Interaction ranges, ionic fluid criticality

We turn now to theories of ionic criticality that encompass nonclassical phenomena. Mean-field-like criticality of ionic fluids was debated in 1972 [30] and according to a remark by Friedman in this discussion [69], this subject seems to have attracted attention in 1963. Arguments in favor of a mean-field criticality of ionic systems, at least in part, seem to go back to the work of Kac et al. [288], who showed in 1962 that in D = 1 classical van der Waals behavior is obtained for a potential of the form ionic fluids with attractive and repulsive Coulombic interactions have little in common with the simple Kac fluid. 

Keywords Criticality, ionic fluids, long-range interactions, computer simulations... 

In this contribution we have reviewed the results from recent simulations directed towards understanding the manifestation of critical phenomena and finite-size scaling in systems with long-range interactions, including the restricted primitive model of ionic fluids, the charged hard dumbbell fluid, and hard spheres with algebraic interactions. The main conclusions from our studies are as follows. 

To conclude this section on the DH theory, we would like to point out that these last two criticisms (neglecting short range repulsive interactions and linearizing the PBE) are the only valid criticisms. In fact the McMillan-Mayer theory (MMM) showed that, provided a correct definition of the "effective interaction potential" is given, the molecular structure of the solvent needs not to be considered explicitly(1) in calculating the thermodynamic properties of ionic solutions. This conclusion has very important consequences the first one is that, as the number density of ion in a typical electrolyte solutions is of the order of 10"3 ions/A, then the solution can be considered as a dilute ionic gas as a consequence the theories available for gases can be used for ionic fluids, provided the "effective potential" (more often called potential of the mean force at infinite dilution) takes the place ot the gas-gas interaction potential. Strictly this is true only in the limit of infinite dilution, but will hold also at finite concentrations, provided the chemical potential of the solvent in the given solution is the same as in the infinitely dilute solutions. This actually... 

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