Nonuniformly charged sphere

O Brien s method was extended to study the electrophoresis of a nonuniformly charged sphere with thin but polarized ion cloud in a symmetric electrolyte [32]. The electrophoretic mobility depends on the charge distribution at the particle surface. It is found that the polarization effect of the ion could leads to different electrophoretic mobilities for particles with different zeta potential distributions but having an identical velocity for the limit of infinite Ka. This intriguing result is due to the fact that the theory for undistorted ion cloud is linear in the distribution of zeta potential, whereas the polarization effects are nonlinear. 

M. L. Grant and D. A. Saville, J. Colloid Interface Sci., 171, 35 (1995). Electrostatic Interactions between a Nonuniformly Charged Sphere and a Charged Surface. 

In 1923, E Hiickel and P Debye, winner of the 1936 Nobel Prize in Chemistry, adapted the Poisson-Boltzmann theory to explain the nonidealities of dilute solutions of strong electrolytes. To visualize Na ions surrounded by CD ions and C1 surrounded by Na at the same time, think of a NaCl crystal that is expanded uniformly. Now add fluctuations, Debye and Hhckel focused on one ion as a charged sphere, and used the linear approximation to the Poisson-Boltzmann equation to compute the electrostatic free energy of creating the nonuniform distribution of its surrounding counterions and co-ions. 

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