Orientational dynamics governs the pathways of entropic crystallization of Brownian squares

Crystallization pathways represent an exciting frontier in dense systems of hard-interacting anisotropic colloids, where the overlap of orientational excluded volumes of the particles couples their translational and rotational dynamics to produce various ordering through configurational reorganization. We elucidate this for a 2D system of osmotically compressed rounded Brownian square platelets, which form hexagonal (HX) and rhombic (RB) crystals at increasing osmotic pressures (Π). By analyzing the contributions of particle dynamics in minimizing the free energy, we have shown that the range of particles' orientational diffusion dictates the system's structural evolution and, thus, the equilibrium ordering at a given Π. At low Π, broader orientational freedom helps rotational configurational entropy minimize the free energy to form HX crystal, whereas, at higher Π, the collective translational fluctuations of particles with restricted rotational diffusion maximize entropy, which induces RB phase. Intriguingly, the system's density has no direct effect on this process. Brownian dynamics simulations confirm our experimental observations, and these results are relevant to all similar systems.