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Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid transitions, such as colloidal gelation, which are due to attractive interactions and aggregation. Using a lattice model, we show that structural correlations shift RP to lower volume fractions. Through molecular dynamics simulations, we show that increasing attraction in colloidal gelation increases structural correlation and thus lowers the RP transition, agreeing with experiments. Hence colloidal gelation can be understood as a RP transition, but occurs at volume fractions far below values predicted by the classical RP, due to attractive interactions which induce structural correlation.
Rheological measurements of model colloidal gels reveal that large variations in the shear moduli as colloidal volume-fraction changes are not reflected by simple structural parameters such as the coordination number, which remains almost a constant.
Rigidity percolation (RP) is the emergence of mechanical stability in networks. Motivated by the experimentally observed fractal nature of materials like colloidal gels and disordered fiber networks, we study RP in a fractal network. Specifically, we
We examine microstructural and mechanical changes which occur during oscillatory shear flow and reformation after flow cessation of an intermediate volume fraction colloidal gel using rheometry and Brownian Dynamics (BD) simulations. A model depletio
We study a lattice model of attractive colloids. It is exactly solvable on sparse random graphs. As the pressure and temperature are varied it reproduces many characteristic phenomena of liquids, glasses and colloidal systems such as ideal gel format
We sandwich a colloidal gel between two parallel plates and induce a radial flow by lifting the upper plate at a constant velocity. Two distinct scenarios result from such a tensile test: ($i$) stable flows during which the gel undergoes a tensile de