Polyelectrolyte (PE) brush-like molecules are very useful in modifying 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 "intermediate"/"short" 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. (C) 2014 The Electrochemical Society. All rights reserved.