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  • 1
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1579-1590 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: 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 Rs [which is given by Rs ≡ 1 - (C2″/C2′), where C2′ is the concentration of the salt in feed solution, and C2″ is the concentration of salt in effluent] were examined with cationic and anionic membranes of block and graft copolymers. For ionic membranes, Rs and K1 are related by K1 = A exp { - BRs}, 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, Rs and K1 for ionically charged membranes are related as described above. This relation significantly differs from that found between Rs 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 Rs with increasing K1 is much less in ionic membranes than in nonionic ones; however, in the high Rs region, K1 for both ionic and nonionic membranes become similar as the dominant mode of water transport changes from flow to diffusion.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1117-1131 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The diffusive permeability of water P, which relates to diffusive flux of water under a concentration gradient of water (measured by diffusion of tritiated water), and the hydraulic permeability of water K, which relates to the water flux under a hydraulic pressure gradient are defined. For the case of diffusive transport one has P = KRT/ν1, where ν1 is the molar volume of water. The relationship between P and K was investigated as a function of hydration H, i.e., the volume fraction of water in swollen polymer membranes. The following characteristic features of water permeability are revealed. (a) In the lowhydration region (H 〈 0.2), water permeates by diffusion even under an applied hydraulic pressure gradient and KRT/ν1 = P. (b) In the higher hydration region KRT/ν1 is greater than P, and the ratio ω = KRT/ν1P increases nearly exponentially with decrease of (1-H)/H. Water in this region moves partly by bulk flow under an applied hydraulic pressure gradient but moves only by diffusion in the absence of a pressure gradient. (c) The dependence of log P on (1-H)/H is nearly linear in regions of both high and low hydration but the slopes are different. The transition occurs in about the same H range where the discrepancy between P and KRT/ν1 becomes significant. Excellent agreement was found between the experimental data for P as a function of H and the theoretical prediction based on the free-volume concept of diffusive transport in hydrated homogeneous membranes.
    Additional Material: 5 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 9 (1971), S. 1537-1551 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: 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 Rs 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/P1v1, 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 Rs can be expressed in terms of P1, the diffusive salt permeability P2, and the effective pressure (Δp - Δπ): \documentclass{article}\pagestyle{empty}\begin{document}$ R_{\rm S} = \{ {\rm \omega } + [P_2 RT/P_1 v_1 (p - {\rm \pi )]\} }^{{\rm - 1}} $\end{document} Experimental results obtained with various hydrophilic polymers are presented as the dependence of Rs 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.
    Additional Material: 4 Ill.
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