Towards a theory of coexistence and criticality in real molten salts

Abstract

To improve our understanding of the liquid-gas phase separation occurring in ordinary molten salts a variety of model ionic fluids is investigated extending from the restricted primitive model (RPM) (composed of hard ions with equal size) to model reactive fluids in which a chemical reaction between ionic and covalent species takes place. In searching to improve the existing linearized theories for the RPM, it is shown that the mean-field approach of Debye-Hückel (DH) theory is very sensitive to successive improvements (ion pairing, hard sphere contribution, dielectric constant), whereas the mean-spherical approximation (MSA) exhibits, under similar conditions, less sensitive behaviour. In particular, it is shown that the good agreement obtained by M. E. Fisher and Y. Levin (1993, Phys. Rev. Lett., 71, 3826) with computer simulation data in implementing the ion-dipole interaction into DH theory with ion pairing worsens significantly if the dielectric medium composed of ion pairs is properly taken into account in a self-consistent way. However, our improved MSA incorporating at the same time ion pairing, ionic solvation and dipole-dipole contributions shows only qualitative agreement with the available simulation data. In order to describe more realistically the world of molten salts a primitive model is introduced of a reactive fluid composed of ionic and covalent (polar or non-polar) species which can interact in accordance with the chemical equilibrium In this model fluid the phase separation is governed mainly by ΔE the energy difference between molecules (C, D) and ions (A+, B-) in their ground states. When ΔE ≳ 0 the concentration of molecules in the fluid is so small that it behaves like the RPM discussed previously. On the other hand, when ΔE < 0 the concentration of molecules becomes significant in both phases (liquid and gas) and the critical point shifts towards higher densities (as compared with the RPM critical point) while the coexistence curve adopts a peculiar arched shape, these features being all the more pronounced when ΔE is more negative. In spite of the key role played by the covalent species, the phase transition is still driven by the ionic population. Thus at the high temperatures of the onset of the phase transition, the molecules behave mostly like ideal species. The theory is next specialized to two highly conducting molten salts, namely NaCl and NH4Cl, as well as a weakly dissociated liquid, water, which is known to ionize under pressure. The calculation permits one to understand why molten salts, like alkali halides, exhibit a very low critical density and low vapour pressure in contrast to other molten salts, where covalent species are in a much more significant concentration, and for which the critical density and the vapour pressure practically match those found with regular liquids. Finally, the difficulty of obtaining a quantitative agreement with experimental data is emphasized and a route for further improvements is indiated.