Computer simulation study of a simple tetrahedratic mesogenic lattice model

Abstract

Over the last 12 years, the possible existence of a tetrahedratic mesophase, involving a third-rank orientational order parameter and no positional order, has been addressed theoretically and predicted in some cases; no experimental realizations of a purely tetrahedratic phase are known at the time being, but various pieces of evidence suggest that interactions of tetrahedral symmetry do play a significant role in the macroscopic properties of mesophases resulting from banana-shaped (bent-core) mesogens. We address a very simple tetrahedratic mesogenic lattice model, involving continuous interactions; we consider particles possessing T(d) symmetry, whose centers of mass are associated with a three-dimensional simple-cubic lattice; the pair potential is taken to be isotropic in orientation space and restricted to nearest-neighboring sites; we let the two orthonormal triads {u alpha, alpha=1,2,3} and {v gamma, gamma=1,2,3} define the orientations of a pair of interacting particles; we let the unit vectors u alpha be combined to yield four unit vectors {e(j), j=1,2,3,4}, arranged in a tetrahedral fashion; we let the unit vectors v gamma be similarly combined to yield the four unit vectors {f(k), k=1,2,3,4}; and finally we let h(jk)=(e(j)f(k)). The interaction model studied here is defined by the simplest nontrivial (cubic) polynomial in the scalar products h(jk), consistent with the assumed symmetry and favoring orientational order; it is, so to speak, the tetrahedratic counterpart of the Lebwohl-Lasher model for uniaxial nematics. The model was investigated by molecular field (MF) theory and Monte Carlo simulations; MF theory predicts a low-temperature, tetrahedrically ordered phase, undergoing a second-order transition to the isotropic phase at higher temperature; on the other hand, available theoretical treatments point to the transition being driven first order by thermal fluctuations. Simulations showed evidence of a first-order transition.