Entropic crystal–crystal transitions of Brownian squares

When a monolayer of hard microscale square platelets, produced lithographically, is osmotically concentrated in a flat plane to raise the particle area fraction ϕ A , an order–order transition occurs between a hexagonal rotator crystal and a rhombic crystal. Strikingly, phases having fourfold symmetry are not observed at any ϕ A . The rhombic lattice angle α increases continuously with ϕ A , as the system maximizes its total rotational and translational entropy. A cage model, based on packing rotationally swept squares, or “squaroids,” reasonably predicts the measured α ( ϕ A ), indicating that rotational entropy and the square particle shape combine to produce the rhombic unit cell.