Abstract
We use Langevin dynamics simulations to investigate the conformation of polyelectrolyte (PE) brushes and the counterions distribution at different grafting densities in direct-current uniform electric fields |E|. The field direction is perpendicular to the substrate surface. Firstly, we observe that |E| larger than a critical electric field |E*| can induce large conformational change of PE brushes. At low grafting densities, the height of chains stretch together with |E| and the brush is in a homogeneous phase. However, at intermediate and high grafting densities, two phases can coexist in the brush. For the intermediate grafting density case, the brush separates into dilute and dense, two-layer phases when |E**|<|E|<|E***| because a fraction of the chains are not stretched. For high grafting density, only few chains are stretched by the electric field. The majority of the chains are non-stretched and form a compact layer with the counterions. The bifurcated brush does not merge into a homogeneous phase in strong electric fields as at the intermediate grafting density. Secondly, the profiles of the counterion distribution change significantly at low and intermediate grafting density when the field strength exceeds |E*|. Below |E*|, the counterion profiles match the monomer distributions due to ion condensation on the chains. Above |E*|, the majority of the ions move toward the substrate surface and the fraction of the condensed counterions decreases. The monomer and ion distributions are studied in detail through calculation of the side-view and top-view densities. Finally, we find that |E*| increases with grafting density and follows the scaling law. A schematic phase diagram is presented, which gives a thorough picture of the PE brush sys-tem over the parameter space grafting densities and |E|.