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We use a Fundamental-Measure density functional for hard board-likepolydisperse particles, in the restricted-orientation approximation, to explainthe phase behaviour of platelet colloidal suspensions studied in recentexperiments. In particular, we focus our attention on the behavior of the totalpacking fraction of the mixture, $\eta$, in the region of two-phaseisotropic-nematic coexistence as a function of mean aspect ratio,polydispersity and fraction of total volume $\gamma$ occupied by the nematicphase. In our model, platelets are polydisperse in the square section, of sidelength $\sigma$, but have constant thickness $L$ (and aspect ratio$\kappa\equiv L/<\sigma><1$, with $<\sigma>$ the mean side length). Goodagreement between our theory and recent experiments is obtained by mapping thereal system onto an effective one, with excluded volume interactions but withthicker particles (due to the presence of long-ranged repulsive interactionsbetween platelets). The effect of polydispersity in both shape and particlesize has been taken into account by using a size distribution function with aneffective mean-square deviation that depends on both polydispersities. We alsoshow that the bimodality of the size distribution function is required tocorrectly describe the huge two-phase coexistence gap and the nonlinearity ofthe function $\gamma(\eta)$, two important features that these colloidalsuspensions exhibit.

Effect of polydispersity, bimodality and aspect ratio on the phase behavior of colloidal platelet suspensions