Structural rearrangement and slow dynamics near the onset of rigidity

A wide variety of amorphous soft materials, such colloidal suspensions and crosslinked biopolymer networks, consist of a bulk fluid phase containing many microscopic immersed solid components. These materials generally develop macroscopic rigidity at a critical value of some system-specific control parameter. For suspensions, the relevant control parameter is the particle volume fraction; for networks, it can be the average connectivity or the magnitude of applied strain. Close to the transition point, these systems share a tendency to display striking rheological signatures of critical slowing down. We show that this slowing is quantitatively controlled by nonaffine (heterogeneous) structural rearrangements that, like critical fluctuations in other systems, grow in magnitude and exhibit a diverging correlation length as the critical point is approached. Near the onset or loss of rigidity, dissipation-limiting rearrangements dominate the macroscopic viscoelastic response, giving rise to diverging relaxation times and power-law rheology. Here, we describe the quantitative relationship between nonaffine rearrangements and excess viscosity in fluid-immersed amorphous materials, and we verify this relationship in rheological simulations of crosslinked networks and dense suspensions.