Charge inversion by flexible polyelectrolytes adsorbed onto charged cylindric surfaces within self-consistent-field theory

Self-consistent-field theory (SCFT) is presented to study the charge inversion phenomena by flexible polyelectrolytes (PE) adsorbed onto oppositely charged cylindric surfaces. We focus on the effect of surface curvature on the charge inversion ratio between the area density of surface charge compensated by the adsorbed polymers and the area density of origin surface charge. Numerical results show that surface curvature does have a strong effect on the charge inversion phenomena. Namely, it can lead to strong charge inversion at high salt concentrations with strong surface-PE short-range non-Coulombic interaction even in a good solvent. In particular, under large surface curvature and strong short-range non-Coulombic interaction conditions, full charge inversion can even happen at low salt concentrations. Moreover, numerical results show that the surface curvature has a different effect on the charge inversion ratio in the regime dominated by the surface-PE electrostatic interaction and in the regime dominated by the surface-PE shortrange non-Coulombic interaction. Increasing surface curvature will decrease the charge inversion ratio in the former case, while it will increase it in the latter case. Also, we numerically obtain a crossover point for the cylinder radius, which approximately equates to 2 times the gyration radius of PE chain. When the cylinder radius becomes larger than it, the surface curvature will lose its effect on the charge inversion. The numerical results give a further demonstration that, in these weakly charged systems, the surface-PE short-range nonCoulombic interaction is the main driving force of charge inversion phenomena. The results are in good agreement with the theoretical and experimental results.