Aggregation vs. Condensation in a Lattice Model of Geometrically Frustrated Assembly

Geometrically frustrated assembly (GFA) has proven to be a useful framework for understanding a wide range of self-assembling systems whose behavior is governed by global constraints that obstruct the uniform extension of some locally preferred order across the entire system. One common response to these imposed constraints is the formation of a state of self-limited assembly where at least one dimension of the equilibrium structure is restricted to a certain finite length that is controlled by the ratio of frustration and inter-particle binding energy. We consider a minimal lattice model of geometrically frustrated assembly and use it to study the statistical mechanics of GFA at variable temperature and concentration. In this talk, we focus on how these systems can escape this size limitation via a condensation transition to a macroscopic bulk phase that is characterized by a finite density of topological defects. Using a combination of numerical and analytical methods, we show that this transition occurs at a critical ratio of frustration and binding energy and that this critical point is largely independent of concentration, consistent with scaling argument comparing dimensions of self-limiting to multi-defect ground states. We conclude with an examination of the affect of temperature on the critical frustration and discuss how the assembly morphologies are impacted by increasing conformational entropy.