TRANSITIONS TO ORDERED PHASES IN SYSTEMS CONTAINING ROD-LIKE PARTICLES .2. CONTINUUM MONTE-CARLO APPROACH VERSUS DISCRETE LATTICE MODELS

The predictions of the new continuous-placement Monte Carlo (CMC) appr oach described in the preceding paper are compared with the results ob tained from the discrete lattice model (DLM) of Flory and Ronca. The c omparison is made for two-dimensional, monodisperse, athermal systems. For this purpose, we have adapted the Flory-Ronca model to two dimens ions, gaining additional insight into the justification for one of the numerical correction factors used in that model. The CMC and DLM appr oaches both predict that a uniform (flat) distribution of rod orientat ions in the anisotropic phase is associated with a first-order isotrop ic-to-nematic transition, while normally distributed orientations lead to a continuous transition with increasing rod concentration. The two models also agree qualitatively with respect to the relative free ene rgies of different rod orientation distributions in the anisotropic ph ase. However, the DLM assigns disproportionately high entropy to short rods (especially at high concentrations) and to disordered phases, so that the DLM does not generate quantitatively reliable phase diagrams .