The authors also carried out a fifth order virial calculation for the equation of state. More accurate predictions of the higher virial contributions for disks were presented in Ref. [21], where simulation results are reported for hard cut spheres and more recently in Ref. [22]. Later simulation work was carried out on polydisperse platelet systems [23] and systems of platelets with different polygonal shapes (e.g. hexagons, triangles) [24]. Further simula- tion results of model circular platelets were reported in Ref. [25] and simulations alongside an integral equation approach for mixtures of rods and disks were carried out in Ref. [26]. Simulations of binary platelet systems have not yet been carried out. 

Binary mixtures of particles of different shape and/or size are interesting due to the richness of the phase diagrams they may exhibit. Binary rod mixtures form a prominent example. Studies include mixtures of thick and thin rods [27] and long and short rods [28] using Onsager theory as well as using Parsons-Lee scaling [29]. The phase behaviour in binary mixtures can include: the fractionation effect, whereby the larger particles go preferentially into the nematic phase; widening of the biphasic region; a re-entrant I → N → I phenomenon on increasing density; the possibility of demixing into two different isotropic states and/or two different nematic states and triphasic equilibria (see e.g. Ref. [27] for examples of these phenomena). Nematic-nematic ( N - N ) demixing, at high enough pressures, can be viewed as a result of competition between orientational entropy of the smaller platelets favouring mixing, and the entropy of mixing [27]. The N - N phase separation for binary mixtures of rods, including the high density regime, is studied in detail in Ref. [30]. 

Binary mixtures of thin and thick platelets have been investigated [31, 65] with the Parsons-Lee scaling of the Onsager functional [32–34]. Studies based on the Zwanzig model for binary hard platelets, where the particles are restricted to occupy only three mutually perpendicular directions, have been carried out for the bulk and interfacial properties of the demixed phases. Rich phase diagrams, involving isotropic and nematic phases have been reported in Refs. [35–37]. A recent review [38] of platelet fluids contains a summary of these results. Recently Verhoeff et al. [39] have investigated experimentally and theoretically the phase behaviour of colloidal platelets with bimodal shape distribution. Their theory is based on the Onsager-Parsons free energy and a cell approach for the columnar ( Col ) state [40]. The authors find agreement between their experimental findings and theoretical predictions for sufficiently large thickness ratios. The phase diagram features an I - N density inversion and triphasic I - N - Col equilibrium. 

