Modification of Mixed Matrix Membranes’ Famous Permeability Prediction Models by Considering the Formed Voids around Nonporous Fillers

New promising generations of mixed matrix membranes (MMMs), which potentially have better separation performances than the neat polymeric membranes, are prepared by the incorporation of proper filler particles within polymeric matrices. However, some undesired phenomena like the void formation around the filler particles limit this potential improvement. Having proper models is necessary to elucidate the impacts of this phenomenon on the MMMs’ separation performance. Different models have been developed but they are not able to predict the impact(s) of formed voids truly and their predicted void permeabilities are usually overestimated. In this study, the new parameter of the modified filler volume fraction 𝜙𝜙𝑑𝑑 ′ considering the MMM swollen structure due to the formed voids around the filler particles, is employed along with the formed voids’ permeabilities correction factor, as ß, to modify the Maxwell, Bruggeman and Pal models for the MMMs’ permeability prediction. Absolute average relative errors (AAREs) of the modified models predicted that MMMs’ permeabilities or selectivities were considerably reduced to 3.16, 29.92, and 21.95 % from those of the Maxwell, Bruggeman, and Pal models as 31.33, 310.64, and 67.10 % respectively. Additionally, the optimum thicknesses of the formed voids around the filler particles rationally agree with the Knudsen flow concepts.