Diffusion Of Gases In Polymers Research Articles

Cold neutron transmission for the in-situ analysis of the gas diffusion in polymers

A novel set-up for monitoring the gas diffusion process in polymers has been developed. This set-up is based on performing neutron radiography and tomography of polymeric materials under high pressures of gas. Information about the absorption kinetics of supercritical CO2 was obtained. Additionally, solubility, diffusivity, and macroscopic changes in the dimensions of the samples can be in-situ obtained through the developed measurement technique. This novel approach can be very helpful to analyze the diffusion kinetics in a wide range of polymers.

In Silico Determination of Gas Permeabilities by Non-Equilibrium Molecular Dynamics: CO2 and He through PIM-1.

We study the permeation dynamics of helium and carbon dioxide through an atomistically detailed model of a polymer of intrinsic microporosity, PIM-1, via non-equilibrium molecular dynamics (NEMD) simulations. This work presents the first explicit molecular modeling of gas permeation through a high free-volume polymer sample, and it demonstrates how permeability and solubility can be obtained coherently from a single simulation. Solubilities in particular can be obtained to a very high degree of confidence and within experimental inaccuracies. Furthermore, the simulations make it possible to obtain very specific information on the diffusion dynamics of penetrant molecules and yield detailed maps of gas occupancy, which are akin to a digital tomographic scan of the polymer network. In addition to determining permeability and solubility directly from NEMD simulations, the results shed light on the permeation mechanism of the penetrant gases, suggesting that the relative openness of the microporous topology promotes the anomalous diffusion of penetrant gases, which entails a deviation from the pore hopping mechanism usually observed in gas diffusion in polymers.

Contributions of diffusion and solubility selectivity to the upper bound analysis for glassy gas separation membranes

Prior analyses of the upper bound of permselectivity versus permeability, both theoretical and empirical, have assumed that this relationship is a consequence of the dependence of gas diffusion coefficients on the molecular diameter of the gases of interest. The solubility selectivity has been assumed to be invariant with permeability (and free volume). However, a few literature sources note that the solubility coefficient for specific families of glassy polymers correlate with free volume. A large database of permeability, diffusivity and solubility coefficients for glassy polymers was compiled to investigate this hypothesis. A critical analysis of the data demonstrates a modest solubility selectivity contribution to permselectivity as a function of free volume and, thus, permeability. The solubility selectivity (Si/Sj) generally decreases with increasing permeability (and free volume) when the diameter of gas j is larger than that of gas i. This empirical trend is likely a consequence of larger gas molecules having less access than smaller molecules to sorption sites as the polymer packing density increases and free volume decreases. The diffusion data permit determination of a diffusivity upper bound, which is modestly different from the permeability-based upper bound relationship. The diffusion data analysis allows a determination of a new set of gas diameters more appropriate for gas diffusion in polymers than prior correlations.

Predicting Solubility and Diffusivity of Gases in Polymers under High Pressure: N2 in Polycarbonate and Poly(ether-ether-ketone)

The aim of this study was to develop a model that predicts the gas solubility and the sorption and desorption kinetics in polymer granulates over large temperature and pressure intervals. Besides the part predicting the solubility and diffusivity, the model involves the simultaneous solution of the diffusion equation and the heat equation in three dimensions using a finite element method (FEM). When the temperature- and pressure-dependent solubility of a specific polymer/gas combination is not known, an improved version of the non-equilibrium lattice fluid model (NELF) is used to predict the solubility. The improvement of the NELF model includes the use of Hansen’s solubility parameters, and it uses pressure–volume–temperature (PVT) data from two new empirical models, which accurately estimate polymer densities over a wide range of temperatures and pressures. The new solubility model predicted the solubility–pressure data of N2 in poly(ethyl methacrylate) and N2 and CH4 in polycarbonate (PC) at pressures ...

Influence of local chain dynamics on diffusion of gases in polymers as determined by pulsed field gradient NMR

AbstractDiffusion of gases in polymers below the glass transition temperature, Tg, is strongly modulated by local chain dynamics. For this reason, an analysis of pulsed field gradient (PFG) nuclear magnetic resonance (NMR) diffusion measurements considering the viscoelastic behavior of polymers is proposed. Carbon‐13 PFG NMR measurements of [13C]O2 diffusion in polymer films at 298 K are performed. Data obtained in polymers with Tg above (polycarbonate) and below (polyethylene) the temperature set for diffusion measurements are analyzed with a stretched exponential. The results show that the distribution of diffusion coefficients in amorphous phases below Tg is wider than that above it. Moreover, from a PFG NMR perspective, full randomization of the dynamic processes in polymers below Tg requires long diffusion times, which suggests fluctuations of local chain density on a macroscopic scale may occur. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 231–235, 2010

Gas Diffusion in Anisotropic Nonhomogeneous Polymers

AbstractIn an effort to address the situation of gas diffusion in polymers that undergo swelling during the absorption process, two mass flux constitutive relations, independent of Fick's law, are evaluated. Both mass flux relations utilize the mass diffusivity as a tensor quantity. The diffusivity tensor considered can be a function of both time and spatial coordinates. For the case of one‐dimensional diffusion, approximations are found relating the diffusivity, when it is considered to be time varying and a function of position in the polymer, to the constant diffusivity assumed by Fick's law and its predicted concentration profile. Analyzing a case of oxygen absorption by glassy poly(ethylene terephthalate) shows a time‐dependent diffusivity with negligible spatial variation.magnified image

Molecular dynamics simulations to compute diffusion coefficients of gases into polydimethylsiloxane and poly{(1,5‐ naphthalene)‐co‐[1,4‐durene‐2,2′‐bis(3,4‐dicarboxyl phenyl)hexafluoropropane diimide

AbstractDiffusion coefficients of N2, O2, CO2 and CH4 at 298 K in polydimethylsiloxane (PDMS) and poly{[(1,5‐naphthalene)‐co‐[1,4‐durene‐2,2′‐bis(3,4‐dicarboxyl phenyl)hexafluoropropane diimide]} (6FDA‐1,5‐NDA) polymers have been estimated using molecular dynamics (MD) simulations. Estimated diffusion coefficients in PDMS decrease systematically with increasing size of the penetrant gas molecules following the experimental observations. For 6FDA‐1,5‐NDA polymer, diffusion coefficients decrease in the same order of magnitude, but differ in their sequential order, due to varying side group interactions of the polymer with the gaseous molecules. Cohesive energy density, solubility parameter and free volume of the polymers were determined using MD simulations. Reliability and accuracy of the simulations have been tested typically with the computed values of the diffusion coefficient of O2 in PDMS polymer, which compare well with the literature data. X‐ray scattering profiles of 6FDA‐1,5‐NDA have been generated to understand the interrelationship between the morphology and diffusion coefficients. The radial distribution function was evaluated to find the contribution of atoms that are important in understanding the molecular interactions during gas diffusion in polymers. Copyright © 2007 Society of Chemical Industry

Effect of compressed CO 2 on crystallization and melting behavior of isotactic polypropylene

Compressed gases such as CO 2 above their critical temperatures provide a highly tunable technique that has been shown to induce changes in phase behavior, crystallization kinetics and morphology of the polymers. Gas induced plasticization of the polymer matrix has been studied in a large number of polymers such as polystyrene, and poly(ethylene terephathalate). The knowledge of polymer–gas interactions is fundamental to the study of phenomena such as solubility and diffusivity of gases in polymers, dilation of polymers and in the development of applications such as foams and barrier materials. In this paper, we describe the interactions of compressed CO 2 with isotactic polypropylene (PP). Crystallization of various PPs in presence of compressed CO 2 was evaluated using a high pressure differential scanning calorimeter (HPDSC). CO 2 plasticized the polymer matrix and decreased the crystallization temperature, T c by ∼8 °C for PP at a pressure of 650 psi CO 2. The decrease as a function of pressure was −0.173 °C/bar and did not change with the molecular architecture of PP. Both crystallization kinetics and melting behavior are evaluated. Since solubility and diffusivity are important thermodynamic parameters that establish the intrinsic gas transport characteristics in a polymer, solubility of CO 2 in PP was measured using a high-pressure electrobalance and compared with cross-linked polyethylene. At 50 °C, solubility followed Henry’s law and at a pressure of 200 psi about 1% CO 2 dissolved in PP. Similar solubility was achieved in PE at a pressure of 160 psi. Higher solubility of CO 2 in PE is attributed to its lower crystallinity and lower T g, than PP. Diffusion coefficients were calculated from the sorption kinetics using a Fickian transport model. Diffusivity was independent of pressure and PE showed higher diffusivity than PP. Preliminary foaming studies carried out using a batch process indicate that both PP and PE can be foamed from the solid state to form microcellular foams. Cell size and cell density were ∼10 μm and 10 8 cells/cm 3, respectively in PE. Differences in morphology between the foams for these polymers are attributed to the differences in diffusivity.

Mathematical Modelling of the Permeation of Gases in Polymers

In this work, we focus on the experiments of permeation in order to characterise the transport coefficients and how they depend on the gas concentration. First, a physical and mathematical modelling approach is presented. Two models are used in order to describe the diffusion of gases in polymers. The mathematical modelling leads thereafter to the construction of an unusual optimisation problem. A work complementary to this approach relates to the study of parameter sensitivity, which characterises the coefficient of diffusion and the maximum gas concentration, unknown in the permeation tests. This method of optimisation does not depend on the initialisation of the parameters and makes it possible to determine a unique set of parameters.

High-precision gravimetric technique for determining the solubility and diffusivity of gases in polymers

An in situ gravimetric technique, employing an electrobalance, is described for determining the solubility and diffusivity of gases in polymers over extended ranges of temperature and pressure. Solubilities of CO2 in polystyrene at 35°C were measured as a test case; the results are in excellent agreement with the literature values determined by the pressure decay method. Solubility and diffusivity results are also reported for PVC-CO2 at 35°C and for PS-1,1,1,2-tetrafluoroethane at 30, 90, and 120°C. A comparison with other studies shows the in situ method to be more efficient and precise than the ones based on weighing the gas-saturated polymer under ambient conditions. The kinetics of gas sorption were analyzed in terms of two data reduction techniques to derive diffusion coefficients. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2025–2032, 1998

Diffusion of Gold and Silver in Bisphenol A Polycarbonate

Diffusion of evaporated gold and silver into Bisphenol A polycarbonate has been studied using the radiotracer technique in combination with ion beam sputtering for serial sectioning. Diffusion coefficients between 4 × 10-14 and 1 × 10-16 cm2 s-1 were measured in the temperature range between 210 and 130 °C. The metal concentration in the polymer turned out to depend strongly on the evaporation rate. An Arrhenius-like temperature dependence with activation energies of 1.02 eV for silver and 1.13 eV for gold was found. The low diffusivities, which are not affected by the polymer dynamics, are interpreted within molecular theories for diffusion of gases in polymers with an additional attractive interaction between metal atoms and polymer chains.

Structural Characterization of Polycarbonates for Membrane Applications by Atomic Level Simulation

Polycarbonate polymers are desirable for use in membrane applications for separating gas mixtures due to their unique properties. Two commercially important membrane polymers, the tetramethyl (TMPC) and tetrabromo (TBPC) derivatives of Bisphenol A polycarbonate, were studied with computer simulation. The volume available to various gas diffusants in these polymers was characterized by calculating the volume of clusters of Delauney tetrahedra between the atoms of an ensemble of bulk molecular mechanics models of the polymer. The inverse of this available volume correlated with the diffusivity of various gases in these polymers. This correlation was able to qualitatively reproduce the gas diffusion consistent with the superior diffusivity and superior selectivity of TMPC and TBPC, respectively. Analysis of the structure of the two polymers suggests a more ordered packing of the TMPC chain which is consistent with the experimentally observed trend in which inhibited packing leads to increased selectivity for gas diffusion in polymers. Despite the model`s neglect of the thermal motion of the polymer, it has potential for use as a tool to suggest other perturbations in polycarbonate structure that may produce superior properties.

Gas sorption and transport in polyisobutylene: Equilibrium and nonequilibrium molecular dynamics simulations

Molecular dynamics calculations are reported on the sorption and diffusion of small gas molecules (He, H2, and O2) in amorphous polyisobutylene. An all-atom force field (with explicit hydrogen atoms) was used. In addition to the standard method of obtaining the diffusion coefficient from an equilibrium calculation via the mean-square displacement we used a nonequilibrium technique that applies a fictitious external field selectively to the gas molecules. To our knowledge, nonequilibrium MD is, for the first time, applied to the problem of gas diffusion in polymers. Results of both techniques are compared. Energy profiles of the jump events underlying gas diffusion through polymers are studied. We also discuss the possible presence of anomalous (non-Einstein) behavior of gas molecules diffusing through an amorphous polymer. Gas solubilities in polyisobutylene are calculated by particle-insertion techniques.

Repeat Unit Structure and Gas Transport Properties of Aromatic Polymers

Abstract Structure/transport-property correlations for a family of aromatic polyesters and polyphenylene oxides are presented. How modification in repeat unit structure changes the packing of bulk polymers, and subsequently the solubility and diffusivity of gases in polymers is addressed in detail. In addition to polymer-gas attraction, polymer packing density is proposed to be an important factor in determining the gas-absorbing capacity of glassy polymers. The observed diffusivity data are strongly correlated with polymer packing. Moreover, scatter in the correlation can be satisfactorily attributed to differences in local chain mobility among the polymers investigated here.

Segmental mobility model for diffusion of gases in polymers

AbstractDiffusion of small molecules in polymers is described quantitatively in terms of segmental mobility processes. The diffusion coefficient depends on a diffusive jump length, which is characteristic of the polymer, and a jump frequency, which is equated to the segmental mobility rate. The presence of a particular solute increases mobility of the surrounding polymer segments by a predictable amount, which is related to the partial molar volume of the solute. The theory is fit to experimental diffusion data, and partial molar volumes are calculated from the fitting parameters. Good agreement with experimental partial molar volumes is obtained.

Limitations of the free‐volume sieving model for diffusion of gases in polymers

Calcul de la distribution des tailles des trous dans un polymere a l'aide de la theorie du volume libre et evaluation du modele en utilisant les donnees experimentales de Van Amerongen sur le caoutchouc naturel. Desaccord avec la distribution du volume libre calculee a partir de considerations thermodynamiques

Investigation on the doping of Polyacetylene Films

We have investigated the oxydation and iodination of (CH)x-films and found that iodine doped samples degrade in oxygen at a lower rate than pure samples. The iodination can be described as a diffusion process, the diffusion constant being D ≈ 10-14 − 10−13 cm2/sec. This value for D is by many orders of magnitude smaller than those normally encountered for diffusion of gases in polymers. The insulator-metal transition, observed at high iodine concentrations, was investigated by optical transmission measurements. The results show that the forbidden gap remains roughly unaffected if the conductivity changes from the semiconducting to the metallic state. Also, below the gap a peak in absorption builds up with increasing iodine concentration but no absorption characteristic for free carriers is observed. These experimental observations are of importance for the selection of models which are to describe the insulator-metal transition and some consequences hereof are discussed.

Diffusion and sorption of gases in poly(ethylene terephthalate)

AbstractThe sorption and diffusion of gases in poly(ethylene terephthalate) (PET) films have been measured by using a newly devised apparatus which gives the sorption rate curves from the initial to the equilibrium state. By analysis of sorption data for carbon dioxide in PET film, it was shown that the diffusion rate, as well as the equilibrium solubilities, could be explained by the dual‐mode sorption mechanism proposed by Vieth et al. Constants of their equation were used in the analysis of our experimental results, in which the apparent diffusion coefficients were dependent on pressure. The result showed that the dual‐mode sorption mechanism indeed applies to diffusion. The value of the real diffusivity obtained in amorphous PET was 5.7 × 10−9 (± 8%) cm2/sec in the range of pressure from 0 to 1 atm. It is believed that this apparatus has wide applicability, not only to diffusion of gases in polymers, but also to the measurement of surface properties, and can be used to study the morphology of a variety of polymers.

Factorization of the activation energies of diffusion of gases in polymers

Factorization of the activation energies of diffusion of gases in polymers

Diffusion of gases in polymers subjected to ionizing radiation

Diffusion of gases in polymers subjected to ionizing radiation