Transitions to Ordered Phases in Systems Containing Rod-like Particles: II. Continuum Monte Carlo Approach versus Discrete Lattice Models

Abstract

The predictions of the new continuous-placement Monte Carlo (CMC) approach described in the preceding paper are compared with the results obtained from the discrete lattice model (DLM) of Flory and Ronca. The comparison is made for two-dimensional, monodisperse, athermal systems. For this purpose, we have adapted the Flory-Ronca model to two dimensions, gaining additional insight into the justification for one of the numerical correction factors used in that model. The CMC and DLM approaches both predict that a uniform (flat) distribution of rod orientations in the anisotropic phase is associated with a first-order isotropic-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 energies of different rod orientation distributions in the anisotropic phase. 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.

Key Words:

• lattice model
• Monte Carlo
• nematic
• phase separation
• rod-like particles
• two-dimensional