Free energy and cluster structure in the coexistence region of the restricted primitive model

The method of thermodynamic integration is used to determine the free energy of the restricted primitive model of electrolytes along two subcritical isotherms. The densities of liquid-gas coexistence derived from these data are found to be in good agreement with recent estimates from Gibbs ensemble Monte Carlo calculations. The difficulties of the free energy approach—which reside in the necessity of obtaining extremely accurate free energy values at near critical temperatures—is stressed. A detailed account is given of the clustering properties of the ions in the vapor phase, including cluster populations and energies, as well as intercluster contributions to the thermodynamic properties. The validity of several cluster theories for the free energy is investigated.