Hard competition: stabilizing the elusive biaxial nematic phase in suspensions of colloidal particles with extreme lengths

We use computer simulations to study the existence and stability of a biaxial nematic $N_b$ phase in systems of hard polyhedral cuboids, triangular prisms, and rhombic platelets, characterized by a long ($L$), medium ($M$), and short ($S$) particle axis. For all three shape families, we find stable $N_b$ states provided the shape is not only close to the so-called dual shape with $M = \sqrt{LS}$ but also sufficiently anisotropic with $L/S>9,11,14, 23$ for rhombi, prisms, and cuboids, respectively, corresponding to anisotropies not considered before. Surprisingly, a direct isotropic-$N_b$ transition does not occur in these systems due to a destabilization of $N_b$ by a smectic (for cuboids and prisms) or a columnar (for platelets) phase at small $L/S$, or by an intervening uniaxial nematic phase at large $L/S$. Our results are confirmed by a density functional theory provided the third virial coefficient is included and a continuous rather than a discrete (Zwanzig) set of particle orientations is taken into account.