Microscopic theory of elasticity and yielding in ultra-dense attractive glass forming suspensions

The combined consequences of repulsive force caging and short-range attractions that induce physical bonds on the linear elastic, structural relaxation, and nonlinear rheological properties of ultra-dense colloidal suspensions and glasses remain an outstanding challenge to theoretically understand at a microscopic level. Questions of interest include glass melting and re-entrancy, non-monotonic evolution of the elastic modulus with attraction strength, and two-step versus one step yielding. We have analyzed these problems under quiescent conditions and in the presence of external forces (with and without deformation-induced structural changes) over a wide range of attraction strengths and spatial ranges with ideal Mode Coupling theory and the Elastically Collective Nonlinear Langevin Equation theory that includes coupled local activated hopping and longer range collective elasticity. The consequences of explicitly treating strong attractive forces, versus only indirectly via changes of pair structure, have also been determined. We find deformation-induced structural evolution, explicit treatment of attractive forces, and activated relaxation are of critical importance in ultra-dense attractive glass forming colloids. Comparisons are made with experimental and simulation studies.