Polyelectrolyte brush in a cylindrical pore: A Poisson–Boltzmann theory

The conformation of a polyelectrolyte (PE) brush grafted to the inner surface of a long cylindrical mesopore was described within analytical Poisson-Boltzmann strong stretching approximation. The internal structure of the PE brush, including brush thickness and radial density profile of monomer units, and radial distribution of electrostatic potential were analyzed as functions of the pore radius, degree of polymerization, and grafting density of the brush-forming PE chains as well as ionic strength of the solution. It is demonstrated that narrowing of the pore leads to a non-monotonous variation of the brush thickness, which passes through a maximum when the brush thickness becomes equal to the pore radius. Variation in the salt concentration triggers conformational transition that leads to the opening or closing of the hollow (PE-free) channel in the pore center that potentially allows controlling of the pore-selective permeability for charged nanocolloidal particles (e.g., globular proteins or viruses). The predictions of the analytical theory were validated by numerical calculations using the Scheutjens-Fleer self-consistent field modeling method. These theoretical findings may be used for the design of highly selective smart mesoporous membranes with PE brush-functionalized pores for, e.g., protein separation and purification.