Monte Carlo Simulations for the Estimation of the Effective Permeability of Mixed-Matrix Membranes

Recent years have seen the explosive development of mixed-matrix membranes (MMMs) for a myriad of applications. In gas separation, it is desired to concurrently enhance the permeability, selectivity and physicochemical properties of the membrane. To help achieving these objectives, experimental characterization and predictive models can be used synergistically. In this investigation, a Monte Carlo (MC) algorithm is proposed to rapidly and accurately estimate the relative permeability of ideal MMMs over a wide range of conditions. The difference in diffusivity coefficients between the polymer matrix and the filler particle is used to adjust the random progression of the migrating species inside each phase. The solubility coefficients of both phases at the polymer−filler interface are used to control the migration of molecules from one phase to the other in a way to achieve progressively phase equilibrium at the interface. Results for various MMMs were compared with the results obtained with the finite difference method under identical conditions, where the results from the finite difference method are used in this investigation as the benchmark method to test the accuracy of the Monte Carlo algorithm. Results were found to be very accurate (in general, <1% error) over a wide range of polymer and filler characteristics. The MC algorithm is simple and swift to implement and provides an accurate estimation of the relative permeability of ideal MMMs. The MC method can easily be extended to investigate more readily non-ideal MMMs with particle agglomeration, interfacial void, polymer-chain rigidification and/or pore blockage, and MMMs with any filler geometry.

Synthesis and Characterization of a Crystalline Imine-Based Covalent Organic Framework with Triazine Node and Biphenyl Linker and Its Fluorinated Derivate for CO2/CH4 Separation

A catalyst-free Schiff base reaction was applied to synthesize two imine-linked covalent organic frameworks (COFs). The condensation reaction of 1,3,5-tris-(4-aminophenyl)triazine (TAPT) with 4,4'-biphenyldicarboxaldehyde led to the structure of HHU-COF-1 (HHU = Heinrich-Heine University). The fluorinated analog HHU-COF-2 was obtained with 2,2',3,3',5,5',6,6'-octafluoro-4,4'-biphenyldicarboxaldehyde. Solid-state NMR, infrared spectroscopy, X-ray photoelectron spectroscopy, and elemental analysis confirmed the successful formation of the two network structures. The crystalline materials are characterized by high Brunauer-Emmett-Teller surface areas of 2352 m²/g for HHU-COF-1 and 1356 m²/g for HHU-COF-2. The products of a larger-scale synthesis were applied to prepare mixed-matrix membranes (MMMs) with the polymer Matrimid. CO₂/CH₄ permeation tests revealed a moderate increase in CO₂ permeability at constant selectivity for HHU-COF-1 as a dispersed phase, whereas application of the fluorinated COF led to a CO₂/CH₄ selectivity increase from 42 for the pure Matrimid membrane to 51 for 8 wt% of HHU-COF-2 and a permeability increase from 6.8 to 13.0 Barrer for the 24 wt% MMM.

Biphenyl-Based Covalent Triazine Framework/Matrimid® Mixed-Matrix Membranes for CO2/CH4 Separation

Processes, such as biogas upgrading and natural gas sweetening, make CO₂/CH₄ separation an environmentally relevant and current topic. One way to overcome this separation issue is the application of membranes. An increase in separation efficiency can be achieved by applying mixed-matrix membranes, in which filler materials are introduced into polymer matrices. In this work, we report the covalent triazine framework CTF-biphenyl as filler material in a matrix of the glassy polyimide Matrimid^®. MMMs with 8, 16, and 24 wt% of the filler material are applied for CO₂/CH₄ mixed-gas separation measurements. With a CTF-biphenyl loading of only 16 wt%, the CO₂ permeability is more than doubled compared to the pure polymer membrane, while maintaining the high CO₂/CH₄ selectivity of Matrimid^®.

Synthesis and Characterization of Covalent Triazine Framework CTF-1@Polysulfone Mixed Matrix Membranes and Their Gas Separation Studies

Covalent triazine framework CTF-1 and polysulfone (PSF) are used to form mixed-matrix membranes (MMMs) with 8, 16, and 24 wt% of the porous filler material CTF-1. Studies on permeability and selectivity are carried out concerning the gases O2, N2, CO2, and CH4. CO2 permeability of the synthesized MMMs increases by 5.4 Barrer in comparison to the pure PSF membrane. The selectivity remains unchanged for O2/N2 and CO2/CH4 but was found to be increased for CO2/N2. Further, comparisons to theoretical models for permeability prediction yield a permeability for CTF-1 which is about six times higher than the permeability of PSF. The inverse of the sum of the free fractional volumes (FFV) of the polymer and the filler correlate linearly to the logarithm of the permeabilities of the gases which conversely indicates that the porosity of the filler contributes to the gas transport through the membrane.

On the Better Understanding of the Surprisingly High Performance of Metal-Organic Framework-Based Mixed-Matrix Membranes Using the Example of UiO-66 and Matrimid

Metal-organic frameworks feature a certain framework flexibility, mainly due to a linker mobility inside the lattice. The latter is responsible for effects like breathing or gate-opening, thus making predictions of the sorption and diffusion behavior quite difficult. Permeation measurements on supported UiO-66 membranes at low temperatures and on polymer-coated UiO-66 membrane layers as well as ²H NMR line shape studies and nitrogen sorption measurements of UiO-66 with deuterated linkers in Matrimid as mixed-matrix membranes (MMM) indicate that the 2-site 180° flips (π-flips) of the aromatic ring are hindered by the presence of (i) the surrounding polymer Matrimid and (ii) residual solvent molecules, thus giving profound insights into the molecular understanding of gas transport through metal-organic framework-based MMMs.

Comparative Study of MIL-96(Al) as Continuous Metal-Organic Frameworks Layer and Mixed-Matrix Membrane

MIL-96(Al) layers were prepared as supported metal-organic frameworks membrane via reactive seeding using the α-alumina support as the Al source for the formation of the MIL-96(Al) seeds. Depending on the solvent mixture employed during seed formation, two different crystal morphologies, with different orientation of the transport-active channels, have been formed. This crystal orientation and habit is predefined by the seed crystals and is kept in the subsequent growth of the seeds to continuous layers. In the gas separation of an equimolar H2/CO2 mixture, the hydrogen permeability of the two supported MIL-96(Al) layers was found to be highly dependent on the crystal morphology and the accompanied channel orientation in the layer. In addition to the neat supported MIL-96(Al) membrane layers, mixed-matrix membranes (MMMs, 10 wt % filler loading) as a composite of MIL-96(Al) particles as filler in a continuous Matrimid polymer phase have been prepared. Five particle sizes of MIL-96(Al) between 3.2 μm and 55 nm were synthesized. In the preparation of the MIL-96(Al)/Matrimid MMM (10 wt % filler loading), the following preparation problems have been identified: The bigger micrometer-sized MIL-96(Al) crystals show a trend toward sedimentation during casting of the MMM, whereas for nanoparticles aggregation and recrystallization to micrometer-sized MIL-96(Al) crystals has been observed. Because of these preparation problems for MMM, the neat supported MIL-96(Al) layers show a relatively high H2/CO2 selectivity (≈9) and a hydrogen permeance approximately 2 magnitudes higher than that of the best MMM.