Carbon Dioxide Diffusion and Plasticization in Fluorinated Polyimides

Molecular dynamics simulation and performance analysis of polyimide/aramid blends

CONTEXT

Polyimide (PI) and aramid, as functional polymer materials, have significant application prospects in special fields such as fire prevention and arc resistance. Blends of materials can not only improve the physical and chemical properties of a single material, but also save costs, so in order to improve the performance of polyimide, it is of great practical importance to study the properties of PI and aramid blends. Molecular dynamics simulation results showed that the two materials are compatible. The solubility parameters of PI tend to stabilize when the polymerization degree exceeded 10; aramid-1313 and aramid-1414 tend to stabilize at polymerization degrees of 10 and 15 or more, respectively. On this basis, the binding energy, diffusion coefficient, and mechanical properties of PI/aramid-1313 and PI/aramid-1414 blends with different mass ratios were analyzed. It was found that with the continuous increase of aramid content, the binding energy of the blends continue to improve, limiting the gas molecules diffusion ability. The mechanical properties of the materials also continue to improve. The simulation results provided in this paper can provide theoretical guidance for experiments on PI blends and shorten the research time and cost.

METHODS

To investigate the properties of PI and aramid blends, the PI/aramid composite system models were constructed using the Amorphous Cell module in Materials Studio software. Subsequently, molecular dynamics simulations of the PI/aramid composite system were performed using the Forcite module, while the interactions between atoms and molecules were described using the COMPASS II force field.

Trajectory-Extending Kinetic Monte Carlo Simulations to Evaluate Pure and Gas Mixture Diffusivities through a Dense Polymeric Membrane

With renewed interest in CO2 separations, carbon molecular sieving (CMS) membrane performance evaluation requires diffusion coefficients as inputs to have a reliable estimate of the permeability. An optimal material is desired to have both high selectivity and permeability. Gases diffusing through dense CMS and polymeric membranes experience extended subdiffusive regimes, which hinders reliable extraction of diffusion coefficients from mean squared displacement data. We improve the sampling of the diffusive landscape by implementing the trajectory-extending kinetic Monte Carlo (TEKMC) technique to efficiently extend molecular dynamics (MD) trajectories from ns to μs time scales. The obtained self-diffusion coefficient of pure CO2 in CMS membranes derived from a 6FDA/BPDA-DAM precursor polymer melt is found to linearly increase from 0.8-1.3 × 10-6 cm2 s-1 in the pressure range of 1-20 bar, which supports previous experimental findings. We also extended the TEKMC algorithm to evaluate the mixture diffusivities in binary mixtures to determine the permselectivity of CO2 in CH4 and N2 mixtures. The mixture diffusion coefficient of CO2 ranges from 1.3-7 × 10-6 cm2 s-1 in the binary mixture CO2/CH4, which is significantly higher than the pure gas diffusion coefficient. Robeson plot comparisons show that the permselectivity obtained from pure gas diffusion data is significantly lower than that predicted using mixture diffusivity data. Specifically, in the case of the CO2/N2 mixture, we find that using mixture diffusivities led to permselectivities lying above the Robeson limit highlighting the importance of using mixture diffusivity data for an accurate evaluation of the membrane performance. Combined with gas solubilities obtained from grand canonical Monte Carlo (GCMC) simulations, our work shows that simulations with the TEKMC method can be used to reliably evaluate the performance of materials for gas separations.

A Molecular Dynamics Study of Single-Gas and Mixed-Gas N2 and CH4 Transport in Triptycene-Based Polyimide Membranes

Fluorinated polyimides incorporated with triptycene units have gained growing attention over the last decade since they present potentially interesting selectivities and a higher free volume with respect to their triptycene-free counterparts. This work examines the transport of single-gas and mixed-gas N2 and CH4 in the triptycene-based 6FDA-BAPT homopolyimide and in a block 15,000 g mol-1/15,000 g mol-1 6FDA-mPDA/BAPT copolyimide by using molecular dynamics (MD) simulations. The void-space analyses reveal that, while the free volume consists of small-to-medium holes in the 6FDA-BAPT homopolyimide, there are more medium-to-large holes in the 6FDA-mPDA/BAPT copolyimide. The single-gas sorption isotherms for N2 and CH4 over the 0-70 bar range at 338.5 K show that both gases are more soluble in the block copolyimide, with a higher affinity for methane. CH4 favours sites with the most favourable energetic interactions, while N2 probes more sites in the matrices. The volume swellings remain limited since neither N2 nor CH4 plasticise penetrants. The transport of a binary-gas 2:1 CH4/N2 mixture is also examined in both polyimides under operating conditions similar to those used in current natural gas processing, i.e., at 65.5 bar and 338.5 K. In the mixed-gas simulations, the solubility selectivities in favour of CH4 are enhanced similarly in both matrices. Although diffusion is higher in 6FDA-BAPT/6FDA-mPDA, the diffusion selectivities are also close. Both triptycene-based polyimides under study favour, to a similar extent, the transport of methane over that of nitrogen under the conditions studied.

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.

Gas Adsorption and Diffusion Behaviors in Interfacial Systems Composed of a Polymer of Intrinsic Microporosity and Amorphous Silica: A Molecular Simulation Study

We investigate the adsorption and diffusion behaviors of CO₂, CH₄, and N₂ in interfacial systems composed of a polymer of intrinsic microporosity (PIM-1) and amorphous silica using grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations. We build model systems of mixed matrix membranes (MMMs) with PIM-1 chains sandwiched between silica surfaces. Gas adsorption analysis using GCMC simulations shows that gas molecules are preferentially adsorbed in microcavities distributed near silica surfaces, resulting in an increase in the solubility coefficients of CO₂, CH₄, and N₂ compared to bulk PIM-1. In contrast, diffusion coefficients obtained from MD simulations and then calibrated using the dual-mode sorption model show different tendencies depending on gas species: CO₂ diffusivity decreases in MMMs compared to PIM-1, whereas CH₄ and N₂ diffusivities increase. These differences are attributed to competing effects of silica surfaces: the emergence of larger pores as a result of chain packing disruption, which enhances gas diffusion, and a quadrupole-dipole interaction between gas molecules and silica surface hydroxyl groups, which retards gas diffusion. The former has a greater impact on CH₄ and N₂ diffusivities, whereas the latter has a greater impact on CO₂ diffusivity due to the strong quadrupole-dipole interaction between CO₂ and surface hydroxyls. These findings add to our understanding of gas adsorption and diffusion behaviors in the vicinity of PIM-1/silica interfaces, which are unobtainable in experimental studies.

Molecular Characterization of Membrane Gas Separation under Very High Temperatures and Pressure: Single- and Mixed-Gas CO2/CH4 and CO2/N2 Permselectivities in Hybrid Networks

This work illustrates the potential of using atomistic molecular dynamics (MD) and grand-canonical Monte Carlo (GCMC) simulations prior to experiments in order to pre-screen candidate membrane structures for gas separation, under harsh conditions of temperature and pressure. It compares at 300 °C and 400 °C the CO₂/CH₄ and CO₂/N₂ sieving properties of a series of hybrid networks based on inorganic silsesquioxanes hyper-cross-linked with small organic PMDA or 6FDA imides. The inorganic precursors are the octa(aminopropyl)silsesquioxane (POSS), which degrades above 300 °C, and the octa(aminophenyl)silsesquioxane (OAPS), which has three possible meta, para or ortho isomers and is expected to resist well above 400 °C. As such, the polyPOSS-imide networks were tested at 300 °C only, while the polyOAPS-imide networks were tested at both 300 °C and 400 °C. The feed gas pressure was set to 60 bar in all the simulations. The morphologies and densities of the pure model networks at 300 °C and 400 °C are strongly dependent on their precursors, with the amount of significant free volume ranging from ~2% to ~20%. Since measurements at high temperatures and pressures are difficult to carry out in a laboratory, six isomer-specific polyOAPS-imides and two polyPOSS-imides were simulated in order to assess their N₂, CH₄ and CO₂ permselectivities under such harsh conditions. The models were first analyzed under single-gas conditions, but to be closer to the real processes, the networks that maintained CO₂/CH₄ and CO₂/N₂ ideal permselectivities above 2 were also tested with binary-gas 90%/10% CH₄/CO₂ and N₂/CO₂ feeds. At very high temperatures, the single-gas solubility coefficients vary in the same order as their critical temperatures, but the differences between the penetrants are attenuated and the plasticizing effect of CO₂ is strongly reduced. The single-gas diffusion coefficients correlate well with the amount of available free volume in the matrices. Some OAPS-based networks exhibit a nanoporous behavior, while the others are less permeable and show higher ideal permselectivities. Four of the networks were further tested under mixed-gas conditions. The solubility coefficient improved for CO₂, while the diffusion selectivity remained similar for the CO₂/CH₄ pair and disappeared for the CO₂/N₂ pair. The real separation factor is, thus, mostly governed by the solubility. Two polyOAPS-imide networks, i.e., the polyorthoOAPS-PMDA and the polymetaOAPS-6FDA, seem to be able to maintain their CO₂/CH₄ and CO₂/N₂ sieving abilities above 2 at 400 °C. These are outstanding performances for polymer-based membranes, and consequently, it is important to be able to produce isomer-specific polyOAPS-imides for use as gas separation membranes under harsh conditions.

The Effect of Molecular Isomerism on the Barrier Properties of Polyimides: Perspectives from Experiments and Simulations

A novel carbazole-containing diamine (M-2,7-CPDA) isomer of our previously reported diamine 2,7-CPDA, has been synthesized using a two-step synthesis. Compared with 2,7-CPDA, the substituted position of amino is changed from para to meta for M-2,7-CPDA. The two diamines were polymerized with pyromellitic dianhydride (PMDA) to prepare two isomeric polyimides (M-2,7-CPPI and 2,7-CPPI), respectively. The effects of para/meta isomerism on microstructures and gas barrier performances of the two isomeric polyimides were studied by positron annihilation test, X-ray diffraction and molecular simulation. The results display that meta-connected M-2,7-CPPI has less ordered chain structure and weaker hydrogen bonding than para-connected 2,7-CPPI, which leads to loose chain stacking and thereby increased free volumes of M-2,7-CPPI. The higher free volumes promote the solubility and diffusivity of gas in M-2,7-CPPI. As a result, the meta-linked M-2,7-CPPI shows a lower gas barrier than its para-linked analog. The work provides guidance for the design and synthesis of high-performance barrier polymers.

Impact of Backbone Amide Substitution at the Meta- and Para-Positions on the Gas Barrier Properties of Polyimide

This study designed and synthesised a meta-amide-substituted dianiline monomer (m-DABA) as a stereoisomer of DABA, a previously investigated para-amide-substituted dianiline monomer. This new monomer was polymerised with pyromellitic dianhydride (PMDA) to prepare a polyimide film (m-DABPI) in a process similar to that employed in a previous study. The relationship between the substitution positions on the monomer and the gas barrier properties of the polyimide film was investigated via molecular simulation, wide-angle X-ray diffraction (WXRD), and positron annihilation lifetime spectroscopy (PALS) to gain deeper insights into the gas barrier mechanism. The results showed that compared with the para-substituted DABPI, the m-DABPI exhibited better gas barrier properties, with a water vapour transmission rate (WVTR) and an oxygen transmission rate (OTR) as low as 2.8 g·m⁻²·d⁻¹ and 3.3 cm³·m⁻²·d⁻¹, respectively. This was because the meta-linked polyimide molecular chains were more tightly packed, leading to a smaller free volume and lower molecular chain mobility. These properties are not conducive to the permeation of small molecules into the film; thus, the gas barrier properties were improved. The findings have significant implications for the structural design of high-barrier materials and could promote the development of flexible display technology.

The influence of additives on polymer matrix mobility and the glass transition

In the region near an interface, the microscopic properties of a glass forming liquid may be perturbed from their equilibrium bulk values. In this work, we probe how the interfacial effects of additive particles dispersed in a matrix can influence the local mobility of the material and its glass transition temperature, Tg. Experimental measurements and simulation results indicate that additives, such as nanoparticles, gas molecules, and oligomers, can shift the mobility and Tg of a surrounding polymer matrix (even for relatively small concentrations of additive; e.g., 5-10% by volume) relative to the pure bulk matrix, thus leading to Tg enhancement or suppression. Additives thus provide a potential route for modifying the properties of a polymer material without significantly changing its chemical composition. Here we apply the Limited Mobility (LM) model to simulate a matrix containing additive species. We show that both additive concentration, as well as the strength of its very local influence on the surrounding matrix material, will determine whether the Tg of the system is raised or lowered, relative to the pure matrix. We demonstrate that incorporation of additives into the simple LM simulation method, which has successfully described the behavior of bulk and thin film glassy solids, leads to direct connections with available experimental and simulation results for a broad range of polymer/additive systems.

High-Barrier Polyimide Containing Carbazole Moiety: Synthesis, Gas Barrier Properties, and Molecular Simulations

A high-barrier polyimide (2,7-CPI) was synthesized through the polymerization of pyromellitic dianhydride (PMDA) and a novel diamine (2,7-CDA) containing carbazole moiety. The synthesized diamine and polyimide were fully characterized by elemental analyses, FTIR and NMR. The 2,7-CPI displays very attractive barrier performances, with oxygen transmission rate (OTR) and water vapor transmission rate (WVTR) low to 0.14 cm³·m⁻²·day⁻¹ and 0.05 g·m⁻²·day⁻¹, respectively. Meanwhile, 2,7-CPI also exhibits exceptional thermal stability with a glass transition temperature (T_g) of 467 °C, 5% weight-loss temperature (T_d5%) of 550 °C under N₂ and coefficient of thermal expansion (CTE) of 3.4 ppm/K. The barrier performances of 2,7-CPI are compared with those of a structural analogue (2,7-CPPI) and a typical polyimide (Kapton). Their barrier performances with respect to microstructure were investigated by molecular simulations, wide angle X-ray diffraction (WAXD), and positron annihilation lifetime spectroscopy (PALS). The results show that 2,7-CPI possesses better coplanar structure and more number of intermolecular hydrogen bonds among the three PIs, which result in tight chain packing and thereby high crystallinity, low free volume, and decreased chains mobility. That is, the high crystallinity and low free volume of 2,7-CPI reduce the diffusion and solubility of gases. Meanwhile, the poor chains mobility further decreases the gases diffusion. The reduced diffusion and solubility of gases consequently promote the improvement of barrier properties for 2,7-CPI. The polyimide has a wide application prospect in the field of flexible electronic packaging industries.

Transport Properties of Thermoplastic R-BAPB Polyimide: Molecular Dynamics Simulations and Experiment

The present work evaluates the transport properties of thermoplastic R-BAPB polyimide based on 1,3-bis(3,3',4,4'-dicarboxyphenoxy)benzene (dianhydride R) and 4,4'-bis(4-aminophenoxy)biphenyl (diamine BAPB). Both experimental studies and molecular dynamics simulations were applied to estimate the diffusion coefficients and solubilities of various gases, such as helium (He), oxygen (O2), nitrogen (N2), and methane (CH4). The validity of the results obtained was confirmed by studying the correlation of the experimental solubilities and diffusion coefficients of He, O2, and N2 in R-BAPB, with their critical temperatures and the effective sizes of the gas molecules, respectively. The solubilities obtained in the molecular dynamics simulations are in good quantitative agreement with the experimental data. A good qualitative relationship between the simulation results and the experimental data is also observed when comparing the diffusion coefficients of the gases. Analysis of the Robeson plots shows that R-BAPB has high selectivity for He, N2, and CO2 separation from CH4, which makes it a promising polymer for developing gas-separation membranes. From this point of view, the simulation models developed and validated in the present work may be put to effective use for further investigations into the transport properties of R-BAPB polyimide and nanocomposites based on it.

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.

Prediction and validation of diffusion coefficients in a model drug delivery system using microsecond atomistic molecular dynamics simulation and vapour sorption analysis

Diffusion of small to medium sized molecules in polymeric medical device materials underlies a broad range of public health concerns related to unintended leaching from or uptake into implantable medical devices. However, obtaining accurate diffusion coefficients for such systems at physiological temperature represents a formidable challenge, both experimentally and computationally. While molecular dynamics simulation has been used to accurately predict the diffusion coefficients, D, of a handful of gases in various polymers, this success has not been extended to molecules larger than gases, e.g., condensable vapours, liquids, and drugs. We present atomistic molecular dynamics simulation predictions of diffusion in a model drug eluting system that represent a dramatic improvement in accuracy compared to previous simulation predictions for comparable systems. We find that, for simulations of insufficient duration, sub-diffusive dynamics can lead to dramatic over-prediction of D. We present useful metrics for monitoring the extent of sub-diffusive dynamics and explore how these metrics correlate to error in D. We also identify a relationship between diffusion and fast dynamics in our system, which may serve as a means to more rapidly predict diffusion in slowly diffusing systems. Our work provides important precedent and essential insights for utilizing atomistic molecular dynamics simulations to predict diffusion coefficients of small to medium sized molecules in condensed soft matter systems.