Theoretical study of the impact of dilute nanoparticle additives on the shear elasticity of dense colloidal suspensions

Motivated by basic issues in soft matter physics and new experimental work on granule-nanoparticle mixtures, we systematically apply naive mode coupling theory with accurate microstructural input to investigate the elastic shear modulus of highly size asymmetric, dense, chemically complex, colloid-nanoparticle mixtures. Our analysis spans four equilibrium microstructural regimes: (i) entropic depletion induced colloid clustering, (ii) discrete adsorbed nanoparticle layers that induce colloid spatial dispersion, (iii) nanoparticle-mediated tight bridging network formation, and (iv) colloidal contact aggregation via direct attractions. Each regime typically displays a distinctive mechanical response to changing colloid-nanoparticle size ratio, packing fractions, and the strength and spatial range of interparticle attractive and repulsive interactions. Small concentrations of nanoparticles can induce orders of magnitude elastic reinforcements typically involving single or double exponential growth with increasing colloid and/or nanoparticle packing fraction. Depending on the system, the elementary stress scale can be controlled by the colloid volume, the nanoparticle volume, or a combination of both. Connections between local microstructural organization and the mixture elastic shear modulus are established. The collective structure factor of the relatively dilute nanoparticle subsystem exhibits strong spatial ordering and large osmotic concentration fluctuations imprinted by the highly correlated dense colloidal subsystem. The relevance of the theoretical results for experimental mixtures with large size asymmetry, particularly in the context of 3D ink printing and additive manufacturing, are discussed.