Abstract

In a charge-stabilized colloidal solution, the large colloidalparticles are surrounded by microions that are up to four ordersof magnitude smaller than the colloidal particles. Because of this sizeasymmetry, it is desirable to obtain an effective one-componentdescription of the mixture where the colloidal particle plus itsionic atmosphere is treated as one, dressed particle. The effectivepair potential between these dressed particles is a screenedCoulomb potential. The screening depends, of course, on thedensity distribution of the small ions around and between the bigcolloidal particles. If the colloidal charge and the concentrationof the ions is not too high, this distribution can beapproximately determined from the linearized Poisson-Boltzmannequation, and the resulting effective pair potentials are Yukawapotentials. In concentrated suspensions, however, the full,non-linear Poisson-Boltzmann equation must be solved to determinethe density distribution of the small ions. In this article, wesuggest a way to obtain effective pair potentials forthis case. We solve the non-linear Poisson-Boltzmann equationaround a colloidal particle that is displaced a certain distancefrom the centre of its Wigner-Seitz cell. From the resultingdensity profile of the ions, we determine the total force actingon the shifted particle as a function of the displacement. Fromthis function one can then estimate the non-linearlyscreened pair forces, and, thus, the effective pair potentials.

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