Phase equilibria in systems of hard disks with thickness polydispersity.

We study isotropic-nematic (I-N) phase equilibria in the Onsager (-Parsons) model for systems of hard colloidal disks allowing for arbitrary polydispersity in thickness. The phase behavior is investigated by analyzing the exact phase equilibrium equations for Gaussian orientational distribution functions. We observe a strong fractionation effect, with the thicker disks found preferentially in the isotropic phase. Due to this effect, the system may undergo an I-N density inversion indicating that the mass density of the isotropic phase becomes higher than that of the coexisting nematic phase. This phenomenon has been observed explicitly in experiment. We also encounter a divergence of the I-N coexistence region for Schulz-distributed parents with polydispersities larger than 46%. An implication of this phenomenon is that the system cannot become fully nematic at high densities but will continue to split off a small fraction of a dilute isotropic phase predominantly containing very thick species.