content_image/372883.jpg content_image/372882.jpg content_image/372881.jpg content_image/372880.jpg content_image/372879.jpg
We define a reduced pressure p ∗ = βpR 3 1 and reduced chemical potentials µ ∗ i = βµ$_{i}$ . Eqs. (31) and (32) are three equations for four unknowns (two state points each characterised by two densities). Therefore, regions of two-phase coexistence depend parametrically on one free parameter. Eqs. (33) and (34) are solved numerically with a Newton-Raphson procedure [60]. The resulting set of solutions yields the binodal. I - N - N triple points are located where the I - N and N - N coexistence curves cross. Therefore, regions of two-phase coexistence depend parametrically on one free parameter (which can be chosen arbitrarily, e.g. as the value of concentration x in one of the phases). 

## G. Equation of State for the Isotropic Phase 

Analytic expressions for the free energy, pressure and chemical potentials for the isotropic phase may be found on insertion of Ψ( θ ) = 1 / (4 π ) into the ideal (5) and excess (22) parts of free energy functional. For this purpose, we use 

and 

<img src='content_image/372883.jpg'>

<img src='content_image/372882.jpg'>

where the integrals I 1 and I 2 are calculated in Appendix A. The expressions for the FMT isotropic free energy, βF$_{iso}$/V , pressure, p ∗ iso and chemical potentials µ ∗ i, iso are 

<img src='content_image/372881.jpg'>

<img src='content_image/372880.jpg'>

<img src='content_image/372879.jpg'>

