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,
email:benjamin.lee@nist.gov)

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.