Planar Assembly ‘Puzzlemer’ Particles: A Coarse Grained Model of Geometrically Frustrated Self-Assembly

Geometrically frustrated assemblies (GFAs) are attractive as they can exhibit self-limiting assembly into equilibrium structures characterized by a finite dimension. Here, we describe a new coarse grained model of a simple GFA building block that we call the “puzzlemer” particle. The taper shape and interactions of this particle promote a locally planar crystal packing that is frustrated by a preferred curvature of the lattice rows. Our central aim is to understand how particle properties control the intra-assembly mechanics, and how these in turn dictate the growth of stresses in the assembly with increased size. In particular, we focus on understanding the relative stiffness to inter-particle bending vs. stretching. This ratio tells us something about how the assembly accommodates frustrated packing: i.e. is it energetically favorable for the monomers to spread out, or flatten their rows? We determine an effective length scale from the ratio, which we hypothesize to be related to the maximal size of self-limiting assembly. We test the predicted connection between pair-wise particle mechanics and self-limiting assembly thermodynamics via numerical studies of the energy landscapes of puzzlemers for variable particle interactions and shape misfits.