Free volume analysis of organic vapor diffusion in polyurethane membranes

Mutual diffusion coefficients of penetrant–polymer systems comprising two organic compounds (benzene and tetrachloroethylene) and four polyurethane membranes (spandex from E.I. du Pont de Nemours & Company, Inc., and three Estane® polymers from B.F. Goodrich Speciality Chemicals) were measured as a function of temperature (30–60°C) and organic vapor activity by performing transient desorption experiments with a McBain quartz-spring microbalance apparatus. Diffusion coefficients increased with temperature and decreased with polymer hard segment content. Fujita’s free volume theory, corrected for the presence of hard segment domains in the polyurethanes, described well the dependence of organic penetrant diffusion on concentration and temperature. Equations correlating the free volume parameters to the polymer morphology, as quantified by the hydrogen bonding index (HBI), were generated. These equations, in combination with the Flory–Rhener equation for benzene and tetrachloroethylene vapor sorption and polymer morphology correlations for the Flory–Rhener parameters, were able to predict to within 12% the mutual diffusion coefficients as a function of concentration, temperature, and hard segment content.