Tracing the phase boundaries of hard spherocylinders

We have mapped out the complete phase diagram of hard spherocylinders as a function of the shape anisotropy $L/D$⁠. Special computational techniques were required to locate phase transitions in the limit $L/D→∞$ and in the close-packing limit for $L/D→0$⁠. The phase boundaries of five different phases were established: the isotropic fluid, the liquid crystalline smectic A and nematic phases, the orientationally ordered solids—in AAA and ABC stacking—and the plastic or rotator solid. The rotator phase is unstable for $L/D⩾0.35$ and the AAA crystal becomes unstable for lengths smaller than $L/D≈7$⁠. The triple points isotropic-smectic-A-solid and isotropic-nematic-smectic-A are estimated to occur at $L/D=3.1$ and $L/D=3.7$⁠, respectively. For the low $L/D$ region, a modified version of the Gibbs–Duhem integration method was used to calculate the isotropic-solid coexistence curves. This method was also applied to the I-N transition for $L/D>10$⁠. For large $L/D$ the simulation results approach the predictions of the Onsager theory. In the limit $L/D→∞$ simulations were performed by application of a scaling technique. The nematic-smectic-A transition for $L/D→∞$ appears to be continuous. As the nematic-smectic-A transition is certainly of first order nature for $L/D⩽5$⁠, the tri-critical point is presumably located between $L/D=5$ and $L/D=∞$⁠. In the small $L/D$ region, the plastic solid to aligned solid transition is first order. Using a mapping of the dense spherocylinder system on a lattice model, the initial slope of the coexistence curve could even be computed in the close-packing limit.