Modeling the Effects of Interfacial Characteristics on Gas Permeation Behavior of Nanotube-Mixed Matrix Membranes

Theoretical approaches that accurately predict the gas permeation behavior of nanotube-containing mixed matrix membranes (nanotube-MMMs) are scarce. This is mainly due to ignoring the effects of nanotube/matrix interfacial characteristics in the existing theories. In this paper, based on the analogy of thermal conduction in polymer composites containing nanotubes, we develop a model to describe gas permeation through nanotube-MMMs. Two new parameters, "interfacial thickness" (a_int) and "interfacial permeation resistance" (R_int), are introduced to account for the role of nanotube/matrix interfacial interactions in the proposed model. The obtained values of a_int, independent of the nature of the permeate gas, increased by increasing both the nanotubes aspect ratio and polymer-nanotube interfacial strength. An excellent correlation between the values of a_int and polymer-nanotube interaction parameters, χ, helped to accurately reproduce the existing experimental data from the literature without the need to resort to any adjustable parameter. The data includes 10 sets of CO₂/CH₄ permeation, 12 sets of CO₂/N₂ permeation, 3 sets of CO₂/O₂ permeation, and 2 sets of CO₂/H₂ permeation through different nanotube-MMMs. Moreover, the average absolute relative errors between the experimental data and the predicted values of the proposed model are very small (less than 5%) in comparison with those of the existing models in the literature. To the best of our knowledge, this is the first study where such a systematic comparison between model predictions and such extensive experimental data is presented. Finally, the new way of assessing gas permeation data presented in the current work would be a simple alternative to complex approaches that are usually utilized to estimate interfacial thickness in polymer composites.