Eur. Phys. J. E 1, 203-214
Beyond Poisson-Boltzmann: Fluctuation effects and correlation functions
R.R. Netz1 - H. Orland2
1 Max-Planck-Institut für
Kolloid- und Grenzflächenforschung,
14424 Potsdam, Germany
2 Service de Physique Théorique,
CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
orland@spht.saclay.cea.fr
Received 8 February 1999 and Received in final form 15 May 1999
Abstract
We formulate the exact non-linear field theory for a fluctuating
counter-ion distribution in the presence of a fixed,
arbitrary charge distribution. The Poisson-Boltzmann equation
is obtained as the saddle-point of the field-theoretic
action, and the effects of
counter-ion fluctuations are included by a loop-wise
expansion around this saddle point.
The Poisson equation is obeyed at each order
in this loop expansion. We explicitly give the
expansion of the Gibbs potential up to two loops.
We then apply our field-theoretic
formalism to the case of a single impenetrable wall
with counter ions only (in the absence of salt ions).
We obtain the fluctuation corrections
to the electrostatic potential and the counter-ion
density to one-loop order without further approximations.
The relative importance
of fluctuation corrections is controlled by a single parameter,
which is proportional to the cube of the counter-ion valency
and to the surface charge density.
The effective interactions and correlation functions
between charged particles close to the charged wall
are obtained
on the one-loop level.
PACS
82.70.-y Disperse systems
-
61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc.
-
82.45.+z Electrochemistry and electrophoresis
Copyright EDP Sciences, Società Italiana di Fisica, Springer-Verlag
