between the isotropic and nematic state of species 2 up to about p ∗ = 0 . 06, suggesting that up to this pressure there is only a small fractionation effect. This fractionation becomes wider on increasing the pressure beyond this point, with the phase boundaries almost reaching x = 0 , 1 by p ∗ = 0 . 1. The re-entrant bend is also a dominating feature of the phase diagram in Fig. 7d for Onsager theory suggesting the FMT phase behaviour is correct, however it is not as pronounced as for FMT and the narrow I - N$_{2}$ handle present at low pressures for FMT is wider for Onsager theory. In Fig. 8 we show the partial nematic order parameters S$_{i}$ in the coexisting nematic phase(s) for λ = 2 , 2 . 5 , 4 and 5, as obtained from FMT. For λ = 2 (Fig. 8a) S$_{1}$ and S$_{2}$ both rise rapidly near zero composition to near unity. S$_{1}$ takes on smaller values than S$_{2}$ for a given mole fraction as has already been observed for the lower size ratios. Hence the (smaller) particles of species 1 are much less ordered than particles of species 2 at a given composition, since the particles of species 2 are high in number and there is more freedom for the smaller particles to rotate in the dense system. Both partial order parameters remain close to unity as the composition x is increased from 0 to about 0.5. The system is at N - N coexistence over this range (see Fig. 4c for the corresponding phase diagram). S$_{tot}$ reaches as low as about 0.5 and S$_{1}$ becomes as small as 0.2 at x = 1. For λ = 2 . 5 (Fig. 8b) the N - N coexistence does not end at a critical point, leaving an interval (in composition) that the curves S$_{i}$ ( x ) do not enter. For λ = 4 (Fig. 8c) S$_{tot}$ varies between about 0.3 and almost 1. This range of S$_{tot}$ increases further for λ = 5 (Fig. 8d) where it reaches as low as about 0.2. For λ = 4 , 5, S$_{tot}$ also increases more rapidly as the composition increases than is the case for the lower size ratios. At high compositions, the (small) particles of species 1 possess very low nematic order, reaching less than 0.1 due to the larger size difference between the two species. Our phase diagrams share several features with those reported in previous studies of binary mixtures of anisometric hard core particles. Widening of the I - N phase coexistence region upon increasing the bidispersity parameter was found in binary mixtures of thick and thin rods [27], long and short rods [28], mixtures of rods and platelets [64], as well as in binary mixtures of platelets using both the Parons-Lee scaling of the Onsager functional [31, 65] and the Zwanzig model [36, 37]. N - N phase coexistence ending in an upper critical point, as we find for an intermediate range of values of size ratios λ , occurs in certain regimes for binary mixtures of rods and platelets. A notable difference to other studies of platelet 21