal gelation, but that different connectivity measures govern ordinary percolation, rigidity percolation, and rheological gelation. These observations reinforce the idea that gelation in homogeneous networks of linked colloids can be understood as a connectivity-controlled, dynamical-mechanical transition, distinct from heterogeneous, nonequilibrium gels, where rigidity often arises from irreversible aggregation and kinetic arrest.

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• Gelation
• Colloidal gel
• Polymer networks
• Viscoelasticity