Electrophoresis of soft particles with charged rigid core coated with pH-regulated polyelectrolyte layer

We present a theoretical study on the electrophoresis of a soft particle with a dielectric charged rigid core grafted with a charge-regulated polyelectrolyte layer. The polyelectrolyte layer possesses either an acidic or a basic functional group and the charge dissociation depends on the local pH and ionic concentration of the electrolyte. The dielectric rigid core is considered to possess a uniform volumetric charge density. The electric potential distribution is determined by computing the Poisson-Boltzmann equation outside the core coupled with a Poisson equation inside the impermeable core along with suitable matching conditions at the core-shell interface. The computed electric field is used to determine the mobility of the particle through an existing analytic expression based on the Debye-Huckel approximation. Our results are found to be in good agreement with the existing solutions for the limiting cases. The influence of the core charge density, ionic concentration, and pH of the electrolyte on the particle mobility is studied for different choice of hydrodynamic penetration length of the polyelectrolyte and dissociation constant of the functional group. The critical value of the pH required to achieve zero mobility is estimated. We find that in a monovalent electrolyte solution, the soft particle with a net negative (positive) charge can have positive (negative) mobility.