Microphase Segregation of Polyelectrolyte Brushes

Polyelectrolyte (PE) brushes are widely used as surface modifiers with tunable response to stimuli. A comprehensive understanding of their structure and mechanical behaviors is essential for the rational design of smart materials. Here, we develop a self-consistent field theory (SCFT) which systematically includes polymer elasticity, solubility, and electrostatic interactions in a unified framework. Particularly, the theory well captures the coupling between the chain conformation and the long-range Coulombic force. Applying the theory to a simple system of uniformly charged PE brush, we find that the brush will undergo microphase segregation to form a multi-layered structure as the electrostatic repulsion increases or the hydrophobicity decreases. The calculation of the end-point distribution reveals that multi-layered brushes are formed by collections of melted mushroom conformations grafted upon each other instead of a pearl-necklace conformation for each chain. To facilitate the experimental validation of the multi-layered structure, the corresponding reflectivity spectra have also been provided. Furthermore, the theory is also applied to describe brushes formed by intrinsically disordered proteins. The theoretical prediction of the salt concentration dependence of the brush height shows quantitative agreement with the experimental measurements. The dramatic change of the brush height near a critical salt concentration is explained by the transition of a purely coil-like layer to a condensed layer coexisting with a coil-like layer.