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

Abstract

Abstract 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 /ν 1 , where ν 1 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 /ν 1 = P . (b) In the higher hydration region KRT /ν 1 is greater than P , and the ratio ω = KRT /ν 1 P 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 /ν 1 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.