Modeling molecular transport in composite membranes with tubular fillers

Dimensional Transformation of Percolation Structure in Mixed-Matrix Membranes (MMMs)

A large number of studies of mixed-matrix membranes (MMMs) have confirmed the possibility of obtaining new materials with unique transport properties, including for solving specific problems in the separation of mixtures of liquids and gases. The choice of particles with a given affinity for the matrix and separable components allows researchers to adjust the selective properties of MMMs in a wide range, which changes the properties of MMMs in a wide range. However, even within the framework of the most complex percolation mechanism of the formation of the MMM structure, it is possible to explain only some of the observed effects. In particular, questions about the required particle concentration and fluctuation of properties in various MMM samples are still the subject of research. The results of the numerical modeling of such structures presented in this paper determined the possible causes of the observed deviations of the experimental results, for example, particle size dispersion, agglomeration, and interaction with the matrix. According to our research, the key factor that qualitatively changes the parameters of percolation structures is the ratio of the geometric dimensions of the system. We have confirmed in a wide range a significant change in the conditions of cluster formation and its power at different particle diameters and lengths (traditional parameters in percolation studies). But in our work, we additionally studied the effect on the cluster parameters of the interfacial layer and the anisotropy of the matrix (the transition from the cube to the film). The results obtained show that changing the parameters of the matrix-particle interaction affects agglomeration, and the degradation of the percolation structure is possible. That is, with an increase in concentration, the parameters of the percolation cluster, its power, and the probability of formation, may decrease. But even more negative changes in percolation structures are observed during the transition from a volumetric matrix to films. The anisotropy of space leads to the formation of percolation through the film in certain areas at low concentrations of particles. At the same time, in a significant part of the matrix, percolation between the film surfaces will be absent, and the effect of changing the properties of MMMs in the matrix as a whole decreases. Our study explains the observed instability of MMM properties at fixed concentrations and parameters of embedded particles, including the effect of reducing the influence of particles with increasing concentration.

The Optimized Preparation Conditions of Cellulose Triacetate Hollow Fiber Reverse Osmosis Membrane with Response Surface Methodology

Reverse osmosis (RO) membrane materials play a key role in determining energy consumption. Currently, CTA is regarded as having one of the highest degrees of chlorine resistance among materials in the RO process. The hollow fiber membrane has the advantages of a large membrane surface area and a preparation process without any redundant processes. Herein, response surface methodology with Box-Behnken Design (BBD) was applied for optimizing the preparation conditions of the cellulose triacetate (CTA) hollow fiber RO membrane. There were four preparation parameters, including solid content, spinning temperature, post-treatment temperature, and post-treatment time, which could affect the permeability of the membrane significantly. In this study, the interaction between preparation parameters and permeability (permeate flux and salt rejection) was evaluated by regression equations. Regression equations can be applied to obtain the optimized preparation parameters of hollow fiber RO membranes and reasonably predict and optimize the permeability of the RO membranes. Finally, the optimized preparation conditions were solid content (44%), spinning temperature (167 °C), post-treatment temperature (79 °C), and post-treatment time (23 min), leading to a permeability of 12.029 (L·m-2·h-1) and salt rejection of 90.132%. This study of reinforced that CTA hollow fiber membrane may promote the transformation of the RO membrane industry.

Utilization of Physical Anisotropy in Metal-Organic Frameworks via Postsynthetic Alignment Control with Liquid Crystal

Metal-organic frameworks (MOFs) represent crystalline materials constructed from combinations of metal and organic units to often yield anisotropic porous structures and physical properties. Postsynthetic methods to align the MOF crystals in bulk remain scarce yet tremendously important to fully utilize their structure-driven intrinsic properties. Herein, we present an unprecedented composite of liquid crystals (LCs) and MOFs and demonstrate the use of nematic LCs to dynamically control the orientation of MOF crystals with exceptional order parameters (as high as 0.965). Unique patterns formed through a facile multidirectional alignment of MOF crystals exhibit polarized fluorescence with the fluorescence intensity of a pattern dependent on the angle of a polarizer, offering potential use in various optical applications such as an optical security label. Further, the alignment mechanism indicates that the method is applicable to numerous combinations of MOFs and LCs, which include UV polymerizable LC monomers used to fabricate free-standing composite films.

Percolation Effects in Mixed Matrix Membranes with Embedded Carbon Nanotubes

Polymeric membranes with embedded nanoparticles, e.g., nanotubes, show a significant increase in permeability of the target component while maintaining selectivity. However, the question of the reasons for this behavior of the composite membrane has not been unequivocally answered to date. In the present work, based on experimental data on the permeability of polymer membranes based on Poly(vinyl trimethylsilane) (PVTMS) with embedded CNTs, an approach to explain the abnormal behavior of such composite membranes is proposed. The presented model considered the mass transfer of gases and liquids through polymeric membranes with embedded CNTs as a parallel transport of gases through the polymeric matrix and a "percolation" cluster-bound regions around the embedded CNTs. The proposed algorithm for modeling parameters of a percolation cluster of embedded tubular particles takes into account an agglomeration and makes it possible to describe the threshold increase and subsequent decrease permeability with increasing concentration of embedded particles. The numerical simulation of such structures showed: an increase in the particle length leads to a decrease in the percolation concentration in a matrix of finite size, the power of the percolation cluster decreases significantly, but the combination of these effects leads to a decrease in the influence of the introduced particles on the properties of the matrix in the vicinity of the percolation threshold; an increase in the concentration of embedded particles leads to an increase in the probability of the formation of agglomerates and the characteristic size of the elements that make up the percolation cluster, the influence of individual particles decreases and the characteristics of the percolation transition determine the ratio of the sizes of agglomerates and matrix; and an increase in the lateral linear dimensions of the matrix leads to a nonlinear decrease in the proportion of the matrix, which is affected by the introduced particles, and the transport characteristics of such MMMs deteriorate.

Hybrid organic-inorganic membranes based on sulfonated poly (ether ether ketone) matrix and iron-encapsulated carbon nanotubes and their application in CO2 separation

The need to reduce greenhouse gas emissions dictates the search for new methods and materials. Here, a novel type of inorganic–organic hybrid materials Fe@MWCNT-OH/SPEEK (with a new type of CNT characterized by increased iron content, 5.80 wt%) for CO₂ separation is presented. The introduction of nanofillers into a polymer matrix has significantly improved hybrid membrane gas transport (D, P, S, and α_CO2/N2), and magnetic, thermal, and mechanical parameters. It was found that magnetic casting has improved the alignment and dispersion of Fe@MWCNT-OH carbon nanotubes. At the same time, CNT and polymer chemical modification enhanced interphase compatibility and membrane CO₂ separation efficiency. The thermooxidative stability, and mechanical and magnetic parameters of composites were improved by increasing new CNT loading. Cherazi's model turned out to be suitable for describing the CO₂ transport through analyzed hybrid membranes. The comparison of the transport and separation properties of the tested membranes with the literature data indicates their potential application in the future and the direction of further research.

Fe@MWCNT-OH/SPEEK hybrid membranes for CO₂ separation! Significant improvement of hybrid membrane's gas transport, magnetic, thermal, and mechanical parameters. Enhancement of interphase compatibility after CNT and polymer chemical modification.

Characteristics of Inorganic–Organic Hybrid Membranes Containing Carbon Nanotubes with Increased Iron-Encapsulated Content for CO2 Separation

Novel inorganic–organic hybrid membranes Fe@MWCNT/PPO or Fe@MWCNT-OH/SPPO (with a new type of CNTs characterized by increased iron content 5.80 wt%) were synthesized for CO2 separation. The introduction of nanofillers into the polymer matrix has significantly improved the hybrid membrane’s gas transport (D, P, S, and αCO2/N2), magnetic, thermal, and mechanical parameters. It was found that magnetic casting has improved the alignment and dispersion of Fe@MWCNTs. At the same time, CNTs and polymer chemical modification enhanced interphase compatibility and the membrane’s CO2 separation efficiency. The thermo-oxidative stability and mechanical and magnetic parameters of composites were improved by increasing new CNTs loading. Cherazi’s model turned out to be suitable for describing the CO2 transport through analyzed hybrid membranes.

Modelling the Molecular Permeation through Mixed-Matrix Membranes Incorporating Tubular Fillers

Membrane-based processes are considered a promising separation method for many chemical and environmental applications such as pervaporation and gas separation. Numerous polymeric membranes have been used for these processes due to their good transport properties, ease of fabrication, and relatively low fabrication cost per unit membrane area. However, these types of membranes are suffering from the trade-off between permeability and selectivity. Mixed-matrix membranes, comprising a filler phase embedded into a polymer matrix, have emerged in an attempt to partly overcome some of the limitations of conventional polymer and inorganic membranes. Among them, membranes incorporating tubular fillers are new nanomaterials having the potential to transcend Robeson's upper bound. Aligning nanotubes in the host polymer matrix in the permeation direction could lead to a significant improvement in membrane permeability. However, although much effort has been devoted to experimentally evaluating nanotube mixed-matrix membranes, their modelling is mostly based on early theories for mass transport in composite membranes. In this study, the effective permeability of mixed-matrix membranes with tubular fillers was estimated from the steady-state concentration profile within the membrane, calculated by solving the Fick diffusion equation numerically. Using this approach, the effects of various structural parameters, including the tubular filler volume fraction, orientation, length-to-diameter aspect ratio, and permeability ratio were assessed. Enhanced relative permeability was obtained with vertically aligned nanotubes. The relative permeability increased with the filler-polymer permeability ratio, filler volume fraction, and the length-to-diameter aspect ratio. For water-butanol separation, mixed-matrix membranes using polydimethylsiloxane with nanotubes did not lead to performance enhancement in terms of permeability and selectivity. The results were then compared with analytical prediction models such as the Maxwell, Hamilton-Crosser and Kang-Jones-Nair (KJN) models. Overall, this work presents a useful tool for understanding and designing mixed-matrix membranes with tubular fillers.

Rational Design of Halloysite Surface Chemistry for High Performance Nanotube-Thin Film Nanocomposite Gas Separation Membranes

The interfacial region has a critical role in determining the gas separation properties of nanofiller-containing membranes. However, the effects of surface chemistry of nanofillers on gas separation performance of thin film nanocomposite (TFN) membranes, prepared by the interfacial polymerization method, have been rarely studied in depth. In this work, pristine and three differently surface-modified halloysite nanotubes (HNTs), by non- (SHNT), moderately (ASHNT), or highly CO₂-philic (SFHNT) agents, are embedded in the polyamide top layer of thin film nanocomposite (TFN) membranes for CO₂/N₂ and CO₂/CH₄ separations. Trimethoxyoctyl silane, 3-(2-aminoethylaminopropyl)trimethoxysilane, and poly(styrenesulfonic acid) are used as modifying agents to quantitatively investigate the effects of interfacial interactions between the polyamide and HNTs on the gas permeation of TFNs. This allows us to provide an interfacial design strategy to fabricate high-performance gas separation membranes. Pure gas permeations conducted on the TFNs at the feed gas pressure of 10 bar showed that CO₂ permeance and CO₂/N₂ and CO₂/CH₄ selectivities were increased by 145%, 130%, and 108%, respectively, after addition of 0.05 w/v% of sulfonated HNTs. The experimental gas permeations through all TFNs/HNTs, except TFNs/SFHNTs, agree well with predictions of a recently developed model, which suggests the importance of considering the neglected role of CO₂ interactions with the HNT/polyamide interface in the model. These results unambiguously proved that designing the interfacial layer thickness in the nanotube-containing membranes is an effective approach to tuning the gas separation properties. The results show that the dispersion of HNTs in the polyamide top layer and the experimental CO₂/gas selectivity was increased with increasing interfacial thickness, a_int, upon surface modification. Moreover, it is quantitatively demonstrated that the thickness of the interfacial layer between the filler and polymer matrix is a function of gas pressure applied on the membrane.

MOF-Based Membranes for Gas Separations

Metal-organic frameworks (MOFs) represent the largest known class of porous crystalline materials ever synthesized. Their narrow pore windows and nearly unlimited structural and chemical features have made these materials of significant interest for membrane-based gas separations. In this comprehensive review, we discuss opportunities and challenges related to the formation of pure MOF films and mixed-matrix membranes (MMMs). Common and emerging separation applications are identified, and membrane transport theory for MOFs is described and contextualized relative to the governing principles that describe transport in polymers. Additionally, cross-cutting research opportunities using advanced metrologies and computational techniques are reviewed. To quantify membrane performance, we introduce a simple membrane performance score that has been tabulated for all of the literature data compiled in this review. These data are reported on upper bound plots, revealing classes of MOF materials that consistently demonstrate promising separation performance. Recommendations are provided with the intent of identifying the most promising materials and directions for the field in terms of fundamental science and eventual deployment of MOF materials for commercial membrane-based gas separations.

Enhancement in pervaporative performance of PDMS membrane for separation of styrene from wastewater by hybridizing with reduced graphene oxide

The removal of styrene from wastewater by pervaporation was investigated by using composite PDMS membranes filled with reduced graphene oxide on PES support layers. Graphene oxide was synthesized through modified Hummers' method and then chemically reduced. The filler was characterized by TEM, SEM, XRD, and AFM. The top layers with different PDMS molecular weights were cast on the PES supports, which were prepared by phase inversion method. The characterizations of prepared membranes were investigated by SEM, AFM, contact angle measurement, TGA, and DSC. It was observed that presence of the filler in the polymeric matrix controls the swelling of the membrane and enhances its solubility parameter in favor of styrene. Moreover, it significantly improves the thermal stability of the membranes. The mechanism of separation in the process was found to be affected mainly by enhancing in the membrane's solubility rather than in its diffusivity. The pervaporative performance of prepared membranes showed their great affinity toward styrene so that the separation factor of the optimum membrane (M2/S) was increased about 250% (600.4 in comparison to 241.4 for the unfilled membrane) while its total flux was decreased from 772.5 g m^-2.h^-1for the unfilled membrane to 321.9 g m^-2.h^-1. Increasing the molecular weight of PDMS lowered the optimal rGO content due to the complexity of the diffusion path and occupation of free volume by longer polymer chains. Accordingly, a lower total flux (124.7 g m^-2.h^-1 for high MW compared to 718.0 g m^-2.h^-1 for low MW) and higher separation factor (822.5 for high MW compared to 230.8 for low MW) were yielded for the same filler content (0.1 wt% rGO).

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.

Modeling Permeation through Mixed-Matrix Membranes: A Review

Over the past three decades, mixed-matrix membranes (MMMs), comprising an inorganic filler phase embedded in a polymer matrix, have emerged as a promising alternative to overcome limitations of conventional polymer and inorganic membranes. However, while much effort has been devoted to MMMs in practice, their modeling is largely based on early theories for transport in composites. These theories consider uniform transport properties and driving force, and thus models for the permeability in MMMs often perform unsatisfactorily when compared to experimental permeation data. In this work, we review existing theories for permeation in MMMs and discuss their fundamental assumptions and limitations with the aim of providing future directions permitting new models to consider realistic MMM operating conditions. Furthermore, we compare predictions of popular permeation models against available experimental and simulation-based permeation data, and discuss the suitability of these models for predicting MMM permeability under typical operating conditions.

Modeling the Effects of Interfacial Characteristics on Gas Permeation Behavior of Nanotube-Mixed Matrix Membranes

Theoretical approaches that accurately predict the gas permeation behavior of nanotube-containing mixed matrix membranes (nanotube-MMMs) are scarce. This is mainly due to ignoring the effects of nanotube/matrix interfacial characteristics in the existing theories. In this paper, based on the analogy of thermal conduction in polymer composites containing nanotubes, we develop a model to describe gas permeation through nanotube-MMMs. Two new parameters, "interfacial thickness" (a_int) and "interfacial permeation resistance" (R_int), are introduced to account for the role of nanotube/matrix interfacial interactions in the proposed model. The obtained values of a_int, independent of the nature of the permeate gas, increased by increasing both the nanotubes aspect ratio and polymer-nanotube interfacial strength. An excellent correlation between the values of a_int and polymer-nanotube interaction parameters, χ, helped to accurately reproduce the existing experimental data from the literature without the need to resort to any adjustable parameter. The data includes 10 sets of CO₂/CH₄ permeation, 12 sets of CO₂/N₂ permeation, 3 sets of CO₂/O₂ permeation, and 2 sets of CO₂/H₂ permeation through different nanotube-MMMs. Moreover, the average absolute relative errors between the experimental data and the predicted values of the proposed model are very small (less than 5%) in comparison with those of the existing models in the literature. To the best of our knowledge, this is the first study where such a systematic comparison between model predictions and such extensive experimental data is presented. Finally, the new way of assessing gas permeation data presented in the current work would be a simple alternative to complex approaches that are usually utilized to estimate interfacial thickness in polymer composites.

Enhancing the permeation selectivity of sodium alginate membrane by incorporating attapulgite nanorods for ethanol dehydration

Hydrophilic AT nanorods with selective channels were applied to fabricate hybrid membranes with high permeation selectivity for ethanol dehydration.

Investigation of cross-linked and additive containing polymer materials for membranes with improved performance in pervaporation and gas separation

Pervaporation and gas separation performances of polymer membranes can be improved by crosslinking or addition of metal-organic frameworks (MOFs). Crosslinked copolyimide membranes show higher plasticization resistance and no significant loss in selectivity compared to non-crosslinked membranes when exposed to mixtures of CO₂/CH₄ or toluene/cyclohexane. Covalently crosslinked membranes reveal better separation performances than ionically crosslinked systems. Covalent interlacing with 3-hydroxypropyldimethylmaleimide as photocrosslinker can be investigated in situ in solution as well as in films, using transient UV/Vis and FTIR spectroscopy. The photocrosslinking yield can be determined from the FTIR-spectra. It is restricted by the stiffness of the copolyimide backbone, which inhibits the photoreaction due to spatial separation of the crosslinker side chains. Mixed-matrix membranes (MMMs) with MOFs as additives (fillers) have increased permeabilities and often also selectivities compared to the pure polymer. Incorporation of MOFs into polysulfone and Matrimid^® polymers for MMMs gives defect-free membranes with performances similar to the best polymer membranes for gas mixtures, such as O₂/N₂ H₂/CH₄, CO₂/CH₄, H₂/CO₂, CH₄/N₂ and CO₂/N₂ (preferentially permeating gas is named first). The MOF porosity, its particle size and content in the MMM are factors to influence the permeability and the separation performance of the membranes.