Salt rejection by polymer membranes in reverse osmosis. II. Ionic polymers

The water permeability K₁ which is related to water flux J₁ per unit membrane area by J₁ = K₁(Δp ? ΔII)/ΔX, where Δp is the pressure difference, ΔII is the osmotic pressure of feed solution, and ΔX is the membrane thickness] of homogeneous ionic polymer membranes in reverse osmosis and their salt rejection R_s which is given by R_s ≡ 1 ? (C_2″/C_2′), where C_2′ is the concentration of the salt in feed solution, and C_2″ is the concentration of salt in effluent] were examined with cationic and anionic membranes of block and graft copolymers. For ionic membranes, R_s and K₁ are related by K₁ = A exp { ? BR_s}, where A and B are constants. This equation was found to be independent of the ion charge, the chemical nature of the polymer, and film morphology. The principle of salt rejection by ionic membranes was explained by the difference in the transport volumes (volume elements available for transport) for mobile co-ions and water. The electric repulsive force between a fixed ion and a mobile co-ion decreases the transport volume of the latter, thus creating a transport depletion of salt flux relative to water transport. This transport depletion is governed by the amount of water sorbed by a fixed ionic site, which also determines the water flux. Consequently, R_s and K₁ for ionically charged membranes are related as described above. This relation significantly differs from that found between R_s and K₁ for nonionic polymer membranes, where the size and the solubility of ions in the membrane are mainly responsible for the transport depletion. The decline of R_s with increasing K₁ is much less in ionic membranes than in nonionic ones; however, in the high R_s region, K₁ for both ionic and nonionic membranes become similar as the dominant mode of water transport changes from flow to diffusion.