Modeling Ion-Specific Effects in Polyelectrolyte Brushes: A Modified Poisson-Nernst-Planck Model

Polyelectrolyte brushes consist of a set of charged linear macromolecules each tethered at one end to a surface. An example is the glycocalyx which refers to hair-like negatively charged sugar molecules that coat the outside membrane of all cells. We consider the transport and equilibrium distribution of ions, and the resulting electrical potential, when such a brush is immersed in a salt buffer containing monovalent cations (sodium and/or potassium). The Gouy-Chapman model for ion screening at a charged surface captures the effects of the Coulombic force that drives ion electrophoresis and diffusion, but neglects non-Coulombic forces and ion pairing. By including the distinct binding affinities of these counter-ions with the brush, and their so-called Born radii, which account for Born forces acting on them when the permittivity is non-uniform, we propose modified Poisson-Nernst-Planck continuum models that show the distinct profiles that may result depending on those ion-specific properties.