Entropic crystallization of Brownian squares through pathways governed by orientational dynamics

In dense systems of hard-interacting colloidal particles having anisotropic shapes, crystallization pathways represent an interesting frontier. The translational and rotational dynamics of such particles become coupled at higher densities, resulting in complex kinetics of their configurational ordering. To elucidate this, we have studied a two-dimensional entropic system of osmotically compressed corner-rounded Brownian square platelets. By analyzing the translational and orientational dynamics of the particles and their respective contributions toward minimizing the free energy, we show that the range of accessible orientational states of the particles principally governs the pathways of structural evolution, as the orientational entropy dictates the minimization of the free energy and, hence, the resulting optimal equilibrium ordering. When the particles have access to a wider range of orientational states, the larger rotational component of configurational entropy minimizes the total free energy, leading to hexagonal ordering. At higher osmotic pressures, the long collective translational fluctuations of the side-aligned particles with restricted rotational fluctuations maximize the entropy with a greater contribution from the translational component, thereby inducing a free energetically favored rhombic crystalline structure. We further show that density influences the crystallization pathways indirectly by setting an upper bound on the range of accessible orientational states. Complementary Brownian dynamics simulations and free-energy calculations further corroborate our findings, and their generalizability is demonstrated using a system of triangular particles. Thus, orientational dynamics is predicted to play a crucial role in governing the pathways for entropic ordering of various anisotropic shapes.