Geometrically Frustrated Self-assembly of Curved Colloidal Particles

Geometrically frustrated systems where local order fails to propagate globally can lead to self-assembly that limits the size of equilibrium structures. We study an example of such geometrically frustrated self-assembly in which plate-like particles with a preferred curvature stack due to an attractive face-to-face interaction. Achieving perfect contact between the curved particles (‘curvamers’) forces them to bend, resulting in an elastic energy cost. The equilibrium size of the self-assembled stacks is finite and determined by the ratio of the bending energy to the adhesive energy. We developed a model of the curvamers and performed molecular dynamics simulations to realize the self-limiting behavior. The model allows us to investigate the geometry of the self-assembled stack and understand the role of the attractive potential between curvamers. In the case of long-ranged potentials, we observe the opening of gaps between curvamers that allows them to ‘escape’ frustration, while in the case of short-ranged potentials, we observe break-up into smaller stacks consistent with self-limiting assembly. Our model, combined with future experiments, helps to elucidate the role of geometric frustration in determining the size and geometry of self-assembled structures.