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.     

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.     

Differential scanning calorimetry of polysulfone at high pressures of CO2 and N2O

Summary Polysulfone is less plasticized by compressed CO₂ than are amorphous vinyl polymers such as atactic polystyrene or poly(methyl methacrylate). N₂O, which is more polar than CO₂, is slightly more effective for plasticizing polysulfone than CO₂. Under the atmosphere of each gas, the depression in T _g is found to be linear with pressure. The dependence of T _g on pressure of CO₂ is −0.52 K·bar⁻¹, while that for N₂O is −0.60 K·bar⁻¹. Chow's thermodynamic model in combination with readily available gas solubility data does not describe well the pressure dependence of T _g in the polysulfone/CO₂ system. Received: 7 June 1999/Revised version: 19 August 1999/Accepted: 23 August 1999     

Molecular simulations of the solubility of gases in polyethylene below its melting temperature

We have employed Monte Carlo simulations in the osmotic ensemble to study the solubility of three different gases (N₂, CH₄, CO₂) in polyethylene. The simulations are performed at temperatures below the polymer melting point. Although under such conditions, polyethylene is in a semicrystalline state, we have used simulation boxes containing only a purely amorphous material. We show that under such circumstances, computed solubilities are 4-5 times larger than experimental data. We therefore introduce an original use of the osmotic ensemble to implicitly account for the effects of the complex morphology of semicrystalline materials on gas solubility. We have made the assumption that i) the network formed by polymer chains trapped between different crystallites and ii) the changes in local density from crystalline regions to purely amorphous regions, may be both represented by an ad-hoc constraint exerted on the amorphous phase. A single constraint value emerges, independent of the gas nature, characteristic of the crystalline degree of the polymer. It is concluded that the role of this constraint is mostly to reproduce the effective density of the permeable phase of the real material, indirectly giving insights into the morphology of a semicrystalline polymer.     

Gas transport in poly(alkoxyphosphazenes)

The permeability of four structurally related poly(alkoxyphosphazenes), three isomers of poly(dibutoxyphosphazenes) (PBuP), and poly(di-neopentyloxyphosphazene) (Pneo-PeP), to 13 gases has been determined by the time-lag method. Systematic variations in chemical structure have shown a large effect of side chains on permeabilities and permselectivities. The permeability of poly(di-n-butoxyphosphazene) (Pn-BuP) is of the order of 10^?8 cm³ (STP) cm/(cm² s cmHg) for many gases, and the value for a large gas is higher than that for a smaller one. For small gases such as He and H₂, poly(di-sec-butoxyphosphazene) (Ps-BuP) is as permeable as Pn-BuP, but its diffusivities for larger gases such as Xe and C₃H₈ are about one order lower than those of Pn-BuP. While the permselectivity of Pn-BuP is determined by the solubility, that of Ps-BuP depends on both the diffusivity and solubility factors. The property of poly(diisobutoxyphosphazene) (Pi-BuP) is intermediate between them. These polymers are constitutionally identical, and the only difference is the arrangements of carbons in the side groups. As the side chains become bulky, the permeability decreases, whereas the permselectivity increases. Further decreases of diffusivity and then permeability are observed for Pneo-PeP, whose side groups have one more methyl group than does Pi-BuP. But the solubility data are not much different from other three polymers and the diffusivity factor becomes more significant in permselectivity. The diffusivity depends on the polymer structure much more than does the solubility. The relationships between chemical structure and gas diffusivity and solubility are discussed.     

Controlling sandwich‐structure of PET microcellular foams using coupling of CO2 diffusion and induced crystallization

Controlling sandwich‐structure of poly(ethylene terephthalate) (PET) microcellular foams using coupling of CO₂ diffusion and CO₂‐induced crystallization is presented in this article. The intrinsic kinetics of CO₂‐induced crystallization of amorphous PET at 25°C and different CO₂ pressures were detected using in situ high‐pressure Fourier transform infrared spectroscopy and correlated by Avrami equation. Sorption of CO₂ in PET was measured using magnetic suspension balance and the diffusivity determined by Fick's second law. A model coupling CO₂ diffusion in and CO₂‐induced crystallization of PET was proposed to calculate the CO₂ concentration as well as crystallinity distributions in PET sheet at different saturation times. It was revealed that a sandwich crystallization structure could be built in PET sheet, based on which a solid‐state foaming process was used to manipulate the sandwich‐structure of PET microcellular foams with two microcellular or even ultra‐microcellular foamed crystalline layers outside and a microcellular foamed amorphous layer inside. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2512–2523, 2012     

Motion and sorption of gas molecules in poly(octadecyl acrylate)

Monte Carlo simulations are reported on the sorption and motion of small gas molecules (CH₄ and CO₂) in poly(octadecyl acrylate), a typical comb-like polymer with biphasic structure. Calculations were performed using a computational procedure recently developed by us, which is suitable to simulate the motion and sorption of small molecules in dense comb-like polymers. To our knowledge, the problem of gas transport in comb-like polymers using explicit penetrant molecules is for the first time studied by computational techniques. The study involves more than 12 million Monte Carlo steps of systems constituted by more than 1470 explicit atoms/pseudoatoms. Solubility coefficients are discussed by comparison with recently reported experimental data.     

Effect of pressure on CO2 transport in poly(ethylene terephthalate)

The CO₂ solubility, permeability, and diffusion time lag in poly(ethylene terephthalate) are reported at 35° and 65°C for CO₂ pressures ranging from 0.07 to 20 atm. The subatmospheric time lag and permeability measurements were made with a glass system at North Carolina State University, while the measurements between 1 and 20 atmospheres, using an identical polymer sample, were made at The University of Texas with a metal system capable of tolerating gauge pressures up to 30 atm. The measured solubility, permeability, and time lag all show strong deviations from the well-known simple expressions for gases in rubbery polymers. The solubility isotherm is non-linear in pressure, and both θ and P are quite pressure dependent, with each showing tendencies to approach low and high pressure asymptotic limits. These effects decrease as temperature increases and would be expected to disappear at or near the glass transition where the amorphous regions become rubbery. The importance of reporting the pressure levels used in transport measurements is emphasized for gas/glassy polymer systems where transport process do not follow linear laws.     

Synthesis of polyarylene homopolymers and copolymers via nickel(0)-catalyzed homocoupling of arylenebismesylates derived from bisphenols

A general and inexpensive procedure for the synthesis of poly(arylene)-type homopolymers and copolymers containing alternating oligophenylene and a functional group (X) (e.g. X = −O−, −CO−, −SO₂−, −C(CH₃)₂−, −CH₂−CH(Et)−, etc) is described. The synthetic method is based on the Ni(0)-catalyzed homocoupling of aryl bismesylates (MsOAr−X−ArOMs) derived from bisphenols. Symmetric X groups lead to regioregular crystalline and insoluble polymers whereas bulky, asymmetric X groups or the incorporation of comonomers yield regioirregular polymers and, respectively, copolymers with decreased crystallinity and increased solubility. This new synthetic method can be applied to the preparation of polymers with controlled rigidity which are amorphous, crystalline or liquid crystalline. Received: 22 January 1997/Accepted: 24 February 1997     

Gas transport in poly(vinyl cyclohexanecarboxylate)

Low-pressure gas permeation measurements were performed on poly(vinyl cyclohexanecarboxylate) to evaluate its transport characteristics. The transport data of CO₂, O₂, N₂, He, and Ar, were presented as a function of temperature ranging from 15 to 85°C. The apparent transport parameters were determined by the time lag method above and below the glass transition temperature and they were compared with other polymers of similar chemical structures. The side chain of the polymer has a bulky cyclohexyl group, which seemed to increase gas diffusivity. The activation energy for diffusion seemed to be related with the polarity of side chain. The relationships between gas diffusivity, physical properties, and chemical structure were qualitatively discussed in comparison with the data on poly(vinyl benzoate) and poly(vinyl acetate).     

Gas transport in poly(vinyl-p-isopropylbenzoate): Comparison and correlation with some other poly(vinyl esters)

Gas permeability in poly(vinyl-p-isopropylbenzoate) (PVp-i-PrB) was determined by a timelag method. The transport properties were discussed from comparison with the permeability data of other poly(vinyl esters), which were studied previously. All these polymers are structurally related, and the size of a side group or the position of its substituent was changed systematically. The isopropyl group of PVp-i-PrB is attached at the para position of a phenyl ring and is the largest in size. As a result gas diffusivity and therefore permeability were increased. The effect of the substituent on gas diffusivity was explained as it increases the interchain and intrachain distances. The discussion was supported from the comparison of the density data between PVp-i-PrB and other poly(vinyl esters). The diffusion coefficients of six glassy poly(vinyl esters) were correlated at their T_g and good correlations were shown to the free volume and its fraction. On the other hand, gas solubility was little affected by the change of an alkyl group on a phenyl ring. The solubility data of PVp-i-PrB and poly(vinyl benzoate) were shown to be clearly correlated with the critical properties of the penetrants. © 1995 John Wiley & Sons, Inc.     

Synthesis of hexafluoroisopropylidene isophthalic polyesters and copolyesters and the relationship between their structure and gas transport properties

Two aromatic polyesters and three copolyesters were synthesized by interfacial polycondensation using 4,4′‐(hexafluoroisopropylidene)diphenol (HFD) and two phthalic dichlorides, isophthaloyl dichloride (ISO) and 5‐tertbutyl‐isophthaloyl dichloride (TERT). The polymers obtained were soluble in common chlorinated solvents. The properties of these aromatic polyesters and copolyesters were characterized by FTIR, density, inherent viscosity, TGA, and DSC. Thermal properties such as glass transition temperature, onset of decomposition, and thermal stability of the homopolymer, poly(hexafluoroisopropilydene)5‐tertbutylisophthalate (HFD/TERT), were higher than those of homopolymer poly(hexafluoroisopropilydene)isophthalate (HFD/ISO). Thermal properties of the copolyesters HFD/TERT‐co‐HFD/ISO depend upon the amounts of the tertbutyl group HFD/TERT, present in the copolymer. Gas permeability coefficients of all polyarylates were measured at 35°C. The effect of different concentrations of the bulky tertbutyl group at the 5‐position in the isophthaloyl moiety on He, O₂, N₂, and CO₂ permeability, diffusion, and solubility coefficients were determined. Gas permeability and diffusivity increase as the concentration of TERT moiety increases in the copolymers. The results indicate that polymers containing the largest amounts of the bulky lateral tertbutyl group show the highest gas permeability. The increment in gas permeability and diffusivity produces a decrease in selectivity, which is attributed to the effect of the large pendant tertbutyl groups in the aromatic polyesters and copolyesters, which decrease the chain packing efficiency and induce a larger fractional free volume. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 2207–2216, 2007     

Measurement and prediction of diffusion coefficients of supercritical CO2 in molten polymers

The solubility and diffusivity of supercritical carbon dioxide (sc‐CO₂) in low‐density polyethylene (LDPE), high‐density polyethylene (HDPE), polypropylene (PP), ethylene‐ethylacrylate copolymer (EEA) and polystyrene (PS) were measured at temperatures from 150°C to 200°C and pressures up to 12 MPa by using the Magnetic Suspension Balance (MSB), a gravimetric technique for gas sorption measurements. The solubility of CO₂ in each polymer was expressed by Henry's constant. The interaction parameter between CO₂ and polymer could be obtained from the solubility data, and it was used to estimate the Pressure‐Volume‐Temperature relationship and the specific free volume of polymer/CO₂ mixtures. The diffusion coefficients were also measured by the MSB for each polymer. The resulting diffusion coefficients were correlated with the estimated free volume of polymer/CO₂ mixture. Combining Fujita's and Maeda and Paul's diffusion models, a model was newly developed in order to predict diffusion coefficients for the polymers studied. Polym. Eng. Sci. 44:1915–1924, 2004. © 2004 Society of Plastics Engineers.     

Diffusion coefficient and equilibrium solubility of water molecules in biodegradable polymers

The diffusion coefficient and solubility of water molecules were measured in polyglycolide (PGA), poly(L ‐lactide) (PLLA), poly[(R)‐3‐hydroxybutyrate] (PHB), poly(ϵ‐caprolactone) (PCL), and Skygreen^R (SG). The diffusion coefficient and equilibrium solubility decreased in the order SG > PCL > PLLA > PHB > PGA and PGA > SG > PLLA > PHB > PCL, respectively. The diffusion coefficient and solubility of water at low sorption temperature in PHB varied according to the initial crystallinity of the matrix polymer even though crystallization of PHB molecules took place during the sorption experiment. In contrast, the amorphous PLLA and the crystalline PLLA showed an almost identical diffusion coefficient and solubility of water, in spite of the fact that the amorphous PLLA remained practically amorphous during the whole sorption procedure. A strong correlation existed between the water solubility and the surface tension or contact angle of the polymer matrix. The water diffusivity in PGA was almost 2 orders of magnitude lower while water was more soluble in PGA with a lower heat of sorption than that corresponding to the other more hydrophobic polymers, indicating that the transport of water molecules in PGA followed the solution–diffusion model. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 1716–1722, 2000     

Investigation of CO2 sorption in molten polymers at high pressures using Raman line imaging

CO₂ sorption in molten poly(ε-caprolactone) (PCL) has been investigated by temporally resolved Raman line imaging, which is introduced here as a new technology for the direct measurement of gas mass fraction profiles inside polymers during transient sorption experiments. Molten PCL was exposed to pressurized carbon dioxide in an optically accessible pressure cell at 80 °C and pressures up to 7.1 MPa. During sorption, Raman spectra were acquired temporally and spatially resolved across the PCL drop, allowing the evaluation of the PCL/CO₂ mutual diffusivity, of the CO₂ solubility in PCL, and the determination of temporal evolution of mass fraction profiles of carbon dioxide inside PCL.     

Supercritical fluid dyeing of PMMA films with azo-dyes

In situ ultraviolet–visible spectroscopy has been used to study diffusion of two azo-dyes in a CO₂-swollen matrix of poly(methyl methacrylate) (PMMA). The diffusivity of both dyes can be tuned simply be changing the system pressure. Higher pressure of CO₂ enhances diffusion of a dye in PMMA. The diffusion of dyes in CO₂-swollen PMMA can also be influenced by specific interactions. The partitioning of the dyes between the polymer phase and the fluid phase was measured, and the partition coefficients are large (10⁴–10⁵). Thus, supercritical fluid dyeing is possible, although the solubility of the dyes in the fluid phase is low. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 911–919, 1998     

Solubility and diffusivity of CO2 in poly(l-lactide)-hydroxyapatite and poly(d,l-lactide-co-glycolide)-hydroxyapatite composite biomaterials

Solubility and diffusivity of supercritical CO₂ in poly(l-lactide)-hydroxyapatite (PLLA-HA) and poly(d,l-lactide-co-glycolide)-hydroxyapatite (PLGA-HA) composite materials were measured using a magnetic suspension balance at a temperature of 313 K and a pressures range of 10-30 MPa. The effect of the HA concentration on the solubility and diffusivity was investigated by varying filler content in the range of 0-50 wt%. For the PLLA-HA composites the solubility decreases with the increase of filler concentration. Diffusivity of the gas in the substrate is also lower as the HA content increases. In the case of PLGA-HA composites, small filler content favors the solubility and diffusivity of CO₂ due to incomplete wetting of the solid particles by the polymer. As the amount of HA increases solubility decreases. The results suggest that dense CO₂ could be used as a ‘green’ processing agent for composite biomaterials when organic solvents or high temperatures should be avoided.     

The physical solubilities and diffusivities of N<Subscript>2</Subscript>O and CO<Subscript>2</Subscript> in aqueous ammonia solutions on the additions of AMP,glycerol and ethylene glycol

Carbon dioxide (CO₂) is a major greenhouse gas, the emissions of which should be reduced. There are various technologies for the effective separation of CO₂. Of these, chemical absorption methods are generally accepted as the most effective. The monoethanolamine (MEA) process is an effective way to remove CO₂, but is an expensive option for the separation of CO₂ from massive gas-discharging plants. Therefore, ammonia solution, which is less expensive and more effective than MEA, was used for the removal of CO₂. In this study, the physical solubility of N₂O in (ammonia+water), (ammonia+2-amino-2-methyl-1-propanol+water), (ammonia+glycerol+water) and (ammonia+ ethylene glycol+water) was measured at 293, 303, 313, 323 K. Additive concentrations of 1, 3, and 5 wt% AMP, glycerol and ethylene glycol were added for each 9 wt% ammonia solution. A solubility apparatus was used to investigate the solubility of N₂O in ammonia solutions. The diffusivity was measured with a wetted wall column absorber. The “N₂O analogy” is used to estimate the solubility and diffusivity of CO₂ in the aqueous ammonia solutions. OriginPro 7.5 was used to correlate the solubility and diffusivity of N₂O in ammonia solutions. The parameters of the correlation were determined from the measured solubility and diffusivity.     

Solubility and diffusion behavior of compressed CO2 in polyurethane oligomer

In CO₂-assisted polyurethane (PU) foaming, the solubility and diffusion coefficient of CO₂ is vitally important to the cell nucleation and growth. This work is aimed at the effect of molecular weights (M _n) and crosslinking densities (V _e) on the solubility and diffusion coefficient of CO₂ in PU oligomers. A series of PU oligomers with different M _n and V _e were synthesized. The solubility and diffusivity of CO₂ in PU oligomers were measured experimentally in the temperature from 80 to 140 °C and with pressures up to 15 MPa. It was shown that the solubility and diffusion coefficients of CO₂ was decreased 20.5 and 21.0%, respectively, with the M _n increasing from 5864 to 153,754 g mol⁻¹ at 80 °C, 15 MPa. The solubility and the diffusion coefficient also decreased 11.1 and 38.0% as the V _e was increased from 64 to 1493 mol m⁻³. Furthermore, the diffusion mechanism of CO₂ in PU oligomers was explored via molecular dynamics simulations. The results indicated that the calculated diffusivity of CO₂ showed the same changing trend as the experimental values, and the smaller M _n or crosslinking degree contributed to an increase in fractional free volume and stronger polymer–CO₂ interactions. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47100.