Unified Dual Mode Description of Small Molecule Sorption and Desorption Kinetics in a Glassy Polymer

Abstract

FTIR-ATR (Fourier transform infrared-attenuated total reflectance) spectroscopy and a conventional gravimetric sorption balance were used to study sorption and desorption kinetics of vapor phase acetonitrile in glassy cellulose acetate. A time delay was observed in the measured concentration at the polymer-crystalinterfacefromtheFTIR-ATRexperimentsthatwaslongerthanexpectedfromapplyingthe simple Fickian diffusion model used to fit the gravimetric data for this system. By using the dual mode sorptionmodelwithtotalimmobilization oftheholepopulationrather thanasimpleFickianframework,the time behavior at the boundary was readily captured. This model in turn was used to fit the FTIR-ATR data fordesorptionkinetics.Thedesorptiondiffusioncoefficientswerefoundtobeconsiderablyhigherthanthose obtainedfor sorption owingtothenecessary redistribution betweenthedissolvedand holepopulations when the classic dual mode sorption model is applied to the desorption isotherm. To resolve this inconsistency and remove the discontinuity in concentration at the penetrant-polymer boundary between sorption and desorption, a unified dual mode model to describe both sorption and desorption is proposed. In this model, a fraction of the dissolved population creates holes during the sorption process at each activity. The new model was applied to the sorption and desorption kinetics data in this study, resulting in unifying dual mode parameters and comparable diffusion coefficients.