Effective pair potentials for charged colloidal particles

Abstract

A general formalism for ionic fluids is presented. We report general and exact expressions for the distribution functions which directly satisfy the Stillinger–Lovett moment conditions. General and exact expressions are also provided for the effective pair potentials among charged colloidal particles. These general expressions are a direct consequence of the multicomponent Ornstein–Zernike (OZ) equations and the asymptotic behavior of the direct correlation functions in charged systems. The effective pair potentials show two distinct parts: short-ranged and electrostatic. For the primitive model (PM) with pointlike small ions the electrostatic component is reduced, for sufficiently large distances, to a screened Coulomb potential with renormalized charges. The general expression of the effective electrostatic interaction gives a clear insight of the specific conditions of validity of the Derjaguin–Landau–Verwey–Overbeek (DLVO) model and of the possible directions in which this model may be improved. We also present results for the PM with pointlike small ions obtained from an implementation of the Zerah–Hansen (ZH) approximation complemented with a new minimization criterion. These results are compared with experimental data to test the accuracy of the predictions of the ZH scheme against those obtained from the DLVO model.