Diffusive and hydraulic permeabilities of water in water‐swollen polymer membranes

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<jats:title>Abstract</jats:title><jats:p>The diffusive permeability of water <jats:italic>P</jats:italic>, 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 <jats:italic>K</jats:italic>, which relates to the water flux under a hydraulic pressure gradient are defined. For the case of diffusive transport one has <jats:italic>P</jats:italic> = <jats:italic>KRT</jats:italic>/ν<jats:sub>1</jats:sub>, where ν<jats:sub>1</jats:sub> is the molar volume of water. The relationship between <jats:italic>P</jats:italic> and <jats:italic>K</jats:italic> was investigated as a function of hydration <jats:italic>H</jats:italic>, 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 (<jats:italic>H</jats:italic> < 0.2), water permeates by diffusion even under an applied hydraulic pressure gradient and <jats:italic>KRT</jats:italic>/ν<jats:sub>1</jats:sub> = <jats:italic>P</jats:italic>. (b) In the higher hydration region <jats:italic>KRT</jats:italic>/ν<jats:sub>1</jats:sub> is greater than <jats:italic>P</jats:italic>, and the ratio ω = <jats:italic>KRT</jats:italic>/ν<jats:sub>1</jats:sub><jats:italic>P</jats:italic> increases nearly exponentially with decrease of (1‐<jats:italic>H</jats:italic>)/<jats:italic>H</jats:italic>. 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 <jats:italic>P</jats:italic> on (1‐<jats:italic>H</jats:italic>)/<jats:italic>H</jats:italic> is nearly linear in regions of both high and low hydration but the slopes are different. The transition occurs in about the same <jats:italic>H</jats:italic> range where the discrepancy between <jats:italic>P</jats:italic> and <jats:italic>KRT</jats:italic>/ν<jats:sub>1</jats:sub> becomes significant. Excellent agreement was found between the experimental data for <jats:italic>P</jats:italic> as a function of <jats:italic>H</jats:italic> and the theoretical prediction based on the free‐volume concept of diffusive transport in hydrated homogeneous membranes.</jats:p>

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