Theory and computer simulation for the cubatic phase of cut spheres

The phase behavior of a system of hard-cut spheres has been studied using a high-order virial theory and by Monte Carlo simulation. The cut-sphere particles are disks of thickness L formed by symmetrically truncating the end caps of a sphere of diameter D. The virial theory predicts a stable nematic phase for aspect ratio L∕D=0.1 and a stable cubatic phase for L∕D=0.15–0.3. The virial series converges rapidly on the equation of state of the isotropic and nematic phases, while for the cubatic phase the convergence is slower, but still gives good agreement with the simulation at high order. It is found that a high-order expansion (up to B₈) is required to predict a stable cubatic phase for L∕D⩾0.15, indicating the importance of many-body interactions in stabilizing this phase. Previous simulation work on this system has focused on aspect ratios L∕D=0.1, 0.2, and 0.3. We expand this to include also L∕D=0.15 and 0.25, and we introduce a fourth-rank tensor to measure cubatic ordering. We have applied a multiparticle move which dramatically speeds the attainment of equilibrium in the nematic phase and therefore is of great benefit in the study of the isotropic-nematic phase transition. In agreement with the theory, our simulations confirm the stability of the nematic phase for L∕D=0.1 and the stability of the cubatic phase over the nematic for L∕D=0.15–0.3. There is, however, some doubt about the stability of the cubatic phase with respect to the columnar. We have shown that the cubatic phase found on compression at L∕D=0.1 is definitely metastable, but the results for L∕D=0.2 were less conclusive.