Solubility and Diffusivity of Gases in Mixed Matrix Membranes Containing Hydrophobic Fumed Silica: Correlations and Predictions Based on the NELF Model

The addition of fumed silica particles to glassy polymers such as PTMSP and Teflon AF 2400 results in an enhancement of gas diffusivity and permeability that is not captured by traditional models for composites because both volume and gas solubility of the composite material are underestimated by the additive rule based on pure component properties. Such effects have been attributed to the creation of additional free volume due to the insertion of filler in the polymeric matrix. In this work, we use the NELF model to relate gas solubility in the composite material to the variations induced by the addition of filler on polymer density and swellability. From these values, the fractional free volume (FFV) increase produced in the polymeric phase by filler incorporation may be evaluated and, in turn, also the diffusivity in the composite material can be calculated as a function of filler content on the basis of its relation to FFV. The gas diffusivity data for n-C4H10 in AF 2400 and AF 2400-based mixed matrices, as well as those relative to N2, CH4, C2H6, C3H8, and n-C4H10 in PTMSP, follow closely the correlation found, which contains only one adjustable parameter for each penetrant-polymer couple.