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Summary: 14174 J. Phys. Chem. 1995,99, 14174-14181
Ion Condensation in the Electric Double Layer and the Corresponding Poisson-Boltzmann
Effective Surface Charge
Phil Attard
Department of Physics, Faculty of Science, Australian National University, Canberra, ACT, 0200,Australia
Received: April 17, 1995; In Final Form: June 23, 1995@
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 0.1 M 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-Boltzmang approximation underestimates the actual surface charge and overestimates the
amount of counterion binding. At high surface charge densities and 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. 0.1 M divalent, 75 %1* per unit surface charge), charge
reversal occurs, due to overscreening by the counterions in the first layer adjacent to the surface.
Introduction
The charge on the surface of a particle is a key quantity in
physical and colloid chemistry that determines the properties
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