Finite ion size and ion permittivity effects on gel electrophoresis of a soft particle

Electrophoresis of a soft particle embedded in a hydrogel medium is studied by considering the hydrated ions as charged dielectric spheres of finite radius. The Nernst-Planck equation for the transport of ions is modified to take into account the ion steric repulsion and the ion-solvent dielectric interactions (MNP-model). The effective polarizability of the hydrated ions lowers the dielectric permittivity of the ionic solution and consequently, the permittivity of the medium varies with local ionic concentration. This spatial variation of the permittivity creates a Born energy difference in ions leading to a Born force experienced by the ions. In addition, ions experience a dielectrophoretic force due to the polarization under the imposed external electric field. The ion steric repulsion are modeled by the Carnahan-Starling equation of state. The convection of ions are governed by the Brinkman extended Navier-Stokes equations. The modified Nernst-Planck equation coupled with the Brinkman NavierStokes equations and the equation for electric field are solved numerically through a control volume approach. The ion steric interactions and ion-solvent interactions create a saturation of mobile ions in the polyelectrolyte layer (PEL) of the soft particle, which leads to an attenuation of the counterion condensation of the PEL. This short range steric repulsion and ion-solvent interactions have significance for higher bulk ionic concentration as well as higher range of charge density of the soft particle. These interactions are elucidated by comparing with the mobility obtained by the standard model (PNP-model). The Dukhin number and the effective charge density of the PEL are determined to illustrate the mobile ion saturation. The discrepancy between the present modified model from the standard model magnifies for the case of salts of multivalent counterions.

Automated summary

The study focuses on the electrophoresis of a soft particle in a hydrogel medium, considering hydrated ions as charged dielectric spheres with finite radius. By modifying the Nernst-Planck equation to account for ion steric repulsion and ion-solvent interactions, the research reveals how the spatial variation of permittivity affects ion transport and mobility in the system. The results highlight the significance of short range steric repulsion and ion-solvent interactions, especially in cases of higher bulk ionic concentration and charge density of the soft particle.