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Modeling water diffusion in polybenzimidazole membranes using partial immobilization and free volume theory
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Revisiting group contribution theory for estimating fractional free volume of microporous polymer membranes
Fractional free volume (FFV) is a commonly used metric for the development of structure–property relationships for polymer membranes. The most common method to calculate FFV uses Bondi's group contribution method, first introduced in 1964. While updated in 1997, there has not been a significant compilation of new structural motifs since the advent of linear microporous polymers. Here, in this study, we critically examined the assumptions in Bondi's original method and provide four recommendations to streamline and improve the accuracy of calculating van der Waals volume (V W ) for any group. Using these recommendations, we created an updated list of (V W ) values for structural groups commonly present in microporous polymers. The (V W ) and FFV values were then calculated for a database of 123 microporous and high free volume polymers from the literature, showing an average 7% decrease in (V W ) and corresponding increase in FFV by a factor of 24% when compared to prior group contribution correlations in the literature. The significant apparent increase in estimated FFV provides a new perspective to understand and interpret the role of free volume on the separation performance of linear microporous polymers. Additionally, standardization of the group contribution method allows for the direct comparison of FFV values across studies.
Quantifying the atomistic free-volume morphology of materials with graph theory
Here, we introduce a new computational methodology for the identification and characterization of free volume within/around atomistic configurations. This scheme employs a three-stage workflow, by which spheres are iteratively grown inside of voxels, and ultimately converted to planar graphs, which are then characterized via a graph-based order parameter. Our approach is computationally efficient, physically intuitive, and universally transferable to any material system. Validation of our methodology is performed on several sets of materials problems: (1) classification of unique free volumes in various crystal phases, (2) autonomous detection and classification of complex surface defects during epitaxial growth simulations, (3) characterization of free volume defects in metals/alloys, and (4) quantification of the spatio-temporal behavior of nano-scale free volume morphologies as a function of both temperature and free-volume size. Our method accurately identifies and characterizes unique free volumes over a multitude of systems and length scales, indicating its potential for future use in understanding the relationship between free volume morphology and material properties under both static and dynamic conditions.
Free volume manipulation of a 6FDA-HAB polyimide using a solid-state protection/deprotection strategy
We report tert-butoxycarbonyl (t-BOC) is a thermally labile moiety that can be used to protect hydroxyl groups on polymers. In this study, t-BOC was appended onto a polyimide consisting of 2,2'-bis-(3,4-dicarboxyphenyl) hexafluoropropane dianhydride (6FDA) and 3,3'-dihydroxy-4,4'-diamino-biphenyl (HAB), after which the polymer was formed into self-standing films. Solid-state thermal treatments were performed to systematically remove t-BOC moieties to alter the physical packing structure and concomitant gas transport properties of the polymer. Despite performing deprotection reactions well below the glass transition temperature of 6FDA-HAB (~300 °C), this free volume manipulation (FVM) approach produced only subtle differences in polymer density, fractional free volume, average free volume element size, and gas transport properties relative to the unprotected polymer. While these findings suggest that thermally removing covalently bound functional groups from polymer films can be used to manipulate free volume and gas transport performance for glassy polymers, more robust polymer systems than linear polyimides are required to preserve the nascent free volume architecture generated from this approach.
Leveraging Free Volume Manipulation to Improve the Membrane Separation Performance of Amine‐Functionalized PIM‐1
Abstract Gas‐separation polymer membranes display a characteristic permeability–selectivity trade‐off that has limited their industrial use. The most comprehensive approach to improving performance is to devise strategies that simultaneously increase fractional free volume, narrow free volume distribution, and enhance sorption selectivity, but generalizable methods for such approaches are exceedingly rare. Here, we present an in situ crosslinking and solid‐state deprotection method to access previously inaccessible sorption and diffusion characteristics in amine‐functionalized polymers of intrinsic microporosity. Free volume element (FVE) size can be increased while preserving a narrow FVE distribution, enabling below‐upper bound polymers to surpass the H 2 /N 2 , H 2 /CH 4 , and O 2 /N 2 upper bounds and improving CO 2 ‐based selectivities by 200 %. This approach can transform polymers into chemical analogues with improved performance, thereby overcoming traditional permeability–selectivity trade‐offs.
Machine learning prediction on the fractional free volume of polymer membranes
Fractional free volume (FFV) characterizes the microstructural level features of polymers and affects their properties including thermal, mechanical, and separation performance. Experimental measurements and theoretical analyses have been used to quantify the FFV of polymers, but challenges remain because of their limitations. Experimental measurements are laborious and based on semi empirical equations, while Bondi’s group contribution theory involves ambiguities like the determination of van der Waals volume and the choice of factor values in the theoretical equation. To efficiently evaluate the FFV of polymers, this study utilizes high-throughput molecular dynamics (MD) simulations to build a large dataset regarding polymer’s FFV. Based on this large dataset, we further build machine learning (ML) models to establish the composition-structure relation. Inspired by group contribution theory which correlates polymer’s functional groups to FFV, our ML models correlate polymer’s substructures or physico-chemical indexes to FFV. Here, our study first benchmarks the MD simulation protocol to obtain reliable FFV of polymers and then carries out high-throughput MD simulations for more than 6,500 homopolymers and 1,400 polyamides. Such a large and diverse dataset makes the well-trained ML models more generalizable, compared with the group contribution theory. The efficiency of a feed forward neural network model is further demonstrated by applying it to a hypothetical polyimide dataset of more than 8 million chemical structures. The predicted FFVs of hypothetical polyimides are further validated by MD simulations. The obtained FFVs of the 8 million polymers, plus their previously reported gas separation performances, demonstrate the promising capability of ML virtual screening for the discovery of polymer membranes with exceptional permeability/selectivity.
Excess free volume and structural properties of inert gas condensation synthesized nanoparticles based CuZr nanoglasses
Abstract Nanoglass (NG) as a new structure-tunable material has been investigated using both experiments and computational modeling. Experimentally, inert gas condensation (IGC) is commonly employed to prepare metallic glass (MG) nanoparticles that are consolidated using cold compression to generate an NG. In computational modeling, various methods have been used to generate NGs. However, due to the high computational cost involved, heretofore modeling investigations have not followed the experimental synthesis route. In this work, we use molecular dynamics simulations to generate an NG model by consolidating IGC-prepared Cu 64 Zr 36 nanoparticles following a workflow similar to that of experiments. The resulting structure is compared with those of NGs produced following two alternative procedures previously used: direct generation employing Voronoi tessellation and consolidation of spherical nanoparticles carved from an MG sample. We focus on the characterization of the excess free volume and the Voronoi polyhedral statistics in order to identify and quantify contrasting features of the glass-glass interfaces in the three NG samples prepared using distinct methods. Results indicate that glass-glass interfaces in IGC-based NGs are thicker and display higher structural contrast with their parent MG structure. Nanoparticle-based methods display excess free volume exceeding 4%, in agreement with experiments. IGC-prepared nanoparticles, which display Cu segregation to their surfaces, generate the highest glass-glass interface excess free volume levels and the largest relative interface volume with excess free volume higher than 3%. Voronoi polyhedral analysis indicates a sharp drop in the full icosahedral motif fraction in the glass-glass interfaces in nanoparticle-based NG as compared to their parent MG.
Structure, Dynamics, and Hydrogen Transport in Amorphous Polymers: An Analysis of the Interplay between Free Volume Element Distribution and Local Segmental Dynamics from Molecular Dynamics Simulations
Polymers are attractive membrane materials owing to their mechanical robustness and relatively inexpensive fabrication. An important indicator of membrane performance are free volume elements (FVE): microporous void spaces created by the inefficient packing of bulky groups along the polymer chain. FVEs tend to degrade over time, as polymer chains reorganize irreversibly. While it is widely accepted that polymer flexibility has an impact on membrane transport properties, the molecular nature of this impact is still not well understood. By the establishment of a correlation between local chain dynamics and the distribution of free volume elements (FVEs), penetrant transport can be regulated more efficiently in amorphous polymer membranes. In this work, we implement all-atom molecular dynamics (MD) simulations to explore the relationship between chain dynamics and free volume in three polymers with different levels of backbone flexibility: polymethylpentene (PMP), polystyrene (PS), and HAB-6FDA thermally rearranged polymer (TRP). We construct these polymers at different temperatures and examine how temperature impacts the FVE distribution and segmental mobility. Our analysis shows that chain segments near FVEs have higher mobility compared with the atoms in the bulk; the extent of this difference increases with chain flexibility. Increasing the chain flexibility by increasing the temperature results in a broader FVE distribution. Rigid polymers such as TRP show the most robust FVE distribution and are not significantly affected by the temperature change. To capture penetrant diffusion through the polymer matrix, hydrogen is inserted and the diffusion is measured at different temperatures; hydrogen mobility is influenced by the FVE structure and overall mobility of polymer chains. Lastly, at low temperatures, hydrogen mobility is influenced by void distribution, while at high temperatures, polymer dynamics dictate hydrogen transport.
Understanding Relationships between Free Volume and Oxygen Absorption in Ionic Liquids
In this report understanding the factors that govern gas absorption in ionic liquids is critical to the development of high-capacity solvents for catalysis, electrochemistry, and gas separations. Here, we report experimental probes of liquid structure that provide insights into how free volume impacts the O 2 absorption properties of ionic liquids. Specifically, we establish that isothermal compressibility - measured rapidly and accurately through small-angle X-ray scattering - reports on the size distribution of transient voids within a representative series of ionic liquids and is correlated with O 2 absorption capacity. Additionally, O 2 absorption capacities are correlated with thermal expansion coefficients, reflecting the beneficial effect of weak intermolecular interactions in ionic liquids on free volume and gas absorption capacity. Molecular dynamics simulations show that the void size distribution - in particular, the probability of forming larger voids within an ionic liquid - has a greater impact on O 2 absorption than the total free volume. These results establish relationships between the ionic liquid structure and gas absorption properties that offer design strategies for ionic liquids with high gas solubilities.
The role of free volume, hydrogen bonds, and crosslinks on physical aging in polymers of intrinsic microporosity (PIMs)
Physical aging rates strongly correlate with the initial free volume of microporous polymers. Introducing hydrogen bonds and crosslinks can reduce the initial free volume and significantly impact gas separation selectivity over time.
Molecular insight into the anion effect and free volume effect of CO 2 solubility in multivalent ionic liquids
For many years, experimental and theoretical studies have investigated the solubility of CO 2 in a variety of ionic liquids (ILs), but the overarching absorption mechanism is still unclear. Currently, two different factors are believed to dominate the absorption performance: (a) the fractional free volume (FFV) accessible for absorption; and (b) the nature of the CO 2 interactions with the anion species. The FFV is often more influential than the specific choice of the anion, but neither mechanism provides a complete picture. Herein, we have attempted to decouple these mechanisms in order to provide a more definitive molecular-level perspective of CO 2 absorption in IL solvents. We simulate a series of nine different multivalent ILs comprised of imidazolium cations and sulfonate/sulfonimide anions tethered to benzene rings, along with a comprehensive analysis of the CO 2 absorption and underlying molecular-level features. We find that the CO 2 solubility has a very strong, linear correlation with respect to FFV, but only when comparisons are constrained to a common anion species. The choice of anion results in a fundamental remapping of the correlation between CO 2 solubility and FFV. Overall, the free volume effect dominates in the ILs with smaller FFV values, while the choice of anion becomes more important in the systems with larger FFVs. Our proposed mechanistic map is intended to provide a more consistent framework for guiding further IL design for gas absorption applications.
Positron annihilation lifetime spectroscopy study of polyvinylpyrrolidone‐added polyvinylidene fluoride membranes: Investigation of free volume and permeation relationships
ABSTRACT Polyvinylidene fluoride (PVDF) membranes were prepared via the phase inversion method from casting solutions containing PVDF, dimethylformamide (DMF), and polyvinylpyrrolidone (PVP) as pore former. PVP was used in the casting solution in a range of 0–5 wt % and extracted. The effect on membranes of using PVP in the casting process was analyzed by X‐ray diffraction, differential scanning calorimetry, scanning electron microscopy, viscosity, and water permeability techniques. With an increase of PVP from 0 to 5 wt %, the PVDF casting solution viscosities increased from 858 to 1148 cP; the resulting PVDF membrane thickness increased; and the crystallinity of PVDF membranes decreased from 40.0 to 33.3%, which indicates that the addition of PVP inhibits the degree of crystallization in the PVDF membranes. SEM results revealed the shape and size of macropores in the membranes; these macropores changed after PVP addition to the casting solutions. The impact of structural changes on free‐volume properties was evaluated using positron annihilation lifetime spectroscopy (PALS) studies. PALS analysis indicated no effect on the average radius (~3.4 Å) of membrane free‐volume holes from the addition of PVP to the casting solution. However, the percentage of o ‐Ps pick‐off annihilation intensity, I 3 , increased from 1.7 to 5.1% with increased PVP content. Further, increasing the PVP content from 0.5 to 5% resulted in an increased final pure water permeability flux. For instance, the 210 min flux for a 14% PVDF + 0.5% PVP membrane was found to be 3.3 times greater than a control membrane having the same PVDF concentration. © 2020 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58 , 589–598
Pentiptycene-based ladder polymers with configurational free volume for enhanced gas separation performance and physical aging resistance
Significance Gas separation membranes are an emerging energy-efficient alternative toward conventional, energy-intensive separation technologies such as cryogenic distillation. Ladder polymers with intrinsic microporosity show exceptional promise toward redefining state-of-the-art gas separation membranes due to their high permeability (throughput) and selectivity (separation efficiency). However, they are typically inhibited by major reductions in permeability over time due to collapsing membrane free volume (open space between polymer chains), forfeiting their greatest asset. This work explores a route toward enhanced aging resistance and overall separation performance by incorporating pentiptycene (an H-shaped scaffold containing five fused arene rings) into ladder-like polymers to incorporate natural, more permanent “micropores” that aren’t susceptible to densification of polymer chains that occurs over time in traditional microporous polymers.
Enhancing acid–gas separations using free volume manipulation for microporous poly(arylene ether)s
H 2 S/CH 4 and CO 2 /CH 4 separations show opposing trends, making simultaneous improvement challenging. This is addressed by increasing free volume to enhance competitive sorption effects and boosting diffusion selectivity through in situ crosslinking.
Leveraging molecular scale free volume generation to improve gas separation performance of carbon molecular sieve membranes
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Role of Side-Chain Free Volume on the Electrochemical Behavior of Poly(propylenedioxythiophenes)
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