{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:15:56Z","timestamp":1777713356232,"version":"3.51.4"},"reference-count":44,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,4,11]],"date-time":"2020-04-11T00:00:00Z","timestamp":1586563200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003407","name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["PON R&I FSE\u2013FESR 2014\u20132020"],"award-info":[{"award-number":["PON R&I FSE\u2013FESR 2014\u20132020"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010434","name":"\u201cla Caixa\u201d Foundation","doi-asserted-by":"publisher","award":["ID100010434"],"award-info":[{"award-number":["ID100010434"]}],"id":[{"id":"10.13039\/100010434","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010434","name":"\u201cla Caixa\u201d Foundation","doi-asserted-by":"publisher","award":["LCF\/BQ\/PR19\/11700011"],"award-info":[{"award-number":["LCF\/BQ\/PR19\/11700011"]}],"id":[{"id":"10.13039\/100010434","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["814804"],"award-info":[{"award-number":["814804"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100011889","name":"Diamond Light Source","doi-asserted-by":"publisher","award":["MT18768-2"],"award-info":[{"award-number":["MT18768-2"]}],"id":[{"id":"10.13039\/100011889","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The most widely used method to measure the transport properties of dense polymeric membranes is the time lag method in a constant volume\/pressure increase instrument. Although simple and quick, this method provides only relatively superficial, averaged data of the permeability, diffusivity, and solubility of gas or vapor species in the membrane. The present manuscript discusses a more sophisticated computational method to determine the transport properties on the basis of a fit of the entire permeation curve, including the transient period. The traditional tangent method and the fitting procedure were compared for the transport of six light gases (H2, He, O2, N2, CH4, and CO2) and ethane and ethylene in mixed matrix membranes (MMM) based on Pebax\u00ae1657 and the metal\u2013organic framework (MOF) CuII2(S,S)-hismox\u00b75H2O. Deviations of the experimental data from the theoretical curve could be attributed to the particular MOF structure, with cavities of different sizes. The fitting procedure revealed two different effective diffusion coefficients for the same gas in the case of methane and ethylene, due to the unusual void morphology in the MOFs. The method was furthermore applied to mixed gas permeation in an innovative constant-pressure\/variable-volume setup with continuous analysis of the permeate composition by an on-line mass-spectrometric residual gas analyzer. This method can provide the diffusion coefficient of individual gas species in a mixture, during mixed gas permeation experiments. Such information was previously inaccessible, and it will greatly enhance insight into the mixed gas transport in polymeric or mixed matrix membranes.<\/jats:p>","DOI":"10.3390\/computation8020028","type":"journal-article","created":{"date-parts":[[2020,4,13]],"date-time":"2020-04-13T04:45:31Z","timestamp":1586753131000},"page":"28","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Gas Transport in Mixed Matrix Membranes: Two Methods for Time Lag Determination"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8355-0141","authenticated-orcid":false,"given":"Alessio","family":"Fuoco","sequence":"first","affiliation":[{"name":"Institute on Membrane Technology, CNR-ITM, Via P. Bucci 17\/C, 87036 Rende (CS), Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8339-062X","authenticated-orcid":false,"given":"Marcello","family":"Monteleone","sequence":"additional","affiliation":[{"name":"Institute on Membrane Technology, CNR-ITM, Via P. Bucci 17\/C, 87036 Rende (CS), Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8561-1510","authenticated-orcid":false,"given":"Elisa","family":"Esposito","sequence":"additional","affiliation":[{"name":"Institute on Membrane Technology, CNR-ITM, Via P. Bucci 17\/C, 87036 Rende (CS), Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6524-3212","authenticated-orcid":false,"given":"Rosaria","family":"Bruno","sequence":"additional","affiliation":[{"name":"Dipartimento di Chimica e Tecnologie Chimiche (CTC), Universit\u00e0 della Calabria, 87036 Rende, Cosenza, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0987-2764","authenticated-orcid":false,"given":"Jes\u00fas","family":"Ferrando-Soria","sequence":"additional","affiliation":[{"name":"Departamento de Qu\u00edmica Inorg\u00e1nica, Instituto de Ciencia Molecular (ICMol), Catedr\u00e1tico Jos\u00e9 Beltr\u00e1n Mart\u00ednez, 2, Universidad de Valencia, 46980 Paterna, Spain"}]},{"given":"Emilio","family":"Pardo","sequence":"additional","affiliation":[{"name":"Departamento de Qu\u00edmica Inorg\u00e1nica, Instituto de Ciencia Molecular (ICMol), Catedr\u00e1tico Jos\u00e9 Beltr\u00e1n Mart\u00ednez, 2, Universidad de Valencia, 46980 Paterna, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8502-8074","authenticated-orcid":false,"given":"Donatella","family":"Armentano","sequence":"additional","affiliation":[{"name":"Dipartimento di Chimica e Tecnologie Chimiche (CTC), Universit\u00e0 della Calabria, 87036 Rende, Cosenza, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4538-6851","authenticated-orcid":false,"given":"Johannes Carolus","family":"Jansen","sequence":"additional","affiliation":[{"name":"Institute on Membrane Technology, CNR-ITM, Via P. Bucci 17\/C, 87036 Rende (CS), Italy"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"eaab0530","DOI":"10.1126\/science.aab0530","article-title":"Maximizing the right stuff: The trade-off between membrane permeability and selectivity","volume":"356","author":"Park","year":"2017","journal-title":"Science (80-)"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1038\/532435a","article-title":"Seven chemical separations to change the world","volume":"532","author":"Sholl","year":"2016","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"7809","DOI":"10.1021\/acs.macromol.7b01718","article-title":"50th Anniversary Perspective: Polymers and Mixed Matrix Membranes for Gas and Vapor Separation: A Review and Prospective Opportunities","volume":"50","author":"Galizia","year":"2017","journal-title":"Macromolecules"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1039\/C8EE02897D","article-title":"Simultaneous production of biomethane and food grade CO2 from biogas: An industrial case study","volume":"12","author":"Esposito","year":"2019","journal-title":"Energy Environ. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2733","DOI":"10.1039\/C9EE01384A","article-title":"Redefining the Robeson upper bounds for CO2 \/CH4 and CO2 \/N2 separations using a series of ultrapermeable benzotriptycene-based polymers of intrinsic microporosity","volume":"12","author":"Chen","year":"2019","journal-title":"Energy Environ. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1016\/j.memsci.2008.04.030","article-title":"The upper bound revisited","volume":"320","author":"Robeson","year":"2008","journal-title":"J. Memb. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/0376-7388(91)80060-J","article-title":"Correlation of separation factor versus permeability for polymeric membranes","volume":"62","author":"Robeson","year":"1991","journal-title":"J. Memb. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"8655","DOI":"10.1021\/acs.chemrev.8b00091","article-title":"Harnessing Filler Materials for Enhancing Biogas Separation Membranes","volume":"118","author":"Chuah","year":"2018","journal-title":"Chem. Rev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3154","DOI":"10.1002\/adfm.201505352","article-title":"Metal Organic Framework Crystals in Mixed-Matrix Membranes: Impact of the Filler Morphology on the Gas Separation Performance","volume":"26","author":"Sabetghadam","year":"2016","journal-title":"Adv. Funct. Mater."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"21381","DOI":"10.1021\/acsami.8b07045","article-title":"Molecular-Scale Hybrid Membranes Derived from Metal-Organic Polyhedra for Gas Separation","volume":"10","author":"Liu","year":"2018","journal-title":"ACS Appl. Mater. Interfaces"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"17086","DOI":"10.1038\/nenergy.2017.86","article-title":"Enhanced selectivity in mixed matrix membranes for CO2 capture through efficient dispersion of amine-functionalized MOF nanoparticles","volume":"2","author":"Ghalei","year":"2017","journal-title":"Nat. Energy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"8828","DOI":"10.1039\/c3ta10438a","article-title":"In Situ growth of metal-organic frameworks on a porous ultrafiltration membrane for gas separation","volume":"1","author":"Nagaraju","year":"2013","journal-title":"J. Mater. Chem. A"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Fuoco, A., Khdhayyer, R.M., Attfield, P.M., Esposito, E., Jansen, C.J., and Budd, M.P. (2017). Synthesis and Transport Properties of Novel MOF\/PIM-1\/MOF Sandwich Membranes for Gas Separation. Membranes, 7.","DOI":"10.3390\/membranes7010007"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1420","DOI":"10.1002\/pen.11041","article-title":"Mixed matrix membrane materials with glassy polymers. Part 1","volume":"42","author":"Mahajan","year":"2002","journal-title":"Polym. Eng. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1002\/pol.1985.180230703","article-title":"A comparative study of approaches applied to the permeability of binary composite polymeric materials","volume":"23","author":"Petropoulos","year":"1985","journal-title":"J. Polym. Sci. Polym. Phys. Ed."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/S0376-7388(97)00194-4","article-title":"Tailoring mixed matrix composite membranes for gas separations","volume":"137","author":"Zimmerman","year":"1997","journal-title":"J. Memb. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.memsci.2011.02.038","article-title":"Prediction of the relative permeability of gases in mixed matrix membranes","volume":"373","author":"Shimekit","year":"2011","journal-title":"J. Memb. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4980","DOI":"10.1021\/cr3003888","article-title":"Predictive models for mixed-matrix membrane performance: A review","volume":"113","author":"Kaliaguine","year":"2013","journal-title":"Chem. Rev."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Maxwell, J.C. (2010). A Treatise on Electricity and Magnetism, Cambridge University Press.","DOI":"10.1017\/CBO9780511709333"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0376-7388(95)00102-I","article-title":"The solution-diffusion model: A review","volume":"107","author":"Wijmans","year":"1995","journal-title":"J. Memb. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Yampolskii, Y., Pinnau, I., and Freeman, B. (2006). The Solution-Diffusion Model: A Unified Approach to Membrane Permeation. Materials Science of Membranes for Gas and Vapor Separation, John Wiley& Sons, Ltd.","DOI":"10.1002\/047002903X"},{"key":"ref_22","unstructured":"Crank, J. (1975). The Mathematics of Diffusion, Clarendon Press. [2nd ed.]."},{"key":"ref_23","first-page":"286","article-title":"The Process of Diffusion through a Rubber Membrane","volume":"97","author":"Daynes","year":"1920","journal-title":"Proc. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/S0376-7388(00)80165-9","article-title":"Kinetic analysis of transient permeation curves","volume":"13","author":"Amarantos","year":"1983","journal-title":"J. Memb. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2185","DOI":"10.1021\/j100538a010","article-title":"Experimental study of a simple anomalous diffusion system by time-lag and transient-state kinetic analysis","volume":"81","author":"Tsimillis","year":"1977","journal-title":"J. Phys. Chem."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1016\/j.memsci.2008.05.050","article-title":"On the permeation time lag for different transport equations by Frisch method","volume":"322","author":"Strzelewicz","year":"2008","journal-title":"J. Memb. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2408","DOI":"10.1063\/1.1733018","article-title":"Anomalous Polymer-Penetrant Permeation","volume":"37","author":"Frisch","year":"1962","journal-title":"J. Chem. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.memsci.2009.11.044","article-title":"Simulation of kinetic curves in mass transfer phenomena for a concentration-dependent diffusion coefficient in polymer membranes","volume":"349","author":"Follain","year":"2010","journal-title":"J. Memb. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/S0376-7388(02)00039-X","article-title":"Experimental evidence and implications of an imperfect upstream pressure step for the time-lag technique","volume":"207","author":"Favre","year":"2002","journal-title":"J. Memb. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Marko\u0161, J. (2011). Particularities of Membrane Gas Separation Under Unsteady State Conditions. Mass Transfer in Chemical Engineering Processes, InTech.","DOI":"10.5772\/659"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"117737","DOI":"10.1016\/j.memsci.2019.117737","article-title":"Transmembrane gas transfer: Mathematics of diffusion and experimental practice","volume":"601","author":"Beckman","year":"2020","journal-title":"J. Memb. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1134\/S2517751619030053","article-title":"Diffusion Transport of Water and Methanol Vapors in Polyvinyltrimethylsilane","volume":"1","author":"Shalygin","year":"2019","journal-title":"Membr. Membr. Technol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2839","DOI":"10.1002\/app.1970.070141117","article-title":"Isobaric measurement of gas permeability of polymers","volume":"14","author":"Yasuda","year":"1970","journal-title":"J. Appl. Polym. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.memsci.2018.04.029","article-title":"A novel time lag method for the analysis of mixed gas diffusion in polymeric membranes by on-line mass spectrometry: Method development and validation","volume":"561","author":"Fraga","year":"2018","journal-title":"J. Memb. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"8098","DOI":"10.1021\/jacs.7b03633","article-title":"Postsynthetic Approach for the Rational Design of Chiral Ferroelectric Metal\u2013Organic Frameworks","volume":"139","author":"Mon","year":"2017","journal-title":"J. Am. Chem. Soc."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5856","DOI":"10.1021\/acs.chemmater.9b01995","article-title":"Efficient Gas Separation and Transport Mechanism in Rare Hemilabile Metal\u2013Organic Framework","volume":"31","author":"Mon","year":"2019","journal-title":"Chem. Mater."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Monteleone, M., Esposito, E., Fuoco, A., Lan\u010d, M., Piln\u00e1\u010dek, K., Friess, K., Bezzu, C., Carta, M., McKeown, N., and Jansen, J.C. (2018). A Novel Time Lag Method for the Analysis of Mixed Gas Diffusion in Polymeric Membranes by On-Line Mass Spectrometry: Pressure Dependence of Transport Parameters. Membranes (Basel), 8.","DOI":"10.3390\/membranes8030073"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.memsci.2010.10.063","article-title":"Organic vapour transport in glassy perfluoropolymer membranes: A simple semi-quantitative approach to analyze clustering phenomena by time lag measurements","volume":"367","author":"Jansen","year":"2011","journal-title":"J. Memb. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/0950-4214(90)80030-O","article-title":"Correlation aspects of the selective gas permeabilities of polymeric materials and membranes","volume":"4","author":"Teplyakov","year":"1990","journal-title":"Gas. Sep. Purif."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Esposito, E., Bruno, R., Monteleone, M., Fuoco, A., Ferrando Soria, J., Pardo, E., Armentano, D., and Jansen, J.C. (2020). Glassy PEEK-WC vs. Rubbery Pebax\u00ae1657 Polymers: Effect on the Gas Transport in CuNi-MOF Based Mixed Matrix Membranes. Appl. Sci., 10.","DOI":"10.3390\/app10041310"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.polymer.2018.09.043","article-title":"Force spectroscopy determination of Young\u2019s modulus in mixed matrix membranes","volume":"156","author":"Longo","year":"2018","journal-title":"Polymer (Guildf)"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1811","DOI":"10.1002\/pol.1969.160071015","article-title":"Effect of immobilizing adsorption on the diffusion time lag","volume":"7","author":"Paul","year":"1969","journal-title":"J. Polym. Sci. Part A-2 Polym. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0376-7388(00)82136-5","article-title":"Effect of immobilizing adsorption on mass transport through polymer films","volume":"8","author":"Grzywna","year":"1981","journal-title":"J. Memb. Sci."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"20121","DOI":"10.1039\/C9TA07159H","article-title":"The origin of size-selective gas transport through polymers of intrinsic microporosity","volume":"7","author":"Fuoco","year":"2019","journal-title":"J. Mater. Chem. 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