Principles of self-assembly of polydisperse chains of spheres

Nature readily uses self-assembly to organize building blocks via programmable interactions into functional entities. These processes serve as an inspiration for materials science to develop a new generation of materials. Using numerical simulations, we study a model system of DNA-coated droplets that initially assemble into a one-dimensional sequence of flavors [1], which subsequently folds into predesigned two-dimensional rigid geometries [2]. Even though the number of possible folded geometries grows exponentially with the chain length, select structures (i.e., foldamers) can still be obtained in near-perfect yields by programming the order of secondary interactions. These foldamers then serve as building blocks for ternary self-assembly of complex supracolloidal architectures. Here, we use spheres of different sizes along the chain to encode a wider range of foldamer shapes. A simple example is the folding of a tetramer chain into a rhombus with a given aspect ratio. Combining rhombi with different aspect ratios according to prescribed matching rules (given by DNA interactions) may be sufficient to make quasicrystals. The study of self-assembling aperiodic tilings could yield general principles for encoding information on nonuniform length scales.

References:

[1] McMullen, A., Holes-Cerfon, M., Sciortino, F., Grosberg, A. Y., Brujic, J., ”Freely Jointed Polymers Made of Droplets”, PRL 121, (2018).

[2] McMullen, A., Muñoz Basagoiti, M., Zeravcic, Z., Brujic, J., “Self-assembly of emulsion droplets through programmable folding”. Nature 610, (2022).