Oxygen transport as a solid‐state structure probe for polymeric materials: A review

Free volume pockets inside a cell membrane play a prominent role in a variety of dynamic processes such as the permeability of small molecules across membranes and the diffusion of, e.g., lipids, drugs, and electron carriers in the plane of the membrane. Nonetheless, by now the chances for characterizing free volume voids in a nonperturbative manner through experiments have been very limited. Here we use lipid membranes as an example to show how positron annihilation spectroscopy (PALS) together with atomistic simulations can be employed to gauge changes in free volume pockets in biological macromolecular complexes. The measurements show that PALS is a viable technique to probe free volume in biomolecular systems. As examples, we consider the gel-to-fluid transition and the role of increasing cholesterol concentration in a lipid membrane. Further applications proposed in this work for PALS are likely to provide a great deal of insight into the understanding of the role of free volume in the dynamics of biomolecular complexes.

Suspension-phase neutralization of an acid-form sulfonated styrenic pentablock copolymer was used to prepare aluminum cross-linked polymer films. Aluminum neutralization was confirmed by 27Al solid state NMR, and the aluminum-neutralized polymer resisted ion exchange to the sodium counterion form when the polymer was soaked in 1 mol/L sodium chloride for 30 days. The effects of aluminum neutralization on polymer morphology, mechanical properties, water and salt transport properties, and free volume were explored. The primary spacing of the morphology, as measured by small-angle X-ray scattering (SAXS), decreased upon neutralization of the sulfonated polymer. The hydrated aluminum-neutralized polymer was mechanically stronger than the non-neutralized polymer, but the dry aluminum-neutralized polymer was more brittle than the non-neutralized polymer. Neutralization of the polymer’s sulfonic acid functionality resulted in a 5.5-fold decrease in water uptake. This water uptake decrease upon aluminum neutralization resulted in a decrease, relative to the non-neutralized polymer, in water and sodium chloride permeability and water vapor transport rate. These decreases in transport rates and water uptake were consistent with one another, based on an analysis of changes in free volume of the material upon aluminum neutralization. Sodium chloride permeability of the aluminum-neutralized polymer was less dependent on salt concentration than that of the non-neutralized polymer, which is consistent with neutralization of the polymer’s charged sulfonate groups. Aluminum neutralization increased the polymer’s water/sodium chloride permeability selectivity because of a 1.8-fold increase in the material’s diffusion selectivity. Free volume element size, characterized by ortho-positronium lifetime, decreased upon aluminum neutralization in both dry and hydrated film samples.

The effect of film thickness on oxygen sorption and transport in dry and water-saturated Kapton® polyimide

Barrier polymers are used for many packaging and protective applications. As barriers they separate a system, such as an article of food or an electronic component, from an environment. Barrier polymers limit movement of substances, called permeants. The movement can be through the polymer or, in some cases, merely into the polymer. After crossing the barrier polymer, the permeant moves to the polymer surface, desorbs, and moves away. Permeant movement is a physical process that has both a thermodynamic and a kinetic component. For polymers without special surface treatments, the thermodynamic contribution is in the solution step. The permeant partitions between the environment and the polymer according to thermodynamic rules of solution. The kinetic contribution is in the diffusion. The net rate of movement is dependent on the speed of permeant movement and the availability of new vacancies in the polymer. The traditional definition of a barrier polymer required an oxygen permeability less than \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}${2{\hskip0.167em}{\hskip0.167em}{\rm{nmol}}/{(}{\rm{m}} {\hskip-0.167em}{\hskip-0.167em}{\cdot{}}{\hskip-0.167em}{\hskip-0.167em} {\rm{s}}{\hskip-0.167em}{\hskip-0.167em}{\cdot{}}{\hskip-0.167em} {\hskip-0.167em}{\rm{GPa}}{)}}$\end{document} (originally, less than \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}${{(}1{\hskip0.167em}{\hskip0.167em}{\rm{cc}}{\hskip-0.167em} {\hskip-0.167em}{\cdot{}}{\hskip-0.167em}{\hskip-0.167em}{\rm{mil}}{)}/{(}100{\hskip0.167em}{\hskip0.167em}{\rm{in}} ^{2}{\hskip-0.167em} {\hskip-0.167em}{\cdot{}}{\hskip-0.167em}{\hskip-0.167em}{\rm{d}} {\hskip-0.167em}{\hskip-0.167em}{\cdot{}}{\hskip-0.167em}{\hskip-0.167em} {\rm{atm}}{)}}$\end{document} ) at room temperature. Poly(ethylene terephthalate) (PET), with an oxygen permeability of \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}${8{\hskip0.167em}{\hskip0.167em}{\rm{nmol}}/{(}{\rm{m}} {\hskip-0.167em}{\hskip-0.167em}{\cdot{}}{\hskip-0.167em}{\hskip-0.167em} {\rm{s}}{\hskip-0.167em}{\hskip-0.167em}{\cdot{}}{\hskip-0.167em} {\hskip-0.167em}{\rm{GPa}}{)}}$\end{document} , is not considered a barrier polymer by the old definition; however, it is an adequate barrier polymer for holding carbon dioxide in a 2‐L bottle for carbonated soft drinks. Many months are required to lose enough carbon dioxide (15% of initial) to be objectionable. The polymers that are good barriers to permanent gases, especially oxygen, have important commercial significance. Vinylidene chloride copolymers are available as resins for extrusion, latices for coating, and resins for solvent coating. Vinylidene chloride copolymers are marketed under a variety of trade names. Saran is a trademark of The Dow Chemical Company for vinylidene chloride copolymers. Other trade names include Daran (W.R. Grace), Amsco Res (Union Oil), and Serfene (Morton Chemical) in the United States; and Haloflex (Imperial Chemical Industries, Ltd.), Diofan (BASF), Ixan (Solvay and Cie SA), and Polyidene (Scott‐Bader) in Europe. Hydrolyzed ethylene–vinyl acetate copolymers, commonly known as ethylene–vinyl alcohol (EVOH) copolymers, are usually used as extrusion resins, although some may be used in solvent‐coating applications. Copolymers of acrylonitrile are used in extrusion and molding applications. Commercially important comonomers for barrier applications include styrene and methyl acrylate. Polyamide polymers can provide a good‐to‐moderate barrier to permeation by permanent gases. Two often‐used polymers have adequate properties for some applications. Poly(ethylene terephthalate) (PET) is used to make films and bottles. Poly(vinyl chloride) (PVC) is a moderate barrier to permanent gases. Plasticized poly(vinyl chloride) is used as a household wrapping film. In regard to water vapor transmission (WVTR) values, those polymers that are good oxygen barriers are often poor water‐vapor barriers and vice versa. Polymer molecules without dipole–dipole interactions, such as polyolefins, dissolve very little water and have low WVTR and permeability values. The permeation of flavor, aroma, and solvent molecules in polymers follows the same physics as the permeation of small molecules, but with two significant differences. For these larger molecules, the diffusion coefficients are much lower and the solubility coefficients are much higher. Furthermore, the large solubility coefficient can lead to enough sorption of the large molecule that plasticization occurs in the polymer, which can increase the diffusion coefficient. Generally, vinylidene chloride copolymers and glassy polymers such as polyamides and EVOH are good barriers to flavor and aroma permeation, whereas the polyolefins are poor barriers. Several physical factors can affect the barrier properties of a polymer. These include temperature, humidity, orientation, and cross‐linking. Typically, the permeability increases 5 to 10% for every increase of 1°C. When a polymer equilibrates with a humid environment, it absorbs water. This can plasticize the polymer and increase the permeability. The effect of orientation on the permeability of polymers is difficult to assess; diffusion in some polymers is unaffected by orientation; in others, increases or decreases are observed. Cross‐linking has been shown in a few cases to decrease the diffusion coefficient. Reasonable prediction can be made of the permeabilities of low molecular weight gases such as oxygen, nitrogen, and carbon dioxide in many polymers. The diffusion coefficients are not complicated by the shape of the permeant, and the solubility coefficients of each of these molecules do not vary much from polymer to polymer. Reasonable predictions of the permeabilities of larger molecules such as flavors, aromas, and solvents are not easily made. The diffusion coefficients are complicated by the shape of the permeant, and the solubility coefficients for a specific permeant can vary widely from polymer to polymer. The permachor method is an empirical method for predicting the permeabilities of oxygen, nitrogen, and carbon dioxide in polymers. In this method a numerical value is assigned to each constituent part of the polymer. An average number is derived for the polymer, and a simple equation converts the value into a permeability. The model has been modified to liquid permeation with some success. For larger molecules, independent predictions of the diffusion coefficients and the solubility coefficients are required. Predicting the diffusion coefficient for a permeant in a polymer requires knowing one other diffusion coefficient in the polymer. The solubility coefficients are more difficult to predict. Although advances are being made, the best method is probably to use a few known solubility coefficients in the polymer to predict others. Measuring the barrier properties of polymers is important for several reasons. The effects of formulation or process changes need to be known, new polymers need to be evaluated, data are needed for a new application before a large investment has been made, and fabricated products need to have performance verified. Two methods of measuring water‐vapor transmission rates (WVTR) are commonly used. The newer method uses a Permatran‐W (Modern Controls, Inc.). The other method is the ASTM cup method. Measuring the permeation of carbon dioxide occurs far less often than measuring the permeation of oxygen or water. The simplest method uses the Permatran‐C instrument (Modern Controls, Inc.). Many methods are used to characterize the transport of flavor, aroma, and solvent molecules in polymers. Each has some value, and no one method is suitable for all situations. Any experiment should obtain the permeability, the diffusion coefficient, and the solubility coefficient. The primary application for barrier polymers is food and beverage packaging. Barrier polymers are also used for packaging medical products, agricultural products, cosmetics, and electronic components and in moldings, pipe, and tubing. The use of safe materials is vital for barrier applications, particularly for food, medical, and cosmetics packaging. Suppliers of specific barrier polymers can provide the necessary details to ensure safe processing and use of barrier polymers.

Using molecular dynamics, a comparative study was performed of two pairs of glassy polymers, low permeability polyetherimides (PEIs) and highly permeable Si-containing polytricyclononenes. All calculations were made with 32 independent models for each polymer. In both cases, the accessible free volume (AFV) increases with decreasing probe size. However, for a zero-size probe, the curves for both types of polymers cross the ordinate in the vicinity of 40%. The size distribution of free volume in PEI and highly permeable polymers differ significantly. In the former case, they are represented by relatively narrow peaks, with the maxima in the range of 0.5–1.0 Å for all the probes from H2 to Xe. In the case of highly permeable Si-containing polymers, much broader peaks are observed to extend up to 7–8 Å for all the gaseous probes. The obtained size distributions of free volume and accessible volume explain the differences in the selectivity of the studied polymers. The surface area of AFV is found for PEIs using Delaunay tessellation. Its analysis and the chemical nature of the groups that form the surface of free volume elements are presented and discussed.

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Ultrahigh permeability polymers are stiff chain glassy polymers that pack very poorly in the solid state, having high values of fractional free volume and a high degree of connectivity of free volume elements. High barrier materials are prepared from stiff chain glassy polymers that pack efficiently in the solid state, with low fractional free volume values. Manipulation of solid state chain packing changes permeability coefficients over many orders of magnitude. Control of chain chemistry and packing structure of stiff chain glassy polymers permits rational tailoring of permeation properties between those of high barriers and those of extremely permeable membranes via systematic manipulation of free volume and free volume distribution.

Different definitions of the free volumes are discussed and related to the total specific volume and to the local free (hole) volume. Positron lifetime measurements are reported for polyethylene, polytetrafluoroethylene, and CR39-copolymers. Two long-lived components appear in polyethylene and polytetrafluoroethylene, which were attributed to o-Ps annihilations in crystalline regions and in holes of the amorphous phase. From a relation between the coefficients of the thermal expansion of macroscopic and hole volume, the fractional hole volume h and from this the number of holes, N, is estimated. Values of Tg = 195 K, hg = 4.5% (polyethylene) and 5.7% (polytetrafluoroethylene) and Ng = 0.73 nm -3 (polyethylene) and 0.36 nm -3 (polytetrafluoroethylene) were obtained. In semicrystalline polymers these values agree with estimates obtained from the densities of the crystalline and amorphous phases. The effect of cross-linking on the free-volume properties of CR39-copolymer networks was studied. The comparison of the hole volume with the specific volume allowed us to estimate the number density of holes to = 1 nm -3 . PACS numbers: 61.41.+e, 65.70.+y, 78.70.—g

The development of polyimide (PI) films with both a low dielectric constant and low dissipation factor at high frequency is an urgent requirement in a new generation of mobile communication technology. Although some breakthroughs have been made in the study of low-dielectric constant polyimide, the main influencing factors and regulation of the high-frequency dissipation factors are still unclear, which severely limits its development and application, and they deserve further study. In this work, we prepared a series of low-dielectric constant polyimide films and measured their high-frequency dielectric properties at different humidity levels by using a homemade system. The free volume and water adsorption of these polyimide films were precisely evaluated by positron annihilation lifetime spectroscopy and the dynamic vapor sorption method, respectively. Our study shows that the main factor affecting the high-frequency dissipation factor of low-dielectric constant PI films is the water adsorption, and the influence of water adsorption capacity and water binding intensity on the increase of the high-frequency dissipation factor is analyzed in detail. The main factors affecting the water adsorption of these polyimide films are the free volume, molecular polarity index (MPI), and morphology. In the case of a similar structure, imide ring density, and morphology, the free volume of DP-BPDA, MDA-BPDA, TPM-BPDA, and FDA-BPDA gradually increases, resulting in an increase in water adsorption and high-frequency dissipation factors. HMDA-BPDA achieves a low water adsorption of 0.44% due to its appropriate free volume, low MPI, and partial crystallinity, thus achieving good comprehensive performance: low dielectric constant (2.84) and low dissipation factor (0.0029) at 50% RH. Therefore, for polymer materials, designing structures with low polarization, appropriate free volume, and low water adsorption will be an effective strategy to achieve both a low dielectric constant and low dissipation factor.

Positron annihilation lifetime spectroscopy (PALS) was used to investigate the phase transitions, mainly the glass transition, of poly(ethylene terephthalate) (PET) and nylon-6 during the thermal treatment of these polymers. The longest-lived component lifetime and intensity, indicative of ortho-positronium pick-off, exhibit thermal dependencies that can be attributed to the free-volume changes associated with structural transitions. Glass transition temperatures and the volume of intermolecular-space holes among polymer chains were obtained from the lifetime, τ3 and intensity of formation, I3, of the long-lived component of ortho-positronium. For PET, the free-volume fraction and thermal expansion coefficients related to the free-volume fraction were also obtained. Double glass transition behavior was noted in the analyzed polymers, which was consistent with their semicrystalline nature as revealed by differential scanning calorimetry. Increases in the slope of the lifetime-temperature plots for nylon-6 and PET were interpreted to suggest that glass transitions are followed by an increased free-volume cavity expansion as temperature is increased. The intensity response for PET was consistent with the association of glass transition with the reduction of crystalline consraint on segmental mobility in the amorphous phase. In contrast, the intensity behavior during the thermal treatment of nylon-6 seems to be governed more by the electronic effects occurring when the polymer chains acquire mobility than by free-volume changes. Since the sensitivity of PALS is in the order of nanometers, it is expected to give an alternative novel technique to estimate phase transitions and relaxations in polymers from the point of view of the free volume. © 1996 John Wiley & Sons, Inc.

A hybrid computational approach based on molecular dynamics simulations and deep learning algorithms facilitate fast and accurate estimation of the free energy of permeation of small drug-like molecules across lipid bilayers.

Selective permeability is a key feature of biological membranes. It is controlled by the physico-chemical properties of the lipid bilayer and by channel-forming membrane proteins. Here we focus on the permeation of small molecules across channel-forming proteins in Gram-negative bacteria called porins and present a new approach based on artificial amino acids. We introduced Hco, a fluorescent amino acid with characteristic excitation and emission wavelengths, into OmpF and measured FRET from Hco to dissolved Bocillin FL using solubilized OmpF porins. We examined four variants of OmpF and by doing so, we were able to show that small molecules, like Bocillin FL, are remaining long enough in the porin in order to undergo FRET and produce a reproducible fluorescence signal. This finding opens the way to quantify translocation in the future by the simultaneous detection of resistive pulses and differential fluorescence with FRET as an example.

Ion beam irradiation is an easily controlled method to modify the chemical structure and microstructure of polymers including the fractional free volume, free volume distribution and chain mobility, thus altering the gas transport properties of the irradiated polymers. The previous paper focused on the impact of H+ ion beam irradiation on chemical structural evolution of the polyimide Matrimid®. This paper focuses on the impact of H+ ion beam irradiation on microstructure and gas permeation properties of Matrimid®. Irradiation at low ion fluence resulted in slight decreases in permeabilities for five gases (i.e., He, CO2, O2, N2, and CH4) with increases in permselectivities for some gas pairs (e.g., He/CH4 and He/N2). In contrast, irradiation at relatively high ion fluences resulted in simultaneous increases in permeabilities and permselectivities for most gas pairs (e.g., He/CH4, He/N2, O2/N2, and CO2/CH4). While Matrimid® has bulk gas permeation properties that are below the range of commercially interesting polymers, samples irradiated at high ion fluences exhibited significant improvement in gas separation performances. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 1670–1680, 2007

Free volume vf is defined as that part of the thermal expansion, or excess volume Δv̄ which can be redistributed without energy change. Assuming a Lennard-Jones potential function for a molecule within its cage in the condensed phase, it can be shown that at small Δv̄ considerable energy is required to redistribute the excess volume; however, at Δv̄ considerably greater than some value δv̄g (corresponding to potentials within the linear region), most of the volume added can be redistributed freely. The transition from glass to liquid may be associated with the introduction of appreciable free volume into the system. Free volume will be distributed at random within the amorphous phase and there is a contribution to the entropy from this randomness which is not present in the entropy of the crystalline phase. According to our model all liquids would become glasses at sufficiently low temperature if crystallization did not intervene. Therefore whether or not a glass forms is determined by the crystallization kinetic constants and the cooling rate of the liquid. The experience on the glass formation is consistent with the generalization: at a given level of cohesive energy the glass-forming tendency of a substance in a particular class is greater the less is the ratio of the energy to the entropy of crystallization.

A semi-rigid co-poly(imide) derived from an isomeric mixture of monomers. Assessing gas transport properties in self-standing polymer membrane