Thermodynamic basis for vapor permeability in Ethyl Cellulose

The vapor permeability in glassy Ethyl Cellulose may show rather different behaviors versus upstream pressure, depending on the penetrant considered, including a monotonous decrease as well as a monotonous increase with increasing pressure. Such a spectrum of behaviors, experimentally well known, is still needing a unifying interpretation and a mathematical description, which we are now proposing in the present work. For each solute, at all different temperatures, the permeability in Ethyl Cellulose is described by means of a simple model with a solid thermodynamic basis. The thermo- dynamic behavior of the polymer/penetrant mixture is given by the nonequilibrium lattice fluid model (NELF), which provides the vapor solubility at different values of T and p. The penetrant permeability is described considering the diffusion coefficient as the product of a purely kinetic factor, the mobility, and a thermodynamic factor related to the dependence of the chemical potential of the diffusing species on its concentration in the polymer. The thermodynamic factor is readily calculated from the NELF model, while the mobility factor is endowed with an exponential dependence on penetrant concentration, as often suggested by experimental data; its expression utilizes only two adjustable parameters: the infinite dilution mobility coefficient and the plasticization factor. The analysis indicates that this simple mathematical theory is able to describe accurately all the different behaviors observed experimentally, for all the penetrants inspected, at all temperatures. In addition, the two model parameters for mobility follow clear and simple correlations: the infinite dilution mobility coefficient scales with the penetrant size, and the plasticization factor is related to the ability of the penetrant to swell Ethyl Cellulose, as quantified by the volume swelling coefficient, which is available from independent information.