Colloidal Droplet Chemistry with Mobile Interfaces

The self-assembly of DNA-functionalized colloids into complex architectures has wide ranging applications from the small-scale manufacture of novel materials to the mimicking of biological binding processes for controlled study. Here we derive a theoretical adhesion model for mobile surface linkers and test it using Brownian DNA-labeled oil droplets in water. The theory takes into account the molecular properties of DNA binders, the entropic penalties associated with binding, and the elasticity of emulsion interfaces, in order to predict the self-assembly of the resulting droplet clusters. The fact that binders can rearrange between droplet-droplet adhesion patches results in free energy minima that correspond to thermodynamically stable colloidal "molecules" of prescribed architecture. In chemistry, when a molecule reacts with another one, it changes its valence according to the rules of quantum mechanics. Analogously, a droplet can change its preferred valence upon binding with a droplet with a different concentration of DNA. This mechanism leads to programmable changes in the colloidal assemblies that are governed by the statistical mechanics of mobile DNA linkers. The theory covers the undeformed and the deformed droplet regime, as a function of surface tension, with applications spanning solid colloids with liquid interfaces, emulsions, all the way to liposomes and cellular membranes.