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) are prepared by incorporation proper filler particles within polymeric matrices and potentially have better separation performances than the neat polymeric membranes. However, some undesired phenomena like 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 were developed but they are not able to predict the formed voids’ impact(s) truly and their predicted void permeabilities are usually overestimated. In this study, new parameter of modified filler volume fraction ϕ_d^' considering the swollen effect of MMM structure due to the formed voids around the filler particles, simultaneously employed with  factor, as the formed voids’ permeabilities correction factor, to modify the Maxwell, the Bruggeman and the Pal models of MMMs permeability prediction. Absolute average relative errors (AAREs) of the modified models predicted MMMs permeabilities or selectivities were considerably reduced to 3.16, 29.92, and 21.95 % from those of the Maxwell, the Bruggeman, and the Pal models as 31.33, 310.64, and 67.10 %, respectively. Additionally, the optimum thicknesses of the formed voids around the filler particles became in rational agreement with the Knudsen flow concepts.