Microscopic Theory of Nonlinear Rheology and Double Yielding in Dense Attractive Glass Forming Colloidal Suspensions

Yielding of amorphous glasses and gels is a mechanically driven transformation of a material from the solid to liquid state on the experimental timescale. It is a ubiquitous fundamental problem of nonequilibrium physics of high importance in material science, biology, and engineering applications such as processing, ink printing, and manufacturing. However, the underlying microscopic mechanisms and degree of universality of the yielding problem remain theoretically poorly understood. We address this problem for dense Brownian suspensions of nanoparticles or colloids that interact via repulsions that induce steric caging and tunable short range attractions that drive physical bond formation. In the absence of deformation, these competing forces can result in fluids, repulsive glasses, attractive glasses, and dense gels of widely varying elastic rigidity and viscosity. Building on a quiescent microscopic theoretical approach that explicitly treats attractive bonding and thermally-induced activated hopping, we formulate a self-consistent theory for the coupled evolution of the transient and steady state mechanical response, and structure as a function of stress, strain, and deformation rate over a wide range of high packing fractions and attraction strengths and ranges. Depending on the latter variables, under step rate shear the theory predicts three qualitatively different transient responses: plastic-like (of two distinct types), static yielding via a single elastic-viscous stress overshoot, and double or 2-step yielding due to an intricate competition between deformation-induced bond breaking and de-caging. A predictive understanding of multiple puzzling experimental observations is achieved, and the approach can be extended to other nonlinear rheological protocols and soft matter systems.