Density functional theory and simulation of the columnar phase of a system of parallel hard ellipsoids with attractive interactions

A simple molecular model consisting of parallel hard oblate ellipsoids with superimposed square-well attractive interactions of variable range is considered for the study of the phase behavior of thermotropic discotic molecules. A density functional theory appropriate for nonuniform fluids is formulated in which the hard-core contributions to the free energy are treated within a nonlocal weighted-density approximation (WDA) while the attractive contributions are treated at a mean-field level. It is shown that the columnar phase becomes stable relative to the nematic phase at fluid densities for a range of values of the range of the attractive well. In these cases, the region of stability of the columnar phase is bounded at high temperatures by a nematic-columnar-solid triple point. The calculations show that if the attractions are made too long ranged (lambda/D> or approximately =0.84 for particles of aspect ratio of L/D=0.1, where lambda/D is the range of the attractive interaction in units of the molecular diameter D), columnar ordering becomes unstable and the nematic phase dominates at all fluid densities. It is shown that columnar ordering is also predicted when the density functional theory is supplemented with the smoothed-density approximation (SDA). Computer simulations have also been carried out for a particular choice of model parameters; our simulation data confirm the stabilization of the hexagonal columnar phase between the solid and nematic phases. A comparison with simulation data allows us to conclude that the WDA provides a fairly good description of the columnar phase and very good agreement for the nematic-columnar transition properties. On the other hand, our calculations show that the SDA largely underestimates the transition pressure and predicts a too-strongly first-order nematic-columnar transition