THE PHASE DIAGRAM OFHARD SPHEROCYLINDERS

We have mapped out the complete phase diagram of hard spherocylinders as a function of the length-to-width ratio . Special computational techniques were required to locate phase transitions in the limit and in the close-packing limit for . 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 0.35 and the AAA crystal becomes unstable for lengths smaller than 7. The triple points isotropic-smectic-A-solid and isotropic-nematic-smectic-A are estimated to occur at =3.1 and =3.5 respectively. For the low 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 isotropic-nematic transition for 10. For large the simulation results approach the predictions of the Onsager theory. In the limit simulations were performed by application of a scaling technique. The nematic-smectic-A transition for appears to be continuous. As the nematic-smectic-A transition is certainly of first order nature for 5, the tri-critical point is presumably located between region, the plastic solid to aligned solid transition is first order. Using a mapping of the dense sphero-cylinder system on a lattice model, the initial slope of the coexistence curve could even be computed in the close packing limit.

• Introduction
• Brief summary of the phase diagram
  • Phase diagram for L/D < 5
  • Phase diagram for L/D>5
• Simulation techniques
  • Equilibration
  • Free energy calculations
    • Isotropic and nematic phases
    • Solid phase
    • Smectic phase
    • Nematic-smectic free energy difference
    • Kappa integration
  • Kofke's Gibbs-Duhem integration
• Phase diagram for L/D < 5
  • Phase behavior for 0 < L/D < 3
  • Phase behavior for 3 < L/D < 5
• The rotator phase
  • Finite densities
  • Close packing limit
• Phase diagram in the L/D = 5-60 region
  • Numerical Techniques
  • Results
  • The AAA crystal phase
• The Onsager limit
  • Scaling
  • Results
  • What is the order of the nematic-smectic transition?
    • Normal periodic boundaries
    • Shifted periodic boundaries
• Conclusion