Intersection of percolation, phase separation and glassy arrest sets minimal conditions for gelation of colloidal systems*

Colloidal gelation is an important phenomenon in the formation of colloidal solids. Although separate mechanisms of colloidal gelation (percolation, arrested phase separation, attractive glass formation) have been well established for attractive colloidal systems, how these different mechanisms interact for a particular system is understudied. Specifically, when different mechanisms predict different thresholds for gelation, it is unclear what determines the minimal conditions for gelation. To resolve this ambiguity, we present a new method to precisely establish locations of arrested states in a colloidal phase diagram that uses modulated quenches in attraction strength to determine the gelation threshold for thermoresponsive systems. We identify three distinct regimes of the gelation threshold, which are shared between all in vitro and in silico systems. A detailed investigation of structural and rheological properties in each regime reveals how percolation, phase separation, and glass transition interact to set the gelation threshold. The gelation threshold can be scaled to collapse the gelation behavior of the systems studied suggesting that this behavior is relevant to a wide range of colloidal systems.