A Brownian quasi-crystal of pre-assembled colloidal Penrose tiles.

Penrose's pentagonal P2 quasi-crystal is a beautiful, hierarchically organized multiscale structure in which kite- and dart-shaped tiles are arranged into local motifs, such as pentagonal stars, which are in turn arranged into various close-packed superstructural patterns that become increasingly complex at larger length scales. Although certain types of quasi-periodic structure have been observed in hard and soft matter, such structures are difficult to engineer, especially over large areas, because generating the necessary, highly specific interactions between constituent building blocks is challenging. Previously reported soft-matter quasi-crystals of dendrimers, triblock copolymers, nanoparticles and polymeric micelles have been limited to 12- or 18-fold symmetries. Because routes for self-assembling complex colloidal building blocks into low-defect dynamic superstructures remain limited, alternative methods, such as using optical and directed assembly, are being explored. Holographic laser tweezers and optical standing waves have been used to hold microspheres in local quasi-crystalline arrangements, and magnetic microspheres of two different sizes have been assembled into local five-fold-symmetric quasi-crystalline arrangements in two dimensions. But a Penrose quasi-crystal of mobile colloidal tiles has hitherto not been fabricated over large areas. Here we report such a quasi-crystal in two dimensions, created using a highly parallelizable method of lithographic printing and subsequent release of pre-assembled kite- and dart-shaped tiles into a solution-dispersion containing a depletion agent. After release, the positions and orientations of the tiles within the quasi-crystal can fluctuate, and these tiles undergo random, Brownian motion in the monolayer owing to frequent collisions between neighbouring tiles, even after the system reaches equilibrium. Using optical microscopy, we study both the equilibrium fluctuations of the system at high tile densities and also the 'melting' of the pattern as the tile density is lowered. At high tile densities we find signatures of a five-fold pentatic liquid quasi-crystalline phase, analogous to a six-fold hexatic liquid crystal. Our fabrication approach is applicable to tiles of different sizes and shapes, and with different initial positions and orientations, enabling the creation of two-dimensional quasi-crystalline systems (and other systems that possess multiscale complexity at high tile densities) beyond those of current self- or directed-assembly methods. We anticipate that our approach for generating lithographically pre-assembled monolayers could be extended to create three-dimensional Brownian systems of fluctuating particles with custom-designed shapes through holographic lithography or stereolithography.