Description of gas transport in perfluoropolymer/SAPO-34 mixed matrix membranes using four-resistance model

Mixed matrix membranes (MMMs) are considered a viable solution for coupling the outstanding gas separationperformances of inorganic porous materials with the ease of fabrication of polymeric membranes.It is known that the heterogeneous system may include a polymer shell of modified permeability surroundingthe filler particles. In addition to that, modifications of the filler were evidenced from the comparisonof the permeability of selective perfluoropolymer/SAPO-34 MMMs with existing extendedMaxwell-like model calculations. This is in agreement with experimental and theoretical evidences ofthe presence of barriers to gas transport in the filler. A 4-phase approach for the transport of gas throughMMMs is proposed here to quantitatively describe the modified layers, both within the Maxwell modeland by finite element analysis. The four phases are: bulk and modified polymer and bulk and modifiedfiller. The latter explicitly accounts for the barriers to mass transport. The changes in the modified layersare quantitatively determined by numerical optimization procedures based on Maxwell’s effective mediumanalytical formula and a finite element solution of the transport differential equations. The newapproach is applied to the minimization of the residuals between each model and an extensive set ofexperimental permeability data (He, H2, CO2, N2) through Hyflon AD60X/SAPO-34 MMMs, including differentfiller particle sizes (0.2, 1.5 and 2 micron), aspect ratios (2, 3 and 9) and loadings (20, 30, 35 and 44 vol%). A MMM subset containing impermeable fillers gives information on the transport properties of thesole matrix. Both the effective medium and the microscopic 4-phase approaches yield physically sounddescriptions of the permeability trends, but FEM simulations also provide spatially resolved gas flows andconcentrations throughout the systems. The focus on the real physical phenomena makes the four-phaseapproach a powerful tool for understanding the MMM transport and improving membrane design