Some approaches for high performance polymer based membranes for gas separation: block copolymers, carbon molecular sieves and mixed matrix membranes

Abstract

The intrinsic characteristics of a membrane process, i.e. efficiency and operational simplicity, high selectivity and permeability for the transport of specific components, compatibility between different membrane operations in integrated systems, low energetic requirements, easy control and scale-up, and high operational flexibility, might be decisive factors in imposing membrane processes in most gas separation fields. This review highlights the research hardware in membrane gas separation, i.e. the membrane material. Emphasis has been devoted to three interesting and important membrane classes for gas separation: block copolymer membranes, carbon membranes and mixed matrix membranes.

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1 Introduction

Gas separation occupies a central position in the chemical feedstock industry:¹ oxygen and nitrogen enrichment of air, hydrogen recovery, natural gas separation and removal of volatile compounds from effluent streams are all current applications. Gas separation by membranes has acquired great economic importance because of its energy efficiency. Some typical examples of membrane gas separations are summarized in Table 1. In particular, the non-cryogenic nitrogen production and hydrogen purification are already present at the industrial level.²

Table 1 Current applications of gas separation membranes

Gas to be separated	Gas pair	Application
a HC = hydrocarbons.
H2	H2/N2	Hydrogen recovery from ammonia purge gas
	H2/HC^a	Refinery hydrogen recovery
	H2/CO,CO2	Synthesis gas ratio adjustment
	H2/CO2	Fuel cells
Air	O2/N2	Oxygen-enriched air for combustion
Acid gases	CO2/CH4	Natural gas sweetening
	H2S/CH4	Sour gas sweetening
	CO2/N2	Digester gas treatment
Drying	H2O/HC^a	Hydrocarbon drying
	H2O/air	Air drying
Hydrocarbons	HC/air	Pollution control; stack gas or solvent recovery
	HC/N2	Upgrading low-BTU gas
Helium	He/HC^a	Helium recovery from gas wells
	He/N2	Helium recovery from diving air

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A MIT (Massachusetts Institute of Technology) study of 2007 predicts that global CO₂ emissions from coal combustion will increase from 9 GTon/year in 2000 to 32 GTon/year in 2050 (55% of projected global CO₂ emissions at that time). Therefore, CO₂ separation by membranes is a great challenge for scientists worldwide.

One way to reduce CO₂ emissions from the atmosphere is carbon capture and sequestration (CCS), i.e. CO₂ is captured from power plant emissions and sequestrated underground in geological structures for long periods of time. Membrane processes have been suggested previously for CO₂ capture from flue gas. Hendricks et al.³ reported as early as 1989 that commercial gas separation membranes available at that time were not competitive with absorption techniques for flue gas treatment.

Recent feasibility studies by Favre and co-workers have rekindled interest in using membranes for CO₂ capture from flue gas.^4,5 Another interesting analysis has been carried out by Merkel et al.⁶ The results for H₂ and CO₂ selective membranes show that by using state-of-the-art membranes (CO₂/H₂ selectivity 15.5, H₂/CO₂ selectivity 5.9), the current requirements concerning CO₂ purity and CO₂ separation degree cannot be fulfilled. A CO₂/H₂ selectivity of 150 for a single CO₂ selective membrane would be needed to obtain power plant efficiency losses below 10% points with separation degrees above 85%. For a cascade concept the needed CO₂/H₂ selectivity would have to be of the order of 60 to achieve the same values. For H₂ selective membranes with a H₂/CO₂ selectivity of 50, separation degrees of 85% at efficiency losses below 10% points can be reached.

Natural gas processing represents the largest market for industrial gas separation processes, and equipment and membrane-based removal of natural gas contaminants is growing faster than any other segment of the membrane gas separation business.²

The oxygen-enriched air produced by membranes has been used in various fields, including chemical and related industries, the medical field, food packaging, etc. In industrial furnaces and burners, for example, injection of oxygen-enriched air (25–35% oxygen) leads to higher flame temperatures and reduces the volume of parasite nitrogen to be heated; this means lower energy consumption. Industrial nitrogen is used in the chemical industry to protect fuels and oxygen-sensitive materials. Membranes today dominate the fraction of the nitrogen market for applications of less than 50 tons/day and relatively low purity (0.5–5% O₂).² What advances have there been in terms of research of membrane materials for the gas separations listed in Table 1?

There are various and interesting opportunities because a vast array of potential materials can be considered as membranes. In this review, the attention has been focused on three promising classes of membrane materials, which are attractive for the gas separation membrane market in terms of performance, reproducibility, processability and cost: carbon molecular sieves (CMSs), block copolymers and mixed matrix membranes (MMMs).

In the case of CMSs, one major disadvantage that hinders their commercialization is their brittleness, meaning they require careful handling. This may be prevented to a certain degree by optimizing precursors and preparation methods. The cost of carbon-based membranes is 1 to 3 orders of magnitude greater per unit area than polymeric membranes. Only when they achieve a much better performance than polymeric membranes might this high investment cost be justified. Several studies report selectivities and permeabilities for CMSs well in excess of the performance of polymeric membranes for difficult cases where the size of the molecules to be separated is very small, such as the CO₂/N₂, the O₂/N₂ and the C₂ and C₃ alkene/alkane pairs. CMS membranes are prepared by pyrolyzing polymers. Unlike zeolites, which have a well-defined pore size distribution, CMSs have been typically plagued by larger pore size distributions, which allow large and condensable molecules to enter and plug the pore network. This traditional picture of CMSs is changing in the last few years thanks to a controlled oxidation technique that is able to finely tune the pore size; this breakthrough is giving a new impetus to the research on CMS membranes.⁷

Block copolymers have gained increasing interest for gas separations involving CO₂ because they show outstanding separation properties. In particular, these materials have become of great interest in nanotechnology, precisely due to their ability to self-assemble in a variety of ordered nanostructures.⁸ The self-assembly process of block copolymers on a substrate is known as the “bottom-up” approach to nanofabrication.⁹ By using block copolymers with different structures, i.e. diblock, triblock and multiblock copolymers, the nanostructure and the properties of these materials can be exquisitely tuned for several specific applications. For instance, the fabrication of nanometric thin membranes from a block copolymer was recently reported.¹⁰ The membranes had thicknesses of less than 100 nm and showed extremely high performance in the separation of carbon dioxide.

MMMs comprise rigid permeable or impermeable particles, such as zeolites, carbon molecular sieves, silica, carbon nanotubes and metal organic frameworks, dispersed in a continuous polymeric matrix. In this approach, using properties of both polymer and inorganic phases, membranes with enhanced permeability, selectivity, mechanical strength, thermal and chemical stability and processability can be prepared.¹¹

The separation performance of homogeneous polymeric films is limited by an upper bound trade-off curve relating permeability and selectivity,¹² while the performance of block copolymers, carbon molecular sieves and mixed matrix membranes can overcome this trade-off curve.

In this review, the separation performance studies of membrane materials based on pure advanced polymers, like block copolymers, CMSs and MMMs for gas separation will be critically reviewed. The outlook of research and development to fully exploit the potential usage of these new membrane materials will be given.

2 Gas separation transport mechanism: theory

Gas transport through dense polymeric membranes is governed by eqn (1):

J_i = P/l(p_il − p_i0) (1)

where J_i is the volume (molar) flux (expressed in terms of cm³(STP) of component i cm⁻² s^-1), P the permeability, l the membrane thickness, p_i0 the partial pressure of component i on the feed side, and p_il the partial pressure of component i on the permeate side. The conventional unit for expressing the permeability, P, is the Barrer, where 1 Barrer is equal to 10⁻¹⁰ cm³ (STP) cm cm⁻² s⁻¹ cmHg⁻¹.

The most commonly used membranes in the gas separation processes are polymeric and nonporous. The separation is based on a solution–diffusion mechanism and the permeability P, defined in eqn (2), represents the ability of molecules to permeate through a membrane:

P = SD (2)

where S is the solubility and D the diffusion coefficient.

Selectivity is a measurement of the membrane's ability to separate the components of a mixture. The ideal selectivity (α_ij) is the ratio of the permeabilities of single gases and it is defined by eqn (3).

α_ij = P_i/P_j = (D_i/D_j) × (S_i/S_j) (3)

The mechanism assumes that each molecule is sorbed by the membrane at one interface, transported by diffusion across the membrane through the voids between the polymeric chains (which make up the so called free volume), and desorbed at the other interface. According to the solution–diffusion model, the permeation of molecules through the membranes is controlled by two major parameters: the diffusion coefficient (D) and the solubility (S).¹³ The diffusion coefficient is a measure of the mobility of the individual molecules passing through the voids between the polymeric chains in a membrane material. The solubility equals the ratio of sorption uptake normalized by the partial pressure at which sorption takes place.¹⁴

Recently, intense research has been directed towards the development of membranes that have more favorable trades-off between selectivity and permeability, such as carbon molecular sieves,¹⁵ zeolites and metal–organic frameworks¹⁶ as membrane materials.

Commercial gas separation membranes are composed of synthetic polymeric materials. Polymers provide a range of desirable properties that are important for gas separation processes including low cost, high permeability, good mechanical stability, and easy processability.¹⁷

Highly permeable rubbers are not very selective and discriminate between gases mainly on the basis of their solubility differences. For separation of permanent gases, less permeable glassy polymers are chosen instead, because of their size selectivity. Glassy polymers have stiffer polymer backbones and therefore let smaller molecules such as H₂ and He pass through more quickly, and larger molecules such as hydrocarbons permeate the membrane slowly. To increase the membrane selectivity, either the diffusivity or the solubility needs to be enhanced; however, polymers that are more permeable are generally less selective and vice versa. Polymeric membranes suffer from a trade-off between their permeability and selectivity. This trade-off was illustrated first by Robeson in 1991 when he plotted polymer selectivity versus permeability, and it later became known as Robeson plots, characterized by “upper-bound trade-off” lines. Owing to improvements during the last decade, Robeson revisited the upper bound curves in 2008.¹²

The trade-off line for each gas pair depicts the permeability–selectivity relation for conventional polymers, and this linear relation has been rationalized in terms of kinetic diameters, free volume and solubility coefficients of gases.

A substantial amount of research effort has been directed to overcoming the limit imposed by the upper bound. Glassy polymers provide high selectivity, but the gas permeability is usually low.

3 Strategies to overcome the upper bound

Common glassy polymers used as membrane materials include polysulfones, polyimides, polyaramides, polycarbonates, polyphenylene oxides and cellulose derivatives.

One of the proposed strategies to alter the trade-off relation was the chemical modification of classical polymers. Sridhar et al.¹⁸ prepared and modified poly(phenylene oxide) (PPO) membranes using chlorosulfonic acid. The CO₂/N₂ selectivity (27.2) for sulfonated PPO membranes was 2.2 times higher than for PPO membranes, while the CO₂ permeability (43.7) decreased by a factor of 2.4. Due to the permeability decrement after the chemical modification, PPO membranes lay well below the upper bound line.

Another strategy is polymer blending. Kapantaidakis et al.¹⁹ prepared membranes by blending polyethersulfone (PES) and polyimide (PI) in different ratios: (20/80), (50/50), (80/20) w/w blends. No significant improvement was observed in selectivity. The ideal selectivity of the CO₂/N₂ gas pair was reported as 40 for the PES/PI (20/80) blend and as 39 for PES/PI (80/20), both being close to the selectivity values of single polymers. Polymer blend membranes of poly(bisphenol A-co-4-nitrophthalic anhydride-co-1,3-phenylenediamine) (PBNPI) and polyphenylsulfone (PPSU) in different weight ratios were prepared and investigated for H₂, CO₂ and CH₄ separations. No improvements in selectivity, but a continuously enhanced permeability has been observed for these gases with increasing PPSU content.²⁰ Asymmetric membranes based on Matrimid® and polysulphone blends with improved permeance and stability, without selectivity increase compared to Matrimid®, have been observed in binary gas (CO₂/CH₄) mixture separations.²¹ Simple modifications of the polymer structure often only lead to a trade-off, as in the examples reported above for polymer blends: one of the parameters is improved, while the other is simultaneously negatively affected.²² This behavior can be explained by the following equations (eqn (4) and (5)).

α_ij=logβ_i/j − λ_ijlogP_i (4)

where P_i is the fast gas permeability, α is the selectivity of species i with respect to j and λ_ij is an empirical model parameter depending on the kinetic diameters of the permeating species. The position of the upper bound line is given by β_i/j; β_i/j depends on gas molecule size as well as solubility (5):

β_i/j= S_i^1+λ_ij/S_jexp{−λ_ij[b − f[(1 − a)/RT]} (5)

where S_i and S_j are the solubility coefficients of the gases. The values of parameter “a” as well as “b” are constant for glassy polymers (a = 0.64, b = 11.5 or 9.2 for glassy and rubbery polymers, respectively), f is a constant dependent upon the polymer..

The theory developed by Freeman²³ justifies the empirical principle of obtaining the best permeability/selectivity properties, up to a limit, i.e. one needs to create a polymeric structure with a stiff backbone (which enhances mobility selectivity at the expense of diffusivity) whilst also disrupting inter-chain packing (to improve permeability). This principle is taken to the extreme with PIMs (polymer of intrinsic microporosity).²⁴ Alentiev and Yampolskii²⁵ showed that the trade-off behavior could be predicted on the basis of a free volume model. Both Freeman²³ and Alentiev and Yampolskii²⁵ indicated that one way to surpass the upper bound is by enhancing the solubility selectivity (S_i/S_j): even if the ratio S_i/S_j is unchanged, a significant improvement can be achieved through an overall increase in S, and hence P.

The upper bound is based on homogeneous polymer films, and several approaches involving heterophase membranes have been demonstrated to exceed the upper bound: a) surface modifications, b) facilitated transport, c) block copolymers, d) MMMs, e) carbon molecular sieve membranes (CMSMs).

Among the methods of membrane surface modifications, UV modification, ion beam surface carbonization,²⁶ and surface fluorination²⁷ are investigated. Facilitated transport membranes rely on a chemical reaction occurring between the gas of interest and a component of the membrane (carrier). The reacted species are readily carried across the membrane, whereas diffusion of non-reactive gases is inhibited. The active carrier is generally basic in nature, given that carbon dioxide is acidic. The driving force for gas transport remains the partial pressure difference across the membrane; however the facilitator carrier increases both the permeability and selectivity of the membrane through the increased loading. The facilitator carrier can be either fixed-sited within the polymeric matrix or mobile.²⁸

More recent patents have focused on hydrogel films from cross-linked hydrophilic polymers, such as polyvinyl alcohol, polyvinylacetate, polyvinyl pyrrolidone, polyethylene oxide, polyacrylamide, blends and copolymers, cast on permeable supports.^29,30 These hydrogels have high water absorbing power and can therefore accommodate considerable loading of the carrier species. Copolymer composite membranes take advantage of the different swelling potential of each polymer component, whereas cross-linking agents are used to generate a strong polymer matrix. As a consequence, even though the membranes are thin, the high water content hydrogel film can retain its shape upon being subjected to pressure. Hence, they can function as a separation membrane with a long service life by exhibiting good water-retention and weatherability.³¹ Fixed carriers are generally polyallylamine, polyethylenimine and polyvinylamine.^32–35

Mobile carriers are basic compounds, and are often a combination of hydroxide salts, organic ammonium salts, aminoacids, carbonates, alkanolamines and polydentate ligands, such as EDTA.^36–38

An extensive treatise of all the approaches to exceed the upper bound is far beyond the scope of this review and further reading of the relevant publications on the subjects of surface modification and facilitated transport, which are not the object of this paper, are recommended. The next paragraphs are focussed on the main aspects and recent advances in the interesting membrane classes of block copolymers, carbon molecular sieve membranes and MMMs.

4 Block copolymer membranes

4.1 Overview of block copolymers

Many years ago scientists and technologists exploited the mixing of two different homopolymers to prepare superior polymeric materials. The polymer mixtures or alloys were denominated polymeric blends; those blends however always presented separated phases (macrodomains) due to the immiscibility of polymers.³⁹ One of the greatest challenges in that time was thus to solve the phase separation or immiscibility that results from the low entropy of mixing two different polymer chains.⁴⁰ One way of reducing the immiscibility was by using a compatibilizer with a chemical similarity to each homopolymer, i.e. surface-active block copolymers coming from two different monomers.^40–42 Those compatibilizers had the feature of self-assembling in the interface of separated phases, thus the size of the macrodomains was reduced. This strategy helped to create heterogeneous materials with improved mechanical,⁴³ barrier,⁴⁴ thermal⁴⁵ and other properties.^46,47

In parallel, and once the features (nanostructure) of block copolymers were known, it was suggested that they could become advanced materials with better properties than blends, so they received more attention due to their ability to self-assemble, especially in the last 20 years.^39,48

Today it is well-known that block copolymers exhibit amphiphilic behaviour, because they are single polymer chains containing two or three different homopolymers covalently bound to each other (Fig. 1), thereby having the ability to form ordered nanostructures, and they are mostly synthesized by living anionic polymerization.⁴⁹ Their properties mainly depend on morphology, i.e. nature, size of the nanostructure and its alignment; the morphology in turn depends on the degree of polymerization of each segment, entire molecular weight, polydispersity of the copolymer and interaction between segments.^50,51

Fig. 1 Schematic representation of linear block copolymers: AB di-block, ABA, BAB and ABC tri-block and AB multi-block copolymers

The phase separation in block copolymers is microscopic, i.e. the size of the separated phases is nanometric. The phase behaviour of block copolymers and the properties of complex nanodomains have been extensively studied; the readers hence are encouraged to read the following reviews.^52–54 Here, we only present a short overview of nanostructures formed by these block copolymers.

The simplest block copolymers are di-block copolymers, they are the most studied and a phase diagram has been constructed by Matsen and Bates.⁵⁵ Four morphologies have been identified, which are body-centered-cubic packed spheres, hexagonal closed packed cylinders, double gyroids, and alternating lamellae (Fig. 2). The morphologies that represent different phases are governed by the Flory–Huggins^56,57 interaction parameter χ, the volume fraction of the blocks and the total degree of polymerization, i.e. these factors direct the equilibrium phase. Nevertheless, it is important to point out that recent studies noticed that not only the degree of polymerization, composition and interaction between segments (thermodynamics) direct the final nanostructure, but so do the kinetics.^58,59

Fig. 2 Di-block copolymer morphologies as a function of volume fraction of each segment. Reproduced with permission from ref. 52. Copyright of Elsevier B. V.

The morphology of a tri-block copolymer is more complex than that of a di-block; this is due to the number of independent molecular parameters, i.e. the addition of a chain segment, either the same as an already existing segment or a completely different one, and thus two types of tri-block copolymers can be identified: ABA and ABC types. Because their morphology is complex, all of them are difficult to show in a short overview, hence only some of the most elaborate nanostructures are shown in Fig. 3A. With the addition of more segments of either A or B, the copolymers become multi-block copolymers, so their morphology is even more complex and can show unexpected nanostructures. Typical multi-block copolymers are those commercially known as thermoplastics; they are engineering materials and have multiple and important applications.^60,61Fig. 3B shows a possible morphological structure of multi-block copolymers; they are two separated micro-phases where amorphous and crystalline structures coexist within each phase. In addition to these phases there is also a microphase (interface) between the amorphous and crystalline structures, this has different properties compared to the separated microphases and can also influence the final properties of the block copolymer.⁶²

Fig. 3 Some typical morphologies of a tri-block copolymer theoretically obtained (A)⁶⁴ and two semi-crystalline separated micro-phases in multi-block copolymers (B) where the blue (left) and red (right) represent the homopolymers. Reproduced with permission from ref. 64. Copyright of American Physical Society.

In general, block copolymers may constitute a combination of flexible and rigid segments, and they can be hydrophobic and/or hydrophilic; therefore depending on the final application, the type and the volume fraction of each segment must be correctly chosen and well-controlled during the synthesis.

4.2 Block copolymers as membrane materials for gas separation

As block copolymers present defined and exquisite nanostructures, they were always of great interest for nanopatterning as a “bottom-up” approach. By using this technique, advanced functional nanostructures and nanodevices can be fabricated,^63,64 but nowadays block copolymers have many applications in other fields too, and membrane technology is one where they have potential as high separation performance materials.

Solubility, diffusivity and permeability of gases through block polymers are important from both the academic and the practical point of view. Knowledge of these properties and their relationships with the nanostructure are the basis to manufacture tailored materials for packaging, perm-selective membranes, protective coating and fibers, among others.

Odani et al.⁶⁵ were perhaps among the first to report on the permeation and diffusion of gases through block copolymers. They investigated poly(styrene-butadiene-styrene) (SBS) block copolymers, and styrene rod-like domains dispersed in butadiene and alternating styrene lamellae domains have been obtained by thermal treatment. Gas permeation and diffusion were correlated with the nanodomain structure (lamellae) by using parallel and series models. Knight and Lyman⁶⁶ were also among the first, but they studied the effect of chemical structure and fabrication variables on the gas permeability of several block copoly(ether-urethane-urea) and copoly(ether-urethane) membranes. The report showed that the type and length of the chains affected the gas permeability in both copolymer systems. The gas permeability variation was also related to the degree of microphase separation and the nature of chain packing. D. R. Paul⁶⁷ in that time developed mixing rules to relate the gas permeation in homogeneous multi-component polymers (block copolymers) to that in pure component polymers. The sorption and diffusion of propane in block copolymers of polydimethylsiloxane (PDMS) and poly(bisphenol-A carbonate) were also studied in that period by Barrie and Williams.⁶⁸ The results were interpreted in terms of composition and length of blocks, i.e. in terms of models where the microdomains are dispersed in a continuous phase. The Cohen group^69,70 has reported several studies on semi-crystalline block copolymers and their gas permeation. For the studied block copolymers, they found that the orientation of the nanodomains strongly influenced the effective gas permeability.

Although the first reports about block copolymers as a membrane material for gas separation were published in the last decade, the self-assembly of block copolymers as a tool to fabricate tailor-made separation membranes is only now being exploited. Block copolymers are however being mostly studied in the fabrication of nanopore membranes, and it is known that for the fabrication of nanopore membranes, the manipulation of the self-assembly process is a great challenge to control the formation of the cylindrical pore structure perpendicular to the surface. Some research has shown that di- and tri-block copolymers form defined nanopores,^58,71,72 and since the size of the pores is uniform they would become the membranes of the future; we say “membranes of the future” because at the moment there is not any technique or method to fabricate these membranes on a square meter scale, and the price of block copolymers is still very high. Recently, Peinemann's group⁵⁸ reported the development of a method to produce membranes on a large scale. The method consists of the combination of two processes: the formation and stabilization of micelles and the well-known phase inversion process.

With respect to the block copolymers for gas separation membranes, the self-assembly process has not been really exploited, only the microphase separation of block copolymers was well correlated with the gas transport.^65,69,73 In this section it will be shown that membranes with a high gas separation performance may be obtained by the self-assembly of block copolymers, on the basis of old reports and recent advances related to block copolymers and membranes. The purpose is to construct strategies to design membranes with tailored properties.

4.3 Di-block and tri-block copolymer membranes

As reported, di- and tri-block copolymers are of great interest for the nanoporous membrane fabrication due to their feature of forming cylindrical and bicontinuous gyroid nanodomains, but these copolymers were studied to a lesser extent for gas separation membranes. Nevertheless, few reports on the correlation of the gas transport properties and the nanostructure geometry can be found in the literature. Barrie and Munday,⁷⁴ for example, in 1983 studied a di-block copolymer containing PS and polydimethysiloxane (PDMS). They reported the dependence of permeability at different temperatures on the composition of the copolymer in terms of models for transport in a continuous phase with an impermeable dispersed phase. Tri-block copolymers such as SBS were already being reported as permeable membranes in 1975.⁶⁵Fig. 4 depicts the geometry for a SBS tri-block copolymer; although this report is old, the authors tried to explain the permeability and diffusivity of inert gases by a simple model of a parallel array of elements (nanodomains formed by polystyrene and polybutadiene). They found that a styrene rod-like membrane dispersed in butadiene exhibited greater permeability and diffusivity than that in alternating styrene lamellae domains, and in conclusion they stated that the permeation and diffusion of inert gases are primarily governed by the rubbery polybutadiene matrix.

Fig. 4 Morphologies of a tri-block copolymer membrane of ABA type (SBS); (A) styrene rod-like domains dispersed in butadiene and (B) alternating styrene lamellae domains. Reproduced with permission from ref. 65. Copyright of Institute for Chemical Research, Kyoto University

The Cohen group from MIT also investigated di-, tri- and tetra-block copolymers as permeable or barrier films.^69,70,76 One of their reports presents a simple model to describe the gas transport through di-block copolymer nanodomains; they proposed, as an upper bound, the lamellae aligned parallel (with respect to the permeation direction) and, as a lower bound, the lamellae aligned in series.⁷⁶ They also calculated that the gas permeation through misoriented lamellae materials and the permeability values were in good agreement with the experimental data. Thus they suggested that materials with tailored permeability and barrier properties can be developed by taking into account the upper and lower bounds. In addition to the nanodomain structure, they also studied how the crystalline structure affects gas permeation (segments that crystallize). Premnath from MIT also⁷⁷ developed a model for permeability through block copolymer membranes, i.e. for systems with perfect orientation in both parallel and series, as well as for random orientation. Kofinas (a former student of the Cohen) group^78,79 also investigated the relationship of different nanodomain orientations and gas permeation in semi-crystalline di- and tri-block copolymers; they generated confined nanopores within the block copolymer domains and increased the gas flux without altering the selectivity.

As seen, the relatively old reports already showed that the self-assembly process of block copolymers can be used as a powerful tool to develop advanced membrane materials. In the last few years only a few papers were published on gas separation membranes from di- and tri-block copolymers. Lokaj et al.⁸⁰ reported the synthesis and gas permeability of block copolymers composed of poly(styrene-b-acrylonitrile) and polystyrene, i.e. by using the di-block copolymer as a macroinitiator, a tri-block copolymer of the ABA type was obtained. The prepared film showed high O₂/N₂ selectivity (>6), so this work showed that the gas selectivity can be improved by adding a third segment to di-block copolymers. In 2004, Patel and Spontak⁷³ explored the properties of a poly(styrene-b-ethylene-oxide-b-styrene) tri-block copolymer and its blend with polyethylene glycol (PEG) as a reverse selective membrane for CO₂ separation. The membrane design as CO₂ selective was based on the unusually high affinity between CO₂ and ethylene oxide; thus by adding PEG, the CO₂ permeability was enhanced, and a composition-dependent transition from alternating lamellar to polyether continuous morphology was evidenced. Li et al.⁸¹ synthesized similar copolymers to those used by Patel and Spontak (PS-PEG-PS); they obtained copolymers with similar molecular weights but different fractions of the crystalline PEG segment. Although the copolymers were not studied as gas separation membranes, the studies showed that the PEG domain can be tuned in terms of the crystalline/amorphous ratio as a gas sensing material. These two works clearly suggest that by tuning the morphology of the tri-block copolymers containing PEG, the affinity between copolymers and CO₂ or certain vapours can be enhanced.

The use of PEG as a hydrophilic phase in block copolymers is important for several industrial applications. A polyacrylonitrile-PEG-polyacrylonitrile tri-block copolymer was for example synthesized and characterized as a pervaporation membrane.⁸² The authors reported that the dehydration of a mixture of acetone with 5% water is considerably improved by using block copolymers; the performance of the membrane mainly depended on PEG content and size of the segment. The transport properties were correlated with the micro-phase separation of the block copolymer and the water solubility in PEG at different temperatures. The effect of nanoscale morphology on ethanol transport through SBS block copolymer membranes was also reported.^83,84 The ethanol selectivity and total flux can be optimized by controlling the size of the block copolymer nanodomains.

In a recent report, the self-assembly of SBS and its behaviour as a membrane for gas separation has been thoroughly studied.⁷⁵ Structural differences of SBS in the copolymer membranes, obtained by manipulation of the self-assembly of block copolymer in solution, have been characterized by means of AFM, TEM and transport properties of three gases (CO₂, N₂ and CH₄). The unexpected CH₄/N₂ ideal selectivity of 7.2 (the highest value ever reported in the literature for block copolymers), with a CH₄ permeability of 41 Barrer, has been attributed to the controlled and improved micro-phase separation of block copolymer, i.e. the hexagonal array of columnar polystyrene cylinders normal to the membrane surface resulted in a membrane with superior gas separation properties. In addition to the unexpected CH₄/N₂, the CO₂/N₂ ideal selectivity of 50, coupled with a CO₂ permeability of 289 Barrer, makes the SBS a good candidate for the preparation of membranes for the post-combustion capture of carbon dioxide. The synthesis and gas transport properties of rigid block copolyaramides were also reported.⁸⁵ The block copolymers containing a highly gas permeable rigid segment and a barrier aramide presented lower permeability values than that in the homopolymer with the higher gas permeability, but the gas transport was well described by a parallel arrangement of nanodomains; hence those models developed in the last century were validated.

Robeson⁸⁶ recently reported a review combining two of the major research areas of Prof. Paul: polymer blends and gas separation membranes. In that review, the morphology of phase separated polymer blends is highlighted as an important variable during the design of materials to enhance the transport properties. We mention this report here to show that the morphology of blends is the same as in block copolymers, i.e. series and parallel models, Maxwell’s model and the continuous model can be used to study the mass transport. The relationship between the transport properties and the morphology are analogous in both systems; the differences, however, are the size of the separated phases (for blends are macro-phases and for block copolymers are micro-phases), and thus this review could be helpful in analysing the gas transport through block copolymer membranes.

It is also worth mentioning the work reported by Querelle et al.⁸⁷ They used a reactive block polymer precursor, and membranes with a bicontinuous nanostructure were obtained. The strategy was to cross-link one phase, thus improving the plasticization effect. The membrane was evaluated for CO₂ separation from CH₄. Although the permeabilities remained the same, the selectivity was slightly reduced; thereby they demonstrated that by this means, cross-linked bicontinuous block copolymer membranes resisted plasticization. One of the latest reports on tri-block copolymers for gas separation was published by Gu and Lodge.⁸⁸ They synthesized a novel tri-block copolymer based on styrene and ionic liquids (IL), i.e. a polystyrene-poly(ionic liquid)-polystyrene named as PS-PIL-PS. The work was inspired by the enhanced transport of PILs developed by Noble’s group.⁸⁹ The developed block copolymer membrane as an ion gel showed enhanced gas transport properties, and the authors pointed out that the thermoreversible nature of this ion gel material offers advantages during processing (solvent-free). The membrane exhibited a high permeability and high CO₂ selectivity over N₂ and CH₄.

4.4 Multi-block copolymer membranes

Many years ago (around 1950) researchers from all over the world were looking for novel polymeric materials with similar properties to those of natural rubber, and thus thermoplastic elastomers were developed. In fact, the above described SBS tri-block copolymer has been developed as a thermoplastic elastomer. Thanks to the advances in polymer synthesis, the segmented or multi block copolymers (linear) have become commercial (thermoplastics and thermoplastic elastomers), and these copolymers have been used in several applications. In membrane technology these multi block copolymers have been mostly studied as gas separation membranes and membranes for fuel cells.^90–93

Multi-block copolymer membranes are composed of copolymers containing flexible and rigid segments, which in turn form the soft and hard phases. Generally, the rigid segment gives mechanical and thermal stability to the material, and it is usually dispersed in the soft phase formed by the flexible segment. An example of a multi block copolymer nanostructure is shown in Fig. 5. The hard phase can be formed by a glassy amorphous polymer with a high glass transition temperature (T_g) or a semi-crystalline polymer, and the soft phase can be formed by a semi-crystalline or amorphous polymers with a low T_g and a relatively low melting temperature (T_m). For gas separation membranes, the segments must be carefully selected before synthesizing a novel polymer, i.e. the combination of both segments should result in high gas permeability, high selectivity and good mechanical and thermal stability.

Fig. 5 Typical multi block copolymer nanostructures (AFM) showing the hard and soft separated phases; (a) poly(ethylene oxide)-poly(buthylene terephthalate) and b) poly(ethylene oxide)-poly(buthylene terephthalate/PEG blend. As seen, the degree of phase separation is different between them, and the hard semi-crystalline poly(buthylene terephthalate) as rod-like domains dispersed in the poly(ethylene oxide) soft phase is clearly distinguished, especially in the blends. Reproduced with permission from ref. 94. Copyright of American Chemical Society.

The most studied multi-block copolymers are polyurethanes, poly(ether-ester)s and poly(ether-amide)s. Polyurethane based membranes were studied in the 1980s as gas separation membranes,^95,96 but nowadays these kinds of copolymers are still being investigated due to their versatility in terms of synthesis. Freeman’s group, for example, recently reported the synthesis of a series of poly(urethane-urea)s containing poly(ether)s.⁹⁷ They tried to synthesize a membrane with improved gas separation properties as a CO₂-selective membrane; they correlated the fractional free volume with the molecular weight of polyethers as well as the gas permeability. Gomes et al.⁹⁸ also investigated polyurethane membranes, but in this case containing ether-siloxane segments. They reported that these copolymers could have potential applications in the separation of n-C₄H₁₀/CH₄. In order to improve the gas permeability or selectivity, nanocomposite membranes from polyurethanes were also prepared;⁹⁹ however, it was unsuccessful because the gas permeability decreased with increasing selectivity or vice-versa (typical trade-off of gas separation membranes).

Poly(ether-amides)s containing poly(ethylene oxide) (PEO) as well as poly(ether-ester)s and polyurethanes were investigated as highly CO₂-selective materials. In recent years, the number of published papers on the development of membranes from block copolymers containing PEO has greatly grown. Since PEG or PEO (i.e. ethylene oxide units) was discovered as a functional group with a high affinity for CO₂,¹⁰⁰ almost all work related to multi-block copolymers containing PEO has been focused on membrane fabrication for CO₂ separation. Poly(ethylene oxide-b-amide) has been one of the most studied block copolymers as a CO₂-selective membrane. Although this copolymer was developed in 1972 as a thermoplastic elastomer (Pebax), only in 1990 was it investigated as a membrane material for gas separation.⁹⁰ However, due to solubility problems, study of this copolymer was not any more intensive; thus new multi-block copolymers were explored. Among these are the poly(ether ester)s, especially the poly(ethylene oxide)-poly(butylene terephthalate), known commercially as Polyactive.¹⁰¹ This multiblock copolymer however presented solubility problems too, hence the studies were also limited.

Pebax membranes form nanostructures of soft and hard phase;¹⁰² the typical hard phases structure has a size of around 6 nm and the longest around 17 nm. Gas permeability generally increases with the size of the polyether domains, but imperfect microphase separation exhibits better gas permeation. The size of the nanodomains of Pebax with a high polyether content depends on the used solvent during casting and on the water content in the membrane.

In recent years, interest in improving the separation performance of Pebax started again thanks to its affinity for CO₂; thereby membranes for CO₂ capture are being developed by using this copolymer. Sridhar et al.¹⁰³ cross-linked Pebax and evaluated its performance for CO₂/CH₄ separation. The gas permeance was decreased to a great extent and the selectivity increased (expectedly), the interesting fact was that CO₂/CH₄ selectivity reached up to 47 (more than twice than that for pristine Pebax). Hamouda et al.¹⁰⁴ and Sridhar et al.¹⁰⁵ studied Pebax membranes filled with silver nanoparticles and reported the water uptake properties and CO₂/CH₄ separation. Car et al.^106,107 reported the modification of Pebax by PEG; they used a simple binary mixture as the solvent (water/ethanol) and studied the gas separation properties with respect to the resulting morphology. They used PEG to increase the number of ethylene oxide units; hence the polymer–CO₂ affinity was enhanced. Thanks to these reports, Pebax copolymer was again considered as a potential membrane material, and later, several reports have been focused on the improvement of this copolymer. Sijbesma et al.¹⁰⁸ for example investigated the water permeation and stability under flow of the flue gas; they suggested that polymeric membranes are viable to directly separate CO₂ from the flue gas. Louie et al.¹⁰⁹ studied the effect of Pebax coating on reverse osmosis (RO) membranes, the RO membranes had defects and by using a thin film of Pebax the gas permeation was greatly decreased but the selectivity was enhanced two-fold. They also suggested that by treating Pebax with different solvents, the morphology can be changed. In general, the separation performance of the Pebax membrane mainly depends on the nature of the block copolymer (Pebax is a trade name of different poly(ether-amide)s), i.e. as a CO₂-selective membrane it depends on PEO content.

Because of their rubber-like properties, Pebax membranes are improved due to their solubility selectivity. But later a report demonstrated that not only is this fact important but so is diffusivity selectivity; and thus it was suggested that by increasing the free volume of Pebax, the CO₂ permeability and selectivity can be simultaneously enhanced.¹¹⁰ Pebax was also blended with PEG-DME (di-methyl ether), and they were investigated following the strategy of increasing the free volume.¹¹¹ The DME end group of PEG hindered PEO crystallization and enhanced the micro-phase separation; thus the CO₂ permeability was increased up to 8-fold, and the CO₂/H₂ selectivity was simultaneously enhanced from 9 to 15. Another similar work was reported by Reijerkerk et al.,¹¹² but instead of PEG-DME they used PEG-PDMS, which improved the Pebax gas permeation due to the presence of PDMS.

The incorporation of quaternary ammonium compounds into the Pebax was also investigated; since the ammonium compounds have a high affinity for CO₂, the gas solubility can be greatly enhanced.¹¹³ The gas permeation with a humid feed revealed that these blend membranes have extremely high permeability (the CO₂ permeability was increased up to 35 fold) without selectivity loss. Pebax/multiwalled carbon nanotube (MWNT) hybrid membranes were also investigated;¹¹⁴ the authors characterized the hybrid membranes by different techniques to understand the effect of MWNTs on the polymer–MWNT interaction, crystallinity, cross-linking degree and gas separation performance. Of interest was the strategy used, i.e. manipulation of the free volume. A Pebax/polyhedral oligosilsesquioxane hybrid membrane was also prepared and investigated for pervaporation,¹¹⁵ but it could also be used for gas separation when water vapour is present.

Recently, a complex Pebax/AgBF₄ thin nano-hybrid membrane was developed;¹¹⁶ the thickness of the thin film was between 100 and 200 nm and the propylene/propane separation was explored. Zeolites were also incorporated into the Pebax membranes and better permeability was observed too.¹¹⁷

A tubular Pebax/ceramic hybrid nanocomposite membrane was also fabricated and examined in terms of separation performance.¹¹⁸ Although the idea of using a ceramic porous support is something interesting, it did not really improve the membrane performance of Pebax; the microphase separation led to the same nanostructure observed when a polymeric porous support is used (hard phase dispersed in a soft amorphous phase).

The use of poly(ether ester)s as a CO₂-selective membrane is also of great interest.¹¹⁹ Poly(ethylene oxide)-poly(butylene terephthalate) block copolymer has been extensively studied by Peineman’s group,^94,120,121 but the first studies of this multi-block copolymer as a gas separation membrane were undertaken by Mulder's group.¹⁰¹ This multi-block copolymer is highly CO₂-selective, and the permeability is similar to or a little bit higher than that for Pebax. Through a detailed investigation, tailor-made membranes were fabricated from this copolymer,¹²⁰ and after understanding the membrane behaviour and morphology, a new CO₂-philic polymer was synthesized. The nanostructured blend membranes from this copolymer exhibited extremely high separation performance, i.e. the CO₂-permeability was increased up to 5-fold without any loss of selectivity.⁹⁴ The authors reported that by choosing the right smart additive, the separation performance of the membrane can be greatly improved. Based on this multi-block copolymer, nanometric thin film membranes with high gas flux and permeability were manufactured.¹²¹ Later, it was demonstrated that by a suitable molecular manipulation of this block copolymer and fabrication process, super permeable membranes with a constrained thickness can be developed for CO₂ capture.¹²²

Other poly(ether ester) multi-block copolymers were also explored and some of them had better gas permeability and selectivity than Pebax and Polyactive. Simmons¹²³ for example patented a series of poly(ester-ether)s as a membrane for gas separation. However, the reported permeability values are higher than those of the commercial poly(ester-ether)s, e.g. for poly(ethylene oxide)-poly(butylene terephthalate) with ∼75% PEG (1500 g mol⁻¹), the CO₂ permeability is higher than 220 Barrer, a similar commercial polymer (Polyactive) has a CO₂ permeability less than 120 Barrer.¹²⁰ Another example is the CO₂ permeability for Pebax, which is reported as ∼150 Barrer, but the CO₂ permeability for the used Pebax reported by other authors is between 70 and 120 Barrer depending on the solvent used for casting.^90,106 Different gas permeation properties (a fact that could depend on the method of processing) can only result due to the different morphologies (separated microphases). As the morphology is a factor that controls the gas transport through block copolymers, it could explain the differences in permeability. Therefore, one can conclude that block copolymers might self-assemble in different ways, due to the different methods used for the preparation of the films.

Block copolymers containing PEO and PPO soft phase and di-amide as the hard phase were also investigated.^124–126 One paper reported by those authors suggested that uniformity of the crystal structure (size) in the hard phase improves the gas separation performance.¹²⁶ Although this could be true to a certain extent, completely amorphous phases in both the hard and soft phase are preferred; thus the hard phase that is considered as impermeable becomes a little permeable due to the presence of flexible segments inter-dispersed between the rigid segments.⁹⁴ Poly(tetramethylene) as the hard phase was also investigated in poly(ether-ester)s as CO₂-selective membranes.¹²⁷ It was interesting that polymers with the same features as Polyactive resulted in being more permeable; this could be explained in terms of chemical structure. A poly(ether-ester) containing poly(tetramethylene) could have a high gas permeability due to the number of methylenes in its glycol moiety; it is called odd-numbered polyester. Even-numbered polyesters are PBT and poly(ethylene terephthalate) (PET), hence a detailed study of poly(ether-ester)s with PET would demonstrate this hypothesis. Block copolymers with polyimide as the hard phase were also reported.¹²⁸ Wessling's group at the University of Twente recently reported an overview of the advances in multi block copolymers and on the limit of gas separation performance.¹²⁹Fig. 6 shows the modified plot of Robeson for CO₂/N₂ separation, where different multi-block copolymers are included.

Fig. 6 Modified Robeson plot, CO₂/N₂ selectivity as a function of CO₂ permeability. Reproduced with permission from ref. 129. Copyright of Elsevier B.V.

4.6 Design and strategy for optimal gas separation membrane fabrication

The versatility of block copolymers in terms of chemical structure and synthesis gives many opportunities to design novel membranes with outstanding properties. Nevertheless, for designing a required membrane material for gas separation, one must simply analyze eqn (2) and consider the following aspects before choosing the segments for the synthesis; (1) the sorption of gas molecules on the membrane surface (upstream), (2) the diffusion of gas through the membrane and (3) the desorption of gas from the membrane (downstream), i.e. by choosing segments that give high sorption properties, high free volume and good mechanical and thermal properties, tailor-made block copolymer membrane might be developed. The three factors described above are well represented by the diffusion–solution model for gas transport through polymeric membranes.¹³⁰

As presented in eqn (3), the overall selectivity can also be split into diffusivity selectivity and solubility selectivity. Therefore, during the design of new block copolymers, we must think about improving both selectivities, as well as the gas permeability. By enhancing both properties simultaneously, one can achieve a breakthrough in membrane science and technology.

In block copolymer membranes, different factors govern the mass transport, such as the chemical nature, the molecular weight and the content of each segment. Those factors are the most important parameters to be controlled during the synthesis. In addition to these parameters, the processability or solubility of the block copolymer in simple solvents must be also taken into account. Generally, the gas transport occurs through the amorphous soft phase; the hard phase is considered to be impermeable and does not contribute to the gas transport, but the importance of the hard phase is due to the physical cross-linking, i.e. it gives mechanical and thermal stability to the material. However, by modifying or manipulating the impermeable hard phase, one can also get some permeability through this phase, which would improve the total permeability.⁹⁴

The self-assembly process of block copolymers was a forgotten aspect during membrane fabrication, i.e. the self-assembly process was not considered a tool to direct the desired morphology that could give high separation properties. The manipulation of block copolymer self-assembly by chemical or physical means may lead to desired nanostructures that give high permeability and high selectivity. Clear examples of improving the gas separation performance of block copolymers by manipulating their self-assembly are described for example in ref. 75, 122, 132.

The use of di-block copolymers containing PEO or functionalized PEO, which form cylindrical nanostructures perpendicular to the surface (as reported in the literature),^131,132 can be used to embed carbon nanotubes, hence instead having PEO only as the permeable phase, the carbon nanotubes embedded within this phase parallel to the direction of gas transport would enhance the gas transport, resulting in a super-permeable nanohybrid membrane. It was reported that carbon nanotubes can be functionalized with PEG or PEO,¹³³ thus it could be easily accommodated into the PEO phase. The challenges would be however to develop carbon nanotubes with controlled sizes, and strategies to embed the carbon nanotubes into the PEO phase. The size (length) of nanotubes should not be more than 100 nm and they should be open. As PEO has a high affinity for CO₂ and the nanotubes exhibited unexpected transport properties,¹³⁴ super-permeable membranes for CO₂ separation might be easily developed. Research is therefore called upon to investigate this kind of nanohybrid material. This hypothesis is shown in Fig. 7, and upon analyzing eqn (2) it is simple to see that the solubility of CO₂ due to PEO, and diffusivity due to the nanotubes, might be enhanced, thus resulting in high permeability. This hypothesis can be also applied to tri-block copolymers and other segments, depending on the gas mixture to be separated.

Fig. 7 Di-block copolymer with a cylindrical nanostructure plus embedded carbon nanotubes; the soft segment could be PEO and the nanotubes could be functionalized with PEG to have a desired dispersion. In addition, the top surface should be free of nanotubes (a condition). Thus the selectivity would not be lost. As a CO₂ selective membrane, this hypothetical membrane would be highly selective due to the presence of PEO, and super-permeable due to the nanotubes.

The addition of other inorganic compounds is also a way to improve the gas separation performance of block-copolymer membranes. The incorporation and well-controlled dispersion of nanoparticles are being extensively studied,^135,136 hence the developed strategies can be also used to design new membranes. Instead of using inorganic nanoparticles and nanotubes, the use of organic or biological compounds that have a high affinity for certain gases and can self-assemble within one phase are also interesting.^137,138

Another way to improve the gas separation membranes by using block copolymers could be the use of organic–inorganic block materials, i.e. a polymer segment bonded to an inorganic material. In fact, Malenfant et al.¹³⁹ investigated the self-assembly of organic–inorganic block copolymers. They reported that this new hybrid block copolymer enables the formation of ordered nanostructures with a tunable morphology and composition. This new block copolymer would be interesting to investigate as a membrane material. Through the polymer segment (soft or hard phase, i.e. rubber or glassy polymer), the gas molecules would permeate and the inorganic phase would give a high mechanical and thermal stability. As the inorganic particles form clusters with nanopores (between particles) of less than 2 nm, this phase of the material would also exhibit a high permeability, especially for condensable gases such as CO₂ and n-butane. For instance, Yave et al. suggested that TiO₂ nanoparticles form clusters (agglomeration of nanoparticles) with small pores through which the n-butane permeated faster than methane due to its condensability; thus the permeability and selectivity in the mixed gas was greatly increased.¹⁴⁰ A recent report by Lau and Chung supports this hypothesis;¹⁴¹ they studied nanohybrid membranes containing nanoparticles that agglomerated, and the agglomeration formed small nanopores that enhanced the CO₂ permeability.

The synthesis of new block copolymers with three or four different segments could be also another option to overcome the state-of-the-art of gas separation membranes. Either the selectivity or the permeability can be improved by adding a new segment. The addition of a third or fourth segment that creates more free volume and improves the solubility of gases would be a challenge. This new segment can even interpenetrate through each segment or self-assemble in a way that enhances the gas permeability and selectivity. An example would be to develop well defined tri-block copolymers containing PEO, PDMS and a rigid segment. Due to the PEO, the CO₂ solubility would be high, the PDMS would contribute to the permeability and the rigid segment would give the mechanical and thermal stability. An additional example would be to develop a di-block copolymer containing PEO and PDMS. A variety of CO₂-selective materials can be developed by manipulating the self-assembly and cross-linking the PDMS. Therefore, and in general, the synthesis of block copolymers containing segments that give a high free volume and high solubility to a certain gas is a topic to be investigated.

5 Carbon molecular sieve membranes

Very selective polymers are not permeable enough, and highly permeable polymers are not very selective. The permeability and the selectivity of polymeric membranes for gas separation is limited by the so called upper bound in a log–log plot of selectivity vs. permeability, also known as a Robeson diagram.^{12,22,142–145} Inorganic membranes are not bound to this restriction, due to the fact that the size of the pores is fixed and true molecular sieving is possible in this case. Examples are zeolites, amorphous silica, metal organic framework (MOF)¹⁴⁶ and carbon molecular sieve (CMS) membranes. With respect to crystalline molecular sieves and MOFs, the pore size of amorphous oxides and CMS membranes is not determined by the lattice constraints of a crystalline material: even though a wide pore size distribution can easily be obtained as a consequence of unsuitable preparation conditions, on the other hand one single precursor can yield several different amorphous oxides or CMSs characterized by different pore sizes and size distributions, depending on the preparation protocol and procedure. In particular, CMSs are versatile materials, more permeable than zeolites, yet with sieving ability, the properties of which may be finely tuned to prepare membranes able to accomplish difficult separations. In fact, several studies report selectivities and permeabilities well in excess of the performance of polymeric membranes for difficult cases where the size of the molecules to be separated is very small, such as the C₂ and C₃ alkene/alkane pairs, the CO₂/N₂ and the O₂/N₂ separations.

In the following section, a non-exhaustive description of the structure, precursors, pyrolysis methods, pre- and post-treatments and separation performances of CMS membranes for gas separation will be given. Details and extensive treatments can be found in the excellent reviews present in the literature.^147–152

5.1 Structure of CMSs and CMS membranes for gas separation

Carbon molecular sieves are produced during the early stages of decomposition of polymeric precursors, and they are classified as amorphous because they do not display a well defined crystalline structure. However, small crystalline regions may coexist with amorphous char, organized in disordered aggregates with very little or no long range order.¹⁴⁸ The graphene flakes in the small crystalline regions are often defective due to the lack of sp² carbons far from the edge, can be haphazardly folded or crumpled together to form a so-called turbostratic structure, and in general the degree of order is so poor that the materials are considered essentially isotropic. Mesoporous carbon membranes are not the subject of the present description. Carbon molecular sieve membranes for gas separation usually have a structure consisting of slit-like cavities of 1–2 nm size (micropores) connected by pore restrictions (ultramicropores) of smaller size. This structure is usually modelled (Fig. 8) as an array of ink-bottle slit-like pores connected by ultramicropores that are able to discriminate between the molecules on the basis of size.^148,153 As evidenced in Fig. 8 (c), the dimensions of these cavities, included the ultramicropore size d_C, are not precisely defined, as is the case in crystalline molecular sieves, but are rather described by size distributions. The basic validity of these assumptions has been confirmed by a recent modelling study on a commercial material (Shirasagi CMS 3 K-161) which indicates that the investigated CMS is a structurally heterogeneous material composed of stacks of slit-shaped, turbostratic carbon nanopores of different sizes embedded in an amorphous carbon matrix.¹⁵⁴

Fig. 8 (a) A schematic representation of a 3D slit-like cavity in a CMS membrane. (b) Cross-section through (a) showing the micropore size (d_TV), the ultramicropore size (d_C), the jump length dimension (d_λ) and the negligible “window thickness” dimension (δ). (c) Representation of the fact that d_TV, d_C and d_λ are actually described by distributions. Reproduced with permission from ref. 153. Copyright of Elsevier B. V.

5.2 Preparation of CMS membranes

In a typical CMS membrane preparation a polymeric precursor is pyrolysed in a vacuum or in an inert purge, usually N₂, by slowly increasing the temperature, in most cases up to 500–800 °C, holding at that temperature for a certain thermal soak time, and then cooling down. The pyrolysis gases evolved leave behind pores, and at the same time the precursor forms the rigid turbostratic structures described in the previous section, along with a severe shrinking (up to 70% in some cases) of the membrane.

Several parameters can be modified in order to finely tune the structure and the performance of CMS membranes: the nature of the precursor polymer, the pyrolysis temperature, the heating rate, the thermal soak time at the maximum temperature and the pyrolysis atmosphere, pre- and post-treatments.

Before we give a detailed description of some of these factors, it is useful to give a basic picture of the carbonization process for Matrimid, a typical polyimide precursor, in vacuum or in an inert atmosphere. The only species released up to 400 °C is water. Large molecules (50–240 Dalton) are only released from 400 to 600 °C, and this gives rise to the formation of micropores. From 550 °C, significant amounts of methane and carbon oxides are given off due to the degradation of imide and benzene rings. The decomposition rigidifies the structure of the precursor, and the release of small molecules reasonably gives rise to the formation of the ultramicropores. From 700 °C upwards, the release of H₂ becomes significant, and leads to the formation of an amorphous carbon material¹⁵⁵ and eventually to graphitic structures. The micropores formed during the low temperature pyrolysis of Matrimid (400–600 °C) shrink at higher temperatures, as evidenced by X-ray diffraction data and gas permeation experiments. The rule of thumb is that higher pyrolysis temperatures bring about a decrease of gas permeability, as well an increase of the gas selectivity in favor of small molecules.¹⁴⁹

The role of the pyrolysis atmosphere has been studied by several researchers. Vacuum pyrolysis of PIs yields more selective but less permeable membranes than inert gas purge pyrolysis,^155–157 and this effect has been explained with an increased heat and mass transfer from the gas phase, which accelerates the carbonization reaction and produces a more open porous matrix.¹⁵⁶ At low flow rates of inert sweep gas, the non volatile by-products are not removed quickly enough, and they can presumably degrade further, to leave carbon deposits on the surface: this may explain the sharp reduction of flux observed in these cases.¹⁵⁶

The role of small amounts of oxygen in the inert sweep gas has been investigated by Koros and co-workers.^159–161 During the pyrolysis of Matrimid membranes, oxygen impurities (3–100 ppm in Ar) reduce both the permeance and the CO₂/CH₄ selectivity of the resulting CMS membranes. For a 6FDA/BPDA-DAM polyimide, instead, the increase of O₂ concentration in the Ar sweep from 4 to 30 ppm brings about a reduction of fluxes but with an increase in CO₂/CH₄ selectivity, whereas 50 ppm O₂ provoke a reduction of flux and selectivity. According to the authors, the oxidation at ppm levels of O₂ takes place preferentially at the more reactive sp² carbon edges of the selective pores, and as a consequence the size of the ultramicropores (d_C in Fig. 8 (a)) is reduced. The oxidation process is controlled by the concentration of oxygen in the inert atmosphere.¹⁶² This oxidative process represents a powerful tool for finely tuning the pore size and the selective transport of CMS membranes.

5.2.1 Precursors of CMS. The most common thermosetting polymers used to date for the preparation of CMSMs are polyacrylonitrile (PAN), polyimides (PIs), phenolic resins (PRs) and poly(furfuryl alcohol) (PFA).^147–152 The first CMS hollow fibres, however, were produced by Koresh and Soffer from cellulose,¹⁵⁸ which is particularly convenient for its low cost when compared to PIs. PIs are considered the best precursors because of the separation performance and mechanical properties of the resulting CMS membranes.^163,164 PFA and PRs are other cheap alternatives to PIs, but since they are liquids, they need to be coated on supports before the pyrolysis step. The other polymers are pre-formed as self-standing membranes, in flat configurations or as hollow fibres, and pyrolized as such, maintaining their shape and morphology.

One strategy for the improvement of the productivity of CMS membranes is the introduction in the precursor membrane of porogens, i.e. species which serve as templates for the formation of microporosity in carbon. This can be accomplished by blending with labile polymers (e.g. polyvinylpirrolidinone, PVP), which completely gasify during the pyrolysis step, by co-polymerization with labile monomers or by the introduction of thermally labile groups (e.g. –SO₃H, –SO₃⁻, alkyl) or ions (NO₃⁻), which decompose.

During the pyrolysis of sulfonated PIs,¹⁶⁹ the sulfur containing groups have already decomposed at 450 °C; when instead the loss of a sulfone moiety requires the breakage of two covalent bonds, the maximum peaks for the release of sulfur oxides are observed at or below 500 °C.¹⁶² In sulfonated poly(2,6-dimethylphenylene oxide) (PPO) the loss of the sulfonic acid group takes place at around 200 °C.¹⁶³ PVP has been used as a porogen in blends with PIs,^170,171 PPO^172–174 and cellulose.^175,176 Silica containing CMS membranes prepared by pyrolysis of poly(imide-co-dimethylsiloxane) on alumina supports demonstrated good separation factors for the He/N₂, H₂/N₂, CO₂/N₂ and O₂/N₂ pairs:^177,178 larger polydimethylsiloxane blocks in the co-polymer caused an increase in permeability at the expense of selectivity.¹⁷⁹

Another strategy for the improvement of the productivity of CMS membranes is the dispersion in the precursor of cations that catalyse the thermal decomposition of the polymer. Trivalent cations (mainly Fe³⁺) introduced as nitrates proved the most effective species for the improvement of the CO₂/CH₄ and O₂/N₂ separation factor of cellulose derived carbon membranes, and MgO increased the H₂/CO₂ selectivity by reducing the CO₂ permeability.¹⁸⁰

Chung and co-workers produced flat CMSMs by cross-linking a polyetherketone with 2,6-bis(4-azidobenzylidene)-4-methylcyclohexanone and pyrolyzing at low temperature (450–650 °C).^181–182 The decomposition of the bis-azide blended with the polymer produces extremely reactive nitrene intermediates, which are able to bind to the surrounding chains and stabilize the thermally labile polyetherketone. The membranes prepared at 550 °C exhibited excellent propene/propane ideal selectivity of 44 with a propane permeability of 48 Barrer, which decreased to 32 and 3.6 Barrer, respectively, with real mixtures.¹⁸¹ Similar membranes prepared at 800 °C displayed a CO₂ permeability of 280 Barrer and ideal CO₂/CH₄ selectivity of 164.¹⁸²

5.2.2 Pre-treatments. The requirement of a precursor polymer for the making of self-supported CMS membranes is that it does not melt before the pyrolysis. The plasticization of the polymer at temperatures higher than the glass transition temperature provokes the thickening of the membrane skin, with the closure of the finer pores present in the porous sublayer. This phenomenon can be exploited to prepare defect-free CMS membranes from defective or even porous precursor membranes,^165,185 but in most cases the densification provokes the formation of a very thick skin layer which, in turn, causes unacceptable reductions in flux.¹⁶⁶ In order to avoid or minimize this phenomenon, the most common pretreatments are the pre-oxidation in air at 100–400 °C and the chemical crosslinking of the precursor membranes. Okamoto and co-workers stabilized asymmetric PI hollow fibres at 400 °C in air for 30 min before pyrolysis in nitrogen at 600–630 °C, obtaining thin skin layers (200 nm) in the resulting CMSMs, higher permeances and sustained selectivities for the C₃H₆/C₃H₈ and the 1,3-butadiene/n-butane pairs.¹⁶⁷

The pre-oxidation stage at 400 °C was accompanied by the decomposition of the sulfone group contained on the aromatic diamine comonomer, giving rise to sulfur oxides in the gas phase. Yoshimune and Haraya pre-oxidised sulfonated poly(phenylene oxide) hollow fibres in air at 260 °C for two hours before pyrolysis under vacuum, obtaining very thin (280 nm) and flexible CMS hollow fibres with high CO₂/CH₄ and H₂/CH₄ separation factors (118 and 392, respectively), and CO₂ permeance in excess of 10⁻⁸ mol m⁻² s⁻¹ Pa⁻¹.¹⁶⁸ Also in this case the sulfur containing groups decomposed almost completely during the pre-oxidation stage.

Another interesting pretreatment which can improve the selectivity of polyimide P84 derived CMSMs is the soaking of the precursor membrane in a linear alcohol (the best effects were given by ethanol) prior to pyrolysis.¹⁸³ The experimental evidence indicates that the weakening of the intramolecular cohesion forces caused by the sorption of ethanol allows a more effective structural re-organization of the polymer chains leading to narrower pores.

5.2.3 Post-treatment. It is not clear whether it is more appropriate to define the synthetic method used by carbon membranes as a post-treatment of CMS membranes or as a real synthesis of a CMS membrane on a carbon porous support.¹⁸⁴ The method introduced by Soffer and co-workers¹⁸⁴ consists of the pyrolytic chemical vapor deposition (CVD) of carbon in the lumen side of the porous carbon hollow fibres derived from cellulose, by using propene as the carbon source. The CVD plugs the pores of the support, but can also create a carbon layer on the surface of the membrane. The CVD is followed by an ‘activation’ step that consists of a high temperature oxidation, which creates a tailored pore structure within the CVD layer.¹⁸⁶

A similar method (propene^187,188 or methane¹⁸⁹ CVD and air oxidation at 250–350 °C) has been adopted by Blue Membranes GmbH for their honeycomb carbon membranes described in a later section.

Pyrolytic carbon deposition of benzene had been also used for the enhancement of the sorption selectivity of activated carbon fibres (ACFs) for pressure swing absorption.^190–192 At a deposition temperature of 900 °C, benzene already pyrolysed in the gas phase to form larger molecules that could not enter the micropores, so that carbon deposited mainly on the external surface of the fibres and produced fibres with limited sorption capacity and poor CO₂/CH₄ sorption selectivity.¹⁹¹

At 727 °C, instead, the experimental evidence indicated that benzene could be sorbed as such into the micropores before pyrolysis, restricting the size of the micropores: as a consequence the sorption amount of CO₂ reduced slightly with respect to the pristine ACFs, whereas a very sharp reduction of CH₄ was observed, with high CO₂/CH₄ sorption selectivity.¹⁹¹

Morooka and co-workers used propene CVD at 650 °C on their supported CMSMs derived from polyimide to reduce the pore size and to increase the O₂/N₂ and CO₂/N₂ selectivity. It turned out that an optimum CVD time was two minutes: at longer times both permeances and selectivity were reduced.¹⁹³

Another popular post-treatment method is oxidation. Morooka and co-workers treated their carbon membranes with 10% and 20% O₂ for 3 h at 300 °C, obtaining a generalized increase of permeance and almost no change in selectivity. The treatment in air at 100 °C for 30 days led to a decrease in permeability with an increase in selectivity; since the former performance could be recovered after heating in N₂ at 600 °C, the authors raised the hypothesis that the 100 °C oxidation produces surface oxides that reduce the size of the ultramicropores.¹⁹⁴

In both cases, the change in elemental composition of the membranes caused by the oxidation at 100–300 °C was modest, suggesting an increase in the micropore volume of the membrane, with almost no change in the pore size distribution.¹⁹⁵

The post-oxidation of PPO derived CMSMs supported on alumina (air at 100–400 °C), instead produced a broadening of the pore size distribution and a drop in all selectivity values.^196–198

BPDA-ODA polyimide (PI) and PEI derived CMS membranes were coated with PPO and pyrolyzed again at 600 °C.¹⁹⁹ The second pyrolysis caused the expansion of the pores of the pristine CMS membranes, and at the same time the decomposition of the thermally labile PPO produced the deposition of carbon at the mouth of the pores. As a result, more permeable and more selective membranes were formed. In particular, the PI derived membrane showed outstanding CO₂ and H₂ permeability (1320 and 1450 Barrer, respectively) coupled with very high CO₂/N₂ (156), CO₂/CH₄ (157) and H₂/CH₄ (172) selectivity.

5.3 CMS membrane modules

The brittleness of carbon molecular sieve membranes is a major problem for the preparation and durability of a module. Carbon Membranes Ltd. (Israel) was the first company to produce high quality hollow fibre membrane modules on an industrial scale.¹⁸⁴ The hollow fibres, 1 m long, had a diameter of 170 μm and a thickness of 9 μm (Fig. 9, left).¹⁸⁶ The packing density was about 2000 m² m⁻³ and each module contained 4 m².¹⁸⁸ Carbon Membranes Ltd. started the commercialization of its membranes and modules at the end of the 1990s, but ceased its activity in 2001.

Blue Membranes GmbH, based in Wiesbaden, Germany, was the second company to develop and construct a CMSM module of a quite different concept,^188,189 in which the membrane and the module are produced at the same time. Bulky ceramic supports severely limit the maximum membrane packing density of the CMSM that can be obtained, and also interfere with the shrinking of the pyrolizing material and introduce mechanical stresses that reduce the resistance of the membrane: the choice of a sheet of paper reinforced with ceramic fibres greatly reduced these risks. The paper was first impregnated with a mixture of a phenolic resin and an epoxy glue dissolved in 2-butanone; then a diagonal pattern was stamped on the dry composite, so that the direction of the wavy motif had a diagonal orientation with respect to the sheet side (Fig. 9a, right). The rippled sheet was then pleated (Fig. 9b, right), creating flow channels for both the feed and the permeate. Next, alternate pairs of folds were sealed at their edges, as shown in Fig. 9c (right), isolating in this way the feed from the permeate side. The pockets that result at this stage of the preparation process resemble the pockets to be glued on the central permeate collector tube in a spiral wound module; in this case, however, no spacer was needed to separate the facing membranes within the pockets. After curing at moderate temperature to bond the points of contact of the sheets, the nascent membranes were pyrolyzed under nitrogen up to 780 °C, then underwent a CVD treatment followed by air oxidation, as described in section 5.2.3, to finely tune the gas separation properties. The structure of the membranes, 50–100 μm thick, comprised a macroporous support with a separating layer of 10–30 μm. The resulting membranes had a high packing density—up to 2500 m² m⁻³—and were housed in modules containing up to 10 m² of membrane area.¹⁸⁸

Fig. 9 SEM pictures of a hollow fibre manufactured by Carbon Membranes Ltd (left). Reproduced with permission from ref. 186. Copyright of Elsevier B.V. Scheme of the preparation of the Blue Membranes GmbH honeycomb CMSM module (right). Reproduced with permission from ref. 188. Copyright of Elsevier B.V.

Fig. 10 Mixed matrix membrane morphologies.

6 MMMs

MMMs are composed of homogeneously interpenetrating polymeric and inorganic particles. Significant improvement in separation properties compared to neat polymers is expected for the resultant mixed matrix membranes (MMMs).²⁰⁰ Generally, the literature has focused on the incorporation of inorganic particles like zeolites, carbon molecular sieves and non-porous silica particles²⁰¹ as a dispersed inorganic phase in a polymer matrix. Inorganic particles added to a polymer matrix can have three effects on the permeability: they can act as molecular sieves altering the permeability, they can disrupt the polymeric structure increasing the permeability too and they can act as barriers reducing permeability.²⁰² However, it has been found that the performance of MMMs is not a simple addition of the intrinsic properties of the individual phase. Many variables may seriously affect MMM performance, making it difficult to understand. Currently, the major concerns in research on MMMs are a suitable combination of polymers and particles, the physical properties of the inorganic fillers (e.g., particle size and particle agglomerations), and the polymer/particle interface morphologies.²⁰³

6.1 Molecular design and key advances in MMMs: choice of the polymer and of the filler

Many variables may affect the performance of MMMs, such as a suitable combination of polymers and particles, the physical properties of the inorganic fillers (particles size, surface area, aspect ratio) and their physical-chemical properties (hydrophilicity, hydrophobicity). Even though the selection of an appropriate inorganic filler was the major concern in the development of MMMs, it has been found that the choice of a suitable polymer as hosting matrix is crucial for MMM performance. In Table 2 an overview of some polymers used for the preparation of MMMs is reported. The transport properties are strongly dependent on the adhesion between the filler and the hosting matrix. Both rubber and glassy polymers are used. The most used rubber polymer is PDMS. Usually the fillers are added before the crosslinking step to enhance the adhesion with the polymeric matrix. It has been shown that successful mixed matrix materials can be formed easily by using flexible polymers, i.e. those with a relatively low glass transition temperature. For example, poly(vinyl acetate) (PVAc) has a low glass transition temperature (35 °C) and for high zeolite loading (e.g. zeolite 4A) the priming of the zeolites before their entrapment in the polymeric solutions is enough to obtain defect free membranes. Priming the zeolites involves adsorbing a layer of polymer onto the surface of the sieve. For rigid polymeric materials i.e. with high T_g, for example PES, Psf, Matrimid PI, 6FDA-6FpDA-DABA, Teflon AF and Hyflon AD (Table 2), the priming step is not sufficient to obtain good adhesion between the polymer and the sieve. Attempts at developing MMMs based on glassy polymers may be classified as fabrication methods with and without modifying the filler surface. The methods used without modifying the filler surface include the use of compatibilizers and the preparation protocols applying high processing temperatures during membrane formation.²⁰⁵ Mahajan et al.²⁰⁶ maintain the polymer flexibility during the membrane formation by applying processing temperatures close to the T_g of polymeric materials, coupled with the use of a non-volatile solvent. In fact, the addition of plasticizers (or compatibilizers) may lower the intrinsic gas separation performance of polymeric materials. Moore and Koros²⁰⁷ summarize the relationships between MMM morphologies and transport properties in five cases. Case 0 represents the ideal case. Case I consists of the presence of a rigidified polymer layer; cases II and III have voids at the interface with the effective void thickness of different size; cases IV and V are both caused by sorption of a strongly held molecule. In particular, in case IV, the strongly held molecule completely prevents the penetrants of interest from entering the zeolites, whereas in case V, the penetrants of interest enter through the zeolite at a slower rate than usual. In Fig. 10, cases 0, I, II and V are represented.

Table 2 Some polymers used for the preparation of MMMs

Polymer	Structure	Polymer	Structure
ABS		PDMS
Teflon® AFs		CA
Hyflon® ADs		PC
6FDA-6FpDA-DABA		Matrimid PI
PMP		PTMSP
PES		PVAc
PSf		PEI

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The addition of a proper silane coupling agent on the zeolite surface may reduce the voids between the unmodified zeolite and the polymer phases.

In Fig. 11 this aspect is illustrated for the preparation of MMMs based on a glassy polymer with high T_g (polyimide, PI84) and surface modified SAPO-34 molecular sieves.

Fig. 11 SEM pictures of MMMs based on PI84 and SAPO-34 molecular sieves functionalized with two types of silane agents containing (a) phenetyl and (b) aminopropyl groups. Overall (left) and magnification (right) of the membrane cross section.

The successful compatibilization between the inorganic and organic phases is due to the presence of amino groups on the surface functionalized SAPO-34 molecular sieves: they react with the imino ring of the polyimide, favoring the interaction with the hosting polymeric matrix.²⁰⁸

In Table 3, an overview of the most used porous fillers for MMMs is given. They are materials with excellent gas separation properties, including zeolites and carbon molecular sieves (CMSs). There are many types of filler other than zeolites and CMSs that have been employed as filler: ordered mesoporous silica, silica spheres, carbon nanotubes and metal organic frameworks (MOFs).

Table 3 Porous fillers used for MMMs

Filler	Category	Pore size (Å)	Structure
3A, 4A, 5A (LTA)	Zeolite	3.2–4.3	3D
ITQ-29 (LTA; Si/Ge = 100-∞)	Zeolite	4.2	3D
SAPO-34 (CHA)	Zeolite	3.8	3D
SSZ-13 (CHA)	Zeolite	3.8	3D
ZSM-2 (FAU)	Zeolite	7.4	3D
Silicalite-1 (MFI)	Zeolite	5.5	3D
ZSM-5 (MFI)	Zeolite	5.5	3D
Beta (BEA)	Zeolite	7.6 × 6.4	3D
Y (FAU)	Zeolite	7.4	3D
CMS	CMS	4–5	2D
MWCNTs	CNTs	20	3D
SWCNT	CNT	20	3D
ZIF-90	MOF	3.5	3D
ZIF-8	MOF	3.4	3D
MOF-5	MOF	6.7	3D
HKUST-1	MOF	9.0	3D
Cu-DHBC-BPY	MOF	3.6 × 4.2	2D
Cu-BPY-HFS	MOF	8.0 × 8.0	2D
Cu-TPA	MOF	5.2	2D
[Cu3(BTC)2]	MOF	9	3D
MIL-53(Al)	MOF	13.0, 7.9	3D
SBA-15	Ordered mesoporous silica	40–140	2D
MCM-41	Ordered mesoporous silica	15–200	1D
Hollow silicalite-1 spheres	Zeolite macrostructures		3D
Halloysite nanotubes	Mineral clays	100–1000	3D

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Non-porous fillers have been proposed and used for MMMs in various studies (Table 4). The most used fillers are silica nanoparticles. The introduction of impermeable particles modifies the packing structure of the polymer matrix. In particular, most of the polymers coupled with non-porous fillers are high free volume polymers (PMP, PTMSP, Teflon AFs). The presence of fumed silica nanoparticles further increases both the size of the larger holes and their fraction, as demonstrated by positron annihilation lifetime spectroscopy (PALS).^209,210

Table 4 Some examples of non porous fillers for MMMs

Filler	Polymer	Ref.
Fumed silica nanoparticles	Teflon AF1600	212
Fumed silica nanoparticles	Teflon AF2400	213,209
Fumed silica nanoparticles	PSf	214
Fumed silica nanoparticles	PIM-1	215
Fumed silica nanoparticles	PTMSP	210,216,217
Fumed silica nanoparticles	PMP	218,219
TiO2	PMP	140
TiO2	Poly(amide-imide)	219,220
Modified fumed silica nanoparticles	PDMS	221–223

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The high free volume reduces the importance of diffusivity selectivity (see section 2, Gas separation transport mechanism: theory), so that solubility selectivity becomes dominant for the overall separation process (reverse selectivity). As we know, in size-selective polymer dense membranes, small molecules preferentially permeate relative to larger ones. However, in membranes with reverse-selective properties, the larger one preferentially permeates in a gas mixture. The presence of nano-sized particles in the polymeric matrix increases the accessible free-volume compared to neat polymer. The resultant MMMs present an improvement in both permeability and selectivity for the larger molecules, with a mechanism very similar to that of microporous carbons, for which selective surface flow and solubility selectivity prevail.²¹¹

6.2 Gas transport models for MMMs

Different theoretical models are used to describe the gas permeabilities in MMMs.

The Maxwell model, originally developed for the estimation of electrical conductivity of composite materials,²²⁴ can be adapted to permeability as:

Where P_r is the relative permeability of the species, P is the effective permeability of the species in MMM, P_m is the permeability of the matrix (continuous phase), ϕ is the volume fraction of the fillers, λ_dm is the permeability ratio P_d/P_m (P_d is the permeability of the species in the dispersed phase).

This model predicts well for a spherical filler with a low-moderate concentration (ϕ < 0.2). It does not take into account the effects of particle distribution, particle shape or aggregation of particles.

A model developed by Cussler is similar in form, but considers a staggered array of high aspect ratio particles (eqn (7)).²²⁵

Where α is the filler aspect ratio (the ratio of the longest to the shortest dimension of the filler). Cussler defines α as half this ratio and his equation differs accordingly. Hence, the Cussler model takes into account the increased tortuosity of the path of the diffusing gas because of the non-spherical shape of the fillers.

The Cussler model is reasonably successful for predicting MMM performance when the aspect ratio is large and the volume is moderate to large (ϕ > 0.2).^225,226 However, there are many combinations of volume fractions and aspect ratios for which neither the Maxwell nor the Cussler models are successful for predicting MMM performance. In eqn (8) a modification of the Cussler model manages to fill much of this gap:

The above models assume ideal contact between the filler particles and the matrix. More often, as reported by Moore and Koros²⁰⁷ the contact between the particles and the matrix phase is defective; dewetting of polymer chains from the filler surface often occurs, resulting in void space between the two phases (Fig. 10, case II). Another possible situation is that the polymer in direct contact with the filler surface becomes rigidified in comparison to the bulk polymer phase (Fig. 10, case I). Therefore, the permeability of a species in the interfacial region surrounding the filler particles is often significantly different from the permeability in the bulk polymer matrix. Mahajan and Koros²²⁷ proposed a three-phase Maxwell model (3MM): the Maxwell model is first applied to a combined sieve and interphase region to estimate an effective permeability (P_I). In eqn (9), ϕ_s is the volume fraction of the sieve phase in the combined sieve and rigidified interfacial matrix layer phase. This effective permeability is then used in the Maxwell model, along with bulk polymer permeability, to estimate the effective permeability of a three-phase system (eqn (10). The 3MM model can predict, in the case of sieve-in-a-cage (SIAC) and leaky interface defects, the dimension of interfacial voids.

Other models, in addition to those reported above, have been proposed and evaluated by Hashemifard et al.²⁰⁴ by using the parameters that reflect the morphology and separation characteristics of the MMMs (matrix or polymer permeability, inorganic permeability, MMM permeability, inorganic loading, inorganic particle size and interphase thickness), the Lewis-Nielsen model, the modified Lewis-Nielsen model and the Felske model.²⁰⁴ Generally, the only parameter that is challengeable is inorganic permeability. Sheffel and Tsapatsis²²⁶ proposed a semi-empirical approach for predicting the performance of mixed matrix membranes. The predictions of this approach were compared to experimental results for two cases studies, PTMSP/silicalite-1 membrane for the separation of normal and iso-butane and the separation of carbon dioxide and methane by MMMs containing CHA-type molecular sieves.

Fig. 12 indicates how to choose a matrix material in order to optimize mixed matrix membrane selectivity.

Fig. 12 Prediction of the selectivity P₂^C/P₁^C of a mixed matrix membrane containing fillers with an aspect ratio of α = 50 and loading of ϕ = 30% as a function of matrix permeability (P₂^M) and selectivity (P₂^M/P₁^M). The colours (right) represent the selectivity of MMMs that would result from forming a membrane based on a matrix with a given permeability (x-axis) and selectivity (y-axis). Reproduced with permission from ref. 226. Copyright of Elsevier B.V.

The Robeson upper bound curve¹² is a guideline about which matrix materials are actually experimentally available. If the Robeson line and the selectivity ridgeline of Fig. 12 (the blue line) intersect at a point where the Robeson line is populated with polymeric materials, this point will provide guidance about which polymer to choose.

For example, for MMMs based on zeolite 4A, the gas separation performance with polymeric matrix as PVAc²²⁸ and Ultem PEI²²⁹ indicates that the higher intrinsic selectivity of Ultem produces MMMs more selective than those based on PVAc. A highly permeable polymer matrix may make the filler useless, because the majority of gas diffusion will occur through the phases with lower transport resistance instead of the filler phase possessing a higher separation performance.

Of interest in evaluating the importance of the physical properties of the zeolite and of the combination polymer/zeolite is the example proposed by Sheffel and Tsapatsis: CO₂/CH₄ separation by means of membranes containing CHA-type molecular sieves (see next paragraph for recent experimental works for this separation).²²⁶Fig. 13 shows the predictions for a mixed matrix membrane containing 30 vol% CHA molecular sieves with an aspect ratio of 30 operating at a feed pressure of 10⁴ kPa.

Fig. 13 Predictions of the CO₂/CH₄ selectivity (P₂^C/P₁^C) of a mixed matrix membrane containing dispersed CHA crystals at a loading of 30 vol% and an aspect ratio of α = 30 as a function of matrix permeability (P₂^M) and selectivity (P₂^M/P₁^M). Reproduced with permission from ref. 226. Copyright of Elsevier B.V.

The upper bound curve CO₂/CH₄, represented by Robeson¹² is shown as a red line.

Fig. 13 shows that a polymer with a CO₂ permeability of 3 × 10⁴ Barrer and a selectivity of 4 makes possible an improvement in selectivity up to 80. For this particular separation, the necessity of using large aspect ratio particles (α = 30) is mandatory; without them the selectivity improvements are perhaps negligible. The second condition is that the MMMs operate at conditions that maximize the effective permeability of the zeolite, i.e. at high operating pressures.

However, the experimental results obtained with the membranes based on a cross-linked polymer and SSZ13 reported by Hillock et al.²³⁰ did show enhanced selectivity and permeability with a filler loading and an aspect ratio different from those proposed by the model; theoretical models need to include a more accurate picture of the experimental membrane geometry, perhaps including interfacial effects.

In Table 5 the experimental combinations (polymer/filler) for CO₂/CH₄ separation are reported; all are based on SAPO-34 (CHA structure) to evaluate the role played by the polymer matrix. Other polymer/filler combinations based on inorganic additives different from SAPO-34 are reported in the next paragraph.

Table 5 Different polymer/SAPO-34 combinations for MMMs intended for CO₂/CH₄ separation

Entry #	Polymer	Separation performance MMMs		Separation performance neat polymer		Ref.
		Permeability CO2 (Barrer)	Ideal selectivity	Permeability CO2 (Barrer)	Ideal selectivity (α)
1	PES	5.12	24.9	2.88	29.4	231
2	PES	1.53	37.4	2.88	29.4	231
3	PPZ	48	17.5	71	15.3	232
4	Poly(RTIL)	477	19	9.2	39	233
5	Poly(RTIL)-[C2 mim][Tf2N]	77	30	44	27	233

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Karatay et al.²³¹ used PES as a polymeric matrix and evaluated the presence of a compatibilizer, 2-hydroxy 5-methyl aniline (HMA) (entry 2, Table 5) to improve the adhesion between the filler and the polymer: only by using HMA the ideal selectivity of MMMs (37.4) improves compared to neat polymer (29.4).

In the case of the PPZ matrix (entry 3, Table 5), which is more permeable to CO₂ and less selective than PES (selectivity CO₂/CH₄ 15.3), a slight improvement has been observed by adding the molecular sieves (17.5), confirming the general consideration that the gas diffusion occurs through the phases with lower transport resistance, instead of the filler phase, which possess higher separation performance.

Polymerizable room-temperature ionic liquid ((Poly(RTIL)) material has been used by Hudiono et al.²³³ with and without room-temperature ionic liquid (RTIL) additives (entries 4 and 5, Table 5). The addition of RTIL in the composite membrane facilitates interaction between the polymer and the inorganic particles of SAPO-34; the selectivity from 19 (entry 4, Table 5) without the compatibilizer increases up to 30 (entry 5, Table 5). Compared to PES and PPZ, the composite membranes show a better performance than the corresponding neat polymer for both permeability and selectivity. The increase in permeability is due to more rapid gas diffusion in the RTIL.

6.3 MMMs: recent progresses

In the present section, some recent advances of MMMs based on conventional fillers (i.e. zeolites and CMS) (Table 6) and unconventional fillers (Table 7) are reported. An overview of interesting examples of MMMs based on non porous fillers is reported above in Table 4. Recent reviews on MMMs by Aroon et al.,²³⁴ Zornoza et al.,²³⁵ provide additional examples and information.

Table 6 Recent advances of MMMs based on zeolites and CMS

Entry#	Filler	Polymer	Gas pair	Separation performance^a		Ref.
				Permeability separated species (Barrer)	Ideal selectivity (α)
a In brackets the separation performance for the neat polymer.
1	SSZ-13	PDMC	CO2/CH4	148 (66.9)	38.9 (36.4)	236
2	4A	PVAc	CO2/CH4	4.33 (2.15)	49.4 (33.5)	237
3	FAU/EMT	6FDA-ODA	CO2/CH4	17.6 (16.5)	80 (53.2)	238
4	ITQ-29	PSf	H2/CH4	21.9 (97.7)	118 (18)	239
5	Hollow silicalite-1 spheres	PSf	H2/CH4	15.4 (11.8)	80.3 (58.9)	240
6	Hollow silicalite-1 spheres	PI	H2/CH4	38.4 (30.4)	180 (132)	240
7	Hollow silicalite-1 spheres	Psf	O2/N2	2.3 (1.6)	6.9 (4.7)	240
8	Hollow silicalite-1 spheres	PI	O2/N2	2.8 (1.9)	8.5 (5.5)	240
9	CMS	PSf Udel P-1700	O2/N2	6.52 (1.58)	6.05 (5.5)	241

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Table 7 Recent advances in MMMs based on MOFs and CNTs

Entry	Filler	Polymer	Gas pair	Separation performance^a		Ref.
				Permeability separated species (Barrer)	Ideal Selectivity (α)
a In brackets the separation performance for the neat polymer. b The MMMs were characterized with a gas mixture CO2/CH4 1 : 1 and the selectivity is not ideal.
1^b	ZIF-90	6FDA-DAM	CO2/CH4	720 (390)	37 (24)	245
2	ZIF-8	Matrimid	CO2/CH4	8.8 (9.8)	81 (43.6)	246
3	ZIF-8	PPEES	O2/N2	1.56 (1.03)	6.2 (5.4)	247
4	ZIF-8	PPEES	H2/N2	17.5 (7.9)	70.0 (41.6)	247
5	MWCNTs	PES	CO2/CH4	6.79 (10.98)	250.13 (51.26)	251
6	MWCNTs	PES	O2/N2	3.19 (2.13)	10.65 (2.56)	251
7	MWCNTs	PES	CO2/N2	4.5 (2.75)	21.8 (20.73)	252
8	MWCNTs	PEBAX1657 (crosslinked)	CO2/N2	17.5 (13.4)	83.2 (55.8)	114
9	MWCNTs	PEBAX1657 (crosslinked)	O2/N2	1.05 (1.19)	7.1 (4.95)	114
10	MWCNTs	PEBAX1657 (crosslinked)	H2/N2	7.18 (5.83)	82.5 (24.8)	114
11	MWCNTs	PI	CO2/CH4	37.31 (16.83)	16.5 (10.9)	253

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Ward and Koros²³⁶ prepared and evaluated MMMs based on SSZ-13 molecular sieves and crosslinkable polyimide (PDMC) for CO₂/CH₄. For unmodified filler (loading 25 wt%) a permeability enhancement of 129% and a decline in selectivity of 4.7% over neat PDMC are reported. The modification of the crystal surface (which presents sylanol groups) consisted in chemical linking to the polymer backbone during the steps of polymerization and polymer crosslinking. MMMs with 25 wt% surface modified crystals exhibit enhancements in both permeability and selectivity of 121% and 6.9%, respectively (entry 1, Table 6). The analysis of interfacial defects has been carried out by using the three-phase Maxwell model described by Mahajan and Koros.²²⁷

The CO₂/CH₄ separation has been investigated too by Adams et al.²³⁷ by using another combination zeolite/polymer, i.e. zeolite 4A and PVAc, respectively (entry 2, Table 6). High particle loading has been used (50 vol %). A selectivity increase of 47% with a lack of significant permeability has been observed.

Overall, it is shown that low performance, low cost polymers, like PVAc, typically not used for gas separation membranes, may be considered in real applications for gas separation.

An excellent combination polymer/zeolite has been proposed and investigated by Nik et al.²³⁸(entry 3, Table 6) for CO₂/CH₄; FAU/EMT intergrowth zeolites grafted with 3-aminopropylmethyldiethoxysilane (APMDES) in a polymeric matrix of 6FDA-ODA polyimide. The ideal selectivity for MMM prepared with the higher loading of aminosilane crystals (0.33 mmol g⁻¹) is 80.0 with an enhancement of selectivity and permeability compared to neat polymer of 50.4% and 6.7%, respectively.

ITQ-29 crystals (entry 4, Table 6) were introduced, at different loadings (4, 8 and 12 wt%), into a commercial polysulfone matrix for the separation of H₂/CH₄, comparing the use of two solvents (tetrahydrofuran and dichloromethane) for the MMMs preparation.²³⁹

The cubic zeolite particles were highly dispersed but sparse for a 4 wt% ITQ-29 loading. This dispersibility decreased at the loading of 8 wt%, with agglomeration at the bottom of the MMM.

Promising results have been obtained for the 4 wt% ITQ-29/polysulfone membrane: the highest H₂ permeability (21.9 Barrer) and a separation factor of 118. MMMs using the novel molecular sieves have potential industrial applications for key separations in energy saving processes, such as hydrogen recovery from flue gases.

Hollow silicalite-1 spheres (Fig. 14),²⁴⁰ obtained by hydrothermal synthesis from solid mesoporous silica spheres, seeded with silicalite 1 nanocrystals, have been used as fillers for two polymeric matrices, polysulfone Udel and polyimide Matrimid (entries 5–8, Table 6). For both the gas separations investigated, i.e. H₂/CH₄ and O₂/N₂, improved selectivity and permeability compared to neat polymers have been obtained.

Fig. 14 Cross section SEM or TEM images (a–c) 8 wt% HZSPSF MMMs; (d) 8 wt% HZSPI MMM. Reproduced with permission from ref. 240. Copyright of Elsevier B.V.

Carbon molecular sieve particles in a polymeric matrix of polysulfone have been explored for gas separation (O₂/N₂) by Rafizah and Ismail (entry 9, Table 6).²⁴¹

The CMS particles were treated with poly(vinyl pyrrolidone) kollidone 15 (PVP K-15) to improve the adhesion to the polysulfone matrix. An enhancement of both the selectivity (10%) and permeability (313%) has been obtained.

For untreated CMS particles a decrease in selectivity of 33% has been observed, confirming the crucial role of the crystal treatment.

Recent advances have shifted towards the addition of new fillers, namely MOFs, carbon nanotubes and layered silicates for the polymer matrix.

MOFs are among the most sophisticated nanostructured materials: their chemical environment can be fine-tuned by selecting the appropriate building blocks²⁴² and/or by post-synthetic modification.²⁴³ The structural diversity of ZIFs is shown in Fig. 15.²⁴⁴

Fig. 15 The single crystal X-ray structures of ZIFs. (Left and center) In each row, the net is shown as a stick diagram (left) and as tiling (center). (Right) The largest cage in each ZIF is shown with ZnN₄ tetrahedra in blue, and, for ZIF-5, InN₆ octahedra in red. H atoms are omitted for clarity. Reproduced from ref. 244 (www.pnas.org).

For each structure, the metal center is solely coordinated by the N atoms of imidazolate to give overall neutral frameworks. The five-membered imidazolate ring serves as the bridging unit between the Zn(II), Co(II), or In(III) centers and imparts an angle of 145° throughout the frameworks via coordinating N atoms in the 1,3-positions of the ring. The organic components of ZIFs provide for organically lined cages and channels rather than a silicate oxide surface as in zeolites.

Submicrometer-sized crystals ZIF-90 crystals were synthesized by non-solvent-induced crystallization and used for the fabrication of MMMs based on poly(imide)s as polymer matrices (entry 1, Table 7).²⁴⁵

ZIF-90 has a sodalite cage-like structure with 0.35 nm pore windows, through which size exclusion of CH₄ (0.38 nm) from CO₂/CH₄ mixtures is possible. In addition, the imidazole linker in ZIF-90 contains a carbonyl group, able to facilitate the transport of CO₂.

MMMs made with 6FDA-DAM (a highly permeable polymer) showed substantial enhancements in both CO₂ permeability (85%) and selectivity (54%), for the gas mixture 1 : 1.

Interestingly, the CO₂/CH₄ mixed-gas selectivity was higher than the ideal selectivity measured by pure-component gas permeation, presumably because of the selective sorption and diffusion of CO₂ in the crystals.

The performances observed by Bae et al.²⁴⁵ of ZIF-90 MMMs based on polymers as Ultem and Matrimid (with the same filler loading of 15 wt %), are lower than those observed for 6FDA-DAM. The Maxwell model (applicable to systems with filler loading <20 vol%) predicts that when the gas permeability of the filler is much larger than that of the polymer matrix, there will be no enhancement in selectivity, even if the dispersed filler is highly selective. The CO₂ permeability of ZIF-90 was found to be approximately 8000 Barrer. The CO₂ permeability for both the polymers Ultem and Matrimid is in the range 1–10 Barrer, whilst for 6FDA-DAM it is 390 Barrer.

However, an improvement in selectivity by using Matrimid as the polymeric matrix and ZIF-8 as the filler, has been observed by Ordoñez et al. (entry 2, Table 7).²⁴⁶ ZIF-8 exhibits, like ZIF-90, the sodalite topology and its pore aperture is 3.4 Å. In this case, higher loading of the filler (50 wt% and 60 wt% ) than that used by Bae et al.²⁴⁵ is responsible for the different behavior. The observed enhancement of the ideal selectivities of the gas pairs containing small gases, such as H₂/O₂, H₂/CO₂, H₂/CH₄ and CO₂/CH₄ demonstrates a transition from a polymer-driven to a ZIF-8 controlled gas transport process. The control experiment using as-synthesized ZIF-8 crystals with filled pores did not show a transition at 50 wt%. These results suggest that additive loading >50 wt% may be required to observe this effect in MMMs.

Diaz et al. (entries 3 and 4, Table 7)²⁴⁷ fabricated MMMs based on ZIF-8 (with loadings of 10, 20 and 30 wt %) using as a polymeric matrix poly(1,4-phenylen ether-ether-sulfone (PPEES). The permeability of all gases increases as the ZIF-8 loading increases, without affecting the ideal selectivity in a significant way, confirming the results of Bae et al.²⁴⁵ Only the selectivity of the MMMs (30 wt %) for the gas pairs O₂/N₂ and H₂/N₂ is close to that marked by the Robeson upper-bound for this pair of gases.

Carbon nanotubes (CNTs) have been considered to be potential fillers for mixed matrix membranes due to their outstanding mechanical, thermal and electrical properties.²⁴⁸

CNTs can be synthesized as singular tubes called single walled carbon nanotubes (SWCNTs) or as a series of shells of different diameters spaced around a common axis, called multi-walled nanotubes (MWCNTs) (Fig. 16).

Fig. 16 Single walled carbon nanotube (left) and multi walled carbon nanotube (right)²⁴⁹ (http://en.wikipedia.org/wiki/Carbon_nanotube)

Recent studies have shown that membranes incorporating CNTs show promise for high selectivity and throughput.²⁵⁰

CNTs possess several possible adsorption sites, such as interstitial channel sites with a high binding energy and pore sites with a large surface area. Moreover, for MWCNTs, the interlayer spaces between the graphite walls provide possible adsorption sites for small molecules exhibiting appreciable adsorption selectivities.

Gas permeation in CNTs was found to be several orders of magnitude faster than in other fillers such as zeolite.

Ismail et al. fabricated and characterized MMMs composed of functionalized MWCNTs and PES. In particular, the MWCNTs were functionalized with 3-aminopropyltriethoxysilane (APTES) to facilitate the dispersion of the fillers in the PES matrix.

The positive effect of the functionalization on the membrane performance (for CO₂/CH₄ and O₂/N₂) can be recognized on the basis of the comparison to the analogue MMMs prepared with MWCNTs unfunctionalized (1 wt % of loading): CO₂/CH₄ selectivity of 30.9 vs. 19.6 and O₂/N₂ selectivity of 6.2 vs. 2.6. The effect of CNTs loading in the range of 0.5–3.0 wt % has been evaluated. The analysis of the MMMs morphology revealed that at 0.5 wt % MWCNTs loading, the nanotubes were well dispersed throughout the PES matrix and a good adhesion of MWCNTs particles with PES matrix also was observed, while at 2 wt % and 3.0 wt % of MWCNTs loading, the nanotubes tended to agglomerate and formed interface void. The highest CO₂/CH₄ and O₂/N₂ selectivities were observed for a loading of 0.5 wt % (entries 5 and 6, Table 7),²⁵¹i.e. 250 and 10.65, respectively. Beyond this loading, a decrease of selectivity with an enhancement of permeability was observed.

Ge et al. (entry 7, Table 7)²⁵² explored PES as a hosting polymeric matrix for MMMs based on MWCNTs. MWCNTs were functionalized via H₂SO₄/HNO₃.

The MMMs have been fabricated via the phase inversion method, exploring a loading range of 1–10 wt%. The gas permeability increased with nanotube loading of 1–5 wt% without loss of selectivity.

Only for the gas pair CO₂/N₂, a slight improvement in selectivity compared to the neat polymer is observed.

The combination Pebax 1657/MWCNTs (loading range of 0–5 wt %) has been evaluated for MMMs for gas separation by Murali et al. (entries 8–10, Table 7).¹¹⁴

Un-functionalized MWCNTs have been used for the fabrication of the MMMs. The polymeric matrix has been crosslinked by using 2,4-toluylene diisocyanate. Characterization by XRD and FTIR showed both physical and chemical interactions within the matrix. Optimization of the gas performance has been realized with a loading of 2 wt% for CO₂/N₂ and H₂/N₂; enhancement of the selectivity of 49% and 233% has been observed, respectively. In the case of O₂/N₂, the selectivity improved by 43% (entry 9, Table 7). By contrast, the un-crosslinked MMMs exhibited high flux with low selectivity.

Aroon et al. evaluated the effect of chitosan as a functionalization agent for MWCNTs.²⁵³ Polyimide (PI) has been used as the polymeric matrix.

The addition of raw MWCNTs to the PI matrix drastically decreases the permeability for both CO₂ and CH₄ gases, compared to neat PI, with an improvement of selectivity of 61%. These contrasting effects collocate the performance of the MMMs below the Robeson's upper bound.

In contrast, by using functionalized MWCNTs, an improvement in both the selectivity (51.4%) and permeability (122%) for the gas pair CO₂/CH₄ has been observed. In both the cases, i.e. raw and functionalized MWCNTs, a loading of 1 wt% was used. For the first case, the decrease in gas permeability can be attributed to the impermeable behaviour of raw MWCNTs (closed ended); in the second case, the increase of permeability with an enhancement in selectivity implies open ended nanotubes with good adhesion between the nanotubes and the polymeric matrix.²⁵³

7 Conclusions

The prediction of R. Baker in 2002,²⁵⁴i.e. that the growth of membrane gas separation technology will take place in the refinery, petrochemical and natural gas industries, is confirmed in the present. Success in these sectors will require membrane materials with high performance (high flux and selectivity), that are able to operate at 70–100 °C. High-cost (in terms of research investment) materials such as block copolymers, CMS and MMMs will displace traditional polymers, such as cellulose–acetate, polysulfone, polyaramide. Carbon membranes 10–100 times more expensive than the polymeric membranes for the separation of interest can only be used in applications in which polymeric membranes completely fail to make the separation and where the competition is distillation.

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