Colloidal Valence as Thermodynamic Equilibrium States predicted by Molecular and Surface Properties

Building complex structures in two or three dimensions by directed self-assembly holds great promise for the efficient synthesis of materials with novel mechanical or optical properties. Self-assembly of colloidal objects also serves as a prototypical system for protein folding or the chemistry of macromolecules. For all these applications, control of the valence of individual objects is crucial. Using colloidal droplets decorated with mobile DNA binders, we show experimentally and theoretically that the mechanical properties of the droplet surfaces and the binder molecules predetermine the droplet-droplet binding characteristics, and in particular determine valence manifested as the spontaneous formation of a predictable number of bond patches between droplets. These valence states are thermodynamic equilibria, and thus offer a robust way of achieving complex self-assembly. Moreover, we show how the molecular properties of the binder (length or stiffness of e.g. dsDNA or ssDNA) govern the size and binder population of bond patches between droplets. Droplet deformation is part of this description, but, contrary to common thinking, is not necessary to establish such patches. We identify guidelines for choices of binder molecules and droplets leading to efficient valence control.