Modeling water diffusion in polybenzimidazole membranes using partial immobilization and free volume theory

Abstract This study extends previous work on modeling water sorption, dilation, and diffusion in polybenzimidazoles (PBIs) by comparing water transport properties of commercial PBI (Celazole®) with three sulfone-containing PBIs. A model is developed combining free volume and partial immobilization theories to describe water diffusion coefficients across a wide range of concentrations and degrees of swelling. Water vapor sorption and dilation follow dual-mode behavior and generally correlate with the availability of strong hydrogen bonding sites on the polymer chains. At low concentrations, water diffusion coefficients are suppressed by partial immobilization of Langmuir species, while at high concentrations, water diffusion coefficients increase due to significant swelling and plasticization. To account for the influence of plasticization on free volume and water mobility, local Henry's law mobility coefficients are correlated with fractional free volume (FFV), where the volume occupied by water molecules is considered to contribute to dynamic free volume and is assumed to be as accessible for water diffusion as unoccupied free volume. Contributions to diffusion coefficients from thermodynamic and convective frame of reference effects and concentration averaging are also considered.