Surface Polarization Effects on Collapse Transition of Polyelectrolyte Brushes

Polyelectrolyte brushes (PEBs) are commonly used to modify surface that have attracted great research interest. The dielectric permittivity of the grafted surface is typically significantly different from that of solution, which results in surface polarization (SP) effect with a jump of electric field. It is thus important to study how SP alters the PEB’s structure and properties. In this work, the SP effects on PEB structure was studied using a statistical thermodynamic theory. The free energy functional to describe SP effect was constructed by using the image-charge method. Meanwhile, the electrostatic potential was solved from a modified Poisson-Boltzmann equation taking the ion solvation effect into consideration. In the absence of SP, the thickness of PEB exhibited a continuous collapse transition when decreasing the solvent quality. In the presence of SP, the collapse became a jump-like transition. Free energy analysis showed that the long-range Coulombic interaction dominated the transition because of the enhanced counterion condensation in the presence of SP. The theory provides an effective tool to study SP effect on PEBs, and the results explain the underlying physics in PEB collapse transition.