A Dual Mode, Local Equilibrium Relaxation Model for Small Molecule Diffusion in a Glassy Polymer

FTIR-ATR (Fourier transform infrared-attenuated total reflectance) spectroscopy and a conventional gravimetric sorption balance were used to study the diffusion of acetonitrile from the vapor phase in glassy cellulose acetate (CA). From the gravimetric experiments, the mass uptake kinetics were well described by a simple Fickian model. However, the experimental data from FTIR-ATR spectroscopy, effectively the concentration at a planar solid boundary, could not be described within the simple Fickian framework. A time delay in the measured concentration at the boundary, longer than expected from the simple Fickian model, strongly suggested that an additional physical phenomenon must be operative. In order to explain the observed behavior, a transport model based on dual mode sorption and total immobilization of the hole population was employed with the assumption of local equilibrium relaxed. The resulting model, incorporating finite hole filling/emptying rates, was able to capture the observed FTIR-ATR data and predict the gravimetric results.