A model for the permeation characteristics of porous membranes with grafted polyelectrolyte brushes

Abstract

The hydraulic permeability and neutral solute diffusion characteristics of a membrane made up of plane parallel channels whose walls are covered by a terminally grafted weak polyelectrolyte are studied theoretically. The measurable quantities of interest, namely the hydraulic and diffusion thicknesses, as well as the selectivity of the pore are predicted in terms of the polymer brush conformations provided by the recent polyelectrolyte brush theory ( Misra et al., Macromolecules 22, 4173 (1989) ). The effects of the brush grafting density, pH, ionic strength, and solute size are investigated. The Debye-Bueche-Brinkman model which visualizes the grafted layer as an obstacle course composed of randomly distributed spherical segments is employed to study both momentum and mass transfer through the channel. The hydrodynamic thickness is found to be a much better characteristic of polymer conformation for brushes than for homopolymer adsorption. This is due to the slower decay of the segment density in brushes—almost parabolic as opposed to almost exponential in homopolymers. Also, the streaming potential is found to be negligibly small due to the highly retarded flow in the polymer brush region where the mobile charge density is high. Concerning the solute permeability, one obtains, in accord with the recent experimental data ( Kim and Anderson, J. Membr. Sci. 47, 163 (1989) ), that the resistance to diffusive transport is less than that for momentum transport, except for fairly large solutes (solute size ∼ two times the segment size). Finally, the computations also reveal that a significant enhancement in selectivity between solutes of different sizes can be achieved with polyelectrolyte grafted membranes.