(562a) a Comprehensive Analysis of Gas Sorption and Transport in Thermally Rearranged Polymers
Michele Galiziaâ¡, Kevin A. Stevens, Zachary P. Smithâ, Donald R. Paul, Benny D. Freeman
J.McKetta Department of Chemical Engineering, 200 E. Dean Keeton Street, 78712 Austin,
and Center for Energy and Environmental Resources, 10100 Burnet Road, 78758 Austin,
The University of Texas at Austin, Texas (USA)
â¡ Permanent address: Department of Chemical, Biological and Materials Engineering, 100 E. Boyd St., 73019 Norman, University of Oklahoma, OK (USA)
â Permanent address: Department of Chemical Engineering, 25 Ames St., 02142 Cambridge, Massachusetts Institute of Technology, MA (USA)
Thermally Rearranged polymers based on PBOs (poly benzoxazoles)  are a class of materials endowed with outstanding separation performance, which abundantly surpass the 2008 Robeson upper bound . As recently reported by Robeson et al. , the outstanding behavior exhibited by TR polymers, uncommon among glassy polymers, derives from a special combination of high gas diffusivity, high gas solubility and high diffusivity-selectivity. In this study, these experimental findings were rationalized on theoretical basis using the Non-equilibrium thermodynamics of glassy polymers . First, solubility, diffusivity and permeability coefficients for H2, N2, CH4, and CO2 in several TR polymers and their polyimide precursor, HAB-6FDA, were measured in a wide temperature (-10 to 50°C) and pressure (up to 32 atm) range. At fixed temperature, gas solubility, diffusivity and permeability coefficients increased with increasing extent of thermal conversion [5,6].
To investigate the molecular origin of the change in gas sorption behavior with increasing TR conversion, the enthalpic and the entropic contributions to the solubility coefficient were calculated. The increase in gas solubility with increasing TR conversion is essentially due to an increase in the entropic contribution, with the enthalpic counterpart being barely affected by thermal conversion. Thus, the increase in gas transport properties observed in TR samples relative to HAB-6FDA polyimide is essentially due to an increase of excess, non-equilibrium fractional free volume. Such analysis justifies the high gas solubility, diffusivity and permeability coefficients exhibited by TR polymers .
A theoretical analysis of gas permeability and diffusivity was also performed. Experimental permeability data were described using the solution-diffusion model. Specifically, solubility coefficients were predicted using the non-equilibrium lattice fluid (NELF) model, and diffusion coefficients were expressed as the product of a mobility factor, L, which was assumed to vary exponentially with concentration, and a thermodynamic factor, which was calculated using the NELF model [4,7]. Interestingly, the mobility factor correlates with the penetrant critical volume,VC , according to the equation:
Â L = k/(VC)Î·
Polymers having large values of Î· exhibit stronger size sieving ability than polymers with smaller values of Î·. TR polymers exhibit greater values of Î· than other glassy polymers, which suggests that the former have stronger size sieving ability than conventional polymers. This result fully agrees with the experimental findings reported by Robeson et al. . The high size sieving ability shown by TR polymers derives from a favorable size and distribution of free volume cavities. This conclusion is supported by PALS analysis and Monte Carlo simulations . So, coalescence of smaller free volume cavities to form larger cavities is believed to take place during conversion of polyimides to PBOs.
 H.B. Park et al., Science 2007 318 254
 L.M. Robeson, J. Membr. Sci. 2008 320 390
 L.M. Robeson et al., J. Membr. Sci. 2017 525 18
 F. Doghieri et al., Macromolecules 1996 29 7885
 K.A. Stevens et al., J. Membr. Sci. 2017, accepted
 M. Galizia et al., Macromolecules 2016 49 8768
 G.C. Sarti et al., J. Membr. Sci. 2013 43 176
 Y. Jiang et al., Polymer 2011 52 2244