Numerical investigation of the contraction of neutral-charged diblock copolymer brushes in electric fields

Using self-consistent field theory (SCFT), the contraction of neutral-charged A-B diblock copolymer brushes in electric fields generated by opposite surface charges on two parallel electrodes has been numerically investigated. The diblock copolymer chains were grafted with the free end of the neutral block to one electrode and immersed in a salt-free solution sandwiched between the two electrodes. The numerical results reveal that the charged monomers, A-B joint segment and the tail exhibit bimodal distributions under external electric fields, which are absent for homopolymer polyelectrolyte brushes. The dependences of the relative populations and peak positions of the two modes on various parameters such as block ratio, grafting density, chain length and strength of the applied electric field were systematically examined and the underlining mechanisms were elucidated. It was found in this study that, if the total amount of surface charges on the grafting electrode is no more than that of the counter-ions in the system, overall charge neutrality is generally maintained inside the brushes when including the contribution of surface charges on the grafting electrode. In such a case, the counter-ions expelled from the brushes are highly enriched in the immediate vicinity of the second electrode and an approximate charge balance between these expelled counter-ions and the opposite surface charges on the second electrode is achieved. (paper)