 
Summary: Testcharge theory for the electric double layer
Yoram Burak* and David Andelman
School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Henri Orland
Service de Physique Théorique, CESaclay, 91191 GifsurYvette cedex, France
(Received 20 January 2004; published 1 July 2004)
We present a model for the ion distribution near a charged surface, based on the response of the ions to the
presence of a single test particle. Near an infinite planar surface this model produces the exact density profile
in the limits of weak and strong coupling, which correspond to zero and infinite values of the dimensionless
coupling parameter. At intermediate values of the coupling parameter our approach leads to approximate
density profiles that agree qualitatively with Monte Carlo simulation. For large values of the coupling param
eter our model predicts a crossover from exponential to algebraic decay at large distance from the charged
plate. Based on the testcharge approach we argue that the exact density profile is described, in this regime, by
a modified meanfield equation, which takes into account the interaction of an ion with the ions close to the
charged plate.
DOI: 10.1103/PhysRevE.70.016102 PACS number(s): 82.45.Gj, 61.20.Qg, 61.20.Gy
I. INTRODUCTION
Interactions between charged objects in solution are deter
mined by the distribution of ions around them. Understand
ing these distributions is thus of fundamental importance for
