CRITICALITY IN THE HARD-SPHERE IONIC FLUID

A physically based mean-field theory of criticality and phase separati on in the restricted primitive model of an electrolyte (hard spheres o f diameter a carrying charges +/- q) is developed on the basis of the Debye-Huckel (DH) approach. Simple DH theory yields a critical point a t T = k(B)Ta/q(2) = 1/16, which is only about 15% above the best rece nt simulation estimates (T-c,T-sim = 0.052-0.056) but a critical dens ity rho(c) = rho(c)a(3) = 1/64 pi similar or equal to 0.005 that is m uch too small (rho(c,sim) = 0.023-0.035). Allowing for hard-core excl usion effects reduces these values slightly. However, correction of th e DH linearization of the Poisson-Boltzmann equation by including pair ing of + and - charges improves rho(c) significantly. Bjerrum's theor y of the (required) association constant is revisited critically, Ebel ing's reformulation is strongly endorsed but makes negligible numerica l difference at criticality and below, The nature and size of the asso ciated, dipolar ion pairs is examined quantitatively and their solvati on free-energy in the residual fluid of free ions is calculated on the basis of DH theory. This contribution to the total free energy proves crucial and leads to a rather satisfactory description of the critica l region. The temperature variation of the vapor pressure and of the d ensity of neutral dipolar pairs correlates fairly well with Gillan's n umerical cluster analysis. Possible improvements to allow for larger i on clusters and to better represent the denser ionic liquid below crit icality are discussed. Finally, the replacement of the DH approximatio n for the ionic free energy by the mean spherical approximation is stu died. Reasonable critical densities are generated but the MSA critical temperatures are all 40-50% too high, in addition, the predicted dens ity of neutral clusters seems much too low near criticality and, along with the vapor pressure, appears to decrease too rapidly by an expone ntial factor below T-c.