Predicting Gas Permeability through Mixed-matrix Membranes Filled with Nanofillers of Different Shapes

Gas permeation through mixed-matrix membranes (MMMs) filled with fillers of non-spherical shapes can be theoretically predicted through different analytical models on the basis of ideal (two-phase) or non-ideal (three-phase) morphology of membrane structure. The predicting capability of different models was evaluated by comparing the estimated carbon dioxide (CO₂) permeance through composite membranes against the available experimental permeation data of Ultrason®/ZIF-300, poly(ethersulfone)/functionalized-CNTs and Matrimid®/graphene oxide hybrid membranes. Experimental-to-theoretical discrepancy in CO₂ permeability for composite membranes containing fillers of different shapes was determined by calculating percentage average absolute relative error (AARE%) for each model. General order of data fitting for different models while considering typical values of morphological parameters was found as: Maxwell < Bruggeman < Lewis‐Nielsen < Pal < Maxwell–Wagner-Sillar < Cussler having AARE% values of 41.2, 34.4, 35.7, 27.6, 8.0 and zero, respectively. Scanning electron microscopic (SEM) images of composite membranes helped to explore the morphology of incorporated filler particles and to improve the predicting capacity of the assumed models. The Maxwell–Wagner-Sillar model adopted for composite membranes containing spheroid- and cylindroid-shaped filler particles best fitted the experimental data while the Cussler model best fitted for hybrid membranes filled with planar flake-shaped filler particles.