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Confinement and free-volume requirements.
Free internal volume requirements of space vehicles for long duration missions from studies of human confinement with elements of isolation and perceptual deprivation
Modeling water diffusion in polybenzimidazole membranes using partial immobilization and free volume theory
Not provided.
Free volume variation with molecular weight of polymers
Free volume measurements were made in several molecular weight fractions of two different geometries of poly(arylene ether ketone)s. Free volumes were measured using positron lifetime spectroscopy. It has been observed that the free volume cell size V(sub f) varies with the molecular weight M of the test samples according to an equation of the form V(sub f) = AM(B), where A and B are constants. The molecular weights computed from the free volume cell sizes are in good agreement with the values measured by gel permeation chromatography.
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.
Free volume in contact lens polymers
We have measured the free volume and gas permeability in several contact lens specimens as part of a Space Commercialization Program. Free volume was measured using positron lifetime spectroscopy, while permeability for O2, N2, and CO2 gases was measured using mass spectrometry and polarography. It has been noted that permeability for all gases increases with the mean free volume cell size in the test samples. As might be expected, the specimens with the highest free volume fraction also exhibit the lowest Rockwell Hardness Number. An interesting corollary of this study is the finding that the presence of fluorine atoms in the lens chemical structure inhibits filling up of their free volume cells. This is expected to allow the lenses to breathe freely while in actual use.
Free volume model for molecular weights of polymers
A free volume model has been developed for determining molecular weights of linear polymers. It is based on the size of free volume cells in two geometries of poly(arylene ether ketone)s. Free volume cell sizes in test samples were measured using positron lifetime spectroscopy. The molecular weights computed from free volume cell sizes are in good agreement with the values measured by gel permeation chromatography, with a low angle laser light scattering photometer as the detector. The model has been further tested on two atactic polystyrene samples, where it predicted the ratio of their molecular weights with reasonable accuracy.
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.
Thermodynamic properties derived from the free volume model of liquids
An equation of state and expressions for the isothermal compressibility, thermal expansion coefficient, heat capacity, and entropy of liquids have been derived from the free volume model partition function suggested by Turnbull. The simple definition of the free volume is used, and it is assumed that the specific volume is directly related to the cube of the intermolecular separation by a proportionality factor which is found to be a function of temperature and pressure as well as specific volume. When values of the proportionality factor are calculated from experimental data for real liquids, it is found to be approximately constant over ranges of temperature and pressure which correspond to the dense liquid phase. This result provides a single-parameter method for calculating dense liquid thermodynamic properties and is consistent with the fact that the free volume model is designed to describe liquids near the solidification point.
Free-volume characteristics of epoxies
Positron annihilation spectroscopy was used to measure free-volume characteristics of selected epoxies. Fluorene resins, a new family of high-temperature thermosetting resins, were selected as the test medium. Experimental results indicate that the free-volume cell size V sub f varies with the molecular weight between the cross-links M sub c according to an equation of the form V sub f = AM sub c sup B, where A and B are structural constants. In two of the samples, the concentration of bulky fluorene groups was increased in the network backbone by replacement of some of the conventional bisphenol A epoxy resin with fluorene-derived epoxy resin. This resulted in an increase in their glass transition temperature for a given level of cross-linking. It was found that in these samples, the Doppler broadening of the annihilation peak decreases with the increasing fluorene content, presumably due to enhanced damping of the chain motions.
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.
Effect of annealing history on free volume in thermoplastics
Two different types of thermoplastic glassy polymers have been investigated for the effects of thermal annealing on their free volumes. It has been observed that free volumes in glassy polymers decrease asymptotically to a steady level after about four thermal anneals lasting for 24 hours at a temperature about 50 C below their glass transition temperatures. These results indicate that composites incorporating properly annealed thermoplastic matrices may not experience any additional internal stresses due to subsequent thermal excursions experienced while in service.
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.
Annealing Reduces Free Volumes In Thermoplastics
Investigation conducted to determine free volumes and water-absorption characteristics of two types of thermoplastic polymide as functions of annealing histories. Reductions reach asymptotic values after several annealing cycles. High-temperature thermoplastics excellent candidates for use in aerospace applications. Graphite-fiber composites containing thermoplastic matrices have wide applicability.