Measurement of diffusion coefficients in polystyrene using xenon-129 NMR

A sample of polystyrene beads, 18 μm in diameter, has been sealed in an NMR tube under 10 atm of xenon gas. Two dimensional,¹²⁹Xe NMR spectra show cross peaks between the resonances corresponding to xenon in the free gas and the sorbed state, indicating that appreciable exchange occurs during the mixing time of the NMR experiment. Selective saturation of the free gas resonance attenuates the integrated intensity of the sorbed xenon resonance as a function of saturation time, thus allowing the accurate measurement of the exchange rates between the gas and the sorbed states. A model has been developed using a slightly modified form of Crank’s treatment of diffusion in a sphere which allows for the accurate determination of the diffusion coefficient for xenon in the sorbed state. The diffusion coefficient for xenon in polystyrene at 25°C is determined to be 2.9·10^?9 cm²/s.