Thermodynamic stability of a smectic phase in a system of hard rods

One of the most remarkable phenomena exhibited by colloidal suspensions of monodisperse rod-like particles is the spontaneous formation of smectic liquid crystals1–5. In these smectic phases, the particles order in periodic layers; on average, the axes of the rods are perpendicular to the layers. Smectics are distinct from crystals in that there is no long-range positional order within the layers. Because the spacing of the smectic layers is of the order of optical wavelengths, white light is separated into colours when scattered, giving rise to beautiful iridescence as in the colour photographs of ref. 2. As early as 1949, Onsager6 showed that nematic ordering may arise from hard-core repulsions between anisometric particles. However, it appears to have been generally accepted in the literature that smectic liquid crystalline ordering demands that attractive forces also operate7. There is nevertheless experimental evidence that smectic ordering does occur in colloidal systems where the particles interact predominantly through repulsive electrostatic interactions. This observation raises the fundamental question of whether smectic ordering can occur in a system of particles with purely repulsive interactions. Inspired by the seminal work of Alder and Wainwright8 on the freezing of a system of hard spheres, we have explored the possibility that smectic ordering occurs in a fluid of hard rod-like particles. Earlier computer simulations on hard parallel spherocylinders9,10 (cylinders with length L and diameter D, capped at each end with hemispheres of the same diameter) indicated that, in this somewhat artificial system, smectic order was indeed possible. Here we present numerical evidence that hard spherocylinders with both translational and orientational freedom can form a thermodynamically stable smectic phase