Bulk phase behaviour of binary hard platelet mixtures from density functional theory Jonathan Phillips 1 ∗ and Matthias Schmidt 1 , 2 $^{1}$H.H. Wills Physics Laboratory, Bristol University, Royal Fort, Tyndall Avenue, Bristol BS8 1TL, United Kingdom $^{2}$Theoretische Physik II, Universit¨ at Bayreuth, Universit¨ atsstraße 30, D-95440 Bayreuth, Germany (Dated: January 29, 2009) Abstract We investigate isotropic-isotropic, isotropic-nematic and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thickness, continuous rotational degrees of freedom and radial size ratios λ up to 5. A fundamental measure density functional theory, pre- viously used for the one-component model, is proposed and results are compared against those from Onsager theory as a benchmark. For λ ≤ 1 . 7 the system displays isotropic-nematic phase coexistence with a widening of the biphasic region for increasing values of λ . For size ratios λ ≥ 2, we find demixing into two nematic states becomes stable and an isotropic-nematic-nematic triple point can occur. Fundamental measure theory gives a smaller isotropic-nematic biphasic region than Onsager theory and locates the transition at lower densities. Furthermore, nematic-nematic demixing occurs over a larger range of compositions at a given value of λ than found in Onsager theory. Both theories predict the same topologies of the phase diagrams. The partial nematic order parameters vary strongly with composition and indicate that the larger particles are more strongly ordered than the smaller particles. PACS numbers: 64.60.Cn,05.20.Jj,64.70.Md,82.70.Dd,64.75.+g arXiv:1001.5438v1 [cond-mat.soft] 29 Jan 2010 ∗ Electronic address: jon.phillips@bristol.ac.uk 1