The upper bound revisited

https://doi.org/10.1016/j.memsci.2008.04.030Get rights and content

Abstract

The empirical upper bound relationship for membrane separation of gases initially published in 1991 has been reviewed with the myriad of data now presently available. The upper bound correlation follows the relationship Pi=kαijn, where Pi is the permeability of the fast gas, αij (Pi/Pj) is the separation factor, k is referred to as the “front factor” and n is the slope of the log–log plot of the noted relationship. Below this line on a plot of log αij versus log Pi, virtually all the experimental data points exist. In spite of the intense investigation resulting in a much larger dataset than the original correlation, the upper bound position has had only minor shifts in position for many gas pairs. Where more significant shifts are observed, they are almost exclusively due to data now in the literature on a series of perfluorinated polymers and involve many of the gas pairs comprising He. The shift observed is primarily due to a change in the front factor, k, whereas the slope of the resultant upper bound relationship remains similar to the prior data correlations. This indicates a different solubility selectivity relationship for perfluorinated polymers compared to hydrocarbon/aromatic polymers as has been noted in the literature. Two additional upper bound relationships are included in this analysis; CO2/N2 and N2/CH4. In addition to the perfluorinated polymers resulting in significant upper bound shifts, minor shifts were observed primarily due to polymers exhibiting rigid, glassy structures including ladder-type polymers. The upper bound correlation can be used to qualitatively determine where the permeability process changes from solution-diffusion to Knudsen diffusion.

Introduction

The separation of gas mixtures employing polymeric membranes has been commercially utilized since the late 1970s. While the ability to separate gas mixtures was recognized much earlier, the commercial reality generated a significant amount of academic and industrial research activity. Membrane separation offers the advantage of low energy cost but has a high initial capital expense relative to the more established gas separation processes (e.g. adsorption and cryogenic distillation). With the increased cost of energy, membrane separation is reemerging as an economic option for various gas separations. Another area of emerging importance could be the recapture of CO2 from industrial processes for reuse or sequestration, and the key separation (CO2/N2) for this area is included in the upper bound analysis. The key parameters for gas separation are the permeability of a specific component of the gas mixture and the separation factor. It was recognized that these are trade-off parameters as the separation factor generally decreases with increasing permeability of the more permeable gas component. This trade-off relationship was shown to be related to an upper bound relationship where the log of the separation factor versus the log of the higher permeability gas yielded a limit for achieving the desired result of a high separation factor combined with a high permeability [1], [2] for polymeric membranes. The upper bound relationship was shown to be valid for a multitude of gas pairs including O2/N2, CO2/CH4, H2/N2, He/N2, H2/CH4, He/CH4, He/H2, H2/CO2 and He/CO2. The upper bound relationship is expressed by Pi=kαijn, where Pi is the permeability of the more permeable gas, α is the separation factor (Pi/Pj) and n is the slope of the log–log limit. It was observed that −1/n versus Δdji (where Δdji is the difference between the gas molecular diameters (dj  di)) yielded a linear relationship. This observation revealed that the diffusion coefficient governed the upper bound limits. Group contribution methods were noted to predict both permeability and separation factors for aromatic polymers and demonstrated the structure–property relationships to optimize membrane separation [3], [4], [5].

The empirical upper bound relationship was shown to be theoretically predicted by Freeman [6] yielding good agreement with the experimental data previously compiled. The value of −1/n was shown to be predicted by activation energy theory to be related to the gas molecular diameters by:1n=djdi21=dj+didi2(djdi)As the term in the square brackets is reasonably constant, the value of −1/n can be approximated by (dj  di) as demonstrated by the empirical relationship. The value of k was predicted by Freeman to be expressed by:k1/n=SiSjSi1/nexp1nbf1aRTwhere Si and Sj are the solubility constants, a has a universal value of 0.64, b has a value of 9.2 for rubbery polymers and 11.5 for glassy polymers and f is a constant dependant upon the polymer and chosen to be 12,600 cal/mol to provide the best fit of the upper bound data. The value of k is referred to as the front factor for the upper bound relationship.

The data utilized for the initial upper bound relationship was from studies listing permeability data on various polymers with limited emphasis on membrane separation. Since the publication of the upper bound concept, a significant number of studies have been directed towards achieving and exceeding the upper bound for various gas pairs. The published data on membrane separation since 1991 now well exceeds the data utilized in the initial correlation and thus provides an excellent comparison of the validity of the upper bound concept and progress towards optimizing the structure/property relationships. This paper will tabulate the data since the initial publication and compare these results versus the original empirical upper bound data. As would be expected, the increased emphasis on membrane separation and the improved structure/property understanding from experimental studies and group contribution approaches has resulted in a number of observations equal to and exceeding the original upper bound. The comment in the original paper [1] “As further structure/property optimization of polymers based on solution/diffusion transport occurs, the upper bound relationship should shift slightly higher. The slope of the line would, however, be expected to remain reasonably constant.” will be shown to be correct. The upper bound relationship is based on homogeneous polymer films and several approaches involving heterogeneous membranes have been demonstrated to easily exceed the upper bound. Surface modification is one method that clearly exceeds the upper bound limits as would be expected from the series resistance model as noted in an earlier paper [2]. UV surface modification [7], ion beam surface carbonization [8] and surface fluorination [9], [10] are among the viable surface modifications yielding such behavior. Another approach initially proposed by Koros and co-workers [11] is typically referred to as a mixed matrix approach where selective molecular sieving structures are incorporated into a polymeric membrane. The mixed matrix approach has been reported in many studies [12], [13], [14] with results exceeding upper bound behavior. Another approach involving carbon molecular sieving membranes produced by carbonization of aromatic polymer membranes [15], [16] also yields permselective properties well above the upper bound relationships. Molecular sieve membranes with well-defined uniform pore structure would, in essence, be considered to be the true upper bound limit for polymeric membranes. A recent paper on a novel approach to molecular sieving type structures [17] employed a solid-state thermal transformation of a polyimide to a benzooxazole-phenylene structure in the main chain yielding a material with remarkable CO2/CH4 separation. The thermal transformation yielded insoluble and infusible polymers with molecular sieving pore dimensions. Achievement of such molecular sieving structures in solution (or melt) processable polymeric membranes is presently not possible and the upper bound correlation is an empirical relationship demonstrating the state-of-the-art for approaching true molecular sieving structures. Heterogeneous membranes, surface modified membranes and molecular sieve membranes are not considered in the same class of polymeric materials employed for establishing the upper bound correlation. It should be noted that several of the polymers comprising points on or near the present empirical upper bound have structural characteristics (e.g. ladder-type polymers) that start approach molecular sieving type structures.

The initial publication on the upper bound allowed for a determination of the state-of-the-art limits for polymeric gas membrane separation. With a specific goal in focus, a large number of studies have resulted with the objective to find polymeric structures which exceeded the empirical upper bound limits. While only modest increases have been observed with some of the gas pairs, there have been gas pairs where important shifts have occurred as discussed in the following data review. The major surprise involves the unique characteristics of a series of perfluorinated commercial polymers relative to He based gas pairs. The importance of ladder-type rigid polymers was at least partly recognized earlier and several examples of these polymers have allowed shifts in the upper bound.

Section snippets

Upper bound relationships

The protocol chosen for data selection involved a similar procedure as noted in the original paper [1]. Data were chosen where the polymer data were utilized from the same study with the same experimental film preparation conditions. Generally these involve soluble (or melt) processible polymers. While the vast majority of the data in the literature appears correct, there are situations where errors have been observed. These can include experimental errors, manuscript errors (“typos”), and

O2/N2 upper bound relationship

The O2/N2 separation remains the most studied gas pair with more data existing in the literature than any of the other pairs. The myriad of data points shows an intensity just below the original upper bound with a few data points emerging above allowing for a new upper bound relationship (Fig. 1). The key points defining the new upper bound are tabulated in Table 1. The position of the one data point above the present upper bound (P(O2) = 18 barrers; α(O2/N2) = 9.0) is questioned as only one

CO2/CH4 upper bound relationship

The second most investigated gas pair for membrane separation is CO2/CH4. The myriad of data points since 1991 confirm the importance of this gas pair (Fig. 2). The ladder polymers (PIM-1 and PIM-7) noted above for O2/N2 separation also show good CO2/CH4 separation capabilities (Table 2). A series of rigid (also ladder-like) polymer variants has been recently published which exhibit even improved separation characteristics [17]. These polymers (TR (thermally rearranged)) comprising

H2/N2 upper bound relationship

The H2/N2 upper bound relationship is shown in Fig. 3 with the key data points listed in Table 3. Although a large amount of data has been generated since 1991, a very minor shift in the upper bound relationship is noted. Again the ladder polymers, PIM-1 and PIM-7 comprise points on the upper bound as with the two gas pairs noted above. The other polymers include polyimide variants at the low permeability end with poly(trimethylsilylpropyne) data points at the high permeability end of the upper

H2/CH4 upper bound relationship

The upper bound relationship for H2/CH4 is illustrated in Fig. 4 with the key data points tabulated in Table 4. As with H2/N2, only a modest shift in the upper bound position has been observed with a significant amount of data points just above the original upper bound. Polyimide variants comprise several of the upper bound positions at the low permeability end with poly(trimethylsilylpropyne) and variants at the high permeability end of the upper bound. Two perfluorinated polymers also have

He/N2 upper bound relationship

The upper bound relationship for He/N2 separation is shown in Fig. 5 with the relevant data points listed in Table 5. The upper bound shift since 1991 is very minor in spite of the much larger dataset available presently. Polypyrrolone and polyimide variants offer data setting the position of the upper bound at lower permeability with poly(trimethylsilylpropyne) data near the higher permeability section of the upper bound. The fluorinated polymer (Hyflon® AD) offers good separation at

He/CH4 upper bound relationship

The upper bound data for He/CH4 separation is illustrated in Fig. 6 with the key data points tabulated in Table 6. Polypyrrolone data comprise the upper bound positions at the lower permeability range with poly(trimethylsilylpropyne) data at the upper end of the permeability. The intermediate data points of interest are all fluorinated polymers as will be noted in many of the separations involving He. A reasonable shift in the front factor has occurred with virtually no change in slope with the

He/H2 upper bound relationship

The upper bound data for He/H2 is shown in Fig. 7 with the important data points tabulated in Table 7. A major change has occurred since the prior upper bound position was noted. This is exclusively due to the appearance of data involving perfluorinated polymers such as those listed in Table 7. Without these data, the upper bound would have virtually remained unchanged. It is of interest to note that one of the data points (Nafion® 117) was noted in the earlier reference but was a singular data

CO2/N2 upper bound relationship

In an earlier reference [2] it was noted that a clear correlation of CO2/N2 did not exist with the data plotted according to the upper bound protocol. Now it appears that sufficient data exists to show a correlation as shown in Fig. 8 with key data points listed in Table 8. Several of the important data points include the PIM-1 and PIM-7 noted above for several other gas pairs. It has been noted in the literature that polymers containing poly(ethylene oxide) units have interesting CO2/N2

N2/CH4 upper bound relationship

The N2/CH4 separation characteristics were not correlated in the previous papers [1], [2] although several more recent references have noted an upper bound relationship [50], [56]. Plotting the available data, an upper bound relationship is observed (Fig. 9) with important data points listed in Table 9. Most of the data points on or very near the upper bound are in the perfluorinated polymer family which are also noted for a number of the gas pairs in this paper which involve He. One data point

H2/CO2 upper bound relationship

The earlier upper bound relationship for H2/CO2 was published in Ref. [2]. The data compiled in this study are illustrated in Fig. 10 with key data points listed in Table 10. A limited shift in the upper bound relationship is noted, primarily a slight slope change resulting from a number of poly(trimethylsilylpropyne) data points at the higher permeability end of the relationship. The limited number of data points at the lower permeability area of the dataset may have skewed the slope versus

He/CO2 upper bound relationship

The initial He/CO2 upper bound relationship was from Ref. [2]. The present data are illustrated in Fig. 11 with important data positions tabulated in Table 11. A shift in position has been observed primarily due to the perfluorinated polymer data now in the literature. These polymers have generally resulted in front factor shifts for all gas pairs comprising He. Without these data only a very small change in the upper bound position would be observed.

Upper bound analysis

The key variables of the upper bound curves from the upper bound relationships (Pi=kαijn) are tabulated in Table 12 for the present upper bound data versus the prior upper bound data.

The slope of the upper bound, n, has been previously shown to be a linear relationship of −1/n versus dj  di. The gas diameter chosen was the Lennard-Jones kinetic diameter reported by Breck [65]. The present data versus prior data from Table 12 are illustrated in Fig. 12a and b. Overall, very minor differences are

Discussion of results

In many cases, the empirical upper bound relationship based on data available in 1991 has not significantly changed even though emphasis has been placed on structural modifications designed to improve the separation capabilities. Of the potential gas pairs comprising He, H2, O2, N2, CO2 and CH4, two additional pairs have been added to those already noted in prior papers [1], [2], namely, CO2/N2 and N2/CH4 both of which could have relevance in commercial applications. A previous attempt to

Conclusions

A review of the permeability data since 1991 when the initial upper bound relationship was proposed has been conducted to determine the shift in the upper bound position for various gas pairs chosen from combination of He, H2, O2, N2, CO2 and CH4. The results show only modest shifts from the 1991 upper bound correlation for O2/N2, H2/N2, H2/CH4, CO2/CH4 and He/N2. From the 1994 correlations of H2/CO2 and He/CO2, H2/CO2 shows only a minor change. Significant shifts in the position of the upper

References (72)

  • D. Sen et al.

    Development of polycarbonate based zeolite 4A filled mixed matrix gas separation membranes

    J. Membr. Sci.

    (2007)
  • C.W. Jones et al.

    Carbon molecular sieve gas separation membranes-I. Preparation and characterization based on polyimide precursors

    Carbon

    (1994)
  • Y.K. Kim et al.

    Preparation and characterization of carbon molecular sieve membranes derived from BTDA-ODA polyimide and their gas separation properties

    J. Membr. Sci.

    (2005)
  • G. Maier et al.

    Gas permeabilities of polymers with indan groups in the main chain. 2. Polyimides

    J. Membr. Sci.

    (1998)
  • F. Hamad et al.

    Performance of gas separation membranes made from sulfonated brominated high molecular weight poly(2,4-dimethyl-1,6-phenylene oxide)

    J. Membr. Sci.

    (2005)
  • P.M. Budd et al.

    Gas separation membranes from polymers with intrinsic microporosity

    J. Membr. Sci.

    (2005)
  • L. Yang et al.

    Gas permeation properties of thianthrene-5,5,10,10-tetraoxide-containing polyimides

    Polymer

    (2001)
  • L. Wang et al.

    Novel copolyimide membranes for gas separation

    J. Membr. Sci.

    (2007)
  • W.-H. Lin et al.

    Gas permeability, diffusivity, solubility, and aging characteristics of 6FDA-durene polyimide membranes

    J. Membr. Sci.

    (2001)
  • G. Polotskaya et al.

    Gas transport properties of polybenzoxazinoneimides and their prepolymers

    Polymer

    (2005)
  • M.E. Rezac et al.

    Transport and thermal properties of poly(ether imide)/acetylene-terminated monomer blends

    J. Membr. Sci.

    (1999)
  • K. Tanaka et al.

    Gas permeation and separation properties of sulfonated polyimide membranes

    Polymer

    (2006)
  • M. Macchione et al.

    Experimental analysis and simulation of the gas transport in dense Hyflon AD60X membranes: influence of residual solvent

    Polymer

    (2007)
  • I. Pinnau et al.

    Gas and vapor transport properties of amorphous perfluorinated copolymer membranes based on 2,2-bistrifluoromethyl-4,5-difluoro-1,3-dioxole/tetrafluoroethylene

    J. Membr. Sci.

    (1996)
  • J.H. Kim et al.

    Effects of CO2 exposure and physical aging on the gas permeability of thin 6FDA-based polyimide membranes. Part 1. Without crosslinking

    J. Membr. Sci.

    (2006)
  • J.H. Kim et al.

    Physical aging of thin 6FDA-based polyimide membranes containing carboxyl acid groups. Part I. Transport properties

    Polymer

    (2006)
  • M.T. Guzmán-Gutierrez et al.

    Gas transport properties of high free volume polyarylates based on isophthalic/terephthalic acid chloride mixtures

    J. Membr. Sci.

    (2007)
  • J.C. Jansen et al.

    On the unusual solvent retention and the effect on the gas transport in perfluorinated Hyflon® AD membranes

    J. Membr. Sci.

    (2007)
  • H. Lin et al.

    Gas solubility, diffusivity and permeability in poly(ethylene oxide)

    J. Membr. Sci.

    (2004)
  • C.J. Orme et al.

    Characterization of gas transport in selected rubbery amorphous polyphosphazene membranes

    J. Membr. Sci.

    (2001)
  • U. Senthilkumar et al.

    Polysiloxanes with pendent bulky groups having amino-hydroxy functionality: structure–permeability correlation

    J. Membr. Sci.

    (2007)
  • M.L. Cecopieri-Gomez et al.

    On the limits of gas separation in CO2/CH4, N2/CH4 and CO2/N2 binary mixtures using polyimide membranes

    J. Membr. Sci.

    (2007)
  • G. Illing et al.

    Towards ultrathin polyaniline films for gas separation

    J. Membr. Sci.

    (2005)
  • Y. Liu et al.

    Chemical cross-linking modification of polyimide membranes for gas separation

    J. Membr. Sci.

    (2001)
  • X.-Y. Wang et al.

    Cavity size distributions in high free volume glassy polymers by molecular simulation

    Polymer

    (2004)
  • Y. Huang et al.

    Physical aging of thin glassy polymer films monitored by gas permeability

    Polymer

    (2004)
  • Cited by (4742)

    View all citing articles on Scopus
    View full text