Sedimentation and multiphase equilibria in suspensions of colloidal hard rods

Sedimentation and multiphase equilibria in a suspension of hard colloidal rods are explored by analyzing the (macroscopic) osmotic equilibrium conditions. We observe that gravity enables the system to explore a whole range of phases varying from the most dilute phase to the densest phase, i.e., from the isotropic (I), to the nematic (N), to the smectic (Sm), to the crystal (K) phase. We determine the phase diagrams for hard spherocylinders with a length-to-diameter ratio of 5 for a semi-infinite system and a system with fixed container height using a bulk equation of state obtained from simulations. Our results show that gravity leads to multiphase coexistence for the semi-infinite system, as we observe I, $I+N,I+N+\mathrm{Sm}$, or $I+N+\mathrm{Sm}+K$ coexistence, while the finite system shows I, N, Sm, K, $I+N,N+\mathrm{Sm},\mathrm{Sm}+K,I+N+\mathrm{Sm},N+\mathrm{Sm}+K$, and $I+N+\mathrm{Sm}+K$ phase coexistence. In addition, we compare our theoretical predictions for the phase behavior and the density profiles with Monte Carlo simulations for the semi-infinite system and we find good agreement with our theoretical predictions.