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

Polyelectrolytes (PEs) have ubiquitous applications in both commodity materials in our everyday life and advanced functional materials to solve emergent challenges. Many biomacromolecules, like proteins, DNA, and RNA, are essentially PEs. Modeling ion correlations in inhomogeneous polymers and soft matters with spatially varying ionic strength or dielectric permittivity remains a great challenge. We develop a new theory which systematically incorporates electrostatic fluctuations into the self-consistent field theory for polymers. Applied to polyelectrolyte brushes, the theory predicts that ion correlations induce non- monotonic change of the brush height: collapse followed by reexpansion. Strong ion correlations can trigger microphase separation, either in the lateral direction as pinned micelles or in the normal direction as oscillatory layers. We also predict that the interactions between two opposing PE brushes show hysteretic feature in the presence of multivalent ions: repulsive in the compression branch and adhesive in the separation branch. Our theoretical predictions are in good agreement with the experimental results reported by Tirrell group. Based on the theory, we develop a computational platform to study neurofilament-derived protein brushes.