(336b) Diffusive Water Transport: Relating Hydraulic Permeability to the Apparent Water Diffusion Coefficient in Water-Swollen Polymers

A dense, nonporous polymer film’s hydraulic water permeability, which is the water flux through the film normalized by the film’s thickness and the pressure difference applied across the film, is a material property that can be measured experimentally to describe water transport.  Permeation of water through dense, non-porous polymer membranes, such as those used in desalination processes (e.g., reverse osmosis (RO)), occurs via a solution-diffusion process where water first sorbs into the polymer at the membrane’s upstream face and then diffuses down a chemical potential and water concentration gradient before desorbing at the downstream face of the membrane, and the diffusion process is the rate-determining step.  The chemical potential and water concentration gradients in these nonporous polymers are generated thermodynamically, and they are related to the pressure difference applied across the polymer film.  In order to relate the measured hydraulic water permeability to the apparent diffusion coefficient of water in the polymer, a constitutive equation is required.  The traditional water transport equation, developed for RO membranes, represents one such constitutive equation, but this equation is only strictly applicable to polymers that sorb relatively little water.  When this limited form of the constitutive equation, which is commonly reported in the literature, is applied to polymers that sorb considerable amounts of water (e.g., hydrogels), the calculated apparent water diffusion coefficients can exceed the self-diffusion coefficient of water.  In several cases in the literature, this observation has been used to incorrectly conclude that water transport occurs via a pore-flow mechanism in dense polymer films.

The traditional and simplified water transport equation does not account for the convective frame of reference terms in Fick’s law and thermodynamic non-ideality of the swollen polymer system.  When these effects are appropriately accounted for, the apparent water diffusion coefficients in highly water swollen polymers, calculated from hydraulic water permeability measurements, are satisfactorily below the self-diffusion coefficient of water indicating diffusive, not pore flow, transport of water.  A review of the full constitutive equation for water transport will be presented, and its use will be demonstrated by analyzing several case studies including data from the literature.