  The specificity and thermal reversibility of DNA interactions have enabled
the self-assembly of crystal structures, self-replicating materials and
colloidal molecules. Grafting DNA onto liquid interfaces of emulsions leads to
exciting new architectural possibilities due to the mobility of the DNA ligands
and the patches they form between bound droplets. Here we show that the size
and number of these adhesion patches (valency) can be controlled. Valence 2
leads to flexible polymers of emulsion droplets, while valence above 4 leads to
rigid droplet networks. A simple thermodynamic model quantitatively describes
the increase in the patch size with droplet radii, DNA concentration and the
stiffness of the tether to the sticky-end. The patches are formed between
droplets with complementary DNA strands or alternatively with complementary
colloidal nanoparticles to mediate DNA binding between droplets. This emulsion
system opens the route to directed self-assembly of more complex structures
through distinct DNA bonds with varying strengths and controlled valence and
flexibility.
