Non-linear screening in concentrated colloidal suspensions

In a charge-stabilized colloidal solution, the large colloidal particles ar e surrounded by microions that are up to four orders of magnitude smaller t han the colloidal particles. Because of this size asymmetry, it is desirabl e to obtain an effective one-component description of the mixture where the colloidal particle plus its ionic atmosphere is treated as one, dressed pa rticle. The effective pair potential between these dressed particles is a s creened Coulomb potential. The screening depends, of course, on the density distribution of the small ions around and between the big colloidal partic les. If the colloidal charge and the concentration of the ions is not too h igh, this distribution can be approximately determined from the linearized Poisson-Boltzmann equation, and the resulting effective pair potentials are Yukawa potentials. In concentrated suspensions, however, the full, non-lin ear Poisson-Boltzmann equation must be solved to determine the density dist ribution of the small ions. In this article, we suggest a way to obtain eff ective pair potentials for this case. We solve the non-linear Poisson-Boltu nann equation around a colloidal particle that is displaced a certain dista nce from the centre of its Wigner-Seitz cell. From the resulting density pr ofile of the ions, we determine the total force acting on the shifted parti cle as a function of the displacement. From this function one can then esti mate the non-linearly screened pair forces, and, thus, the effective pair p otentials.