Theoretical study of kinetic arrest, shear elastic modulus, and yielding in simple biphasic colloidal mixtures

Based on integrating microscopic statistical mechanical theories for structure and ideal kinetic arrest at the naive mode coupling level, we study dynamic localization, the linear elastic shear modulus, applied stress induced modulus softening, and the absolute yielding of simple biphasic binary mixtures composed of equal diameter hard and attractive spheres. The kinetic arrest map is a rich function of total packing fraction, strength of attraction, and mixture composition. The gel to attractive ideal glass transition, the degree of glass melting re-entrancy, and the crossover boundary separating repulsive glasses from attractive glasses vary with the mixture composition. Exponential and/or apparent (high) power law dependences of the elastic shear modulus on the total packing fraction are predicted with effective exponents or exponential prefactors that are sensitive to mixture composition and location in the kinetic arrest map. An analysis of the effective mean square force on a tagged particle that induces dynamic localization reveals a compensation effect between structural correlations and degree of particle localization, resulting in the emergence of a weaker dependence of the shear modulus on mixture composition at very high attraction strengths. Based on a microrheologically inspired formulation of how external stress weakens particle localization and the shear modulus, we analyze mechanical-induced modulus softening and absolute yielding, defined as a discontinuous solid-to-fluid stress-induced transition that can occur in either one or two steps. Estimates of the corresponding yield strains predict that the binary mixture becomes more brittle with increasing sticky particle composition and/or attraction strength.