Sedimentation profiles and phase stacking diagrams in polydisperse hard rounded rectangle fluids

We analyze the sedimentation behavior of a polydisperse two-dimensional liquid-crystal fluid using a local density-functional theory based on scaled particle theory. Polydispersity is incorporated through variations in the roundness of hard rectangular particles interacting solely via excluded area effects. Despite its simplicity, the model displays a rich phenomenology. In bulk, the fluid exhibits isotropic, nematic, and tetratic phases. In sedimentation, we obtain complex phase stacking diagrams featuring multiphasic stacking sequences with up to four stacks of different bulk phases, inverted stacking sequences such as top isotropic and bottom nematic together with top nematic and bottom isotopic, as well as stacking sequences with reentrant stacks such as tetratic and nematic stacks floating between two isotropic stacks. This phenomenology arises as a result of an intricate coupling between particle polydispersity and the effect of gravity. Our approach can be easily adapted to investigate the sedimentation behavior of other polydisperse colloidal systems.