Analytic Expression for Electrophoretic Mobility of Soft Particles with a Hydrophobic Inner Core at Different Electrostatic Conditions

This paper presents a simplified model for the electrophoresis of a soft particle with a nonwettable rigid core with charged polyelectrolyte corona under a weak-field and low-charge density consideration. We have derived a closed form solution for the mobility, which reduces to the well-known expressions for mobility as derived by Ohshima for limiting cases such as a hydrophilic charged core coated with an uncharged polymer (Ohshima, H. J. Colloid Interface Sci. 2002, 252, 119-125) or an uncharged no-slip core coated with a polyelectrolyte layer (Ohshima, H. Electrophoresis 2006, 27, 526-533). The generalized mobility expression reduces to the existing expression for mobility of a rigid hydrophobic colloid as the soft layer shrinks to zero. The general form of the mobility expression involves elliptic integrals, which can be computed easily through a software like Mathematica. We have derived analytical solutions for mobility pertaining to several particular cases. The occurrence of mobility reversal when the core and polyelectrolyte layer has a charge of opposite polarity is demonstrated in this paper.