Eur. Phys. J. E 5, 557-574 (2001)
Electrostatistics of counter-ions at and between planar charged walls: From Poisson-Boltzmann to the strong-coupling theory
R.R. NetzMax-Planck-Institut für Kolloid-und Grenzflächenforschung, 14424 Potsdam, Germany netz@mpikg-golm.mpg.de
(Received 13 February 2001)
Abstract
The Poisson-Boltzmann (PB) approach gives asymptotically exact
counter-ion density profiles around macroscopic charged objects
and forces between macroscopic charged objects
in the weak-coupling limit
of low counter-ion valency, low surface-charge density,
and high temperature. In this paper
we derive, using field-theoretic methods,
a theory which becomes exact in the opposite
limit of strong coupling (SC). Formally, it corresponds to a
standard virial expansion. Long-range divergences
render the virial expansion intractable for
homogeneous bulk systems, giving rise to
non-analyticities in the
low-density expansion of the free-energy density of
electrolyte solutions.
We demonstrate that for the case
of inhomogeneous density distribution functions
at macroscopic charged bodies these divergences
are renormalizable
by a systematic expansion in powers of the fugacity.
For a single planar charged wall, we obtain the
counter-ion density profile in the SC limit,
which decays exponentially, in contrast to the PB result, which
predicts algebraic decay, and in agreement with previously
published numerical results.
Similarly and highly charged plates in the presence of
multivalent counter-ions attract each other in the SC limit and form
electrostatically bound states, in contrast to the PB limit,
where the interaction is always repulsive.
By considering next-leading corrections to both the PB and
SC theories, we estimate the range of validity
for both theories.
82.70.-y - Disperse systems; complex fluids.
82.45.-h - Electrochemistry and electrophoresis.
61.20.Qg - Structure of associated liquids: electrolytes, molten salts, etc..
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001
