Numerical self-consistent field theory study of the response of strong polyelectrolyte brushes to external electric fields.

The response of strong polyelectrolyte (PE) brushes grafted on an electrode to electric fields generated by opposite surface charges on the PE-grafted electrode and a second parallel electrode has been numerically investigated by self-consistent field theory. The influences of grafting density, average charge fraction, salt concentration, and mobile ion size on the variation of the brush height against an applied voltage bias were investigated. In agreement with molecular dynamics simulation results, a higher grafting density requires a larger magnitude of voltage bias to achieve the same amount of relative change in the brush height. In the experimentally relevant parameter regime of the applied voltage, the brush height becomes insensitive to the voltage bias when the grafting density is high. Including the contribution of surface charges on the grafting electrode, overall charge neutrality inside the PE brushes is generally maintained, especially for PE brushes with high grafting density and high average charge fraction. Our numerical study further reveals that the electric field across the two electrodes is highly non-uniform because of the complex interplay between the surface charges on the electrodes, the charges on the grafted PE chains, and counterions.