Diffusiophoretic mobility of charge-regulating porous particles

Abstract

The diffusiophoresis of a charge-regulating porous sphere, such as polyelectrolyte coil, with an arbitrary thickness of the electric double layer in an electrolyte solution prescribed with a concentration gradient is analytically studied for the first time. The ionogenic functional groups and hydrodynamic frictional segments distribute uniformly within the permeable particle, and a charge regulation model for the association and dissociation reactions of the functional groups relates the fixed charge density to the local electric potential. The electrokinetic equations governing the electric potential, ionic electrochemical potential, and fluid velocity distributions are solved as power-series expansions in the basic fixed charge density. An explicit formula for the diffusiophoretic mobility of the particle, which vanishes at the isoelectric point, is derived from a force balance. The effects of charge regulation on the diffusiophoretic mobility, which depend on various particle and electrolyte characteristics such as the reaction equilibrium constants of the ionogenic functional groups, are significant and interesting. The variation in the bulk concentration of the charge-determining ions can produce more than one reversal in the direction of the diffusiophoretic velocity. The obtained results differ conspicuously from those of impermeable particles and provide valuable information for the interpretation of experimental data.

Keywords: Charge regulation; Chemiphoresis; Diffusiophoresis; Electrophoresis; Porous sphere.