Renormalization group analysis of frustrated self-assembly

The self-assembly of shapes that do not fit exactly together can lead to geometrical frustration, and previous numerical simulations have shown that this frustration tend to favor slender self-assembled structures. However, the relationship between the microscopic shape, and the size, structure and dimensionality of the emerging aggregate have yet to be understood.

To elucidate this relationship, we propose to apply real space renormalization to an on-lattice aggregation model. This will enable us to determine the relevant features of the interaction between complex particles, thus providing us with a general classification of local interactions resulting in fibrous, crystalline, or finite-size aggregates, respectively.

The emergence of these distinct morphologies may be relevant to the aggregation of misfolded proteins into pathological fibers, in neurodegenerative and other diseases.