Third case Generally, the permeability of the gases through the dispersed phase lies between the two extreme cases discussed above, and « « The fillers exhibit an intrinsic finite permeability. This 0 Pd ∞. permeability will be different from that of the polymer matrix and its behaviour must be described by the complete Maxwell equation . This requires that the MOFs are well distributed within the polymer matrix and adhere to the polymer without pore blockage. The three cases are schematically indicated in Figure 1. Figure 1: Graphic representation of gas transport properties of the previous cases as a function of the filler concentration. The dashed lines delimit the range of permeabilities predicted by the Maxwell model. The points indicate an example where the filler in the MMM slightly increases the permeability of the polymer matrix. Fourth case This is a special example of the previous situation, in which the permeability of the continuous phase is exactly equal to that of the dispersed phase, In this case, simplifies to: Pc=Pd. This means that the presence of the nanoparticles has no influence on the transport properties of the membrane for a specific gas. In this case, the mixed matrix membrane will show an identical permeability to the neat polymer membrane for this gas, but since different gases are probably affected differently by the filler particles, the selectivity might change with respect to the neat polymer. Experimental Materials All starting materials and solvents were purchased from Sigma-Aldrich, except for chromium nitrate nonahydrate (Cr (NO3)3.9H2O, Alfa, 98%) and sodium hydroxide (NaOH, Fisher Chemical). All chemicals were used as received. Single gases were supplied by Pirossigeno at a minimum purity of 99.9995%. Certified gas mixtures were supplied by Sapio at a purity of ±0.01%
Third case Generally, the permeability of the gases through the dispersed phase lies between the two extreme cases discussed above, and 0 « Pd « ∞. The fillers exhibit an intrinsic finite permeability. This permeability will be different from that of the polymer matrix and its behaviour must be described by the complete Maxwell equation . This requires that the MOFs are well distributed within the polymer matrix and adhere to the polymer without pore blockage. The three cases are schematically indicated in Figure 1. Figure 1: Graphic representation of gas transport properties of the previous cases as a function of the filler concentration. The dashed lines delimit the range of permeabilities predicted by the Maxwell model. The points indicate an example where the filler in the MMM slightly increases the permeability of the polymer matrix. Fourth case This is a special example of the previous situation, in which the permeability of the continuous phase is exactly equal to that of the dispersed phase, Pc=Pd. In this case, simplifies to: This means that the presence of the nanoparticles has no influence on the transport properties of the membrane for a specific gas. In this case, the mixed matrix membrane will show an identical permeability to the neat polymer membrane for this gas, but since different gases are probably affected differently by the filler particles, the selectivity might change with respect to the neat polymer. Experimental Materials All starting materials and solvents were purchased from Sigma-Aldrich, except for chromium nitrate nonahydrate (Cr (NO3)3.9H2O, Alfa, 98%) and sodium hydroxide (NaOH, Fisher Chemical). All chemicals were used as received. Single gases were supplied by Pirossigeno at a minimum purity of 99.9995%. Certified gas mixtures were supplied by Sapio at a purity of ±0.01%
PIM_1_UiO_MMMs_Manuscript_Rev1_Final.docx