Haloing, flocculation, and bridging in colloid-nanoparticle suspensions

Integral equation theory with a hybrid closure approximation is employed to study the equilibrium structure of highly size asymmetric mixtures of spherical colloids and nanoparticles. Nonequilibrium contact aggregation and bridging gel formation is also qualitatively discussed. The effect of size asymmetry, nanoparticle volume fraction and charge, and the spatial range, strength, and functional form of colloid-nanoparticle and colloid-colloid attractions in determining the potential-of-mean force (PMF) between the large spheres is systematically explored. For hard, neutral particles with weak colloid-nanoparticle attraction qualitatively distinct forms of the PMF are predicted: (i) a contact depletion attraction, (ii) a repulsive form associated with thermodynamically stable "nanoparticle haloing," and (iii) repulsive at contact but with a strong and tight bridging minimum. As the interfacial cohesion strengthens and becomes shorter range the PMF acquires a deep and tight bridging minimum. At sufficiently high nanoparticle volume fractions, a repulsive barrier then emerges which can provide kinetic stabilization. The charging of nanoparticles can greatly reduce the volume fractions where significant changes of the PMF occur. For direct and interfacial van der Waals attractions, the large qualitative consequences of changing the absolute magnitude of nanoparticle and colloid diameters at fixed size asymmetry ratio are also studied. The theoretical results are compared with recent experimental and simulation studies. Calculations of the real and Fourier space mixture structure at nonzero colloid volume fractions reveal complex spatial reorganization of the nanoparticles due to many body correlations.