Calculation of the Electrophoretic Mobility of a Particle Bearing Bound Polyelectrolyte Using the Nonlinear Poisson-Boltzmann Equation

A numerical method for determining the electrophoretic mobility of a polyelectrolyte-coated particle is presented. The particle surface is modeled as having a permeable layer of polyelectrolyte molecules anchored to its surface. Fluid flow within the polyelectrolyte layer is subject to Stokes drag arising from the polyelectrolyte segments. The method allows arbitrary distribution of polymer segments and charge density normal to the surface to be used. The hydrodynamic plane of shear may also be varied. The potential profile is determined by a numerical solution to the nonlinearized Poisson-Boltzmann equation. The potential profile is then used in a numerical solution to the Navier-Stokes equation to give the required mobility. The use of the nonlinearized Poisson-Boltzmann equation extends the results to higher charge density/lower ionic strength conditions than previous treatments. The surface potentials and mobilities for three limiting charge distributions are compared for both the linear and nonlinear treatments to delimit the range of validity of the linear treatment. The utility of the numerical, nonlinear treatment is demonstrated by an improved fit to the electrophoretic mobility of human erythrocytes as a function of ionic strength in the range 10 to 150 mM.