Phase equilibria in the polydisperse Zwanzig model of hard rods

We study the phase behavior of the Zwanzig model of suspensions of hard rod s, allowing for polydispersity in the lengths of the rods. In spite of the simplified nature of the model (rods are restricted to lie along one of thr ee orthogonal axes), the results agree qualitatively with experimental obse rvations: the coexistence region broadens significantly as the polydispersi ty increases, and strong fractionation occurs, with long rods found prefere ntially in the nematic phase. These conclusions are obtained from an analys is of the exact phase equilibrium equations. In the second part of the pape r, we consider the application of the recently developed "moment free energ y method" to the polydisperse Zwanzig model. Even though the model contains nonconserved densities due to the orientational degrees of freedom, most o f the exactness statements (regarding the onset of phase coexistence, spino dals, and critical points) derived previously for systems with conserved de nsities remain valid. The accuracy of the results from the moment free ener gy increases as more and more additional moments are retained in the descri ption. We show how this increase in accuracy can be monitored without relyi ng on knowledge of the exact results, and discuss an adaptive technique for choosing the extra moments optimally. (C) 2000 American Institute of Physi cs. [S0021-9606(00)50238-4].