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we provide conclusions and an outlook on possible future work. 

## II. DENSITY FUNCTIONAL THEORY FOR BINARY HARD PLATELET MIX- TURES 

A. Pair Interactions and Model Parameters 

We consider a binary mixture of hard circular platelets with vanishing thickness and continuous positional and orientational degrees of freedom. Species 1 and species 2 have radii R$_{1}$ and R$_{2}$ respectively, with R$_{2}$ > R$_{1}$ . The pair potential u$_{ij}$ between two particles i and j , where i, j = 1 , 2, is infinite if the geometrical shapes of the two platelets overlap and zero otherwise and is hence given by 

where r and r ′ are the positions of the particle centres and ω and ω ′ are unit vectors indicating the particle orientations (normal to the particle surface). The size ratio 

<img src='content_image/371660.jpg'>

<img src='content_image/371659.jpg'>

characterises the radial bidispersity and is the only control parameter in the model. We characterise the thermodynamic state by two dimensionless densities c$_{1}$ = ρ$_{1}$R 3 1 and c$_{2}$ = ρ$_{2}$R 3 $_{1}$, where ρ$_{1}$ and ρ$_{2}$ are the number densities of the two species, ρ$_{i}$ = N$_{i}$/V , where N$_{i}$ is the number of particles of species i = 1 , 2 and V is the system volume. The composition (mole fraction) of the (larger) species 2 is x = ρ$_{2}$/ ( ρ$_{1}$ + ρ$_{2}$ ) and the total dimensionless concentration is c = R 3 $_{1}$( ρ$_{1}$ + ρ$_{2}$ ) = c$_{1}$ + c$_{2}$ . 

B. Grand Potential Functional and Minimisation Principle 

Density functional theory (DFT) is formulated on the one-body level of the density dis- tributions ρ$_{i}$ ( r , ω ). The variational principle [41] states that the true equilibrium density profile is the one which minimises the grand potential functional Ω and so obeys 

<img src='content_image/371662.jpg'>

