  Grafting linkers with open ends of complementary single-stranded DNA makes a
flexible tool to tune interactions between colloids,which facilitates the
design of complex self-assembly structures. Recently, it has been proposed to
coat colloids with mobile DNA linkers, which alleviates kinetic barriers
without high-density grafting, and also allows the design of valency without
patches.However, the self-assembly mechanism of this novel system is poorly
understood.Using a combination of theory and simulation, we obtain phase
diagrams forthe system in both two and three dimensional spaces, and find
stable floppy squareand CsCl crystals when the binding strength is strong, even
in the infinite bindingstrength limit. We demonstrate that these floppy phases
are stabilized by vibrational entropy, and "floppy" modes play an important
role in stabilizing the floppy phases for the infinite binding strength limit.
This special entropic effect in the self-assembly of mobile DNA-coated colloids
is very different from conventional molecular self-assembly, and it offers new
axis to help design novel functional materials using mobile DNA-coated
colloids.
