Correlation of Gas Permeability in a Metal-Organic Framework MIL-101(Cr)-Polysulfone Mixed-Matrix Membrane with Free Volume Measurements by Positron Annihilation Lifetime Spectroscopy (PALS)

Abstract

Hydrothermally stable particles of the metal-organic framework MIL-101(Cr) were incorporated into a polysulfone (PSF) matrix to produce mixed-matrix or composite membranes with excellent dispersion of MIL-101 particles and good adhesion within the polymer matrix. Pure gas (O2, N2, CO2 and CH4) permeation tests showed a significant increase of gas permeabilities of the mixed-matrix membranes without any loss in selectivity. Positron annihilation lifetime spectroscopy (PALS) indicated that the increased gas permeability is due to the free volume in the PSF polymer and the added large free volume inside the MIL-101 particles. The trend of the gas transport properties of the composite membranes could be reproduced by a Maxwell model.

Figure 1

Schematic representation of a mixed-matrix membrane indicating different, also simultaneous possible sizes, shapes and components for the inorganic filler materials. 10 µm is a typical length scale of the particles, compared to the thickness of the polymer film of 100 µm.

Figure 2

Building blocks for MIL-101, [Cr₃(µ₃-O)(F,OH)((BDC)₃(H₂O)₂], generated from the deposited X-ray data file at the Cambridge Structure Database (CSD-Refcode OCUNAK) [86] using the program DIAMOND [87]. Trinuclear {Cr₃O} building units and bridging benzene-1,4-dicarboxylate ligands form pentagonal and hexagonal rings (a) which are assembled into mesoporous cages (b). The yellow spheres in the mesoporous cages with diameters of 29 or 34 Å, respectively, take into account the van-der-Waals radii of the framework walls (water-guest molecules are not shown) [86]. The different objects in this figure are not drawn to scale.

Figure 3

Polysulfone repeating unit.

Figure 4

Schematic presentation of sample preparation for positron annihilation lifetime spectroscopy (PALS).

Figure 5

O₂/N₂ permeability and separation performance of pure polysulfone (PSF) and MIL-101/PSF membranes with different MIL wt % loadings (graphics with revised MIL-101 wt % [94] values compared to reference [85]).

Figure 6

SEM photographs of MIL-101/PSF membranes based on 400 mg of PSF with different loadings of MIL-101. Left: membranes surface; right: cross section view.

Figure 7

CO₂/N₂ permeability and separation performance of pure PSF and MIL-101/PSF membranes with different MIL wt % loadings.

Figure 8

CO₂/CH₄ permeability and separation performance of pure PSF and MIL-101/PSF membranes with different MIL wt % loadings.

Figure 9

Comparison of CO₂/N₂ separation performance of MIL-101/PSF with other metal-organic framework (MOF)-containing mixed-matrix membranes from literature data (for further details on MOF-mixed-matrix membrane (MMM) data points see Table S2 and Table S4, Figure S6). The Robeson upper bound for polymer separation performance as defined 2008 is shown [10].

Figure 10

Comparison of CO₂/CH₄ separation performance of MIL-101/PSF with other MOF-containing mixed-matrix membranes from literature data (for further details on MOF-MMM data points see Table S3 and Table S5, Figure S7). The Robeson upper bounds for polymer separation performance as defined in 1991 and 2008 are shown [9,10].

Figure 11

Calculated permeability and selectivity for the MIL-101/PSF-MMMs using the Maxwell model under the assumption of a highly permeable dispersed (filler, MOF) phase, i.e., P_d >> P_c and β ≈ 1. Part (a) is to be compared with Figure 5 and (b) with Figure 7.

Figure 12

Pore radii of the average free volume as function of wt % MIL-101 in MMM. For details see Section 2.6.2.

Figure 13

o-Ps intensities as function of wt % MIL-101 in MMM. The o-Ps intensity is related to the relative contribution of annihilation events in the respective phase of the sample. For details see Section 2.6.2.