  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. The scaling analysis elucidates the competition between the
repulsive osmotic pressure due to translational entropy and the attraction
induced by ion correlations. We also clarify the absence of causal relationship
between the brush collapse-reexpansion and the inversion 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 in the literature.
