Electrophoretic mobility of soft particles. A soft step function model

A simple approximate analytic expression is derived for the electrophoretic mobility of a soft particle consisting of the hard particle core covered with an ion-penetrable surface layer of polyelectrolytes. The effect of the inhomogeneous distribution of the polymer segments is taken into account by modeling the surface layer as a soft step function with the inhomogeneous distribution width δ. The mobility expression, which is derived on the basis of the non-linear Poisson–Boltzmann equation, improves an approximate mobility expression previously derived by using the linearized Poisson–Boltzmann equation.