  We explore the conditions under which colloids can be stabilized by the
addition of smaller particles. The largest repulsive barriers between colloids
occur when the added particles repel each other with soft interactions, leading
to an accumulation near the colloid surfaces. At lower densities these layers
of mobile particles (nanoparticle halos) result in stabilization, but when too
many are added, the interactions become attractive again. We systematically
study these effects --accumulation repulsion, re-entrant attraction, and
bridging -- by accurate integral equation techniques.
