Criticality of charged systems. I. The restricted primitive model

Abstract

A new method, which improves upon the mean spherical approximation (MSA), is developed by including the ionic-pairing contribution using a recent theory of association. The association constant of the new approximation is obtained through the second ionic virial coefficient. In the simplest version of our theory, which we call the pairing MSA 1 (PMSA1), we neglect the activity coefficient of the fully associated ionic-pairs, which are regarded as a separate dipolar species, and obtain the critical point (ρc*, Tc*) at (0.025, 0.075). In the second PMSA ( or PMSA2), we include the activity coefficient of these dipolar particles at the MSA level. The new critical point is located at (0.023, 0.073). In the third PMSA ( or PMSA3), we further include the effect of the presence of the dipolar-particle cores. The final critical point is located at (0.0245, 0.0745). These critical points are considerably closer than the MSA result (0.014, 0.079) to the most recent Monte Carlo estimates of ρc* from 0.025 to 0.04 and Tc* from 0.053 to somewhat over 0.057. Both PMSA2 and PMSA3 appear to improve the critical values of pressure and the degree of association significantly over PMSA1. All expressions for the thermodynamic properties in the PMSA1, PMSA2, and PMSA3 are of simple analytic form. The equation of state in the PMSA3 reduces to the very accurate Carnahan-Starling equation of state for hard spheres if the charges are turned off, and it reduces to an accurate equation of state for a mixture of hard spheres and hard dumbbells if the charges of the associated pairs are turned off. A comparison is made between our theory and that of a recent approach of Fisher and Levin, which is in good agreement with the simulation results if the hard-core contribution to the thermodynamics is neglected, but which falls out of agreement when an accurate core contribution is included. A discussion of the importance of an accurate core term in the treatment of the restrictive primitive model is given. Finally, the most likely reasons that the Tc* predicted by the PMSA is somewhat too high are briefly noted.