Correlated rigidity percolation and colloidal gels

Rigidity percolation occurs when mechanical stability emerges in disordered networks as more components or constraints are introduced. Classical theories of rigidity percolation elucidated critical phenomena at the rigidity percolation transition in systems where components are uncorrelated. Many experimental systems, such as colloidal gels, involve components that exhibit interactions which induce positional correlation. In this talk, we discuss the effect of correlation at the rigidity percolation transition and discuss its implications for colloidal gels. We find, through numerical simulations of site-diluted triangular lattices, that short-range positional correlation shifts the rigidity percolation transition to lower volume fraction, while keeping the same critical exponents, consistent with the scenario that correlation acts as an irrelevant perturbation at rigidity percolation. We further explore the emergence of rigidity in colloidal gels through molecular dynamics simulations and structural rigidity analysis. In particular, we examine the relation between the emergence of rigidity and the gelation transition at different temperatures, aiming at understanding the origin of structural rigidity in colloidal gels, as solid materials at extra-low volume fractions.