A unified state diagram for the yielding transition of soft colloids

Concentrated colloidal suspensions and emulsions are amorphous soft solids, widespread in technological and industrial applications and studied as model systems in physics and material sciences. They are easily fluidized by applying a mechanical stress, undergoing a yielding transition that still lacks a unified description. Here, we investigate yielding in three classes of repulsive soft solids, using analytical and numerical modelling and experiments probing the microscopic dynamics and mechanical response under oscillatory shear. We find that at the microscopic level yielding consists in a transition between two distinct dynamical states, which we rationalize by proposing a lattice model with dynamical coupling between neighboring sites, leading to a unified state diagram for yielding. Leveraging the analogy with Wan der Waals's phase diagram for real gases, we show that distance from a critical point plays a major role in the emergence of first-order-like vs second-order-like features in yielding, thereby reconciling previously contrasting observations on the nature of the transition.