Electrostatic potential of polyelectrolyte molecules grafted on charged surfaces: A poisson-boltzmann model

Polyelectrolyte (PE) brush-likemolecules are very useful inmodifying the physical properties of surfaces in solution. Polyelectrolytes strongly influence the electrostatic potential of the PE-covered surface of nanoparticles and also the ion concentration near the surface. These parameters further affect the mobility and ion dynamics that play a significant role in applications such as electrophoretic deposition (EPD). In this work we use a 1D Poisson-Boltzmann model to simulate the effect of the surface charge on the electrostatic potential at the surface and at the polyelectrolyte/solution interface. This extends existing models that treat neutral surfaces with PE molecules. From the analysis of the numerical results of our model, we define long and intermediateshort PE brushes according to the amount of screening of the electrostatic field inside the PE brush. We also find novel analytical expressions for the potential of brush/bulk interfaces and the Donnan potential for a pH-dependent PE brush. Finally, we show that the case of intermediate/short brush is realistic for typical values of surface charge and experimental PE lengths.