@article{85afc8f8c10f44e0b7cf186e7ae5cf63,
title = "Modeling water diffusion in polybenzimidazole membranes using partial immobilization and free volume theory",
abstract = "This study extends previous work on modeling water sorption, dilation, and diffusion in polybenzimidazoles (PBIs) by comparing water transport properties of commercial PBI (Celazole{\textregistered}) with three sulfone-containing PBIs. A model is developed combining free volume and partial immobilization theories to describe water diffusion coefficients across a wide range of concentrations and degrees of swelling. Water vapor sorption and dilation follow dual-mode behavior and generally correlate with the availability of strong hydrogen bonding sites on the polymer chains. At low concentrations, water diffusion coefficients are suppressed by partial immobilization of Langmuir species, while at high concentrations, water diffusion coefficients increase due to significant swelling and plasticization. To account for the influence of plasticization on free volume and water mobility, local Henry's law mobility coefficients are correlated with fractional free volume (FFV), where the volume occupied by water molecules is considered to contribute to dynamic free volume and is assumed to be as accessible for water diffusion as unoccupied free volume. Contributions to diffusion coefficients from thermodynamic and convective frame of reference effects and concentration averaging are also considered.",
keywords = "Diffusion, Free volume, Partial immobilization, Plasticization, Polybenzimidazole",
author = "Moon, \{Joshua D.\} and Michele Galizia and Hailun Borjigin and Ran Liu and Riffle, \{Judy S.\} and Freeman, \{Benny D.\} and Paul, \{Donald R.\}",
note = "Funding Information: Local mobility coefficients, Lloc, which represent a weighted average of Henry's law and Langmuir mobilities, also increase with concentration and follow a similar trend with concentration as FFV. Local diffusion coefficients, Dloc, follow similar trends with concentration as local mobilities with the exception of downwards curvature at average concentrations around 25?50 cm3(STP)/cm [3]. This behavior is most evident for TADPS-OBA (cf., Fig. 8). Local diffusion coefficients are about 1?3 times greater than local mobility coefficients due to additional thermodynamic contributions to diffusion (i.e., Q). Q ranges from 1 to about 3, with values around unity at zero concentration, increasing to a maximum of 2.5?3 at average concentrations around 25?50 cm3(STP)/cm [3], then decreasing to values around 1.2?1.5 at high concentrations (see supporting information). Similar trends have been observed for methanol in Celazole? and CO2 in PET [80,81]. This behavior suggests strong water-polymer interactions enhance diffusion at low concentrations, as values of Q greater than unity often indicate favorable penetrant-polymer interactions [80,90]. TADPS-IPA and TADPS-OBA have only slightly higher values of Q than TADPS-TPA and Celazole?. This behavior suggests the higher diffusion coefficients of TADPS-IPA and TADPS-OBA relative to TADPS-TPA and Celazole? are due primarily to increases in mobility from enhanced chain flexibility and not primarily from enhanced sorption thermodynamics.The materials, supplies, conference travel, and a portion of B.D.F.?s time was supported by the U.S. Department of Energy Office of Science, Office of Basic Energy Sciences under Award Number DE-FG02?02ER15362. B.D.F.?s role in supervising the research from January to July 2017 was partially supported by the Australian-American Fulbright Commission for the award to B.D.F of the U.S. Fulbright Distinguished Chair in Science, Technology and Innovation sponsored by the Commonwealth Scientific and Industrial Research Organization (CSIRO). J.D.M's work on this research project was supported in part by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1610403. Funding Information: The materials, supplies, conference travel, and a portion of B.D.F.{\textquoteright}s time was supported by the U.S. Department of Energy Office of Science, Office of Basic Energy Sciences under Award Number DE-FG02–02ER15362 . B.D.F.{\textquoteright}s role in supervising the research from January to July 2017 was partially supported by the Australian-American Fulbright Commission for the award to B.D.F of the U.S. Fulbright Distinguished Chair in Science, Technology and Innovation sponsored by the Commonwealth Scientific and Industrial Research Organization (CSIRO). J.D.M{\textquoteright}s work on this research project was supported in part by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1610403 . Publisher Copyright: {\textcopyright} 2020 Elsevier Ltd Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = feb,
day = "17",
doi = "10.1016/j.polymer.2020.122170",
language = "English",
volume = "189",
journal = "Polymer",
issn = "0032-3861",
publisher = "Elsevier",
}