Department of Physics, Faculty of Science, Australian National University, Canberra, ACT, 0200, Australia.
J. Phys. Chem. 99, 14174-14181 (1995)
Abstract
The effective surface charge obtained by fitting
the Poisson-Boltzmann approximation to measured data
is related to the actual surface charge.
Evaluation of the formally exact expression,
which depends upon the wall-ion direct correlation function,
gives a precise measure of the amount of ion condensation
in the planar double layer.
Results are presented for 0.001, 0.01, and 0.1M monovalent
and divalent restricted primitive model electrolytes
using the singlet hypernetted chain closure with the first
bridge diagram.
In general the apparent surface charge is less than the
actual surface charge, due to the influence of ion-ion correlations.
Thus the Poisson-Boltzmann approximation underestimates
the actual surface charge and overestimates the amount of counterion binding.
At high surface charge densities the apparent surface charge saturates,
and there is a maximum surface charge density that a
given electrolyte will appear to support.
At surface charge densities beyond this and high concentrations,
(e.g. 0.1M divalent, 75\AA $^2$ per unit surface charge),
charge reversal occurs,
due to over-screening by the counterions in the first layer
adjacent to the surface.
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