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The results for the spinodals were checked by running the self-consistency program for the solutions of the coupled ODFs (29) and (30) with the trial functions 1 / 4 π ; the locus of c values (for a given value of λ ) for which the maximum number of iterations occured was found to agree numerically very well to the I - N spinodal. To calculate the spinodals in the ( x, p ∗ ) representation we insert the ( x, c ) values which form the spinodal into the expression for the isotropic pressure (38). In the monodisperse limit, one needs to solve the following cubic polynomial to calculate the bifurcation point c ∗ 

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where the bifurcation concentration is c ∗ = 8 /π 2 = 0 . 811 for Onsager theory and c ∗ = 0 . 434 for FMT, the latter much closer to the limit of stability of the isotropic phase as observed in simulations [26]. 

I. Symmetry-Conserved Demixing Spinodals 

A thermodynamic phase is locally stable if the determinant of the Hessian matrix of the Helmholtz free energy density with respect to the species densities is positive. The spinodal is the limit of stability, defined by det N = 0, where 

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For the I - I spinodals, we insert Ψ$_{1}$( θ ) = Ψ$_{2}$( θ ) = 1 / 4 π into the free energy (37). This yields an analytic solution of Eq. (46) for Onsager theory, given by 

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