Biphasic Colloidal Mixtures: Theory of Dynamic Solidification, Linear Elasticity and Yielding

We apply ideal naive mode coupling theory to treat dynamical arrest, the elastic shear modulus, and stress-driven yielding of binary mixtures of equal diameter hard and attractive spheres. A rich kinetic arrest behavior emerges from the competition between excluded volume caging forces and attraction-induced physical bond formation. A homogeneous fluid, partially localized state (repulsive spheres remain fluid but attractive spheres gel), and doubly localized attractive and repulsive glasses are predicted. The shear elastic moduli vary as a power law with total volume fraction with effective exponents that decrease with increasing sticky colloid composition and attraction strength. The partial localization scenario and aforementioned power law scaling of the elastic modulus for different sticky particle compositions are in good agreement with experiments of Lewis and coworkers, although the absolute magnitudes of the latter are overpredicted presumably due to mixture composition dependent nonequilibrium clustering effects. Predictions for the perturbative yield stress are also obtained and favorably compared to experiment. The binary mixture becomes more brittle (smaller yield strain) with increasing sticky particle composition and attraction bond strength.