(336h) A Variational Field Theory for Ion/Charge Correlations in Electrolyte Systems

Many biological systems and industrially important formulations
consist of solutions containing highly charged colloidal particles.
For these solutions, electrostatic and dispersion forces typically
play a major role in determining their structure and thermodynamic
properties.  Much of our understanding of the role of electrostatic
interactions in these systems is based on Poisson-Boltzmann theory
which, although quite successful, has many well documented
limitations, such as its failure for systems with multivalent ions
where ion-ion correlations are significant.  In this work, a
variational field theory approach is developed, which removes many of
these limitations.

The key physical motivation behind the theory is to treat the short
and long wavelength fluctuations in the system within different
approximation schemes.  At short range, the systems are strongly
coupled, and at long range the systems are weakly coupled.  To
describe both these regimes within a single theory, we split the
interaction into a short and long range contribution.  The long range
behavior is often well approximated by a mean field theory, or
including first order fluctuation corrections, while the short range
behavior can be captured by a virial expansion, or other liquid state
methods suitable to describe particles with short range pair
interactions.

This approach is able to properly account for the many-body effects of
the electrostatic interactions, even for strongly charged particles,
and it also naturally handles the coupling between electrostatic,
induction, and dispersion interactions.  For weakly coupled systems,
this theory approaches the Poisson-Boltzmann theory, while for
strongly coupled systems, the theory resembles the strong coupling
expansion.  The theory also performs well for intermediate couplings.
In addition, the accuracy of the theory can, in principle, be
systematically improved.

The theory can be applied to a wide variety of problems, such as
systems with different geometries and conditions (e.g., dielectric
interfaces) and particles with different shapes and charge
distributions.  We examine its application to determine the effective
interaction between charged, low dielectric particles in electrolyte
solutions.  This fairly simple system exhibits a range of interesting
phenomena, such as like-charge attraction and electrostatic depletion,
that can not be captured with mean field approximations.  The
resulting theory is shown to gives accurate predictions in comparison
to Monte Carlo simulation results.