Cavity size, sorption and transport characteristics of thermally rearranged (TR) polymers

Modelling Sorption and Transport of Gases in Polymeric Membranes across Different Scales: A Review

Professor Giulio C. Sarti has provided outstanding contributions to the modelling of fluid sorption and transport in polymeric materials, with a special eye on industrial applications such as membrane separation, due to his Chemical Engineering background. He was the co-creator of innovative theories such as the Non-Equilibrium Theory for Glassy Polymers (NET-GP), a flexible tool to estimate the solubility of pure and mixed fluids in a wide range of polymers, and of the Standard Transport Model (STM) for estimating membrane permeability and selectivity. In this review, inspired by his rigorous and original approach to representing membrane fundamentals, we provide an overview of the most significant and up-to-date modeling tools available to estimate the main properties governing polymeric membranes in fluid separation, namely solubility and diffusivity. The paper is not meant to be comprehensive, but it focuses on those contributions that are most relevant or that show the potential to be relevant in the future. We do not restrict our view to the field of macroscopic modelling, which was the main playground of professor Sarti, but also devote our attention to Molecular and Multiscale Hierarchical Modeling. This work proposes a critical evaluation of the different approaches considered, along with their limitations and potentiality.

Single-gas and mixed-gas permeation of N2/CH4 in thermally-rearranged TR-PBO membranes and their 6FDA-bisAPAF polyimide precursor studied by molecular dynamics simulations

High-performance polymers with polybenzoxazole (PBO) structures, formed via thermal rearrangement (TR) of aromatic polyimide precursors, have been developed for gas separation applications. The present work compares the transport of N₂ and CH₄ in a 6FDA-bisAPAF polyimide precursor and in its TR-PBO derivative using molecular dynamics (MD) simulations. The modelling closely mimicked the experimental approach by transforming a 6FDA-bisAPAF atomistic model into its corresponding TR-PBO structure via a specific algorithm. The densities and void spaces of both precursor and TR polymers were found to compare well to experimental data. An iterative technique was used to obtain the single-gas sorption isotherms of N₂ and CH₄ at 338.5 K in both polymers over a range of feed pressures up to and exceeding 65 bar. CH₄ was systematically found to be more soluble than N₂. Solubilities in both matrices were quite similar with those in TR-PBO being slightly higher due to its larger fraction of significant volume. Volume dilation analyses confirmed a higher resistance to plasticization for TR-PBO. Extended single-gas N₂ and CH₄ simulations and 2 : 1 binary CH₄/N₂ mixed-gas simulations were then conducted in both matrices at 338.5 K and at a pressure of ∼65 bar corresponding to natural gas processing conditions. Mixed-gas sorption was modelled using a modification of the aforementioned iterative method, which fixed the pressure and iterated to convergence the number of molecules of each type of penetrant. The gas diffusion coefficients were estimated using the Trajectory-Extending Kinetic Monte Carlo (TEKMC) procedure. As found experimentally, significantly higher diffusivities and permeabilities were observed in the TR polymer, which led to a slightly lower ideal N₂/CH₄ permselectivity for TR-PBO (∼2.6) when compared to its 6FDA-bisAPAF precursor (∼3.8). However, both models showed a reduced N₂/CH₄ separation efficiency under 2 : 1 binary CH₄/N₂ mixed-gas conditions bordering on the loss of selectivity. For 6FDA-bisAPAF, both permeabilities decreased in the mixed-gas case, but more for N₂ than for CH₄. For TR-PBO, the permeability of the faster N₂ decreased while the permeability of the slower CH₄ increased under mixed-gas conditions. This confirms that single-gas simulations are not sufficient for the prediction of the actual mixed-gas permselectivity behaviour in such polymers.

Molecular Methods for Assessing the Morphology, Topology, and Performance of Polyamide Membranes

The molecular-scale morphology and topology of polyamide composite membranes determine the performance characteristics of these materials. However, molecular-scale simulations are computationally expensive and morphological and topological characterization of molecular structures are not well developed. Molecular dynamics simulation and analysis methods for the polymerization, hydration, and quantification of polyamide membrane structures were developed and compared to elucidate efficient approaches for producing and analyzing the polyamide structure. Polymerization simulations that omitted the reaction-phase solvent did not change the observed hydration, pore-size distribution, or water permeability, while improving the simulation efficiency. Pre-insertion of water into the aggregate pores (radius ≈ 4 Å) of dry domains enabled shorter hydration simulations and improved simulation scaling, without altering pore structure, properties, or performance. Medial axis and Minkowski functional methods were implemented to identify permeation pathways and quantify the polyamide morphology and topology, respectively. Better agreement between simulations and experimentally observed systems was accomplished by increasing the domain size rather than increasing the number of ensemble realizations of smaller systems. The largest domain hydrated was an order of magnitude larger by volume than the largest domain previously reported. This work identifies methods that can enable more efficient and meaningful fundamental modeling of membrane materials.

Molecular dynamics simulation for membrane separation and porous materials: A current state of art review

Computational frameworks have been under specific attention within the last two decades. Molecular Dynamics (MD) simulations, identical to the other computational approaches, try to address the unknown question, lighten the dark areas of unanswered questions, to achieve probable explanations and solutions. Owing to their complex microporous structure on one side and the intricate biochemical nature of various materials used in the structure, separative membrane materials possess peculiar degrees of complications. More notably, as nanocomposite materials are often integrated into separative membranes, thin-film nanocomposites and porous separative nanocomposite materials could possess an additional level of complexity with regard to the nanoscale interactions brought to the structure. This critical review intends to cover the recent methods used to assess membranes and membrane materials. Incorporation of MD in membrane technology-related fields such as desalination, fuel cell-based energy production, blood purification through hemodialysis, etc., were briefly covered. Accordingly, this review could be used to understand the current extent of MD applications for separative membranes. The review could also be used as a guideline to use the proper MD implementation within the related fields.

Enhanced gas separation and mechanical properties of fluorene-based thermal rearrangement copolymers

A series of thermal rearrangement (TR) copolymer membranes were prepared by the copolymerization of 9,9-bis(3-amino-4-hydroxyphenoxyphenyl) fluorene (BAHPPF), 9,9-bis(3-amino-4-hydroxyphenyl)fluorene (BAHPF) and 2,2'-bis(3,4'-dicarboxyphenyl)hexafluoropropane dianhydride (6FDA), followed by thermal imidization and further thermal rearrangement. The effects of molar ratio of diamines on the structure and properties of copolymer membranes were studied. The copolymer precursors CP-4:6 and CP-5:5 exhibited excellent mechanical properties. The mechanical properties of precursor membranes rapidly decreased with the increase of thermal treatment temperatures, but the tensile strength of TRCP-4:6 still reached 21.2 MPa. In general, the gas permeabilities of TR copolymers increased with the increase of BAHPF content. Comparatively, TRCP-3:7 and TRCP-4:6 showed higher gas permeabilities, coupled with high O2/N2 and CO2/CH4 selectivities. Especially, the H2, CO2, O2, N2 and CH4 permeabilities of TRCP-4:6 reached 244.4, 269.0, 46.8, 5.20 and 4.60 Barrers respectively, and the selectivities for CO2/CH4 and O2/N2 were 58.48 and 9.00, which exceeded the 2008 upper bound. Therefore, these TR copolymer membranes are expected to be one of the candidate materials for gas separation applications.

Preparation and characterization of polyimide membranes modified by a task-specific ionic liquid based on Schiff base for CO2/N2 separation

In order to increase CO₂/N₂ selectivity of polyimide (PI) dense membranes, task-specific ionic liquid (TSIL), 1-aminoethyl-3-buthylimidazolium hexafluorophosphate ([NH₂ebim][PF₆]), has been grafted to polymer chains as large side groups by forming the structure of Schiff base for the first time. The modified membranes were characterized by Fourier transform infrared spectroscopy (FT-IR), elemental analysis, thermogravimetric analysis (TGA), X-ray diffraction (XRD), dynamic thermomechanical analysis (DMA), and stress-strain testing. The results showed that TSIL had been successfully linked to PI chains by forming "C=N." The modified membranes had more free volume, which was favorable to the improvement of CO₂ permeability. The reduction of spin degree of freedom means the rigidity increment of polymer chains, which indicated that the selectivity of CO₂/N₂ can be enhanced. As a result, CO₂ permeability of the modified membrane (TSIL-0.8 wt%) was increased from 5.28 to 10.2 Barrer, and CO₂/N₂ selectivity was increased from 21.9 to 92.8 at 30 °C and 0.1 MPa. Meanwhile, the effects of different feed pressures (0.1-0.6 MPa) and different operating temperatures (30-60 °C) on CO₂/N₂ transport properties were also investigated, and it was found that the separation performances of the modified membranes had already exceeded Robeson's upper bound.

Optical Analysis of the Internal Void Structure in Polymer Membranes for Gas Separation

Global warming by greenhouse gas emissions is one of the main threats of our modern society, and efficient CO2 capture processes are needed to solve this problem. Membrane separation processes have been identified among the most promising technologies for CO2 capture, and these require the development of highly efficient membrane materials which, in turn, requires detailed understanding of their operation mechanism. In the last decades, molecular modeling studies have become an extremely powerful tool to understand and anticipate the gas transport properties of polymeric membranes. This work presents a study on the correlation of the structural features of different membrane materials, analyzed by means of molecular dynamics simulation, and their gas diffusivity/selectivity. We propose a simplified method to determine the void size distribution via an automatic image recognition tool, along with a consolidated Connolly probe sensing of space, without the need of demanding computational procedures. Based on a picture of the void shape and width, automatic image recognition tests the dimensions of the void elements, reducing them to ellipses. Comparison of the minor axis of the obtained ellipses with the diameters of the gases yields a qualitative estimation of non-accessible paths in the geometrical arrangement of polymeric chains. A second tool, the Connolly probe sensing of space, gives more details on the complexity of voids. The combination of the two proposed tools can be used for a qualitative and rapid screening of material models and for an estimation of the trend in their diffusivity selectivity. The main differences in the structural features of three different classes of polymers are investigated in this work (glassy polymers, superglassy perfluoropolymers and high free volume polymers of intrinsic microporosity), and the results show how the proposed computationally less demanding analysis can be linked with their selectivities.

Syntheses of Colorless and Transparent Polyimide Membranes for Microfiltration

Herein, poly(amic acid) (PAA) was synthesized using 4,4’-(hexafluoroisopropylidene) diphthalic anhydride (6FDA) as a dianhydride and 2,2-bis(3-aminophenyl)hexafluoropropane (6FAm) and 2,2-bis(3-amino-4-hydroxyphenyl)hexafluoropropane (6FAm-OH) as diamines. Poly(vinyl alcohol) (PVA) at various contents (0–5.0 wt%) was blended with PAA to prepare a composite material. Then, colorless and transparent polyimide (CPI) composite films were prepared by applying various stages of heat treatment using the PAA/PVA blend film as a precursor. These film-type composites were immersed in water to completely dissolve PVA, a water-soluble polymer, and their pore sizes were investigated to determine their potential as a porous membrane. According to the results of scanning electronic microscopy (SEM), as the concentration of PVA increased from 0 to 5.0 wt% in the CPI/PVA composite films, the size of the pores resulting from the dissolution of water-soluble PVA increased. Further, the micrometer-sized pores were uniformly dispersed in the CPI films. The thermal properties, morphology, and optical transparency of the two types of CPI membranes synthesized using 6FAm and 6FAm-OH monomers were examined and compared.

Molecular Modeling Investigations of Sorption and Diffusion of Small Molecules in Glassy Polymers

With a wide range of applications, from energy and environmental engineering, such as in gas separations and water purification, to biomedical engineering and packaging, glassy polymeric materials remain in the core of novel membrane and state-of the art barrier technologies. This review focuses on molecular simulation methodologies implemented for the study of sorption and diffusion of small molecules in dense glassy polymeric systems. Basic concepts are introduced and systematic methods for the generation of realistic polymer configurations are briefly presented. Challenges related to the long length and time scale phenomena that govern the permeation process in the glassy polymer matrix are described and molecular simulation approaches developed to address the multiscale problem at hand are discussed.

Engineered Transport in Microporous Materials and Membranes for Clean Energy Technologies

Many forward-looking clean-energy technologies hinge on the development of scalable and efficient membrane-based separations. Ongoing investment in the basic research of microporous materials is beginning to pay dividends in membrane technology maturation. Specifically, improvements in membrane selectivity, permeability, and durability are being leveraged for more efficient carbon capture, desalination, and energy storage, and the market adoption of membranes in those areas appears to be on the horizon. Herein, an overview of the microporous materials chemistry driving advanced membrane development, the clean-energy separations employing them, and the theoretical underpinnings tying membrane performance to membrane structure across multiple length scales is provided. The interplay of pore architecture and chemistry for a given set of analytes emerges as a critical design consideration dictating mass transport outcomes. Opportunities and outstanding challenges in the field are also discussed, including high-flux 2D molecular-sieving membranes, phase-change adsorbents as performance-enhancing components in composite membranes, and the need for quantitative metrologies for understanding mass transport in heterophasic materials and in micropores with unusual chemical interactions with analytes of interest.

Soluble, optically transparent polyamides with a phosphaphenanthrene skeleton: synthesis, characterization, gas permeation and molecular dynamics simulations

Soluble, optically transparent polyamides with a phosphaphenanthrene skeleton: synthesis, characterization, gas permeation and molecular dynamics simulations.

Computational insights on the role of film thickness on the physical properties of ultrathin polysulfone membranes

A pioneering work to elucidate physical properties of ultrathin membrane films from atomistic point of view in Materials Studio.

Claisen thermally rearranged (CTR) polymers

Thermally rearranged (TR) polymers, which are considered the next-generation of membrane materials because of their excellent transport properties and high thermal and chemical stability, are proven to have significant drawbacks because of the high temperature required for the rearrangement and low degree of conversion during this process. We demonstrate that using a [3,3]-sigmatropic rearrangement, the temperature required for the rearrangement of a solid glassy polymer was reduced by 200°C. Conversions of functionalized polyimide to polybenzoxazole of more than 97% were achieved. These highly mechanically stable polymers were almost five times more permeable and had more than two times higher degrees of conversion than the reference polymer treated under the same conditions. Properties of these second-generation TR polymers provide the possibility of preparing efficient polymer membranes in a form of, for example, thin-film composite membranes for various gas and liquid membrane separation applications.

A comparison of homopolymer and block copolymer structure in 6FDA-based polyimides

Two homopolyimides and the corresponding block copolyimide, all based on the 4,4'-(hexafluoroisopropylidene)diphthalic dianhydride (6FDA), have been synthesized and fully atomistic models have been studied using molecular dynamics (MD) simulation. The respective diamines were 1,3-phenylenediamine (mPDA) and 2,3,5,6-tetramethyl-1,4-phenylenediamine (durene). These polyimides are potential candidates for gas separation applications. The synthesized polymers were processed as dense flat membranes. The effects of diamine structure were investigated at the molecular level and an attempt to compare the structural features of homo- and block copolyimides was made. Amorphous models were generated using a hybrid pivot Monte Carlo-MD sampling preparation technique. Average model densities were validated against experimental measurements on the dense films. Cohesive energies, Hildebrand solubility parameters, conformational characteristics, intermolecular interactions and available void spaces were analysed for each system. The durene diamine was found to hinder stacking and increase the available space. This is associated with the steric effect of the methyl substituents. In general, 6FDA-mPDA/durene exhibits an intermediate behaviour with respect to its base polyimides. For most of the examined properties, the differences between different size simulated systems were minor with the exception of the free volume distribution.