ELECTROLYTE CRITICALITY AND GENERALIZED DEBYE-HUECKEL THEORY. Benjamin
P. Lee* and Michael E. Fisher, University of Maryland, College Park, MD,
USA. (*Building 224, room B210, NIST, Gaithersburg, MD 20899, 301-975-2113,
Experiments on phase separation in electrolytes can exhibit, surprisingly, either mean-field or Ising-like criticality, a discrepancy which has stimulated much theoretical study. The usual starting point is the restricted primitive model (RPM) of charged, equisized hard spheres, for which it has been shown that Debye-Hueckel (DH) based theories not only give exact results in the low-density limit, but also provide an adequate description of the near-critical thermodynamics. We generalize the DH approach to the case of non-uniform ion densities p+(r) and p-(r), which allows calculation of ion correlation functions via functional techniques. Our results offer many improvements over the conventionally assumed DH correlations: (I) the charge-charge correlation function satisfies explicitly the Stillinger-Lovett second-moment condition and exhibits charge oscillations for densities above a Kirkwood line in the (p,T) plane, (ii) the density-density correlation length is non-trivial, and found to be exact and universal in the low-density limit, and (iii) the thermodynamic consistency built into our approach yields a diverging correlation length at the critical point. The latter result allows us to formulate a Ginzburg criterion for the expected range of the critical region. From this we find that the RPM should be Ising-like, and thus appears not to be a sufficient model for describing the full range of experiments.