Ion correlation induced non-monotonic height change and microphase separation of polyelectrolyte brushes

We develop an electrostatic-fluctuation augmented self-consistent field theory (SCFT) which will be an important progress in modeling inhomogeneous polyelectrolyte systems. The theory systematically incorporates different components of the electrostatic fluctuations into a unified framework and self-consistently capture the coupling between electrostatics and chain conformation. The theory is particularly useful for inhomogeneous systems with spatially varying ionic environment and dielectric permittivity. We apply the theory to polyelectrolyte (PE) brushes grafted on a surface which are widely used to regulate transport and control wettability, adhesion, antifouling, and lubrication. We find that the morphological response of PE brushes in the presence of multivalent salt is significantly different from that of monovalent salt. Ion correlation induces a non-monotonic salt concentration dependent of brush height: collapse at low salt concentrations followed by a re-expansion at high salt concentrations. The brush heights predicted by our theory are in quantitative agreement with the experimental data reported by Matthew Tirrell group. We elucidate that there is no casual relationship between brush re-expansion and charge inversion. Furthermore, for strong ion correlations, e.g. trivalent ions, we predict that PE brush will undergo microphase separation, in good agreement with experimental and simulation results. The microphase separation either forms domains in the lateral direction at lower grafting densities or leads to oscillatory multi-layers in the normal direction at higher grafting densities.