A simple equation of state (EOS) for dilute solutions of hard convex bodies (HCBâs) (i.e., large hard spheres or prolate or oblate spherocylinders) in much smaller spherical solvent water molecules is proposed as the repulsive backbone for a statistical associating fluid theory (SAFT) treatment of aqueous micellar solutions. The Onsager-Parsons-Lee formalism , which incorporates the hard sphere EOS  and hard convex body (HCB) occupied and pair excluded volumes, is applied to obtain an EOS for the isotropic liquid phase of HCB pure fluids and mixtures. The compressibility factor versus packing fraction (single-phase behavior) of several isotropic hard-body pure fluids and mixtures including hard spheres and prolate or oblate hard spherocylinders was predicted and compared with available molecular simulation data. Good-to excellent results were observed for pure hard spheres and hard sphere mixtures, especially for dilute solutions of large spheres in small spheres characteristic of spherical micelles in water. Furthermore, fair-to-very good predictions were generally obtained for pure prolate and oblate hard spherocylinders and mixtures of these shapes with hard spheres (models for cylindrical and planar micelles respectively with solvent) up to moderate packing fractions; however, results deteriorated slightly at high packing fractions. These findings suggest that good results should be expected for any of the model micellar shapes in water, where the small solvent hard-spheres are in large excess.
Wertheimâs first-order thermodynamic perturbation theory (TPT1)  was applied to obtain expressions for the free energy and compressibility factor of chain formation from individual aggregates. Micellar structural data (shape, average aggregation number and size) were used to construct some representative model systems for study including aqueous solutions of: 1) monodisperse spherical, cylindrical or planar micelles; 2) polydisperse cylindrical micelles; and 3) chains of cylindrical (wormlike) micelles. Phase stability criteria were applied to identify regions of phase instability (two isotropic liquid phases). Finally, consideration of the EOS attractive terms for dispersion and hydrogen bonding in future work is discussed.
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