Electrophoretic mobility of interacting colloidal spheres

The electrophoretic mobility μ of charged colloidal spheres suspended in deionized water was measured as a function of the packing fraction Φ increasing from about ${10}^{-6}$ to $2\times {10}^{-3}.$ With increasing packing fraction, the mobility first increases linearly with the logarithm of the packing fraction and then saturates at a high value unaffected by the freezing transition. The electrostatic potential $\Psi \mathrm{}\left(r\right)\mathrm{}$ was calculated numerically by solving the nonlinearized Poisson-Boltzmann equation in a cell model under conditions of charge regulation. The potential first is constant at low packing fraction and then decreases roughly linearly with $\log \left(\Phi \right).\mathrm{}$ In both cases the qualitative change in packing fraction dependence occurs once $\kappa a$ significantly (typically 10–20%) increases above ${\kappa }_{0}a$ given by the residual small ion concentration. Qualitatively similar behavior was found for particles of different size and surface chemistry and also under conditions of added salt. None of the theoretical approaches presently available is able to capture this interesting and complex behavior observed under low salt conditions.