Rigidity percolation: what can we learn about the elasticity of colloidal gels? 

Dispersed adhesive particles within a suspension can aggregate and spontaneously self-organize into a robust, percolating structure known as a gel. These network-like structures are prevalent in nature and play a critical role in many industrial processes, including those involving batteries, food products, and pharmaceutical formulations. In this talk, we will examine the emergence of elasticity in colloidal gels. We will show that gelation is governed by a rigidity percolation transition. We identify a characteristic correlation length that quantifies the extent of elastic and structural inhomogeneities, which diverges at the critical point. Our findings reveal that, regardless of the interaction types, the particle concentration, or the specific route to non-ergodicity (as defined by the preparation protocol), the elastic moduli and vibrational properties of gels can be accurately predicted using a mean-field model, in which the bending modes of fractal clusters — approximately the size of this correlation length — dominate under small deformations.

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