Self-assembly of Archimedean tilings with enthalpically and entropically patchy polygons.

Considerable progress in the synthesis of anisotropic patchy nanoplates (nanoplatelets) promises a rich variety of highly ordered two-dimensional superlattices. Recent experiments of superlattices assembled from nanoplates confirm the accessibility of exotic phases and motivate the need for a better understanding of the underlying self-assembly mechanisms. Here, we present experimentally accessible, rational design rules for the self-assembly of the Archimedean tilings from polygonal nanoplates. The Archimedean tilings represent a model set of target patterns that (i) contain both simple and complex patterns, (ii) are comprised of simple regular shapes, and (iii) contain patterns with potentially interesting materials properties. Via Monte Carlo simulations, we propose a set of design rules with general applicability to one- and two-component systems of polygons. These design rules, specified by increasing levels of patchiness, correspond to a reduced set of anisotropy dimensions for robust self-assembly of the Archimedean tilings. We show for which tilings entropic patches alone are sufficient for assembly and when short-range enthalpic interactions are required. For the latter, we show how patchy these interactions should be for optimal yield. This study provides a minimal set of guidelines for the design of anisostropic patchy particles that can self-assemble all 11 Archimedean tilings.