Electrophoresis of composite soft particles with differentiated core and shell permeabilities to ions and fluid flow.

Within the framework of analytical theories for soft surface electrophoresis, soft particles are classically defined by a hard impermeable core of given surface charge density surrounded by a polyelectrolyte shell layer permeable to both electroosmotic flow and ions from background electrolyte. This definition excludes practical core-shell particles, e.g. dendrimers, viruses or multi-layered polymeric particles, defined by a polyelectrolytic core where structural charges are distributed and where counter-ions concentration and electroosmotic flow velocity can be significant. Whereas a number of important approximate expressions has been derived for the electrophoretic mobility of hard and soft particles, none of them is applicable to such generic composite core-shell particles with differentiated ions- and fluid flow-permeabilities of their core and shell components. In this work, we elaborate an original closed-form electrophoretic mobility expression for this generic composite particle type within the Debye-Hückel electrostatic framework and thin double layer approximation. The expression explicitly involves the screening Debye layer thickness and the Brinkman core and shell hydrodynamic length scales, which favors so-far missing analysis of the respective core and shell contributions to overall particle mobility. Limits of this expression successfully reproduce results from Ohshima's electrophoresis theory solely applicable to soft particles with or without hard core.

Ion partitioning effect on the electrophoresis of a soft particle with hydrophobic core.

A theoretical study on the electrophoresis of a soft particle made up of a charged hydrophobic inner core surrounded by polyelectrolyte layer (PEL) is made. The dielectric permittivity of the PEL and aqueous solution are considered to be different, which creates the ion partitioning effect. The ion partitioning effect, which is accounted by the Born energy difference, modifies the distribution of mobile ions in the PEL and hence alters the particle electrophoresis. The combined effects of core hydrophobicity and the ion partitioning effect on the mobility are determined based on the Debye-Huckel approximation under a thin Debye layer assumption. An analytic expression for the electrophoretic mobility taking into account the core hydrophobicity and ion partitioning effect is obtained. The occurrence of zero mobility and reversal of mobility of the soft particle is illustrated.