Analytical theory of solution of attracting molecules of different size derived from hypernetted-chain equation for radial distribution function

Abstract

The Flory–Huggins formula of mixing entropy of different size molecules originally proved for polymer solution is generally proved for attracting spherical molecules different in size. The Scatchard formula of the excess energy known for application in the solubility parameter is also proved theoretically. The proof is based on analytical solutions of the radial distribution functions for mixture and does not rely on the lattice model. The hypernetted-chain (HNC) equation is perturbed taking hard-sphere system as reference and the attractive force as perturbation. The obtained equation for the perturbed radial distribution function for mixture is solved analytically under simplifying assumptions, which enabled to give the equation of state in analytical form. In order to give the excess Gibbs free energy in explicit form, the vapor pressure of liquid mixture is obtained by applying a phase equilibrium condition corresponding to the Maxwell’s equal-area rule to mixture. The excess entropy and enthalpy are derived directly.