  In self-assembling systems, geometric frustration leads to complex states
characterized by internal gradients of shape misfit. Frustrated assemblies have
drawn recent interest due to the unique possibility that their thermodynamics
can sense and select the finite size of assembly at length scales much larger
than constituent building blocks or their interactions. At present,
self-limitation is chiefly understood to derive from zero-temperature
considerations, specifically the competition between cohesion and
scale-dependent elastic costs of frustration. While effects of entropy and
finite temperature fluctuations are necessarily significant for self-assembling
systems, their impact on the self-limiting states of frustrated assemblies is
not known. We introduce a generic, minimal model of frustrated assembly, and
establish its finite-temperature and concentration dependent thermodynamics by
way of simulation and continuum theory. The phase diagram is marked by three
distinct states of translation order: a dispersed vapor; a defect-riddled
condensate; and the self-limiting aggregate state. We show that, at finite
temperature, the self-limiting state is stable at intermediate frustration.
Further, in contrast to the prevailing picture, its thermodynamic boundaries
with the macroscopic disperse and bulk states are temperature controlled,
pointing to the essential importance of translational and conformational
entropy in their formation.
