Customized Microscale Self-assembly through Thermodynamic Valence Control

The spontaneous assembly of individual objects not just to rafts or clusters, but to complex structures in two or three dimensions is an important goal of both fundamental and applied research, providing insight into processes like protein folding and the synthesis of branched macromolecules. To control this process, one has to control the valence of the constitutive objects. It is shown here that microscale droplets uniformly coated with mobile DNA molecules bind to each other reversibly with well-defined valence determined by the overall DNA coverage of each droplet. This experimental finding is explained by a purely thermodynamic theory, demonstrating that proper accounting of free energy contributions from molecular interactions and entropy predicts selection of a preferred number of binding patches. The theory shows how varying the properties of binder molecules and droplets allows for customization of valence, and thus of the self-assembled structures.