Elastic Frustration In Self-Assembly

Self-assembly of identical particles, if the particles fit together, leads to space filling aggregates. However, in the case of misfitting particles, the resulting aggregates may have limiting sizes due to the frustration. One of the ways of the frustration occurs is the shape misfit of building blocks such that particles need to deform elastically in order to fit each other. The energy cost of elastic deformation competes with a surface tension which drives the particle into assembly. In the regime in which these two energies are comparable, it is very little known about what type of structures and shapes the aggregates have due to the elastic frustration. We tackle the frustrated self-assembly using a coarse grained, continuum model. We determine a phase diagram which shows favorable shapes of aggregates for given parameters. The phase diagram shows us that incompressibility and existence of soft modes favors the fibrillar structures for aggregates.