Salt rejection by polymer membranes in reverse osmosis. I. Nonionic polymers

An attempt is made to analyze the relationship between salt rejection and water flux of nonionic polymer membranes in reverse osmosis on the basis of the movement of water in the membranes. The salt rejection R_s is a consequence of transport depletion of salt in relation to water flux. The transport depletion can be quantitatively expressed through knowledge of the mode of water transport and by application of free-volume theory to membrane transport phenomena. Water permeation can be characterized by a parameter ω = RTK₁/P_1v1, K₁ denoting hydraulic permeability, P₁ diffusive water permeability, v₁ the molar volume of water. Thus polymer membranes can be classified in three categories: ω = 1 (diffusion membranes); ω > 1 (diffusion-flow membranes); and ω ? 1 (flow membranes). Salt rejection R_s can be expressed in terms of P₁, the diffusive salt permeability P₂, and the effective pressure (Δp ? Δπ): Experimental results obtained with various hydrophilic polymers are presented as the dependence of R_s on the logarithm of water flux. Good agreement was found between the experimental data and the calculated curve. Excessive swelling of membranes results in bulk flow of water (high ω) with coupled transport of salt. Hence the salt rejection decreases quickly as water flux in creases beyond a threshold value above which water flux can be characterized as bulk flow.