Isotropic-nematic density inversion in a binary mixture of thin and thick hard platelets

We study the phase behavior of a binary mixture of thin and thick hard platelets, using Onsager's second virial theory for binary mixtures in the Gaussian approximation. Higher virial terms are included by rescaling the excluded volume part of the Onsager free energy using a modified form of the Carnahan-Starling free energy for hard spheres (Parsons approach). Our calculations provide a simple explanation for the isotropic-nematic (I-N) density inversion, as experimentally observed in systems of polydisperse gibbsite platelets by Van der Kooij et al. (J. Phys. Chem. B 2001, 105, 1696). In these systems, a nematic upper phase was found to coexist with an isotropic bottom phase. We confirm the original conjecture of the authors, which states that the phenomenon originates from a pronounced fractionation in thickness between the phases, such that the thick platelets are largely expelled from the nematic phase and preferentially occupy the isotropic phase. Our calculations show that the inverted state is found in a major part of the I-N coexistence region. In addition, a nematic-nematic demixing transition is located at sufficiently high osmotic pressures for any thickness ratio L-2/L-1 > 1. The N-N coexistence region is bounded by a lower critical point which shifts toward lower values as the thickness ratio is increased. At high thickness ratios (L-2/L-1 > 3.3), a triphasic coexistence is found at which two nematic phases coexist with an isotropic phase. We show that the demixing transition is driven by a small O(LID) contribution to the excluded volume entropy.