Electrophoretic mobility of a highly charged soft particle: Relaxation effect

An approximate analytic expression is derived for the electrophoretic mobility of a soft particle, that is, a hard particle of radius a covered with an ion-penetrable surface layer of polyelectrolytes of thickness d in an electrolyte solution of concentration n under conditions at which κa ≫ 1, κd ≫ 1, λa ≫ 1, and λd ≫ 1 (where κ = Debye–Hückel parameter and 1/λ = softness parameter). The obtained expression is an improvement of a previously derived mobility expression [Ohshima, J. Colloid Interface Sci., 163 (1994) 474; ibid. 228 (2000) 190] by taking into account the relaxation effect for the region outside the surface charge layer so that it can be applicable for arbitrary values of the density N of fixed-charges in the surface charge layer. It is observed that the electrophoretic mobility plotted as a function of N or n exhibits a maximum due to the relaxation effect.