Self-Limitation and Condensation in Geometrically Frustrated Assembly

Geometric frustration has become an important paradigm for understanding a wide range of self-assembling systems whose behavior is controlled by intra-assembly strain gradients. This strain, which scales super-extensively with domain size, prevents the system from assembling into a uniform, defect-free bulk state and drives the system, instead, towards either a dispersed, a self-limited or a defect-riddled condensed phase. Which of these states a particular system exhibits is determined by the interplay of five key parameters: frustration, inter-particle cohesion and elasticity, concentration and temperature. In this talk, we use a minimal lattice model of geometrically frustrated assembly to investigate how the ratio between frustration and cohesion mediates a transition between the self-limited and the defect-riddled condensed phases. We investigate this using both analytic and numerical methods through the use of a continuum version of our model that was developed alongside an algorithm for performing numerical Monte Carlo simulations on the original lattice model. We present the phase diagram for finite temperature geometrically frustrated assembly, delineating the boundaries between dispersed, (finite width) aggregates and bulk condensed states.