Thermal stability and secondary aggregation of self-limiting, geometrically-frustrated assemblies: Chain assembly of incommensurate polybricks

Abstract

In geometrically frustrated assemblies, equilibrium self-limitation manifests in the form of a minimum in the free energy per subunit at a finite, multi-subunit size which results from the competition between the elastic costs of frustration within an assembly and the surface energy at its boundaries. Physical realizations -- from ill-fitting particle assemblies to self-twisting protein superstructures -- are capable of multiple mechanisms of escaping the cumulative costs of frustration, resulting in unlimited equilibrium assembly, including elastic modes of ``shape-flattening'' and the formation of weak, defective bonds that screen intra-assembly stresses. Here we study a model of 1D chain assembly of incommensurate ``polybricks'', and determine its equilibrium assembly as a function of temperature, concentration, degree of shape frustration, elasticity and inter-particle binding, notably focusing on how weakly cohesive, defective bonds give rise to strongly temperature-dependent assembly. Complex assembly behavior derives from the competition between multiple distinct local minima in the free energy landscape, including self-limiting chains, weakly-bound aggregates of self-limiting chains, and strongly-bound, elastically defrustrated assemblies. We show that this scenario, in general, gives rise to anomalous {\it multiple aggregation} behavior, in which disperse subunits first exhibit a primary aggregation transition to self-limiting chains (at intermediate concentration and temperature) which are ultimately unstable to condensation into unlimited assembly of finite-chains through weak binding at a secondary aggregation transition (at low temperature and high concentration). We show that window of stable self-limitation is determined both by the elastic costs of frustration in the assembly as well as energetic and entropic features of inter-subunit binding.