Comparison of Numerical Modeling of Water Uptake in Poly(vinyl chloride)-Based Ion-Selective Membranes with Experiment

A dual-sorption-site model in which both miscible and phase-separated water droplets are present in ion-selective, poly(vinyl chloride) (PVC)-based membranes is applied to data obtained for the H 2 O concentration profiles during the later stages of water uptake. A finite difference algorithm for calculating the concentration profiles is presented, and the calculated curves are shown to match the experimental data over the entire equilibration period. A relaxation process is identified which is associated with an increasing content of immobilized H 2 O, C im, as described by C im = C ° im (1 − y e - β t ), where y = 0.7, β = 0.27 h - 1 for membranes with about 45 mM salt added, and y = 0.6, β = 0.40 h - 1 with 5 mM added salt. Calculations are presented showing water equilibration times required for 40−100 μm thick membranes contacted by water on both sides, a solid on one side, or a 10−40 μm thick hydrogel serving as an inner electrolyte reservoir on one side. For membranes thinner than 200 μm that are contacted on both sides by H 2 O, the slow relaxation phenomenon dominates water uptake rather than the diffusion process. The presence of an internal reservoir, which must be hydrated by transport across the membrane, slows equilibration drastically.