Thermodynamics and phase behavior of the lamellar Zwanzig model

Binary mixtures of lamellar colloids represented by hard platelets are studied within a generalization of the Zwanzig model for rods, whereby the square cuboids can take only three orientations along the $x$, $y$ or $z$ axes. The free energy is calculated within Rosenfeld's ''Fundamental Measure Theory'' (FMT) adapted to the present model. In the one-component limit, the model exhibits the expected isotropic to nematic phase transition, which narrows as the aspect ratio $\zeta=L/D$ ($D$ is the width and $L$ the thickness of the platelets) increases. In the binary case the competition between nematic ordering and depletion-induced segregation leads to rich phase behaviour.