Limiting electrophoretic mobility of a highly charged soft particle in an electrolyte solution: solidification effect

Abstract

It is known that the electrophoretic mobility of a spherical rigid particle in an electrolyte solution with large kappaa (where kappa=Debye-Hückel parameter and a=particle radius) and large Dukhin number (Du>>1) tends to a nonzero constant value in the limit of high zeta potentials. A highly charged liquid drop exhibits the same limiting mobility value. That is, a liquid drop behaves as if it were a rigid particle (the solidification effect). In the present paper we derive the corresponding mobility expression for a highly charged spherical soft particle (i.e., a polyelectrolyte-coated particle) consisting of the particle core of radius a covered with an ion-penetrable surface layer of thickness d in a symmetrical electrolyte solution of valence z. It is shown that for kappaa>> and kappad>>1, the magnitude of the scaled limiting mobility mu((infinity)) is given by |mu((infinity))|=2epsilon(r)epsilon(o)kT/3etaze x (1+a(3)/2b(3)) x 2 ln 2, where epsilon(r) is the relative permittivity of the electrolyte solution, epsilon(o) is the permittivity of a vacuum, e is the elementary electric charge, and kT is the thermal energy. When a approximately b, the obtained limiting mobility expression tends to the result for a rigid sphere. That is, the solidification effect is observed also for a soft particle.