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Polymer Blends in Membrane Transport Processes Lloyd M. Robeson* Lehigh UniVersity (Adjunct Professor), Center for Polymer Science and Engineering, Materials Science and Engineering Department, 1801 Mill Creek Road, Macungie, PennsylVania 18062
Polymer blend technology and gas membrane separation have been two research areas where Prof. Don Paul has had major contributions. The combination of these topics has been chosen as the subject of this review paper. The morphology of phase separated polymer blends is an important variable in the design of enhanced transport properties. The fundamentals of polymer blends in transport processes will be discussed along with situations where polymer blends may be desired. These areas include barrier polymers, gas membrane separation, percolation networks for electrical conductivity, proton exchange membranes, and polymers employed in optoelectronic devices. The predictions of the series, parallel, Maxwell, and equivalent box models are applied where relevant to these examples. Introduction The subject of this paper was chosen to combine two of the major research areas of Prof. Don Paul into a single topic. Prof. Paul has been a leading global contributor to two important topics in polymer science and engineering in the past four decades; namely, polymer blends and membrane separation of gases.1–4 This author has been involved with these subjects in an industrial career5–8 and is well-aware of Don’s seminal contributions. In the field of polymer blends, several examples of significant contributions by Paul and co-workers deserve mention. The analog heat of mixing concept to predict the heat of mixing of high molecular weight polymers using low molecular weight analog compounds yielded a novel method for predicting miscibility in polymer blends from heat of mixing data.9 Such data cannot be directly determined on high molecular weight polymers as the viscous heating obscures experimental results. The mean field theory (also referred to as “specific rejection”) demonstrated another novel method for predicting miscibility windows in copolymers.10 This theory (also mentioned independently in other publications11,12) noted that intramolecular repulsion in copolymers could lead to situations where miscibility could be observed in blends with other homopolymers or copolymers. Paul and co-workers demonstrated the viability of this concept in many papers of which only a few are noted.13–15 In addition, Paul and co-workers reported many miscible blend combinations illustrating that polymer blend miscibility was more prevalent than initially expected In the area of polymer permeability and permselectivity, examples of highly cited contributions of Paul include description of gaseous diffusion using fluctuation theory,16 the derivation of the copolymer equation for copolymers with application to miscible blends,17 derivation of the solution-diffusion process relevant to reverse osmosis transport,18 and a group contribution method for glassy polymers with excellent correlation with experimental data.19 The experimental data from Paul and coworkers was noted to be a major contribution to the development of the empirical upper bound7 as well as in an updated version.8 A recent paper20 coauthored with Paul and several co-workers correlated the vast amount of experimental data that illustrated the relevance of the Freeman theory on the upper bound21 to * To whom correspondence should be addressed. E-mail: lesrob2@ verizon.net.
typical polymer data and allowed for a determination of a new set of kinetic diameters correlating with polymer permeability data. Fundamentals of Polymer Blends in Transport Processes. The most important aspect of polymer blends related to transport processes involves the phase behavior.22 The extremes of phase behavior (miscibility and phase separation) will be delineated in the following discussions of their predicted transport properties. In these discussions, permeability will be discussed as the primary transport property but thermal conductivity, electrical conductivity, ion conductivity, and proton conductivity follow the same relationships. The initial discussion will involve transport in miscible blends. Transport Properties of Miscible Blends. The key equation for predicting the permeability of miscible blends is ln Pb ) φ1 ln P1 + φ2 ln P2
(1)
where Pb, P1, and P2 are the permeability coefficients of the blend and components 1 and 2 (unblended). φ1 and φ2 are the respective volume fractions of components 1 and 2. This relationship has been shown to predict random copolymer permeability as a function of composition and has been employed for group contribution methodology.23,24 This equation was empirically proposed in early publications,25 and the theoretical derivation of this equation is attributed to Don Paul.17 With miscible polymers exhibiting strong specific interactions, deviation of experimental results from this relationship was predicted by Paul and demonstrated for several miscible blends.26–28 With specific interactions, densification occurs resulting in modest reduction of the diffusion coefficient and the solubility constants of the blend relative to the predicted logarithmic relationship for these variables. Transport Relationships for Phase Separated Blends. The relationships for phase separated blends are more complex as the blend composition changes from component 1 as the continuous phase to component 2 as the continuous phase. For intermediate compositions between the percolation limits, both components contribute to the continuous (and discontinuous) phase morphology. At the extremes of composition, the parallel and series models are often employed as upper and lower bounds of the expected transport behavior. These models are expressed by the following equations: Pb ) φ1P1 + φ2P2
10.1021/ie100153q 2010 American Chemical Society Published on Web 04/23/2010
parallel model
(2)
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Pb ) P1P2 /(φ1P2 + φ2P1)
series model
(3)
Another model commonly employed involves spheres of one component dispersed in a matrix of another component, and the permeability relationship is usually expressed by Maxwell’s equation:29
[
Pb ) Pm
Pd + 2Pm - 2φd(Pm - Pd) Pd + 2Pm + φd(Pm - Pd)
]
(4)
where b, m, and d represent the blend, the matrix phase, and the dispersed phase. This model predicts values slightly below and above the upper bound parallel model and the lower bound series model for the matrix phase and the dispersed phase, respectively. The parallel and series models and Maxwell’s model offer reasonable predictions where one phase is entirely the continuous phase at both ends of the composition range. In the intermediate compositions, these relationships do not apply. The best approach in the intermediate range is referred to as the equivalent box model (EBM) proposed by Kolarik30–32 and employing DeGennes percolation theory33 to predict the continuous and dispersed phase contributions. This model employs a combination of parallel and series model contributions to the phase separated blend. In the case of permeability, the equations for the EBM analysis are Pb ) P1φ1p + P2φ2p + φs2 /
[
φ2s φ1s + P1 P2
]
Figure 1. Combination of parallel and series contributions of the equivalent box model.
Figure 2. Illustration of generalized morphology for various conductivity or permeability models. (Reprinted with permission from ref 61. Copyright 2007 Elsevier.)
where φs ) φ1s + φ2s
(5)
where φ1p, φ2p, φ1s, φ2s, and φs are defined by the expressions φ1p ) [(φ1 - φ1cr)/(1 - φ1cr)]T1 ;
φ1s ) φ1 - φ1p
(6) φ2p ) [(φ2 - φ2cr)/(1 - φ2cr)]T2 ;
φ2s ) φ2 - φ2p
(7) where Pb, P1, and P2 are the respective permeabilities of the blend and components 1 and 2, φ1cr and φ2cr are the critical threshold percolation values of components 1 and 2. T1 and T2 are the critical universal exponents for the components. φ1cr, φ2cr, T1, and T2 can be considered adjustable parameters for fitting experimental data or universal parameters if the percolation theory is employed. For discrete spherical domains, φ1cr ) φ2cr ) 0.156 and T1 ) T2 ) 1.833 as predicted from DeGennes’s percolation theory33 (3-dimensional array). In the regions of low concentration where 0 < φ1 < φ1cr or (0 < φ2 < φ2cr); φ1p ) 0 and φ1s ) φ1 or (φ2p ) 0 and φ2s ) φ2). As with the parallel, series, and Maxwell’s models, thermal conductivity, K, and electrical, ion or proton conductivity, σ, can be substituted for permeability, P, in the above equations. The equivalent box model is illustrated in Figure 1 to show the combination of a series and parallel contribution to the overall permeability. The graphical illustration of the phase separated models is shown in Figure 2. The generalized permeability behavior of polymer blends predicted by the models discussed above is illustrated in Figure 3 for blends of polymer 1 with a permeability of 1 barrer and polymer 2 with a permeability of 100 barrers. As the data illustrates, the permeability data of the blend is very dependent upon the phase behavior and resultant morphology. Note that
Figure 3. Illustration of specific data applied to the models discussed above.
Figure 4. Illustration of cross-sectional morphology of unoriented versus biaxially oriented polymer blend.
the permeability value of barrers is typically employed in the literature as (1 barrer )10-10 cc (STP-cm/(cm2 s cm Hg))). An example of the application of these models to real examples involves the addition of low volume fractions of a barrier polymer to a matrix of a more permeable polymer. With biaxial orientation of the blend, the dispersed polymer goes from a spherical structure to a plateletlike morphology with the platelet oriented perpendicular to the transport direction as illustrated in Figure 4. This concept was the basis of barrier multicomponent films commercialized by DuPont (Selar) employing polyamide as the dispersed polymer and polyethylene as the matrix to yield a film or blow molded container with good barrier properties to both water and oxygen.34 The unoriented polymer blend can be modeled by the parallel or
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Figure 5. Upper bound data for O2/N2 membrane separation. (Reprinted with permission from ref 8. Copyright 2008 Elsevier.)
Maxwell’s model and the biaxially oriented polymer blend by the series model. As noted in Figure 3, the series model will yield a significantly lower permeability. For the series model to be relevant, the dispersed polymer phase aspect ratio should be high. Membrane Separation of Gases. A correlation of membrane separation data offering an analysis of the limits of polymer permselectivity is often referred to as the upper bound. The vast amount of data plotted as the log of the separation factor alpha (Rij ) Pi/Pj) versus the permeability of the more permeable gas (Pi) yields a linear line on this plot where virtually all the experimental data points are below the line.7,8 This empirical correlation has been predicted from basic permeability relationships by Freeman.21 Many of the data points employed for determining the empirical upper bound are from work reported by Paul and co-workers including values on the upper bound. The upper bound relationship for O2 and N2 membrane separation is illustrated in Figure 5. The upper bound model is only valid for homogeneous polymer films. It has been well-demonstrated that laminated films with different permeability values can yield values above the upper bound particularly if the individual component films exhibit upper bound properties. This is predicted from the series resistance model and is an inherent characteristic of surface modified films. Surface modification processes such as fluorination and fluorooxidation,35–37 UV exposure,38,39 ion beam exposure,40,41 plasma exposure,42 and chemical cross-linking43 have been of interest as the composite films often exhibit excellent permselectivity values with observations well above the upper bound. Miscible blends comprised of two upper bound polymers will have permselectivity properties on the upper bound at each composition assuming the blends follow the predictions of eq 1. The parallel model predicts permselectivity of phase separated polymers with upper bound properties to exhibit permselectivity values below the upper bound relationship at all compositions. It is of interest to determine how a typical phase separated blend will perform if comprised of two upper bound properties when the equivalent box model is utilized. This comparison is made with two values from the O2/N2 data (1) P(O2) ) 0.3028 barrers; P(N2) ) 0.02019 barrers; R(O2/N2) ) 15.0 and (2) P(O2) ) 152.9 barrers; P(N2) ) 30.58 barrers; R(O2/N2) ) 5.0. These values are arbitrarily chosen to
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Figure 6. Model predictions of blends of two upper bound polymers as superimposed on the upper bound plot (miscible blend model is also the upper bound line).
Figure 7. Model predictions of R(O2/N2) versus volume fraction of the lower permeability component.
illustrate situations similar to surface modification examples. The observed sensitivity of the comparison is a function of the distance between the upper bound points chosen. The results are illustrated in Figure 6 where the data are illustrated compared in the plot of R(O2/N2) versus P(O2). The results show that the EBM predictions show only interesting results (above the upper bound) at very low permeability where the low permeability polymer is entirely the continuous phase. The same data plotted as R(O2/N2) versus volume fraction is illustrated in Figure 7. This demonstrates that the EBM predictions yield values above the upper bound above the percolation threshold limit (>0.844 volume fraction) where the lower permeability polymer is entirely in the continuous phase. These results demonstrate that phase separated polymer blends will have limited utility in membrane separation applications unless the morphology can be attained where the lower permeability polymer exhibits complete continuous phase structure as predicted by the series resistance model. This is, of course, the case for surface modified polymers where the noted surface modifications often lead to greatly reduced permeability of a very thin layer. This is further illustrated in Figure 8 where the volume fraction of the surface modified layer is noted on the plot to demonstrate the desired position maximizing both
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Figure 8. Series resistance model applied to surface modification of a dense polymer film.
permeability and permselectivity as judged by the largest deviation from the upper bound curve. That value is between 0.002 and 0.005 volume fraction of the surface modified layer for the example shown. The results in Figure 8 are within the range of data reported in the literature for surface modification experiments where the surface modified layer can exhibit several orders of magnitude lower permeability than the unmodified polymer substrate. While these results may appear to be a obvious approach to enhancing the permselectivity of specific polymers and yield results well-above the upper bound, the practical limits of this approach, however, may be more of a problem. For membrane separation, the thickness of the dense membrane separating layer is usually in the range of 100 nm. At a 0.005 volume fraction, the surface modified layer would be 0.5 nm. In practice, surface modification processes often yield modified layers in the range of 100 nm. An example where this process has shown viability is with extremely highly permeable polymers such as poly(trimethylsilylpropyne) where surface modifications are in the range of 100 nm (such as fluorooxidation).35 The surface modified layer often involves crosslinking reactions that are conducted under solid-state conditions thus yielding highly nonequilibrium pore size and pore size distribution. These conditions could lead to a narrow pore size distribution more similar to molecular sieves than typically observed with polymer films with a more equilibrium relaxation of the chain dimensions during normal film preparation. An analysis of the cross-linked surface of a diamine cross-linked polyimide43 showed surface permselectivity higher than the upper bound. Mixed Matrix Membranes. Another area of interest in membrane separation involving phase separated systems is with mixed matrix membranes. These systems are polymer composites and not polymer blends, but they are worthy of discussion. The concept first proposed by Koros and co-workers44 involves the addition of molecular sieve particles (generally spherical) to a polymer matrix. It was noted in that reference that Paul and Kemp45 investigated a mixed matrix membrane of 5A zeolite in silicone rubber showing increased time lag but only modest changes in steady-state permeation. The molecular sieve
has properties well-above the upper bound relationship, and it has been shown with specific examples that these composites can exceed the upper bound. Further studies by Koros and coworkers and others are noted in refs 46–52. A review of mixed matrix membrane studies53 demonstrates significant activity in this area. Mixed matrix membranes are often modeled with Maxwell’s equation where the polymer is the matrix and molecular sieves are dispersed.44 It has been shown that modifications of Maxwell’s equation are often required to account for interfacial effects47 as well as molecular sieve pore blockage and polymer chain rigidification.54,55 A recent publication details the prediction of mixed matrix membrane permeability employing various theoretical models.56 The addition of molecular sieves to an upper bound polymer will be considered with two cases. The first case (which is the prominent case in experimental studies) involves spherical or low aspect ratio molecular sieves. The second (and idealized) case involves molecular sieving thin platelets with very high aspect ratio added to the polymer matrix transverse to the permeation direction. The first case will be modeled with Maxwell’s equation, and the second case will be modeled using the series resistance model. The molecular sieve transport data will be chosen to be the same as reported44 for zeolite 4A (P(O2) ) 0.77 barrers and R(O2/N2) ) 37.0). An intermediate point will be chosen for the polymer on the upper bound where P(O2) ) 1.0 barrers and thus R(O2/N2) ) 12.15. As Figure 9 illustrates, this approach can yield compositions above the upper bound relationship with the second case offering improved permselectivity over the conventional case. Molecular sieves with very high aspect ratio may be of interest in these studies. Percolation in Phase-Separated Polymer Blends. A unique feature of phase separated polymer blends is where the interface between the components constitutes a percolation network (at intermediate compositions of the blend). An area receiving interest has been with electrical conductivity. If a conductive particle concentrates at the interface, the threshold of conductivity can be at much lower levels than if dispersed in either unblended polymer. This was initially demonstrated by Gubbels et al.57,58 This behavior has also been observed with conductive
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Figure 11. Generalized behavior of water sorption (immersion) of emulsion cast films compared to solution cast films.
Figure 9. Prediction of molecular sieve addition to an upper bound polymer.
Figure 12. Upper bound relationship for proton exchange membranes. (Reprinted with permission from ref 61. Copyright 2007 Elsevier.)
Figure 10. Graphical comparison of well-dispersed conductive particles in a homogeneous polymer or blend and percolation at the interface in a phase separated polymer blend or cast emulsion film.
carbon black particles added to aqueous based emulsions where the carbon black will concentrate at the particle interfaces upon water evaporation.59 This concept is illustrated in Figure 10. Another example where the percolation concept yields significant differences between a homogeneous polymer or miscible blend and a phase separated blend involves the water sorption in emulsion cast films. Upon casting an emulsion film and devolatilization of water, the resultant morphology of a phase separated blend leaves an interface where the surfactant and water sensitive initiation fragments reside. For homogeneous or miscible blends, the interface disappears due to the diffusion of polymer molecules across the interface. With immersion of the dry samples in water, significant differences result. For the phase separated blend, the initial water sorption rate is quite high due to the influx of water into the percolated interfacial regions containing the water sensitive species. The peak water sorption is much lower than that for the homogeneous or miscible blends as the percolation pathway that permits water influx also allows the water sensitive species to diffuse out of the sample into the water phase shifting the equilibrium water
sorption. Solution cast films of the same polymer or blend without water sensitive species present shows a much lower equilibrium water sorption value. This generalized behavior is illustrated in Figure 11. Specific examples illustrating this behavior are noted in ref 60. Additional Polymer Blend Membrane Related Transport Processes. Proton conductivity in proton exchange membranes (PEMs) is a area of present intense investigation with the goal of maximizing proton conductivity while minimizing the water sorption of the membrane. While higher values of proton conductivity are offer observed with PEMs exhibiting high water sorption values, low water sorption is desired to limit the PEM swelling with varying operating conditions. Lower water sorption will reduce the membrane electrode assembly failure resulting from expansion and contraction of the membrane as the relative humidity changes. An empirical upper bound relationship has been noted where virtually all the experimental data lie below the relationship in a plot of log proton conductivity versus log water sorption.61 This is illustrated in Figure 12 for hydrogen based proton exchange membrane fuel cells (PEMFCs). While relevance may exist for direct methanol fuel cells (DMFCs), the analysis is only for hydrogen based fuel cells with water as the proton carrier phase. In the case of a polymer blend comprised of different points on the upper bound line, the models discussed show that the parallel model and also the equivalent box model yield desired values above the line expected for miscible blends or copolymers as illustrated in Figure 13. This behavior has also been noted experimentally in a paper where sulfonated poly(aryl ether ketone) blends with
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Figure 13. Model predictions for proton conductivity comprised of a low conductivity and a higher conductivity polymer blend. (Reprinted with permission from ref 61. Copyright 2007 Elsevier.)
polyetherimide where the sulfonated polymer was aligned parallel with the conduction direction in an electric field.62 The alignment of domain structures in a block copolymer comprising hydrated poly(styrene sulfonic acid) blocks showed anisotropic proton conductivity.63 Polymer blends have also been noted in lithium battery separator applications. While the vast majority of separators are based on microporous polymer membranes, gel polyelectrolyte layers and solid polyelectrolyte layers have been noted numerous times in the literature. A summary of polymer blend activity in this area has been noted in a recent polymer blends book.6 Another area where polymer blends have been investigated involve the optoelectronic applications for light emitting diodes, photovoltaic devices, and electrochromic applications also summarized in the noted book. With light emitting diodes, polymer blends offering improved performance over blend component values and achieving the proper color balance (including white light) have been noted in various publications. With photovoltaic devices, the combination of phase separated donor-acceptor polymer blends for heterojunctions in the light harvesting layer of the device has been an area of significant investigation. In this case, the heterojunction interface allows the photon absorption in the polymer creating an exciton which degenerates into a hole and an electron.64,65 The holes and electrons migrate to the appropriate electrode generating a current in the device. The phase separated morphology is desired to be cocontinuous presumably enhanced by a spinodal decomposition phase separation process. A review of polymer blends in optoelectronic applications is noted in ref 6. Summary Polymer membranes are utilized in a litany of applications involving transport processes including gas and liquid permeability, membrane separation processes, barrier polymers, lithium ion battery microporous membrane separators, proton exchange membranes for fuel cells, and ultrathin membranes employed in optoelectronic devices for hole and electron injection and transport as well as light emission (light emitting diodes) and light harvesting (photovoltaic devices). Polymer blends have been widely studied in these transport processes and in specific cases offer advantages over single component polymer systems. The phase behavior (and morphology) of phase separated polymer blends is the important variable related to the observed advantages. These cases are reviewed in this paper employing the relevant transport models typically utilized
to relate morphology with transport properties. One of the prime examples involves surface modification of gas separation membranes to yield permselectivity well-above the upper bound relationship as predicted by the series resistance model. In another example involving proton exchange membranes, enhanced performance is predicted (and observed experimentally) with morphology predicted by the parallel model. Percolation concepts are also discussed involving electrical conductivity enhancement and novel water transport in emulsion blends involving immiscible emulsion polymer components. The contributions to the literature involving polymer blends and permeability/permselectivity in polymeric membranes by Dr. Donald R. Paul has provided a significant background to the understanding of transport processes in polymeric materials. His leadership in polymer materials science is well-recognized worldwide both in academia as well as in industry. He has been an excellent educator as judged by the success of the students he has mentored. Most important, I and his many professional colleagues consider Don to be a friend with the highest level of professional ethics and behavior including a sincere passion and respect for the profession as well as its participants. Literature Cited (1) Paul, D. R., Newman, S., Eds.; Polymer Blends; Academic Press: New York, 1978; Vol. 1 and 2. (2) Paul, D. R., Bucknall, C. B., Eds.; Polymer Blends; John Wiley & Sons: New York, 2000; Vol 1 (Formulation) and Vol. 2 (Performance). (3) Paul, D. R., Yampol’skii, Y. P., Eds.; Polymeric Gas Separation Membranes; CRC Press: Boca Raton, 1994. (4) Paul, D. R.; Stannett, V. T.; Koros, W. J.; Lonsdale, H. K.; Baker, R. W. Recent Advances in Membrane Science and Technology. AdV. Polym. Sci. 1979, 32, 69. (5) Olabisi, O.; Robeson, L. M.; Shaw, M. T. Polymer-Polymer Miscibility; Academic Press: New York, 1979. (6) Robeson, L. M. Polymer Blends: A ComprehensiVe ReView; Hanser Gardner Publications: Cincinnati, 2007. (7) Robeson, L. M. Correlation of Separation Factor Versus Permeability for Polymeric Membranes. J. Membr. Sci. 1991, 62, 165. (8) Robeson, L. M. The Upper Bound Revisited. J. Membr. Sci. 2008, 320, 390. (9) Cruz, C. A.; Barlow, J. W.; Paul, D. R. The Basis for Miscibility in Polyester-Polycarbonate Blends. Macromolecules 1979, 12, 726. (10) Paul, D. R.; Barlow, J. W. A Binary Interaction Model for Miscibility of Copolymers in Blends. Polymer 1984, 25, 487. (11) Kambour, R. P.; Bendler, J. T.; Bopp, R. C. Phase Behavior of Polystyrene/Poly(2,6-dimethyl-1,4-phenylene oxide) and Their Derivatives. Macromolecules 1983, 16, 753. (12) ten Brinke, G.; Karasz, F. E.; MacKnight, W. J. Phase Behavior in Copolymer Blends: Poly(2,6-dimethyl-1,4-phenylene oxide) and HalogenSubstituted Styrene Copolymers. Macromolecules 1983, 16, 1827. (13) Chu, J. H.; Paul, D. R. Interaction Energies for Blends of SAN with Methyl Methacrylate Copolymer with Ethyl Acrylate and n-Butyl Acrylate. Polymer 1999, 40, 2687. (14) Gan, P. P.; Paul, D. R. Phase Behavior of Blends of Styrene/Maleic Anhydride Copolymers. J. Appl. Polym. Sci. 1994, 54, 317. (15) Nishomoto, M.; Keskkula, H.; Paul, D. R. Blends of Poly(styreneco-acrylonitrile) and Methyl Methacrylate Based Copolymers. Macromolecules 1990, 23, 3633. (16) DiBenedetto, A. T.; Paul, D. R. An Interpretation of Gaseous Diffusion Through Polymers Using Fluctuation Theory. J. Polym. Sci.: Part A 1964, 3, 1001. (17) Paul, D. R. Gas Transport in Homogeneous Multicomponent Polymers. J. Membr. Sci. 1984, 18, 75. (18) Paul, D. R. Reformulation of the Solution-Diffusion Theory of Reverse Osmosis. J. Membr. Sci. 2004, 241, 371. (19) Park, J. Y.; Paul, D. R. Correlation and Prediction of Gas Permeability in Glassy Polymer Membrane Materials via a Modified Free Voume Based Group Contribution Method. J. Membr. Sci. 1997, 125, 23. (20) Robeson, L. M.; Freeman, B. D.; Paul, D. R.; Rowe, B. W. An Empirical Correlation of Gas Permeability and Permselectivity in Polymers and its Theoretical Basis. J. Membr. Sci. 2009, 341, 178. (21) Freeman, B. D. Basis of Permeability/selectivity Tradeoff Relations in Polymeric Gas Separation Membranes. Macromolecules. 1999, 32, 375.
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ReceiVed for reView January 22, 2010 ReVised manuscript receiVed March 4, 2010 Accepted March 9, 2010 IE100153Q
