Effect of ion partitioning on diffusiophoresis of a soft particle with hydrophobic core

A theoretical study on the diffusiophoresis of a soft particle consisting of a hydrophobic rigid core covered with a charged polymer layer migrating in an electrolyte medium under an imposed concentration gradient is carried out. The dielectric permittivity of the soft layer is considered to be different from that of the adjoining electrolyte medium, yielding the ion partitioning effect due to the self-energy difference of ions. The electrolyte concentration is assumed to be sufficiently high to create a thin Debye layer around the particle so that the particle surface can be treated planer and the curvature effects can be ignored. A general diffusiophoretic mobility expression, which is applied to an arbitrarily charged soft particle with a hydrophobic inner core is derived, considering the ion partitioning effect. The general mobility expression is further approximated under the low particle charge limit to deduce a closed-form analytical solution for the diffusiophoretic mobility of a weakly charged soft particle. A simplified mobility expression obtained with a thinner hydrodynamic screening length consideration is provided as well, which is pertinent to a soft particle with a hydrophilic core in the presence of the ion partitioning effect. The cumulative effects of core hydrophobicity and ion partitioning on the particle motion are illustrated. The hydrophobic core has a strong effect when both the electrophoresis and chemiphoresis parts work in combination. A mobility reversal occurs on reduction of the soft layer permittivity for the case where the electrophoresis and chemiphoresis components oppose each other. The influence of ion partitioning is potent at a larger slip length and a thicker hydrodynamic screening length where the effective charge of the soft particle is high.