Modeling Permeation through Mixed-Matrix Membranes: A Review

Recent advancements in polyurethane-based membranes for gas separation

Gas separation membranes are critical in a variety of environmental research and industrial applications. These membranes are designed to selectively allow some gases to flow while blocking others, allowing for the separation and purification of gases for a variety of applications. Therefore, the demand for fast and energy-efficient gas separation techniques is of central interest for many chemical and energy production diligences due to the intensified levels of greenhouse and industrial gases. This encourages the researchers to innovate techniques for capturing and separating these gases, including membrane separation techniques. Polymeric membranes play a significant role in gas separations by capturing gases from the fuel combustion process, purifying chemical raw material used for plastic production, and isolating pure and noncombustible gases. Polyurethane-based membrane technology offers an excellent knack for gas separation applications and has also been considered more energy-efficient than conventional phase change separation methodologies. This review article reveals a thorough delineation of the current developments and efforts made for PU membranes. It further explains its uses for the separation of valuable gases such as carbon dioxide (CO2), hydrogen (H2), nitrogen (N2), methane (CH4), or a mixture of gases from a variety of gas spillages. Polyurethane (PU) is an excellent choice of material and a leading candidate for producing gas-separating membranes because of its outstanding chemical chemistry, good mechanical abilities, higher permeability, and variable microstructure. The presence of PU improves several characteristics of gas-separating membranes. Selectivity and separation efficiency of PU-centered membranes are enhanced through modifications such as blending with other polymers, use of nanoparticles (silica, metal oxides, alumina, zeolite), and interpenetrating polymer networks (IPNs) formation. This manuscript critically analyzes the various gas transport methods and selection criteria for the fabrication of PU membranes. It also covers the challenges facing the development of PU-membrane-based separation procedures.

How 2D Nanoflakes Improve Transport in Mixed Matrix Membranes: Insights from a Simple Lattice Model and Dynamic Mean Field Theory

Mixed matrix membranes (MMMs), incorporating graphene and graphene oxide structural fragments, have emerged as promising materials for challenging gas separation processes. What remains unclear is the actual molecular mechanism responsible for the enhanced permeability and perm-selectivity of these materials. With the fully atomistic models still unable to handle the required time and length scales, here, we employ a simple qualitative model based on the lattice representation of the physical system and dynamic mean field theory. We demonstrate that the performance enhancement results from the flux-regularization impact of the 2D nanoflakes and that this effect sensitively depends on the orientation of the nanoflakes and the properties of the interface between the nanoflakes and the polymer.

The Difference in Performance and Compatibility between Crystalline and Amorphous Fillers in Mixed Matrix Membranes for Gas Separation (MMMs)

An increasing number of high-performing gas separation membranes is reported almost on a daily basis, yet only a few of them have reached commercialisation while the rest are still considered pure research outcomes. This is often attributable to a rapid change in the performance of these separation systems over a relatively short time. A common approach to address this issue is the development of mixed matrix membranes (MMMs). These hybrid systems typically utilise either crystalline or amorphous additives, so-called fillers, which are incorporated into polymeric membranes at different loadings, with the aim to improve and stabilise the final gas separation performance. After a general introduction to the most relevant models to describe the transport properties in MMMs, this review intends to investigate and discuss the main advantages and disadvantages derived from the inclusion of fillers of different morphologies. Particular emphasis will be given to the study of the compatibility at the interface between the filler and the matrix created by the two different classes of additives, the inorganic and crystalline fillers vs. their organic and amorphous counterparts. It will conclude with a brief summary of the main findings.

Mixed Matrix Membranes for Carbon Capture and Sequestration: Challenges and Scope

Carbon dioxide (CO₂) is a major greenhouse gas responsible for the increase in global temperature, making carbon capture and sequestration (CCS) crucial for controlling global warming. Traditional CCS methods such as absorption, adsorption, and cryogenic distillation are energy-intensive and expensive. In recent years, researchers have focused on CCS using membranes, specifically solution-diffusion, glassy, and polymeric membranes, due to their favorable properties for CCS applications. However, existing polymeric membranes have limitations in terms of permeability and selectivity trade-off, despite efforts to modify their structure. Mixed matrix membranes (MMMs) offer advantages in terms of energy usage, cost, and operation for CCS, as they can overcome the limitations of polymeric membranes by incorporating inorganic fillers, such as graphene oxide, zeolite, silica, carbon nanotubes, and metal-organic frameworks. MMMs have shown superior gas separation performance compared to polymeric membranes. However, challenges with MMMs include interfacial defects between the polymeric and inorganic phases, as well as agglomeration with increasing filler content, which can decrease selectivity. Additionally, there is a need for renewable and naturally occurring polymeric materials for the industrial-scale production of MMMs for CCS applications, which poses fabrication and reproducibility challenges. Therefore, this research focuses on different methodologies for carbon capture and sequestration techniques, discusses their merits and demerits, and elaborates on the most efficient method. Factors to consider in developing MMMs for gas separation, such as matrix and filler properties, and their synergistic effect are also explained in this Review.

A molecular simulation study on amine-functionalized silica/polysulfone mixed matrix membrane for mixed gas separation

Polysulfone (PSF) based mixed matrix membranes (MMMs) are one of the most broadly studied polymeric materials used for CO₂/CH₄ separation. The performance of existing PSF membranes encounters a bottleneck for widespread expansion in industrial applications due to the trade-off amongst permeability and selectivity. Membrane performance has been postulated to be enhanced via functionalization of filler at different weight percentages. Nonetheless, the preparation of functionalized MMMs without defects and its empirical study that exhibits improved CO₂/CH₄ separation performance is challenging at an experimental scale that needs prior knowledge of the compatibility between the filler and polymer. Molecular simulation approaches can be used to explore the effect of functionalization on MMM's gas transport properties at an atomic level without the challenges in the experimental study, however, they have received less scrutiny to date. In addition, most of the research has focused on pure gas studies while mixed gas transport properties that reflect real separation in functionalized silica/PSF MMMs are scarcely available. In this work, a molecular simulation computational framework has been developed to investigate the structural, physical properties and gas transport behavior of amine-functionalized silica/PSF-based MMMs. The effect of varying weight percentages (i.e., 15-30 wt.%) of amine-functionalized silica and gas concentrations (i.e., 30% CH₄/CO₂, 50% CH₄/CO₂, and 70% CH₄/CO₂) on physical and gas transport characteristics in amine-functionalized silica/PSF MMMs at 308.15 K and 1 atm has been investigated. Functionalization of silica nanoparticles was found to increase the diffusion and solubility coefficients, leading to an increase in the percentage enhancement of permeability and selectivity for amine-functionalized silica/PSF MMM by 566% and 56%, respectively, compared to silica/PSF-based MMMs at optimal weight percentage of 20 wt.%. The model's permeability differed by 7.1% under mixed gas conditions. The findings of this study could help to improve real CO₂/CH₄ separation in the future design and concept of functionalized MMMs using molecular simulation and empirical modeling strategies.

Filler Models Revisited: Extension of the Nielson Model with Respect to the Geometric Arrangements of Fillers

Models describing how fillers affect the barrier properties of polymers remain an important research topic to improve applications such as hydrogen storage or food preservation. The Nielsen model, one of the earliest models for such predictions, is still one of the most widely used in the literature. However, it does not provide quantitative information on arrangements of fillers inside a polymer matrix, which is crucial for the definition of suitable filler distributions in barrier materials. Therefore, the channel model was developed in this work, which extends the Nielsen model by determining the relative distances between the fillers in regular filler arrangements in polymer matrices. This allows us to relate the permeation properties of filled polymer membranes to the geometric properties of the filler arrangement in simulations and experimental measurements. Simulations with geometries defined according to the channel model showed good agreement with the predictions of the Nielsen model. This demonstrated that the channel model can be a valuable tool for predicting at least mean geometric distances in studied polymer membranes. The validity range of the channel model was limited to a value range of the filler volume fraction 0.01≤ϕf≤0.5 based on theoretical considerations.

A Review of the Recent Progress in the Development of Nanocomposites Based on Poly(ether-block-amide) Copolymers as Membranes for CO2 Separation

An inspiring challenge for membrane scientists is to exceed the current materials' performance while keeping the intrinsic processability of the polymers. Nanocomposites, as mixed-matrix membranes, represent a practicable response to this strongly felt need, since they combine the superior properties of inorganic fillers with the easy handling of the polymers. In the global strategy of containing the greenhouse effect by pursuing a model of sustainable growth, separations involving CO2 are some of the most pressing topics due to their implications in flue gas emission and natural gas upgrading. For this purpose, Pebax copolymers are being actively studied by virtue of a macromolecular structure that comprises specific groups that are capable of interacting with CO2, facilitating its transport with respect to other gas species. Interestingly, these copolymers show a high versatility in the incorporation of nanofillers, as proved by the large number of papers describing nanocomposite membranes based on Pebax for the separation of CO2. Since the field is advancing fast, this review will focus on the most recent progress (from the last 5 years), in order to provide the most up-to-date overview in this area. The most recent approaches for developing Pebax-based mixed-matrix membranes will be discussed, evidencing the most promising filler materials and analyzing the key-factors and the main aspects that are relevant in terms of achieving the best effectiveness of these multifaceted membranes for the development of innovative devices.

PIM-1/Holey Graphene Oxide Mixed Matrix Membranes for Gas Separation: Unveiling the Role of Holes

PIM-1/holey graphene oxide (GO) mixed matrix membranes (MMMs) have been prepared and their gas separation performance for CO₂/CH₄ mixtures assessed. Nanopores have been created in the basal plane of gas-impermeable GO by chemical etching reactions, and the resulting holey flakes have been further chemically functionalized, either with octadecylamine (ODA) or with PIM-1 moieties, to aid their dispersion in PIM-1. It is found that nanopores barely promote gas transport through the graphene-like nanofiller for fresh membranes (tested right after preparation); however, the prepared hybrid PIM-1/holey GO membranes exhibit higher CO₂ permeability and CO₂/CH₄ selectivity than the pure polymer membrane 150 days after preparation and 13 and 15% higher CO₂ permeability for filler contents of 0.1% of octadecylamine-functionalized holey GO and 1% of (PIM-1)-functionalized holey GO, respectively. The most significant improvement is observed for the mitigation of physical aging, as MMMs using 10% of (PIM-1)-functionalized holey GO nanofillers are capable of maintaining up to 70% of their initial CO₂ permeability after 150 days, whereas only 53% is kept for pure PIM-1 after the same period. The gas permeability of the nanofiller has been rationalized with the aid of the Maxwell-Wagner-Sillars equation.

Application of the dynamic mean field theory to fluid transport in slit pores

We explore the applicability of the lattice model and dynamic mean field theory as a computationally efficient tool to study transport across heterogeneous porous media, such as mixed matrix membranes. As a starting point and to establish some basic definitions of properties analogous to those in the off-lattice systems, we consider transport across simple models of porous materials represented by a slit pore in a chemical potential gradient. Using this simple model, we investigate the distribution of density and flux under steady state conditions, define the permeability across the system, and explore how this property depends on the length of the pore and the solid-fluid interactions. Among other effects, we observe that the flux in the system goes through a maximum as the solid-fluid interaction is varied from weak to strong. This effect is dominated by the behavior of the fluid near the walls and is also confirmed by off-lattice molecular dynamics simulations. We further extend this study to explore transport across heterogeneous slit pore channels composed of two solids with different values of solid-fluid interaction strengths. We demonstrate that the lattice models and dynamic mean field theory provide a useful framework to pose questions on the accuracy and applicability of the classical theories of transport across heterogeneous porous systems.

3D Modelling of Mass Transfer into Bio-Composite

A three-dimensional model structure that allows considering interphase layer around permeable inclusions is developed to predict water vapor permeability in composite materials made of a matrix Poly(3-HydroxyButyrate-co-3-HydroxyValerate) (PHBV) including Wheat Straw Fiber (WSF) particles. About 500 two-phase structures corresponding to composites of different particles volume fractions (5.14-11.4-19.52 % v/v) generated using experimental particles' size distribution have permitted to capture all the variability of the experimental material. These structures have served as a basis to create three-phase structures including interphase zone of altered polymer property surrounding each particle. Finite Element Method (FEM) applied on these structures has permitted to calculate the relative permeability (ratio between composite and neat matrix permeability P/Pm). The numerical results of the two-phase model are consistent with the experimental data for volume fraction lower than 11.4 %v/v but the large upturn of the experimental relative permeability for highest volume fraction is not well represented by the two-phase model. Among hypothesis made to explain model's deviation, the presence of an interphase with its own transfer properties is numerically tested: numerical exploration made with the three-phase model proves that an interphase of 5 µm thick, with diffusivity of Di≥1×10-10 m2·s-1, would explain the large upturn of permeability at high volume fraction.

A Molecular Simulation Study of Silica/Polysulfone Mixed Matrix Membrane for Mixed Gas Separation

Polysulfone-based mixed matrix membranes (MMMs) incorporated with silica nanoparticles are a new generation material under ongoing research and development for gas separation. However, the attributes of a better-performing MMM cannot be precisely studied under experimental conditions. Thus, it requires an atomistic scale study to elucidate the separation performance of silica/polysulfone MMMs. As most of the research work and empirical models for gas transport properties have been limited to pure gas, a computational framework for molecular simulation is required to study the mixed gas transport properties in silica/polysulfone MMMs to reflect real membrane separation. In this work, Monte Carlo (MC) and molecular dynamics (MD) simulations were employed to study the solubility and diffusivity of CO₂/CH₄ with varying gas concentrations (i.e., 30% CO₂/CH₄, 50% CO₂/CH₄, and 70% CO₂/CH₄) and silica content (i.e., 15–30 wt.%). The accuracy of the simulated structures was validated with published literature, followed by the study of the gas transport properties at 308.15 K and 1 atm. Simulation results concluded an increase in the free volume with an increasing weight percentage of silica. It was also found that pure gas consistently exhibited higher gas transport properties when compared to mixed gas conditions. The results also showed a competitive gas transport performance for mixed gases, which is more apparent when CO₂ increases. In this context, an increment in the permeation was observed for mixed gas with increasing gas concentrations (i.e., 70% CO₂/CH₄ > 50% CO₂/CH₄ > 30% CO₂/CH₄). The diffusivity, solubility, and permeability of the mixed gases were consistently increasing until 25 wt.%, followed by a decrease for 30 wt.% of silica. An empirical model based on a parallel resistance approach was developed by incorporating mathematical formulations for solubility and permeability. The model results were compared with simulation results to quantify the effect of mixed gas transport, which showed an 18% and 15% percentage error for the permeability and solubility, respectively, in comparison to the simulation data. This study provides a basis for future understanding of MMMs using molecular simulations and modeling techniques for mixed gas conditions that demonstrate real membrane separation.

A Review on Mixed Matrix Membranes for Solvent Dehydration and Recovery Process

Solvent separation and dehydration are important operations for industries and laboratories. Processes such as distillation and extraction are not always effective and are energy-consuming. An alternate approach is offered by pervaporation, based on the solution-diffusion transport mechanism. Polymer-based membranes such as those made of Polydimethylsiloxane (PDMS) have offered good pervaporation performance. Attempts have been made to improve their performance by incorporating inorganic fillers into the PDMS matrix, in which metal-organic frameworks (MOFs) have proven to be the most efficient. Among the MOFs, Zeolitic imidazolate framework (ZIF) based membranes have shown an excellent performance, with high values for flux and separation factors. Various studies have been conducted, employing ZIF-PDMS membranes for pervaporation separation of mixtures such as aqueous-alcoholic solutions. This paper presents an extensive review of the pervaporation performance of ZIF-based mixed matrix membranes (MMMs), novel synthesis methods, filler modifications, factors affecting membrane performance as well as studies based on polymers other than PDMS for the membrane matrix. Some suggestions for future studies have also been provided, such as the use of biopolymers and self-healing membranes.

Mitigating the Agglomeration of Nanofiller in a Mixed Matrix Membrane by Incorporating an Interface Agent

Nanodiamonds (ND) have recently emerged as excellent candidates for various applications including membrane technology due to their nanoscale size, non-toxic nature, excellent mechanical and thermal properties, high surface areas and tuneable surface structures with functional groups. However, their non-porous structure and strong tendency to aggregate are hindering their potential in gas separation membrane applications. To overcome those issues, this study proposes an efficient approach by decorating the ND surface with polyethyleneimine (PEI) before embedding it into the polymer matrix to fabricate MMMs for CO₂/N₂ separation. Acting as both interfacial binder and gas carrier agent, the PEI layer enhances the polymer/filler interfacial interaction, minimising the agglomeration of ND in the polymer matrix, which is evidenced by the focus ion beam scanning electron microscopy (FIB-SEM). The incorporation of PEI into the membrane matrix effectively improves the CO₂/N₂ selectivity compared to the pristine polymer membranes. The improvement in CO₂/N₂ selectivity is also modelled by calculating the interfacial permeabilities with the Felske model using the gas permeabilities in the MMM. This study proposes a simple and effective modification method to address both the interface and gas selectivity in the application of nanoscale and non-porous fillers in gas separation membranes.

Paper and Other Fibrous Materials-A Complete Platform for Biosensing Applications

Paper-based analytical devices (PADs) and Electrospun Fiber-Based Biosensors (EFBs) have aroused the interest of the academy and industry due to their affordability, sensitivity, ease of use, robustness, being equipment-free, and deliverability to end-users. These features make them suitable to face the need for point-of-care (POC) diagnostics, monitoring, environmental, and quality food control applications. Our work introduces new and experienced researchers in the field to a practical guide for fibrous-based biosensors fabrication with insight into the chemical and physical interaction of fibrous materials with a wide variety of materials for functionalization and biofunctionalization purposes. This research also allows readers to compare classical and novel materials, fabrication techniques, immobilization methods, signal transduction, and readout. Moreover, the examined classical and alternative mathematical models provide a powerful tool for bioanalytical device designing for the multiple steps required in biosensing platforms. Finally, we aimed this research to comprise the current state of PADs and EFBs research and their future direction to offer the reader a full insight on this topic.

Gas Permeation Model of Mixed-Matrix Membranes with Embedded Impermeable Cuboid Nanoparticles

In the packaging industry, the barrier property of packaging materials is of paramount importance. The enhancement of barrier properties of materials can be achieved by adding impermeable nanoparticles into thin polymeric films, known as mixed-matrix membranes (MMMs). Three-dimensional numerical simulations were performed to study the barrier property of these MMMs and to estimate the effective membrane gas permeability. Results show that horizontally-aligned thin cuboid nanoparticles offer far superior barrier properties than spherical nanoparticles for an identical solid volume fraction. Maxwell’s model predicts very well the relative permeability of spherical and cubic nanoparticles over a wide range of the solid volume fraction. However, Maxwell’s model shows an increasingly poor prediction of the relative permeability of MMM as the aspect ratio of cuboid nanoparticles tends to zero or infinity. An artificial neural network (ANN) model was developed successfully to predict the relative permeability of MMMs as a function of the relative thickness and the relative projected area of the embedded nanoparticles. However, since an ANN model does not provide an explicit form of the relation of the relative permeability with the physical characteristics of the MMM, a new model based on multivariable regression analysis is introduced to represent the relative permeability in a MMM with impermeable cuboid nanoparticles. The new model possesses a simple explicit form and can predict, very well, the relative permeability over an extensive range of the solid volume fraction and aspect ratio, compared with many existing models.

Diffusion coefficients in nanoporous solids derived from membrane permeation measurements

Based on the molecular understanding of the interplay of diffusion and adsorption, new membrane materials can be developed and the operational conditions of gas separation membranes can be optimized. Therefore, numerous diffusion and adsorption studies are conducted to optimize membrane materials. However, in an opposite way, transport or Fickian diffusion coefficients DT can be derived from membrane permeation studies with surprising accuracy. From measuring the gas transport through nanoporous supported thin-layer membranes or through mixed matrix membranes with nanoporous fillers in a polymer matrix, the transport diffusion coefficients DT of gases in novel nanoporous materials such as zeolites, MOFs, COFs… can be estimated.

A Review on Computational Modeling Tools for MOF-Based Mixed Matrix Membranes

Computational modeling of membrane materials is a rapidly growing field to investigate the properties of membrane materials beyond the limits of experimental techniques and to complement the experimental membrane studies by providing insights at the atomic-level. In this study, we first reviewed the fundamental approaches employed to describe the gas permeability/selectivity trade-off of polymer membranes and then addressed the great promise of mixed matrix membranes (MMMs) to overcome this trade-off. We then reviewed the current approaches for predicting the gas permeation through MMMs and specifically focused on MMMs composed of metal organic frameworks (MOFs). Computational tools such as atomically-detailed molecular simulations that can predict the gas separation performances of MOF-based MMMs prior to experimental investigation have been reviewed and the new computational methods that can provide information about the compatibility between the MOF and the polymer of the MMM have been discussed. We finally addressed the opportunities and challenges of using computational studies to analyze the barriers that must be overcome to advance the application of MOF-based membranes.

Comparative Study of the Performances of Al(OH)3 and BaSO4 in Ultrafine Powder Coatings

Ultrafine powder coatings are one of the development directions in the powder coating industry, as they can achieve thin coatings with good leveling and high surface smoothness comparable to liquid coatings. Compared to regular coatings, they experience a higher sensitivity to any incompatibilities, e.g., filler from coating components. The properties of fillers play a great role in the performance of coating films. Aluminum trihydrate (Al(OH)3) is a well-known filler in solvent-based coatings and other polymer industries. To study and evaluate the performances of Al(OH)3 in ultrafine powder coatings, a popular filler, barium sulfate (BaSO4) is used for comparison. Both fillers are added in ultrafine powder coatings based on two of the most commonly used resin systems (polyester-epoxy and polyester). The differences of physical and chemical properties between both fillers have significant influences on several properties of powder paints and coating films. The polar groups (hydrogen bond) in Al(OH)3 result in the strong interaction between inorganic filler and organic polymer matrix, thus decreasing the molecular network mobility and influencing the chain formation, which is verified by differential scanning calorimetric (DSC). The bed expansion ratio (BERs) of powder paints incorporated with Al(OH)3 are much higher than those with BaSO4, which indicate more uniform gas-solid contact during the spraying process. Samples with Al(OH)3 exhibit much lower specular gloss at 60°, which are expected to achieve remarkable matting effects. Superior corrosion resistances can be observed for almost all the coated panels incorporated with Al(OH)3 in contrast to those with BaSO4. Other aspects are slightly influenced by the difference between the two fillers, such as the angle of repose values (AORs) of powder paints, the impact resistance and flexibility of coating films.

Special Issue on “Transport of Fluids in Nanoporous Materials”

Understanding the transport behavior of fluid molecules in confined spaces is central to the design of innovative processes involving porous materials and is indispensable to the correlation of process behavior with the material structure and properties typically used for structural characterizations such as pore dimension, surface texture, and tortuosity. [...]