Evidence of dual mobility in sulfur dioxide‐polyarylate system: An integral sorption analysis

Ranade, G. R.; Chandler, Robin R.; Plank, Charles A.; Laukhuf, Walden L. S.

doi:10.1002/pen.760250304

Cited by 9 publications

(6 citation statements)

References 13 publications

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“…All sorption isotherms are concave to the pressure axis, which were as expected on the basis of the typical behavior of glassy amorphous polymers and of the dual mode sorption model. Penetrants sorbed in Henry’s sites ( C D ) is believed to be same as gas dissolution in a rubbery polymer, while penetrants sorbed in Langmuir sites ( C H ) has a capacity limit due to a hole-filling process behavior. ,,− ,, …”

Section: Resultsmentioning

confidence: 99%

“…It is well-known that solubility is determined by (1) the inherent condensability of the penetrant, (2) the polymer−penetrant interactions, and (3) the amount and distribution of excess free volume in the glassy polymer. [13][14][15][16][17][18][19][20][21][22]28,29,[34][35][36][37][38][39][40]48 In this study, Figure 2 shows the sorption isotherms as a function of CH 4 , CO 2 , C 3 H 8 , and C 3 H 6 and their pressures at 35 °C. All sorption isotherms are concave to the pressure axis, which were as expected on the basis of the typical behavior of glassy amorphous polymers and of the dual mode sorption model.…”

Section: Resultsmentioning

confidence: 99%

“…Therefore, the total sorption ( C ) is written as C = C normalD + C normalH = k normalD p + C normalH ′ b p 1 + b p where C is the concentration of the gas sorbed in the polymer with a unit of gas volume (cm 3 ) per polymer volume (cm 3 ), p (atm) is the pressure of the feed gas in contact with the polymer, C D and C H are the concentrations of the gas penetrant sorbed at the Henry sites and Langmuir sites, respectively, k D is the Henry’s law constant indicating gas dissolution into the equilibrium-defined polymer matrix, C H ′ is the Langmuir capacity of the glassy polymer that is related to the unrelaxed volume, which is a measure of the departure from equilibrium in the glassy state, and b is the Langmuir affinity parameter describing the affinity of the gas to a Langmuir site. The Langmuir capacity can be viewed as a measurement of the excess free volume of a polymer. − ,,,− The solubility coefficient ( S ) of a gas in a glassy polymeric membrane is described as the ratio of the equilibrium gas concentration to the applied gas pressure, as written in eq : S = C p = k normalD + C normalH ′ b 1 + b p Gas sorption may display an unusual isotherm if a gas is polar in nature and highly condensable. Since one can conduct the gas sorption isotherm experimentally, the three dual-mode sorption parameters ( k D , C H ′ , and b ) can be obtained by curve fitting using a nonlinear least-squares method. − …”

Section: Introductionmentioning

confidence: 99%

“…The Langmuir capacity can be viewed as a measurement of the excess free volume of a polymer. − ,,,− The solubility coefficient ( S ) of a gas in a glassy polymeric membrane is described as the ratio of the equilibrium gas concentration to the applied gas pressure, as written in eq : S = C p = k normalD + C normalH ′ b 1 + b p Gas sorption may display an unusual isotherm if a gas is polar in nature and highly condensable. Since one can conduct the gas sorption isotherm experimentally, the three dual-mode sorption parameters ( k D , C H ′ , and b ) can be obtained by curve fitting using a nonlinear least-squares method. − …”

Section: Introductionmentioning

confidence: 99%

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Permeability, Solubility, Diffusivity, and PALS Data of Cross-linkable 6FDA-based Copolyimides

Askari

Chua

Chung

2014

Ind. Eng. Chem. Res.

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The intrinsic gas transport properties of thermally treated cross-linkable 6FDA-based copolyimide membranes have been studied. Grafting various sizes of cyclodextrin (CD) to the copolyimide matrix and then thermally decomposing CD at elevated temperatures are an effective method to micromanipulate microvoids and free volume as well as gas sorption and permeation. The pressure-dependent solubility and permeability coefficients were found to follow the dual-mode sorption model and partial immobilization model, respectively. Solubility and permeability coefficients of CH 4 , CO 2 , C 3 H 6 , and C 3 H 8 were conducted at 35 °C for different upstream pressures. The Langmuir saturation constant, C H ′ , increases with an increase in annealing temperature. On the other hand, Henry's solubility coefficient k D and Langmuir affinity constant b do not change noticeably. The CH 4 permeability decreases with pressure, while some membranes exhibit serious plasticization with an increase in CO 2 , C 3 H 6 and C 3 H 8 pressures. The diffusivity coefficient of the Henry mode (D D ) and Langmuir mode (D H ) were calculated from the permeability and solubility data and their ratio, F, is higher for membranes thermally treated at 425 °C than those treated at 200 °C. Data from positron annihilation lifetime spectroscopy (PALS) confirm that free-volume and the number of micropores increases while the radius of pore sizes decreases during the high temperature annealing process. All CD grafted membranes thermally treated at 425 °C have almost equal or lower solubility selectivity than the original membrane for CO 2 / CH 4 and C 3 H 6 /C 3 H 8 separations but the former has much higher diffusion selectivity than the latter. As a result, diffusion selectivity plays a more important role than solubility in determining the permselectivity of the CD grafted membranes thermally treated at 425 °C.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Permeability, Solubility, Diffusivity, and PALS Data of Cross-linkable 6FDA-based Copolyimides

Askari

Chua

Chung

2014

Ind. Eng. Chem. Res.

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“…Gas sorption may display an unusual isotherm if a gas is polar in nature and highly condensable. Since gas sorption isotherm can be experimentally performed, the three dual-mode sorption parameters (k D , C' H , and b) can be obtained by the curve fitting using a nonlinear least squares method [32][33][34][35][36][37][38].…”

Section: Theory and Background 21 Dual-mode Sorption Modelmentioning

confidence: 99%

CO2/CH4 Sorption Behavior of Glassy Polymeric Membranes Based on Dual Mode Sorption Model

Askari¹

2017

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Among the various transport models for gas separation via membrane, the best description is done by solution-diffusion model. The main parameters of this model are the sorption and diffusion of the penetrant through the membrane. Studies conducted by various researchers in the field of gas separation indicate that the thermodynamic interaction (sorption effects) in glassy polymers has the major role in the diffusivity, permeability, and selectivity of the membrane, especially in the multi-component gas mixture. In glassy polymers, dual-mode sorption model is frequently used to describe the equilibrium sorption behavior of a polymer-gas system and, based on this sorption model; the permeation behavior is described by the partial immobilization model. In this study, the difference between the sorption mechanism of CO2 and CH4 in glassy polymeric membranes was analyzed by separating the sorption mode and introducing P50/50 parameter (the pressure at which the contribution of both Henry and Langmuir sorption is equal), which was done using the available experimental data in the scientific references for the sorption values of CO2 and CH4. The contribution of the sorbed molecules in Henry and Langmuir sites was investigated and its changes with pressure were evaluated for CO2 and CH4 permeation. This study was also attempted to provide a correct definition of F factor, used in references, in the form of the multiplication of mobile concentration ratios (CHmobile/CH) by the diffusivity coefficients in two modes (DH/DD).

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Numerical examination of the dual‐mode sorption model for sorption rate experiments with an extension for a mobile langmuir component

Riedl

Spencer

1990

J of Applied Polymer Sci

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SynopsisNumerical methods were applied to the dual-mode sorption model for sorption rate experiments with an immobilized Langmuir component over broad ranges of polymer characteristics and experimental conditions. The variation of the diffusion coefficient evaluated using a single scaling procedure was examined. The numerical procedure was also applied to the model for infinite volume sorption and to sorption allowing for mobility of the Langmuir component of the penetrant.

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Evidence of dual mobility in sulfur dioxide‐polyarylate system: An integral sorption analysis

Cited by 9 publications

References 13 publications

Permeability, Solubility, Diffusivity, and PALS Data of Cross-linkable 6FDA-based Copolyimides

Permeability, Solubility, Diffusivity, and PALS Data of Cross-linkable 6FDA-based Copolyimides

CO2/CH4 Sorption Behavior of Glassy Polymeric Membranes Based on Dual Mode Sorption Model

Numerical examination of the dual‐mode sorption model for sorption rate experiments with an extension for a mobile langmuir component

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