content_image/348274.jpg content_image/348272.jpg content_image/348271.jpg
where the kernel L ( θ, θ ′ , θ ′′ ) is 

<img src='content_image/348274.jpg'>

The full form of the excess free energy, as used in the calculations described below, is given by the sum of Eqs. (13) and (27). In practice, along with Eqs. (12) and (28), these require numerical computation on a grid as described in the following. 

## E. Self-consistency equations for the orientational distribution functions 

The minimisation principle (3) together with the FMT approximation (22) for F$_{exc}$ ([ ρ$_{1}$, ρ$_{2}$ ]) leads to two coupled Euler-Lagrange equations for the ODFs: 

<img src='content_image/348272.jpg'>

<img src='content_image/348271.jpg'>

where the constants Z$_{1}$ and Z$_{2}$ are such that the normalisation ∫ d ω Ψ$_{i}$( ω ) = 1, for i = 1 , 2. Neglecting terms of order c 2 in the exponentials, the equations for FMT reduce to the Euler-Lagrange equations of Onsager theory. We solve Eqs. (29) and (30) numerically with 

