Modeling of the Salt and pH Effects on the Permeability of Grafted Porous Membranes

Abstract

A simple theoretical model describing the effects of pH and salt concentration on the permeability and counterion transport number of variable permeability membranes has been presented and validated experimentally for the case of poly(vinylidene fluoride) membranes graft modified with poly(acrylic acid) chains by radiation-induced grafting. The model incorporates explicitly the statistical conformations of a polyacid chain grafted onto the pore surface. The electrostatic interactions between the bound charges in the chains are screened according to the Debye−Hückel theory. The charged capillary model for porous membranes is then used to evaluate the permeability and counterion transport number of the membrane. This theoretical approach is able to describe the experimental trends observed for a range of KCl concentrations and pH values when the grafting ratios are low. In particular, the fact that the membrane permeability changes by several orders of magnitude when the properties of the external solution are varied can be rationalized in terms of very simple physical principles.