Atomistic molecular dynamics simulations of gas diffusion and solubility in rubbery amorphous hydrocarbon polymers

Diffusion coefficients D of H₂, He, O₂, N₂, and CO₂ in different rubbery amorphous polymeric matrices were estimated by atomistic molecular dynamics simulations at 298 K using the Einstein relationship, and compared with the relevant experimental values, where available. The simulated diffusion coefficients D of all the gases in all polymers considered almost regularly decreased with increasing molecular gas volumes and increasing polymer glass transition temperature. Further, solubility coefficients and heats of solution were obtained for all gases from Grand Canonical Monte Carlo simulations, which were also used to calculate sorption isotherms. In general, there is a good agreement between experimental and simulated values of diffusion and solubility coefficients for all gases considered.     

Molecular dynamics simulation of diffusion and permeation of gases in polystyrene

Molecular dynamics simulations are performed to study the diffusion and permeation of gases, including argon, nitrogen, methane, carbon dioxide, and propane, in polystyrene over a wide range of temperatures. A jumping mechanism is observed for the diffusion of diffusants in polymer. The calculated diffusion coefficients agree well with the experimental data and with the results of former simulation studies. The relation between the diffusion coefficient and the molecular diameter is confirmed by the results. Our calculated results on the temperature-dependence of diffusion coefficients show that for some gases a break is seen, at the glass transition temperature, in the Arrhenius plot of ln (D) versus 1/T, while for some other light gases, argon and nitrogen, the plot is linear over the whole temperature range. We have also calculated the permeability coefficients, using the diffusion coefficients calculated in this work and our recently published solubility coefficients [Eslami and Müller-Plathe, Macromolecules 2007; 40:6413]. Our results show that the calculated permeability coefficients are higher than the experimental data by almost the same trend observed in the solubility calculations, but the ratios of calculated permeabilities are in a very good agreement with experiment.     

Molecular simulations of gas transport in nitrile rubber and styrene butadiene rubber

Nitrile rubber (NBR, 39:61 wt% of acrylonitrile:butadiene) and styrene butadiene rubber (SBR, 50:50 wt% of styrene:butadiene) matrices have been equilibrated by molecular dynamics (MD) simulations. Transition-state approach is used to calculate the diffusion and solubility coefficients of small penetrants in these matrices, indicating quite low values in NBR and reasonable agreement with experimental results. MD simulations have been performed to analyze water diffusion in these matrices. Aggregation of water molecules is observed in the hydrophobic matrix SBR. MD simulations with fictitious nonpolar water molecules inhibit aggregation and lead to enhanced diffusion in SBR. In NBR there is a slight increase in diffusion for fictitious water molecules. The lower diffusion constants in NBR result from slower local relaxation of the matrix due to tighter intermolecular packing and higher cohesive energy density. The free volume distribution that affects solubility coefficients is not a major determining factor for the diffusion coefficients in these matrices.     

Molecular dynamics simulation of diffusion of O2 and CO2 in amorphous poly(ethylene terephthalate) and related aromatic polyesters

The diffusion of small molecules through polymers is important in many areas of polymer science, such as gas barrier and separation membrane materials, polymeric foams, and in the processing and properties of polymers. Molecular simulation techniques have been applied to study the diffusion of oxygen and dioxide of carbon as small molecule penetrants in models of bulk amorphous poly(ethylene terephthalate) and related aromatic polyesters. A bulk amorphous configuration with periodic boundary conditions is generated into a unit cell whose dimensions are determined for each of the simulated aromatic polyesters in the cell to have the experimental density. The aim for this research is to explore and investigate the diffusion of gases through bulk amorphous poly(ethylene terephthalate) and related aromatic polyesters. The diffusion coefficients for O₂ and CO₂ were determined via NVE molecular dynamics simulations using the Dreiding 2.21 molecular mechanics force field over a range of temperatures (300, 500 and 600 K) using up to 30 ns simulation time. We have focussed on the influence of the temperature, polymer dynamics, number of aromatic rings, ortho-, meta-, para-isomers, density and free volume distribution on the diffusion properties. Correlation of diffusion coefficients with free volume, temperature, number of aromatic rings, ortho-, meta- and para-isomers was found.     

The atomistic simulation of the gas permeability of poly(organophosphazenes). Part 2. Poly[bis(2,2,2-trifluoroethoxy)phosphazene]

Self-diffusion and sorption of seven gases (He, H₂, O₂, N₂, CH₄, CO₂, and Xe) in poly[bis(2,2,2-trifluoroethoxy)phosphazene] (PTFEP) have been investigated by molecular dynamics and Grand Canonical Monte Carlo (GCMC) simulations of two amorphous cells and an α-orthorhombic crystalline supercell. In the case of MD simulation of diffusion coefficients, values obtained for both amorphous and crystalline PTFEP are similar and comparable to experimental values reported for semicrystalline samples. These results indicate that gas diffusion is unrestricted in the crystalline state of PTFEP as has been reported for poly(4-methyl-1-pentene) (PMP) and, more recently, for a crystalline form of syndiotactic polystyrene (sPS).In contrast to both PMP and sPS that have low-density crystalline forms, only He exhibits any solubility in the α-orthorhombic crystalline cells of PTFEP during simulation. In addition, values of the solubility coefficients obtained from simulation of the amorphous cells are three to five times larger than would be expected by extrapolating values reported for semicrystalline samples to 100% amorphous content. These results suggest that while the crystalline domains do not restrict gas diffusivity in PTFEP, they significantly reduce gas solubility in semicrystalline PTFEP through the reduction of amorphous content and through some additional effect of the crystallites on amorphous-phase solubility, possibly through chain immobilization of the amorphous phase. Similar solubility behavior has been suggested for polyethylene on the basis of recent simulation studies.As reported in a prior communication, the solubility of CO₂ in PTFEP is very high compared to other gases due to a weak quadrupole-dipole interaction between CO₂ and the trifluoroethoxy group of PTFEP. As a result, the solubility coefficients of CO₂ obtained from GCMC simulation of the amorphous cells and from permeability measurements of semicrystalline samples are both larger than predicted by a simple correlation of gas solubility coefficients with the Lennard-Jones potential well parameter, ε/k, of other gases as proposed by Teplyakov and others. A modified form of this correlation that includes a Flory interaction term is shown to fit all gas solubility data for this polymer including that of CO₂.     

Cavity size, sorption and transport characteristics of thermally rearranged (TR) polymers

Within a polymer thin film, free volume elements have a wide range of size and topology. This broad range of free volume element sizes determines the ability for a polymer to perform molecular separations. Herein, six permeable thermally rearranged (TR) polymers and their precursors were studied. Using atomistic models, cavity size (free volume) distributions determined by a combination of molecular dynamics and Monte Carlo methods were consistent with experimental observation that TR polymers are more permeable than their precursors. The cavity size distributions determined by simulation were also consistent with free volume distributions determined by positron annihilation lifetime spectroscopy. The diffusion, solubility and permeation of gases in TR polymers and their precursors were also simulated at 308 K, with results that agree qualitatively with experimental data.     

Molecular dynamics simulation of diffusion of O2 and CO2 in blends of amorphous poly(ethylene terephthalate) and related polyesters

The diffusion of small molecules through polymers is important in many areas of polymer science, such as gas barrier and separation membrane materials, polymeric foams, and in the processing and properties of polymers. Molecular dynamics simulation techniques have been applied to study the diffusion of oxygen and carbon dioxide as small molecule penetrants in models polyester blends of bulk amorphous poly(ethylene terephthalate) and related aromatic polyesters. A bulk amorphous configuration with periodic boundary conditions was generated into a unit cell whose dimensions were determined for each of the simulated polyester blends in the cell having the experimental density. The diffusion coefficients for O₂ and CO₂ were determined via NVE molecular dynamics simulations using the Dreiding 2.21 molecular mechanics force field over a range of temperatures (300, 500 and 600 K) using up to 40 ns simulation time. We have focussed on the influence of the temperature, polymer dynamics, density and free volume distribution on the diffusion properties. Correlation of diffusion coefficients with free volume distribution was found.     

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]}

Diffusion 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     

Molecular simulations of small gas diffusion and solubility in copolymers of styrene

The objective of this study is to investigate the relationship between gas permeability and the chemical structure and conformational properties for copolymers of styrene and its homopolymer. The diffusion and the solubility coefficients of small gas molecules (He, H₂, Ne, O₂, N₂, CH₄, Ar, CO₂) in amorphous structures of poly (styrene-alt-maleic anhydride) copolymer (SMA), poly (styrene-stat-butadiene) rubber (SBR), and atactic polystyrene (PS) are investigated by the transition state approach. Simulation results are found to be in good agreement with the experimentally measured values. The transport behavior of H₂O molecules is also studied in the same bulk structures by fully atomistic molecular dynamics simulations. In general, the diffusion coefficients of the gases in these matrices decrease in the following order: SBR>PS>SMA, whereas the solubility coefficients follow the reverse order. The differences in the mobility of the matrices seem to be the dominant determining factor for diffusion. And the solubility coefficients depend on the free volume distribution of the matrices.     

Molecular dynamics simulation of diffusion of gases in pure and silica-filled poly(1-trimethylsilyl-1-propyne) [PTMSP]

Nanocomposites have been extensively applied, and molecular dynamics simulation techniques have been applied to study the diffusion of gases (H₂, O₂, N₂, CO₂, CH₄, n-C₄H₁₀) through pure and filled with silica particle poly(1-trimethylsilyl-1-propyne) [PTMSP]. The aim for this research is to explore and investigate the effect of silica particle on the diffusion of gases in polymer. The diffusion coefficients of gases were determined via NVT molecular dynamics simulation using the COMPASS force field up to 500 or 1000 ps simulation time. We have focused on the effect of the concentration and the size of the silica particles on diffusion coefficients of gases and the changes of free volume and translational dynamics and intermolecular energies. It has been found that the addition of silica particle to PTMSP increased the diffusion coefficients of gases by enhancing the free volume of polymer.     

Gas transport in ethylene-propylene-diene (EPDM) elastomer: Molecular simulation and experimental study

Time lag permeation measurements with ethylene-propylene-diene (EPDM) elastomer have been undertaken in an effort to characterize the gas transport properties of this barrier material. The derived solubility and diffusivity of a series of probe gases including helium, hydrogen, neon, argon, krypton, oxygen, nitrogen, carbon dioxide and methane were measured and compared with molecular simulation predictions. Molecular Dynamics (MD) and Grand Canonical Monte Carlo (GCMC) calculations were performed to provide estimates for diffusivity and solubility, respectively. Agreement between the molecular simulations and experimental data is obtained for simple spherical monatomic probe gases, with greater deviation observed for non-spherical polyatomic gases. Additionally, agreement between semi-empirical correlations based on the effective cross-sectional area of the diffusing species and the effective Lennard-Jones interaction constant of the sorbed species is better than widely used correlations based on gas critical properties. Furthermore, the molecular simulations provide a meaningful representation for the elastomer studied and additionally appear to capture the fundamental principles of sorption and diffusion of the chosen probe gases.     

Effect of styrene grafting on diffusion and solubility of gases in polyethylene

Diffusion and solubility coefficient data of gases for styrene-grafted high-density polyethylene obtained by γ-irradiation are reported. Diffusion coefficients were determined by the time lag method. Solubility coefficients were determined by a new, more accurate static method. Densities and volume fractions of grafted polystyrene were calculated from the observed values of extent of grafting and density of the graft copolymer films. The solubility coefficients obey simple additivity in terms of volume fraction of side-chain polystyrene and amorphous polyethylene. However, behavior of the diffusion coefficients is more complex. Inasmuch as diffusion is a kinetic process, it is influenced by morphology. The experimental results reported here, together with x-ray diffraction and DSC data, provide a basis for discussing the morphology of the graft copolymers.     

Diffusion of low‐molecular‐weight permeants through semi‐crystalline polymers: combining molecular dynamics with semi‐empirical models

A molecular dynamics‐based computational approach was used to study the diffusion of oxygen through a model semi‐crystalline polymer, namely linear low‐density polyethylene. The simulated molecules were validated by comparing the predicted properties with experimental values of available free volumes, on atomic scale, using positron annihilation lifetime spectroscopy and measured values of density. The semi‐crystalline polymer was considered as a composite network of a continuous amorphous phase and a dispersed crystalline phase. Based on this observation, the overall diffusion was simulated, including the diffusion through the crystalline phase, which has not been previously reported. A tight correlation was then achieved between experimental and simulated data by utilising several semi‐empirical and analytical models developed for composite materials. The proposed methodology in this work can be effectively used as a basis for designing polymer networks with controlled diffusion characteristics in a bottom‐up approach. © 2018 Society of Chemical Industry     

Gas transport properties of polyaniline membranes

The transport properties of He, H₂, CO₂, O₂, N₂, and CH₄ gases in solvent cast, HCl doped, and undoped polyaniline (PANi) membranes were determined. Measurements were carried out at 40 psi pressure from 19°C to 60°C. An excellent correlation was found between the diffusion coefficients and the molecular diameters of gases. The solubility coefficients of gases were found to correlate with their boiling points or critical temperatures. The sepa-ration factors for CO₂/N₂ and CO₂/CH₄ are dominated by the high solubility of CO₂. These correlations enable us to predict the permeability, diffusion, and solubility coefficients of other gases. After the doping-undoping process, the fluxes of gases with kinetic diameters smaller than 3.5 Å increased but those of larger gases decreased. This results in a higher separation factor for a gas pair involving a small gas molecule and a larger one. © 1996 John Wiley & Sons, Inc.     

Effect of absorbed water on oxygen transport in EVOH matrices. A molecular dynamics study

We performed molecular dynamics simulations on oxygen transport in dry and hydrated (with 3 and 13 wt% water content) amorphous ethylene-vinyl alcohol (EVOH) copolymers. As the water content increases, the intermolecular hydrogen bonding in the matrix decreases and the cavity sizes increase, which result in increased diffusion coefficients. The local chain mobility increases significantly only at 13% water content. The predicted glass transition temperatures fall into reported experimental ranges. The solubility coefficients of oxygen slightly decrease with increasing water content, which indicates that the excessive increase in permeability mainly results from increased diffusion rates.     

Molecular dynamics simulation of diffusion of hydrogen and its isotopic molecule in polystyrene

Polystyrene is one of the target materials used in Inertial Confinement Fusion (ICF). Molecular dynamics simulations are performed in this report to study the diffusion of gases, including hydrogen and its isotopic molecule under normal temperature and pressure. According to the Mean Square Displacement (MSD) of the gas moving in polystyrene, the diffusion coefficient of hydrogen, deuterium and tritium in different molecular weight polystyrene were obtained. The calculated diffusion coefficients agree well with the results of former simulation studies. The diffusion coefficients of polystyrene of the same molecular weight gradually decrease along with the increase of mass fraction of hydrogen isotopes (hydrogen, deuterium and tritium). The study also finds that diffusion coefficients will decrease along with the increasing of polystyrene molecular weight. Moreover, the pair correlation functions, cohesive energy density and fractional free volume were studied corresponding to hydrogen isotopes diffusion coefficients.     

Force fields for classical atomistic simulations of small gas molecules in silicalite-1 for energy-related gas separations at high temperatures

High temperature (>573 K) molecular dynamics studies of gas diffusion in microporous zeolites require consideration of the zeolite framework flexibility. Pore windows can expand and contract at high temperatures, affecting phase space and material properties. No studies to date have addressed the application of the condensed-phase optimized molecular potentials for atomistic simulation studies or the consistent valence force field to simulate gas diffusion and adsorption in siliceous MFI (silicalite-1). The current study seeks to validate these intramolecular and intermolecular potentials along with another zeolite-specific force field reported by Nicholas et al. (JACS 113:4792–4800, 1991) for silicalite-1, one of the most extensively investigated zeolites, with respect to diffusion of several gas molecules. The experimental diffusion coefficients of H₂, CO₂, CH₄, O₂ and N₂ in silicalite-1 obtained using pulse-field gradient-nuclear magnetic resonance and quasi-elastic neutron scattering methods were compared to theoretically derived diffusion coefficients employing these force fields in molecular dynamics simulations. The diffusion coefficients obtained using the three force fields for H₂, CO₂, CH₄, O₂ and N₂ agreed well with these experimental data. The zeolite-specific force field of Nicholas et al. was employed in grand canonical Monte Carlo simulations to obtain adsorption isotherms of these gases. The adsorption isotherms and isosteric heats of adsorption predicted were also in agreement with the expected range of available experimental and theoretical adsorption data reported in the literature.     

Preparation and C3H8/Gas Separation Properties of a Synthesized Single Layer PDMS Membrane

In this paper, a new polydimethylsiloxane (PDMS) membrane was synthesized and its ability for separation of heavier gases from lighter ones was examined. Sorption, diffusion, and permeation of H₂, N₂, O₂, CH₄, CO_2, and C₃H₈ in the synthesized membrane were investigated as a function of pressure at 35°C. PDMS was confirmed to be more permeable to more condensable gases such as C₃H₈. This result was attributed to very high solubility of larger gas molecules in hydrocarbon?based PDMS in spite of their low diffusion coefficients relative to small molecules. The synthesized membrane showed much better gas permeation performance than others reported in the literature. Increasing upstream pressure increased solubility, permeability and diffusion coefficients of C₃H₈, while these values decreased slightly or stayed constant for other gases. Local effective diffusion coefficient of C₃H₈ and CO₂ increased with increasing penetrant concentration which indicated plasticization effect of these gases over the range of penetrant concentration studied. C₃H₈/gas solubility, diffusivity and overall selectivities also increased with increasing feed pressure. Ideal selectivity values of 4, 13, 18, 20, and 36 for C₃H₈ over CO₂, CH₄, H₂, O_2, and N₂, respectively, at upstream pressure of 7 atm, confirmed the outstanding separation performance of the synthesized mebrane.     

MOLECULAR DIFFUSION OF VOLATILE-LIQUID VAPORS INTO AIR

Diffusion coefficients of vapors diffused into stagnant air were determined at room temperature and atmospheric pressure. Experimental data on diffusion coefficients were obtained from the steady-state open-tube evaporation method modified for this study. No fresh air is passed over the top end of a diffusion tube, and amounts of volatile liquids evaporated in the diffusion tube are measured with a balance rather than a change of the liquid level in a diffusion tube. Experimental molecular diffusion coefficients are obtained by applying experimental data of mass losses of volatile liquidsversusevaporation durations to a diffusion equation developed suitable for the novel open-tube evaporation method. Three main experimental errors of the novel open-tube evaporation method are described in detail. Predicted diffusion coefficients are calculated with the Wilke-Lee method and compared with experimental values obtained from this diffusion study.     

Functional barriers in PET recycled bottles. Part I. Determination of diffusion coefficients in bioriented PET with and without contact with food simulants

A major outcome for recycled plastics consists of making food packaging materials. However, any contamination of collected plastics with chemicals may then be of concern for public health. A solution to mind migration is to use a layer of virgin polymer, named functional barrier, intercalated between the recycled layer and the food. This article aims to provide experimental values of diffusion coefficients (D) of model pollutants (surrogates) in poly(ethylene terephthalate) (PET) to be used for modeling migration through functional barriers. Diffusion coefficients of a large set of surrogates at low concentrations in PET were measured in various conditions. A solid‐to‐solid diffusion test was designed to avoid the use of a solvent that may induce plasticizing of the material and partitioning effects at the interface. Using [Log D = f(molecular weight)] correlations, the values of diffusion coefficients and activation energies of the surrogates measured by this method were shown to be consistent with the literature data obtained for gases, in permeation experiments, where no plasticization occurred. Migration from PET into food simulants was then studied. Migration into an aqueous medium is largely influenced by the solubility of the surrogates, the less soluble ones being not detected, despite high D values. With ethanol solvent, there were no partitioning effects, and the high plasticization effect of PET by ethanol considerably increases the apparent diffusion coefficients. The effects of temperature and plasticization on the relationship between diffusion coefficients and molecular weight are discussed. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 2845–2858, 2004