Numerical Study of Two Opposing Weak Polyelectrolyte Brushes by the Self-consistent Field Theory

The self-consistent field theory (SCFT) was employed to numerically study the interaction and interpenetration between two opposing weak polyelectrolyte (PE) brushes formed by grafting weak PE chains onto the surfaces of two long and parallel columns with rectangular-shaped cross-section immersed in a salty aqueous solution. The dependences of the brush heights and the average degree of ionization on various system parameters were also investigated. When the brush separation is relatively large compared with the unperturbed brush height, the degree of interpenetration between the two opposing PE brushes was found to increase with increasing grafting density and bulk degree of ionization. The degree of interpenetration also increases with the bulk salt concentration in the osmotic brush regime. Numerical results further revealed that, at a brush separation comparable to the unperturbed brush height, the degree of interpenetration does not increase further with increasing bulk degree of ionization, bulk salt concentration in the osmotic regime and grafting density. The saturation of the degree of interpenetration with these system parameters indicates that the grafted PE chains in the gap between the two columns retract and tilt in order to reduce the unfavorable electrostatic and steric repulsions between the two opposing PE brushes. Based on salt ion concentrations at the midpoint between the two opposing brushes, a quantitative criterion in terms of the unperturbed brush height and Debye screening length was established to determine the threshold value of the brush separation beyond which they are truly independent from each other.