(332d) Ion Correlation Induced Non-Monotonic Height Change and Microphase Separation of Polyelectrolyte Brushes

Modeling ion correlations in inhomogeneous polymers and soft matters with spatially varying ionic strength or dielectric permittivity remains a great challenge. Here, 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. We perform the scaling analysis to elucidate the essential role of the electrostatics as the competition between the repulsive osmotic pressure due to translational entropy and the attraction induced by ion correlations. Four regimes are identified in the height response: osmotic, salted, collapsed and neutral. We clarify the absence of causal relationship between the brush collapse-reexpansion and the charge inversion practically defined as the reversal of the surface electrostatic potential. Furthermore, strong ion correlations can trigger microphase separation, either in the lateral direction as pinned micelles or in the normal direction as oscillatory layers. Our theoretical predictions are in good agreement with the experimental results reported by Tirrell group. The easy access of our theory to the high dimensional calculation enables us to explore the rich morphological behaviors of PE brushes and other ion-containing polymer systems.