A lattice-based activity coefficient model for gas sorption in glassy polymers

Energetics of gas sorption in glassy polymers

A compressible lattice model with holes, the glassy polymer lattice sorption model (GPLSM), was used to model the sorption of carbon dioxide, methane, and ethylene in glassy polycarbonate and carbon dioxide in glassy tetramethyl polycarbonate. For glassy polymers, an incompressible lattice model, such as the Flory–Huggins theory, requires concentration‐dependent and physically unrealistic values for the lattice site volumes in order to satisfy lattice incompressibility. Rather than forcing lattice incompressibility, GPLSM was used and reasonable parameter values were obtained. The effect of conditioning on gas sorption in glassy polymers was analyzed quantitatively with GPLSM. The Henry's law constant decreases significantly upon gas conditioning, reflecting changes in the polymer matrix at infinite dilution. Treating the Henry's law constant as a hypothetical vapor pressure at infinite dilution, gas molecules in the conditioned polymer are less “volatile” than those in the unconditioned polymer. Flory–Huggins theory was used to model the sorption of carbon dioxide, methane, and ethylene in silicone rubber. Above the glass transition temperature, the criterion of lattice incompressibility for Flory‐Huggins theory was satisfied with physically realistic and constant values for the lattice site volumes. © 1992 John Wiley & Sons, Inc.

Mixed gas sorption in glassy polymers: Equipment design considerations and preliminary results

Analysis of dual-mode model parameters for gas sorption in glassy polymers

Theories and models are presented for gas sorption in polymers above and below the glass transition temperature. With the exception of predictive theories that do not represent the data well, the models are fit to data for the carbon dioxide/silicone rubber and carbon dioxide/polycarbonate systems for the purposes of comparison. During the past decade, a number of new models and theories have been proposed specifically for gas sorption in glassy polymers. Each new model attempts to incorporate aspects of the gas sorption process that are unique to polymers below the glass transition temperature. This review discusses these recent advances, the assumptions used in their development and their advantages and disadvantages.

ADVERTISEMENT RETURN TO ISSUEPREVArticleA lattice-based activity coefficient model for gas sorption in glassy polymers [Erratum to document cited in CA114(24):229894q]R. M. Conforti, T. A. Barbari, P. Vimalchand, and M. D. DonohueCite this: Macromolecules 1991, 24, 20, 5740Publication Date (Print):September 1, 1991Publication History Published online1 May 2002Published inissue 1 September 1991https://pubs.acs.org/doi/10.1021/ma00020a044https://doi.org/10.1021/ma00020a044research-articleACS PublicationsRequest reuse permissionsArticle Views21Altmetric-Citations-LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-AlertscloseSupporting Info (1)»Supporting Information Supporting Information Get e-Alerts

A molecular modeling investigation of dilation effects induced by sorbed gas molecules in two glassy polymers is presented. As experimental reference, integral sorption of CO2 and CH4 was measured for polysulfone (PSU) and a polyimide (6FDA‐TrMPD, PI4) at 308 K and a pressure of 10 bar. Simultaneously, the gas induced swelling effect was measured with a dilatometer based on a capacitive distance sensor recorded. The experimental evidence of the (on the observed time scale and concentration levels) elastic nature of the gas induced dilation is supported by the dilation and contraction behavior observed in molecular dynamics (MD) simulations of respective detailed atomistic packing models. These models were constructed in accordance with gas concentration levels obtained from the experimental sorption results. Quantitative deviations between simulated and measured dilations are discussed as a consequence of an anelastic response of the polymer matrix which is too fast to be resolved in the experiments whose kinetics is dominated by diffusional processes. In the simulation, the initial insertion of penetrant molecules into equilibrated packing models “circumvents” the slow diffusional process of the experiment and allows a reasonable representation of the dilation process as well as a closer investigation. Our simulation approach reveals a different behavior for PSU and PI4 on the corresponding time scale. Most likely, the different chain mobility of the two polymers is responsible for the respective response to the inserted amount of gas molecules which is discussed in terms of the different chain mobilities of the two polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 59–71, 2008

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTContinuous-site model for Langmuir gas sorption in glassy polymersGeorge H. Weiss, John T. Bendler, and Michael F. ShlesingerCite this: Macromolecules 1992, 25, 2, 990–992Publication Date (Print):January 1, 1992Publication History Published online1 May 2002Published inissue 1 January 1992https://doi.org/10.1021/ma00028a074RIGHTS & PERMISSIONSArticle Views139Altmetric-Citations25LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (372 KB) Get e-Alerts Get e-Alerts

Modeling of vapor sorption in glassy polymers using a new dual mode sorption model based on multilayer sorption theory

ABSTRACTAlthough gas sorption in glassy polymers is a well‐studied phenomenon, no general microscopical model is developed which is able to describe the gas sorption in a wide temperature range using only characteristics of polymer and gas molecule. In this work, sorption isotherms and desorption kinetics of O2, Ar, and N2 for glassy poly(ethyl methacrylate) have been measured in the temperature range from 160 to 308 K. To describe both the phenomena, the model is developed which postulates that, in the frozen structure of glassy polymer, any cavities between macromolecules are the sorption sites for small molecules. The cavities of small size can expand elastically to accommodate a gas molecule. The sorption sites are considered to be the potential wells and their depths are distributed according to Gaussian law. The concentration of sorption sites, their mean depth and depths dispersion, and the frequency of molecules oscillations in the sorption sites are the only parameters which determine both the gas transport and sorption. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018, 56, 288–296

The suitability of the Guggenheim–Anderson–De Boer (GAB) model for the parameterization of gas sorption isotherms and their dependences on temperature is explored. The GAB model implies that molecules adsorb on inner surfaces of the polymer in multilayers, which contrasts with the assumptions of the classical Dual Mode Sorption (DMS) model which implies the simultaneous occurrence of Henry-like dissolution and Langmuir's case I adsorption. The GAB model shows similar efficacy of the parameterization of the gas sorption isotherms in polymers as the DMS model. The isosteric heat of adsorption shows clear dependence on relative surface coverage for carbon dioxide sorption in cellulose acetate, polyethylene terephthalate, and the first polymer of intrinsic microporosity (PIM-1), thus allowing for the occurrence of adsorption multilayers. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014, 52, 1490–1495

Published in J. Polym. Sci. Part B; Polym. Phys. 52, 1490–1495 (2014) Page 1493, top: Table 1: The units for Ap were incorrectly given in kPa. The correct units should be 103 atm. Page 1495, bottom: Table A1: The units for Ap were incorrectly given in kPa. The correct units should be 103 atm. We apologize for any inconvenience this error may have caused.

A model of continuous-site distribution for gas sorption in glassy polymers is examined with sorption data of CO2 and Ar in polycarbonate. A procedure is presented for determining from a measured isotherm the number of sorption sites in a polymer, an important parameter that previously had to be assumed. With this parameter value and solubility data obtained at zero pressure, the model can reasonably predict sorption isotherms of CO2 in glassy polycarbonate for a wide temperature range. The number of sorption sites and the average site volume evaluated from CO2 sorption isotherms are employed for the prediction of Ar sorption isotherms with zero-pressure solubility data and the independently measured partial molar volume of Ar. A reasonable fit to the measured isotherms of Ar is achieved. With the proposed procedure, the continuous-site model shows several advantages over the conventional dual-mode sorption model. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 883–888, 2000

A model of continuous-site distribution for gas sorption in glassy polymers is examined with sorption data of CO2 and Ar in polycarbonate. A procedure is presented for determining from a measured isotherm the number of sorption sites in a polymer, an important parameter that previously had to be assumed. With this parameter value and solubility data obtained at zero pressure, the model can reasonably predict sorption isotherms of CO2 in glassy polycarbonate for a wide temperature range. The number of sorption sites and the average site volume evaluated from CO2 sorption isotherms are employed for the prediction of Ar sorption isotherms with zero-pressure solubility data and the independently measured partial molar volume of Ar. A reasonable fit to the measured isotherms of Ar is achieved. With the proposed procedure, the continuous-site model shows several advantages over the conventional dual-mode sorption model. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 883–888, 2000

A thermodynamic framework for the analysis of gas sorption in glassy polymers is established in the limit of low sorption levels. The results represent an extension of the Flory‐Huggins theory to materials with nonzero internal energy changes due to deformation; the Flory‐Huggins theory is recovered in the limit of zero polymer bulk modulus. The sorption isotherm is expressed in terms of the penetrant vapor‐phase activity, polymer physical properties, the penetrant partial molar volume, and the heat of mixing. The qualitative form of the isotherm is shown to be unrelated to the presence of excess free volume in the polymer; only quantitative predictions are influenced. The downward curvature of the isotherm is due to the thermodynamics of solid deformation. Explicit relationships between the parameters of this work and the dual‐mode model are given for the low‐sorption/high‐bulk modulus limit.