Polymer materials for solving actual problems of membrane gas

Technologies of gas mixture separation by polymer membranes have been actively developed since the mid-1970s. Particularly in this period, asymmetric membranes with a non-porous selective layer based on poly(vinyltrimethylsilane) (PVTMS)1,2 and on polysulfone (PSF)1--3 appeared almost simultaneously to be used for separation of oxygen/nitrogen mixtures as air components and for hydrogen recovery in ammonia synthesis. Currently, membrane gas separation is one of the most rapidly developing and knowledge-intensive fields of membrane technology. In this field, various problems are solved mainly using asymmetric or composite membranes based on both glassy and rubbery synthetic polymers with selective layers several tens to several hundreds of nanometres thick.2–4 The manufacture of these membranes is a separate problem. To address this problem, it is necessary to have a selection of known polymers, or synthesize new polymers possessing optimal separating behaviour and optimal characteristics such as molecular weight distribution, mechanical strength, chemical and thermal stability, cost, etc.2–4 Currently, most membranes are manufactured on the basis of commercial mass-produced polymers.3,4 The requirements to materials for various gas separation purposes are considerably different. For example, one of the traditional processes of separation of air components (production of technical-grade nitrogen and oxygen-enriched air) does not require high thermal stability or mechanical strength, since the process takes place at a low pressure drop and at ambient temperature. In this case, the most important parameters are gas separation characteristics of the proper membrane and the process parameters; therefore, this task can be accomplished with a broad range of polymers (Table 1, Fig. 1), such as PVTMS, PSF, tetrabromo-polycarbonate (TBPC), polyphenylene oxide (PPO), polyimides (PIs) and so on. Meanwhile, another traditional problem, hydrogen recovery during the ammonia synthesis, requires the use of thermally and chemically stable and mechanically strong polymers, for example PIs, because this process occurs at elevated temperatures and pressures in the presence of ammonia traces. The large-scale recovery of acid gases (CO₂, H₂S) from natural gas has been implemented since the early 1980s with cellulose acetate (CA), membranes, the main advantages of which are low cost and ready availability of the polymer. However, in recent years, CO2-selective polymers such as poly(ethylene oxide) copolymers, PEBAX or PolyActive have been considered to be most promising for CO2 recovery (see Fig. 1). The recovery of C₂–C₄ hydrocarbons from natural and associated gases is performed using membranes made of rubbery polymers: polydimethylsiloxane (PDMS) or other polysiloxanes (see Fig. 1);3,5 however, there is an alternative trend that implies the use of highly permeable polyacetylenes such as polytrimethylsilylpropyne (PTMSP), but this trend is held up by the instability of the membrane material properties with time.3 Quite a few gas separation problems related to the use of polymer membranes have not yet been solved. For example, nitrogen recovery from natural gas or biogas has not been practically implemented as yet, but is at the stage of laboratory research or pilot tests (see Table 1). The problem of separation of olefins and paraffins,5 which is of crucial importance for the large-scale production of plastics, has not been solved either. As a rule, polymers with economically feasible separation characteristics for industrial implementation of membrane processes in these cases have not been found. Although only a narrow range of polymers find practical application, apart from optimization of separation designs using existing membranes, new membrane-forming polymer materials possessing separation and physicochemical characteristics needed for particular processes are being searched for, with the goal to extend the scope of practical applicability of the membrane separation technologies3--5 (see Table 1). The main gas separation problems and some membrane materials used to solve them are presented in Table 1.3--5 The chemical structures of the main commercial polymeric materials are depicted in Fig. 1. In this review, we consider only mixtures of non-condensable (permanent) gases, which include helium, hydrogen, oxygen, nitrogen, carbon monoxide and dioxide and methane. The issues of hydrocarbon separation are beyond the scope of this review.

Table 1

\[ \]

Main gas separation problems and membrane materials to address these problems.^2-5

(1)

Fig. 1

Chemical structures of the main commercial polymer membrane materials.

Membrane gas separation implies separation of gases in a stream. The feed stream is separated into a stream that passes through the membrane (permeate), which is enriched in the more permeable component, and the stream left above the membrane (retentate), which is enriched in the less permeable component (Fig. 2).

Fig. 2

Scheme of membrane separation.

Gas transport in polymer membranes with a thin non-porous selective layer, like that in non-porous polymer films, occurs by the dissolution--diffusion mechanism:2--­4,6,7 the gas is adsorbed on the inlet surface of the membrane (film), diffuses through the membrane under the action of the arising concentration gradient and is desorbed from the outer surface of the membrane (film).

In this case, flux J through the membrane is described by Fick's law for one-dimensional diffusion in an isotropic medium. In the case of steady-state flux at a constant temperature, a linear concentration gradient in the membrane and the lack of dependence of the diffusion coefficient (D) on the concentration of the permeating component (which is usually the case for gases at low pressures), Fick's law is simplified to the expression2,4,6

(1)

where Δc is the gas concentration gradient across the membrane, l is the membrane thickness. The gas concentration in the membrane is a function of pressure c=f(p) according to the equilibrium isotherm of gas sorption in the membrane material. At low gas pressures, all types of isotherms are reduced to the Henry isotherm.2,4,6 In this case, Δc=SΔp, where S is the gas solubility coefficient in the polymer, Δp is the pressure drop across the membrane.

Then the gas flux through the membrane is directly proportional to the pressure drop and inversely proportional to the membrane thickness

(2)

The permeability coefficient P acts as the proportionality factor in this case

(3)

In the membrane materials science literature, P is usually expressed using arbitrary units called Barrers: 1 Barrer=10^–10 cm³(STP) cm (cm² s cm Hg)^–1. The expression is not reduced because cm³(STP) refers to the amount of permeating gas (at STP), while cm and cm² refer to polymer film characteristics. Nevertheless, there are quite a few other non-SI units, including those involving various reductions.7 In SI units, P is defined in mol(m s Pa)^–1. Membranes with unknown thickness of the selective layer are characterized by gas permeability value Q=P/l. In modern publications, Q is measured, most often, in GPU units: 1 GPU=10^–6 cm³ (STP) (cm² s cm Hg)^–1. In the membrane-related literature, D is usually expressed in cm² s^–1, while S is measured in either cm³ (STP) (cm³ cm Hg)^–1 or cm³ (STP) (cm³ atm)^–1. Correspondingly, in SI units, this is m² s^–1 and mol (m³ Pa)^–1.

A factor characterizing the efficiency of a gas separation process is the selectivity of separation of gases i and j

(4)

In view of expressions (3) and (4), gas separation selectivity (permeation selectivity, ideal selectivity or, more often, selectivity) α_ij is the product of diffusion selectivity α_ij^D=D_i/D_j and the solubility selectivity α_ij^S=S_i/S_j.

The P, D and S values, the selectivity α_ij, and the diffusion α_ij^D and solubility α_ij^S selectivities are considered to be parameters of the polymer-gas system at a constant temperature and moderate pressure drops.2--4,6 The greater P for more permeable component i and the higher the separation selectivity for a particular pair of gases α_ij, the more favourable the use of this polymer as a membrane material. However, the permeability and selectivity values follow a trade-off relationship: as the permeability increases, the selectivity decreases.4,6 Therefore, the efficiency of a polymer material for the separation of a particular pair of gases is determined by the position in the permeability--selectivity diagrams (Robeson plots) with respect to the so-called upper bound relationship.8--13 Since the practical applicability of a polymeric material is determined not only by its separation properties, but also by many other characteristics, the position of the polymer in the permeability--selectivity plots is a clue for further materials science research. The upper bounds in the Robeson plots are formed by polymers with the most favourable permeability/selectivity combinations and are described by the empirical relation8,9

(5)

As time goes on, the upper bound position in these plots (Table 2) shifts to higher permeability (increase in k) and higher selectivity (increase in n), because the total number of the synthesized and studied polymers with a favourable combination of permeability and selectivity to solve various gas separation problems increases over time. The same time dependence was reported by Alentiev and Yampolskii.14 A calculation similar to that reported by Alentiev and ­Yampolskii14 carried out using the data of Table 2 shows that for the polymer with P(O₂)=100 Barrer, the O₂/­N₂ selectivity corresponding to the upper bound increases from 4.2 at 1991 to 5.4 in 2008 and reaches 8.2 in 2015. When the polymer has P(CO₂)=100 Barrer, the CO₂/CH₄ selectivity corresponding to the upper bound of 1991 amounts to 34, that for 2008 is 62, and the selectivity for 2019 is 170.

Table 2

\[ \]

Parameters of equation (5) for Robeson upper bounds of 1991⁸ and 2008⁹ and current corrections (present) reported in 2015¹⁰ and 2019.^11,12

(2)

Currently, the transport parameters for the polymer-gas systems have been collected into extensive databases, some of which are available to users;15,16 in particular, the Russian database of TIPS RAS is available.17

Since the permeability coefficients of gases are determined by their diffusion and solubility coefficients and by their ratio, for evaluating the transport and separation capabilities of a polymer, it is important to identify the factors that affect these values. According to linear correlations known from the literature, the gas diffusion coefficients in a polymeric material depend on the effective cross-sectional area of the gas molecule, i.e., on the squared kinetic diameter d (Refs 18, 19)

(6)

The solubility coefficients depend on the effective Lennard-Jones potential for the gas-gas interaction ε/k (Refs 18, 19)

(7)

The effective kinetic diameters and the effective ­Lennard-Jones parameters of non-condensable gases reported in the literature18,19 for polymers are summarized in Table 3.

Table 3

\[ \]

Effective kinetic diameters (d) and effective Lennard-Jones parameters (ε/k) of non-condensable gases for polymers.^18,19

(3)

Correspondingly, it follows from Eqns (3), (6) and (7) that

(8)

According to Teplyakov and Meares,19 K₁ for glassy and rubbery polymers varies insignificantly, by no more than 23%. The K₃ value varies by no more than 46%, which is also not much. A greater contribution to P is made by the product K₄(ε/k), since K₄ may vary by approximately 90% depending on the polymer structure, while (ε/k) may vary 38-fold depending on the considered gas (see Table 3). The term K₂d² makes even a greater contribution to the permeability coefficient, as K₂ was reported 19 to vary by a factor of 9.5 depending on the particular polymer and d² may differ by a factor of 4.3 depending on the considered gas (see Table 3).

From Eqns (4) and (8), it follows that

(9)

Thus, in most cases, from the relationship between d² and ε/k, it can be determined for each pair of gases which of the mixture components would pass through the membrane, i.e., which component would be present in higher amount in the permeate and in lower amount in the retentate. The expected selectivity level, i.e., the degree of permeate enrichment (and retentate depletion) in this component, can also be estimated.

Depending on the target component of the mixture, either permeate or retentate can be the target flow. For example, when air is separated on any non-porous polymer membrane, the permeate is enriched in oxygen [α(O₂/­N₂)>1], because d(O₂)<d(N₂) and ε/­k(O₂)> ε/­k(N₂). Consequently, for the production of ­technical-grade nitrogen, the target flow is the retentate. Since air contains 78% nitrogen and only 21% oxygen, the retentate can be easily depleted in oxygen even at a moderate gas separation selectivity.2--4,6 Thus, to attain this goal, the polymer with the highest permeability is most advantageous for air separation, all other conditions being equal. When hydrogen-containing mixtures formed in ammonia synthesis are separated, hydrogen is the target product, while unreacted nitrogen is the main contaminant. According to the data of Table 2, d(H₂)<<d(N₂) and, hence, d²(N₂) is two times greater than d²(H₂); however, ε/­k(H₂)< ε/k(N₂). Nevertheless, the ε/k(N₂) and ε/k(H₂) values differ by 25% (see Table 2), i.e., the difference between ε/k cannot counterbalance the difference between the squared kinetic diameters; therefore, hydrogen as the more permeable component tends to enrich the permeate. In view of the fact that hydrogen content in the mixture is about 60%,20 the polymer with the highest gas separation selectivity is most advantageous, all other conditions being equal.

In this review, we use both the positions of polymers in the permeability-selectivity plots and the relationships between d² and ε/k for the specified gas pairs according to Eqn (9) to evaluate the applicability of existing commercial polymers and prospective materials, including those studied since 2018, for the solution of practical problems of gas separation.

The separation of air components and, in particular, nitrogen production from air, occupies a special place among membrane gas separation processes. Thus, production of nitrogen-enriched mixtures accounts for more than 50% of the market of membrane gas separation technologies.5,21 The ready availability of raw material, the ease of obtaining these mixtures in the retentate, moderate requirements to the membrane material22 and the wide scope of applicability of nitrogen mixtures22--24 are responsible for the prevalence of this technology. For example, mixtures containing 90 to 98% nitrogen are used for the storage of various foodstuffs. A nitrogen content of 95% is sufficient to form an inert atmosphere for power engineering, for soldering in electronics, for processing of plastics and in chemical reactors. Mixtures containing 90 to 95% nitrogen form a fire-safe atmosphere; therefore, these nitrogen mixtures are used for filling fuel tanks, tankers and pipelines. For the storage of drugs and in metal working, 97% content of nitrogen is needed, while laser cutting requires 99.9%.23 The technical-grade nitrogen of various concentrations is used in synthesis gas production processes.24 In all of the above cases, one-, two- or three-stage process designs are implemented, depending on the membrane material and the required purity of the resulting gas.22

Today, the commercial-scale production of oxygen is mainly performed by cryogenic and adsorption methods, including the short-cycle adsorption process, as these methods provide high productivity and the required purity of oxygen at a relatively low oxygen concentration in the initial mixture. Meanwhile, according to feasibility studies,25 small-scale production of oxygen-enriched mixtures, for example, for medicine and agriculture, could also be effectively performed by membrane separation methods,26 particularly using polymer membranes with a non-porous selective layer.27,28 Furthermore, for small-scale processes, important factors are the compactness and mobility of the production units, which is provided by the application of membrane technologies and combinations of membranes with other types of separation and purification methods. Currently, mixtures enriched in oxygen by means of membrane technologies are used in therapeutic and preventive medicine (24-82%) and to prevent the decompression illness in divers (32-36%);23 even one-stage separation process may be sufficient for this goal. However, when the required oxygen content in the mixture is 90% or more, e.g., for catalyst regeneration, paper making industry, wastewater treatment, etc.,23 the use of one-stage air enrichment in oxygen using polymer membranes is no longer possible.29 Meanwhile, 90% O₂ purity can be attained by using two or three stages, depending on the type of the membrane.29 Apart from polymer membranes, these processes can be implemented using inorganic (e.g., carbon) membranes,30 which provide 70% oxygen content upon one-stage treatment of air. However, the cost of these membranes significantly exceeds the cost of polymer membranes; therefore, the search for new polymeric materials and the development of new composite membranes in order to achieve economically viable results is still relevant. For example, it was shown29 that increase in the membrane permeability, with the selectivity being maintained, leads to a very fast decrease in the cost of oxygen production without deterioration of the product purity. Meanwhile, an increase in the selectivity with invariable permeability does not affect the production cost, but increases the product purity.

Thus, the search for new polymeric materials with increased permeability and selectivity for air separation is stimulated by optimization of the production processes of both oxygen-enriched air and technical-grade nitrogen.

In the permeability-selectivity diagram (Robeson plot)8--10 for the oxygen-nitrogen pair (Fig. 4), the position of the upper bound considerably changed as new classes of polymers were investigated. In 1991, the upper bound was defined by highly permeable polyacetylenes, in particular, PTMSP, TBPC and step-ladder polypyrrolone.8 The upper bound of 2008 was defined by polyimides, polypyrrolones and highly permeable ladder polymers with intrinsic microporosity (PIM-1 and PIM-7) 9 (Fig. 3). Finally, in 2015, the upper bound was defined only by highly permeable semiladder polymers and polyimides based on them.10,31 Other polymers located near the upper bound of 2015 are ultrapermeable semiladder polymers with triptycene moieties in the backbone12,13,21,32 (see Fig. 3, Fig. 4) and some thermally rearranged (TR) polymers (rigid-chain polybenzoxazoles produced by solid-phase thermochemical reaction) with backbone kinks, e.g., Tröger's bases33 (see Fig. 3, Fig. 4) and some polyimides with bulky side groups.32,34,35

Fig. 3

Synthetic polymers considered in the review.

Fig. 4

Robeson plot for O₂/N₂. The plot shows the upper bounds of 1991,⁸ 2008 (Ref. 9) and 2015¹⁰ and polymers studied after 2018 and containing triptycene units,^{12,13,21,32,36-38} spiro moieties^13,21,39-48 and Tröger's bases^13,21,49-52 and TR polymers,^33,37,53-63 CANAL polymers,^52,64,65 PNBIs⁶⁶ and commercial polymers^67-72 currently used for air separation membranes (see Table 4).

For polyimides with bulky side groups, it is believed that the increase in the permeability is provided by increasing free volume caused by increasing hindrance of rotation of the backbone.35 One more type of ladder polymers are so-called CANAL polymers, which combine norbornene moieties with Tröger's base units64 or with rigid cycloaliphatic motifs65 in the backbone (see Fig. 3). In the permeability--selectivity diagram (see Fig. 4), these polymers are located above the upper bound of 2008.9 In the case of ladder polymers with rigid sites of contortion (kinks), this behaviour is caused by not only specific design elements leading to increased free volume and, therefore, high permeability,13,31,32 but also enhanced diffusion selectivity,32 resulting apparently from ordered chain packing in the polymer matrix.32,73 Owing to particularly this effect, other semiladder polymers that are not highly permeable such as polypyrrolones8,9 and poly(naphthoylenebenzimidazoles) (PNBIs)66 (see Fig. 3) are also located close to the upper bounds of the 1991 and 2008 in the permeability-selectivity diagram (see Fig. 4). Indeed, PNBIs66 are located at the upper bound of 1991 (see Fig. 4). The selectivity of the rigid semiladder polymers with kinks in the backbone tends to increase upon physical ageing due to the increase in the diffusion selectivity. For example, α^D(O₂/N₂) of semiladder polymers containing triptycene units in the backbone increases twofold or more as a result of physical ageing for 300--700 days.12 In the permeability-selectivity diagram (see Fig. 4), these polymers are located above the upper bound of 2015.10,31 The CANAL polymers with cycloaliphatic motifs65 reach the upper bound of 2015 during the physical ageing 10,31 (see Fig. 4). This result is attributable to an approximately twofold increase in the diffusion selectivity in 55 days.65 Apparently, these polymer units are also characterized by an ordered packing of chains in the polymer matrix formed during physical ageing,32,73 but this issue requires further investigation.

A comparison of the data given in Fig. 4 and in Table 4 clearly evidences that none of the commercial polymers reaches even the upper bound of 1991.8 Table 4 presents the deviations of the selectivity values (Δα, %) from the upper bound of 1991,8 which are calculated as

(10)

where α(1991) is found from known P(O₂) using the upper bound equation proposed by Robeson.8 Considering the Δα values, TBPC and PI P84 (13-15%) are located most closely to the upper bound. Meanwhile, Δα for PVTMS, which is unfortunately not manufactured now, is even lower, amounting to 9%. The deviations for PPO and Teflon AF2400 are 21-23%, while PI Upilex-R and PSF, which have been long and widely used, are characterized by the greatest Δα among the membrane polymers (36 to 40%). Although all currently used membrane materials are below the upper bound of 1991, the existence of effective processes for membrane production based on them and the stability of transport parameters over time are favourable for their use in modern industry.

Table 4

\[ \]

Modern commercial membranes for separation of air components and selective layer materials

(4)

The prospective membrane materials, including those shown in Fig. 2, despite their promising gas transport and separation characteristics, still have a few significant drawbacks. For example, highly permeable PTMSP, which determines the upper bound position of 1991,8 is unstable over time and subject to physical ageing.3,74 Meanwhile, the synthesis of time-stable PTMSP has recently been reported;75--77 therefore, this polymer can be considered to be promising for the production of technical-grade nitrogen. Thermally stable PNBIs,66 which are located near the upper bound of 1991 (Δα=2-9%) and surpass commercial polyimides in the combination of permeability and selectivity (see Table 4), are stable over time and are of great practical interest, but the manufacture of membranes from these polymers is still far from industrial implementation. Polymers containing spiro moieties13,21,39--48 or Tröger's bases 13,21,49--52 are unstable over time,31 and their synthesis also has not yet been sufficiently elaborated to be implemented on an industrial scale. Nevertheless, studies along this line are in progress, and at least PIM-1, which defines the upper bound of 2008,9 is considered to be an advantageous material, in particular for the separation of air components.21 New methods for the synthesis of PIM-1 and its copolymers 41,44,45,47,48,78 and their modifications39,40,42,43,46,79 are being developed. The triptycene-containing polymers12,13,21,32,36--38 and CANAL polymers52,64,65 are considered to be interesting new materials; however, their synthesis is fairly expensive and, considering the instability of these polymers over time,12,52,64,65 the prospects for their practical application are now obscure. Nevertheless, the situation with the synthesis of time-stable PTMSP76 (30 years later than the primary gas separation data appeared) makes it possible to classify this group of polymers as promising materials, in particular for the separation of oxygen/nitrogen mixtures. Thermally rearranged polymers,33,37,53--63 which arouse high interest for their gas transport characteristics, unfortunately do not currently possess the necessary mechanical characteristics for manufacture of commercial membranes; however, some of these polymers13 may be of interest in the future.

The recovery of helium from natural gas is an important engineering problem. Since the helium content in most deposits is extremely low (0.05-0.60 vol.%), it is isolated, most often, by the cryogenic method; hence, the cost of helium is quite high. According to various estimates, from a quarter to a third of the explored reserves of helium in the world are located in Russian oil and gas fields; however, the Russia's share of world helium production is about 3%. High concentrations of helium (0.15-1%) are present in the natural gas of the fields in Eastern Siberia and the Republic of Sakha (Yakutia), but cryogenic recovery of helium from helium-containing gases in Eastern Siberia is not always technologically possible or economically feasible. Thus, the use of membrane gas separation to recover helium from natural sources in Russia is a highly important goal for increasing the production of helium in Russia.

For the He/CH₄ pair of gases, d(He)<<d(CH₄) ­(see Table 2) and, hence, d²(CH₄) is 3.2 times as high as d²(He); hence, the He diffusion coefficient is much greater than that of CH₄. However, the ε/k(He) value is 16 times lower than ε/k(CH₄) (see Table 2). In the case of medium- and low-permeability glassy polymers with high K₂ values,19 the He/CH₄ selectivity is determined by the diffusion selectivity; therefore, helium as the more permeable component enriches the permeate, while CH4 is concentrated in the retentate. Since helium concentration in natural gas is low, successful recovery of the maximum amount of helium from natural gas requires high gas separation selectivity, while the membrane permeability can often be significantly sacrificed. Therefore, the key membrane materials for the recovery of helium from natural gas are highly selective and high-strength polyimides (Table 5). Although quite a few companies attempt to use their own hollow-fiber membranes for this purpose, UBE membranes are most successful. In recent years, hollow-fiber polyimide membranes are used for He/CH₄ separation80 (the membrane material is not disclosed).

Table 5

\[ \]

Modern commercial membranes for helium recovery from natural gas and selective layer materials

(5)

In the case of rubbery (e.g., PDMS74,81) or highly permeable glassy polymers,17,74 for which K₂ in Eqn (7) is low,19 the He/CH₄ selectivity is determined by high solubility of methane and can be close to 1 (Refs 12, 74) or be lower than 1.17,74,81 For polymers located in the vicinity of the Robeson upper bound of 1991,8 the He/CH₄ selectivity is close to 1 for P(He) of approximately 5000 Barrer, while for polymers near the Robeson upper bound of 2008,9 it is equal to 1 for P(He) of approximately 19000 Barrer. These helium permeability values are quite attainable for highly permeable polyacetylenes and triptycene-based ladder polymers (see Fig. 3).17 Thus, increase in the permeability of polymeric materials to solve the problem of helium recovery from natural gas is unreasonable, as this may invert the selectivity.

In the permeability-selectivity diagrams8,9,11 for the helium/methane pair (Fig. 5), the position of the upper bound of 1991 was determined by highly permeable PTMSP, fluorinated polyimides and polycarbonate and by low-permeable polymethyl methacrylate.8 The upper bound of 2008 was mainly defined by fluorinated polypyrrolones and perfluorinated amorphous polymers9 (Fig. 6). The position of these polymers at the upper bound is usually attributed to decrease in the methane solubility in perfluorinated polymers and, hence, increase in the selectivity.82 The effect of fluorinated groups on gas separation selectivity 83 is, in principle, explained similarly to that for perfluorinated polymers.82 In 2019, Wu et al.11 proposed a separate upper bound for the He/CH₄ pair of gases and perfluorinated polymers (see Fig. 5). For example, amorphous Teflons AF,71 other perfluorodioxoles 82,84 and amorphous polyhexafluoropropylene (PHFP) and its copolymers with tetrafluoroethylene82,85 (see Fig. 6) are located above the upper bound of 1991 and near the upper bound of 2008. Meanwhile, PHFP and its copolymers with tetrafluoroethylene annealed above the glass transition temperature are arranged above the upper bound of 2008,82,85 thus defining the upper bound position of 2019 for perfluorinated polymers.11 In the case of annealed PHFP, Δα value in excess of the upper bound of 2019 is approximately 170%. Nevertheless, the application of perfluorinated amorphous polymers for helium recovery from natural gas is doubtful due to their high cost, although it is beneficial, in view of high gas separation characteristics of these polymers.

Fig. 5

Robeson plot for He/CH₄. The plot shows the upper bounds of 1991,⁸ 2008 (Ref. 9) and 2019¹¹ and polymers studied after 2018 and containing triptycene units,^{12,13,21,32,36-38} spiro moieties^13,21,39-48 and Tröger's bases,^13,21,49-52 TR polymers,^33,37,53-63 perfluorinated polymers,^84,89-92 PNBIs⁶⁶ and commercial polymers^67,70-72 currently used in membranes for helium recovery from natural gas (see Table 5).

Fig. 6

Perfluorinated amorphous polymers.

A relatively cheaper method for the manufacture of fluorinated membrane materials is the surface fluorination of the membrane materials that already exist in the market; for a number of highly permeable polymers, this leads to high He/CH₄ selectivities virtually without the loss of productivity.86--88 However, for large-scale processes such as the helium recovery from natural gas, this type of membrane modification has not yet found wide application.

In Table 5, Δα was calculated by Eqn (10) in which α(1991) was found from known P(He) using the upper bound equation proposed by Robeson8 (see Table 2). Comparison of the data presented in Fig. 6 and in Table 5 indicates that none of the commercial materials (except for perfluorinated AF2400) approaches the upper bound of 1991. Nevertheless, PI Upilex-R is used most widely to separate the helium/methane pair, owing to its the high selectivity, particularly in industrial modules. Although perfluorinated AF2400 lies near the upper bound of 2008, its use for the large-scale process of helium recovery from natural gas is also unreasonable due to both low selectivity and high cost of the polymer.

The problem of hydrogen recovery from industrial gas mixtures is especially acute today in relation to industry transition to hydrogen energy production. Since the late 1970s, the key goals that have been addressed using membrane separation of hydrogen-containing mixtures were hydrogen recovery in the synthesis of ammonia and control of the synthesis gas composition in the synthesis of methanol. Both processes occur at high temperatures and pressures; therefore, even after cooling of the gas mixture down to temperatures suitable for polymer membrane technologies, it is desirable to carry out processes at high pressures (100 atm in the former case and more than 70 atm in the latter case).

A typical gas mixture in ammonia synthesis consists of 58-60% of hydrogen, approximately 25-26% of nitrogen and 15-16% of methane in the presence of residual ammonia.20 Therefore, the most important pairs of gases that require separation in this case are H₂/N₂ and H₂/CH₄.

In the case of methanol synthesis, the initial gas mixture consists of hydrogen (more than 60%); nitrogen, carbon dioxide and methane (approximately 11% each); and carbon monoxide (more than 3%).20 Hence H₂/N₂, H₂/CO, H₂/CO₂ and H₂/CH₄ should be considered as the target gas pairs. As a rule, in these processes, like in other petrochemical processes, residual CO₂ is removed by absorption methods (e.g., amine treatment). When hydrogen is obtained from synthesis gas of various compositions, the first high-temperature stage (>700 °C; steam reforming of natural gas or gasification of coal, other natural compounds, polymer waste or pulp-and-paper waste) is followed by a lower-temperature stage (250-300 °C), that is, water gas reaction, in which the CO content in the synthesis gas can often be neglected.93 However, the residual product contains water vapour. Hence, in this case, H₂/CO₂ is the target pair of gases to be separated. Naturally, it would be economically more advantageous to recover hydrogen at high temperatures; however, commercial polymer membranes are unstable at high temperatures; therefore, the gas mixture has to be cooled, which accounts for additional energy cost. Despite significant problems faced in the separation of this mixture using polymer membranes, the possible approaches developed in recent years are discussed below.

The H₂/CH₄ pair of gases is characterized by d(H₂)<<d(CH₄) (see Table 2). Thus, d²(CH₄) is 2.2 times higher than d²(H₂) and, hence, the diffusion coefficient of H₂ is greater than that of CH₄ by a large factor. However, the ε/k(H₂) value is also 2.5 times lower than ε/k(CH₄) (see Table 2). Therefore, as in the case of He/CH₄ pair, the H₂/­CH₄ selectivity of rubbery polymers (e.g., PDMS74,81) or some ultrapermeable glassy polymers,17 characterized by very low K₂ in Eqn (7),19 can also be dictated by the high solubility of methane and be close to or even lower than unity.17 In the case of polymers located near the Robeson upper bound of 1991,8 the H₂/CH₄ selectivity is close to 1 for P(H₂) of approximately 18000 Barrer, while for the polymers located near the Robeson upper bound of 2008,9 it is close to 1 for P(H₂) of approximately 27000 Barrer. Such hydrogen permeability values are known for highly permeable polyacetylenes.17,74 In the case of medium- and low-permeable glassy polymers with high K₂ values,19 the H₂/­CH₄ selectivity is determined by the diffusion selectivity; hence, hydrogen as the more permeable component enriches the permeate, while CH₄ is concentrated in the retentate. If the hydrogen concentration in a mixture is high, then, as in the case of production of oxygen-enriched air, it is necessary to markedly increase the selectivity rather than to increase the H₂ permeability of the membrane. Thus, like in the recovery of helium from natural gas, highly selective polyimides are used most often as the materials of usually hollow-fiber membranes for the separation of hydrogen-methane mixtures (Table 6), while the use of highly permeable polymers is unreasonable.

Table 6

\[ \]

Modern commercial membranes for hydrogen recovery and selective layer materials

(6)

In the Robeson plot8--10,13 for the hydrogen-methane pair (Fig. 7), the position of the upper bound of 1991 was mainly defined by highly permeable polyacetylenes, in particular PTMSP, fluorinated polyimides and polymethyl methacrylate.8 The upper bound of 2008 was defined by polyacetylenes, fluorinated polyimides and perfluorinated amorphous polymers9 (see Fig. 6). Finally, according to the latest data of 2015-2020, the upper bound position is defined by semiladder polymers with kinks in the backbone10 (see Fig. 3) and by TR polymers with similar units in the backbone13 (see Fig. 7). The use of perfluorinated amorphous polymers is considered to be promising for the separation of both H₂/CH₄ and He/­CH₄ pairs.11 Perfluorinated polymers such as amorphous Teflons AF71 and other perfluorodioxoles 82,84 as well as amorphous PHFP and its copolymers with tetrafluoroethylene82,85 (see Fig. 6) are located near the upper bound of 1991. Meanwhile, PHFP and its copolymers with tetrafluoroethylene annealed above the glass transition temperature are situated above the upper bound of 2008 82,85 (see Fig. 7). For annealed PHFP, the Δα values above the upper bound of 2008 are approximately 120%. The effect of fluorine present in the polymer molecule, as in the case of He/CH₄ gas pair, is attributed to decreasing solubility of methane in perfluorinated polymers, while the effect of annealing is explained as being due to the sharp decrease in its diffusion coefficient. Hence, both effects lead to a pronounced increase in the selectivity.82 Nevertheless, the application of perfluorinated polymers for the separation of H₂/CH₄ gas pair is restricted by their high cost. Interestingly, PNBI containing a hexafluoroisopropylidene bridge in the backbone66 (see Fig. 3) is also beyond the upper bound of 1991 (see Fig. 7), with the Δα value relative to the upper bound of 1991 being 15%. Other PNBIs lie at the upper bound of 1991.66 The influence of fluorinated groups on the gas separation selectivity 83 is, in principle, explained similarly to that for perfluorinated polymers.82 Polymers with fluorinated CANAL side groups94 and fluorinated polyimides based on 6FDA dianhydride and diamines with norbornene groups, i.e., CANAL-PI 52 are also located at the upper bound of 2008.9 However, CANAL polymers containing Tröger's bases64 and rigid cycloaliphatic motifs65 (see Fig. 3) are located above the upper bound of 2008 9 and, in some cases, above the upper bound of 2015 10,31,65 (see Fig. 7). Apparently, like in the case of semiladder polymers with rigid kinks in the backbones,12,13,21,32 this can be attributed to enhanced diffusion selectivity32 resulting from ordering of chain packing in the polymer matrix.32,73

Fig. 7

Robeson plot for H₂/CH₄.The plot shows the upper bounds of 1991,⁸ 2008⁹ and 2015¹⁰ and polymers studied after 2018 that contain triptycene units,^{12,13,21,32,36-38} spiro moieties^13,21,39-48 and Tröger's bases,^13,21,49-52 TR polymers^33,37,53-63 CANAL polymers,^52,64,65 PNBIs,⁶⁶ perfluorinated polymers^84,89-92 and commercial polymers^67-72 currently used in membranes for H₂/CH₄ separation (see Table 6).

For the H₂/N₂ pair of gases, d(H₂)<<d(N₂) (see Table 2); hence, d²(N₂) is two times higher than d²(H₂) and, consequently, the diffusion coefficient of H₂ is much higher than the diffusion coefficient of N₂. However, ε/k(H₂) is only 1.3 times lower than ε/k(N₂) (see Table 2). Thus, the solubility of nitrogen cannot play a significant role in the H₂/N₂ separation selectivity, even if K₂ in Eqn (7) is exceptionally low.19 Indeed, for example, for polymers located near the Robeson upper bound of 1991,8 the H₂/N₂ selectivity can be equal to 1 for P(H₂) of approximately 53000 Barrer. There are no polymers with this level of hydrogen permeability coefficients.17 As a consequence, the H₂/N₂ selectivity is determined by the diffusion selectivity, and hydrogen as the more permeable component is concentrated in the permeate, while N₂ is concentrated in the retentate. If the hydrogen concentration in hydrogen-containing mixtures is high (about 60%),20 successful separation of the H₂/N₂ mixture, like separation of the He/CH₄ mixture, requires increase in the selectivity rather than increase in the permeability of the membrane material. Hence, as in the case of hydrogen--methane mixture, highly selective polyimides are the most promising membrane materials for the separation of H₂/N₂ mixtures (see Table 6). Nevertheless, as in the above cases, polysulfone membranes are used owing to their ready accessibility, relatively low cost and higher gas permeability compared to that of polyimides, despite their much lower selectivity.20

The upper bound of 1991 in the Robeson diagrams8--­10,13 for the hydrogen--nitrogen pair, like for the hydrogen--methane pair, was mainly defined by highly permeable polyacetylenes, in particular PTMSP, and polymethyl methacrylate.8 The upper bound of 2008 was defined by polyacetylenes, fluorinated polyimides and highly permeable semiladder polymers with intrinsic microporosity (PIM-1 and PIM-7).9 Finally, according to the latest data of 2015-2020, the upper bound position is defined by semiladder polymers containing rigid kinks10 and by TR polymers with the same moieties13 (Fig. 8). Perfluorinated amorphous polymers are not promising for the separation of this pair of gases, as they do not reach even the upper bound of 1991,82,85 whereas all PNBIs are located at the upper bound of 1991⁶⁶ (see Fig. 8). In view of the high selectivity of PNBIs and their chemical and thermal stabilities, which exceed these parameters for polyimides, these polymers can provide the basis for a selective membrane layer, especially for the hydrogen recovery in ammonia synthesis taking account of high pressure and temperature of the mixture.20 However, the manufacture of membranes from these polymers is still far from industrial implementation. The currently studied CANAL polymers52,64,65,94 are usually located near the upper bound of 20089 (see Fig. 8). However, CANAL polymers with rigid cycloaliphatic motifs65 go beyond the upper bound of 2015 during physical ageing.10,31 This effect might also be attributable to an increase in diffusion selectivity and ordering of chain packing in the polymer matrix,32,73 but this requires further investigation. The increase in the diffusion selectivity by a factor of three or more during physical ageing during 300-700 days is also observed for triptycene-based semiladder polymer;12 particularly these polymers are beyond the 2015 upper bound for the H₂/N₂ pair.10,31 The high selectivities of CANAL polymers containing rigid cycloaliphatic motifs,65 observed after physical ageing [α(H₂/N₂)>100 for P(H₂)>1000 barrer], point to their obviously good prospects. However, the problems of synthesis and stability of properties of the above polymers, like for other semiladder polymers with rigid kinks in the backbones or TR polymer, which define the Robeson upper bounds, still preclude the use of these polymers for membrane manufacturing.

Fig. 8

Robeson plot for H₂/N₂. The plot shows the upper bounds of 1991,⁸ 2008⁹ and 2015¹⁰ and polymers studied after 2018 that contain triptycene units,^{12,13,21,32,36-38} spiro moieties^13,21,39-48 and Tröger's bases,^13,21,49-52 TR polymers,^33,37,53-63 CANAL polymers,^52,64,65 PNBIs⁶⁶ and commercial polymers^67-72 currently used in membranes for H₂/N₂ separation (see Table 6).

While discussing the possibility of H₂/CO separation, it is necessary to note that d(CO)=d(N₂) (see Table 2) and, hence, all considerations of the diffusion selectivity for the H₂/N₂ pair of gases are also applicable to H₂/CO. However, the ε/k(CO) value is 20% greater than ε/k(N₂) and, consequently, ε/k(H₂) is 1.6 times lower than ε/k(N₂) ­(see Table 2). Correspondingly, P(CO)>P(N₂) for any polymer, and the H₂/CO selectivity is lower than the H₂/­N₂ selectivity. Moreover, according to Alentiev et al.,95 if there is no specific interactions between CO and the membrane material, the CO permeability coefficient can be calculated with high accuracy via P(N₂) by the equation

(11)

Hence, the selectivity can be found as

(12)

and the upper bound parameters of the permeability--selectivity plots can be found (see Table 7).

Table 7

\[ \]

Upper bounds of the permeability-selectivity plot for the H₂/CO pair of gases calculated from Eqn (11)

(7)

Due to the higher solubility of CO compared to N₂, for polymers located near the 1991 Robeson upper bound,8 the H₂/CO selectivity may be equal to 1 for P(H₂) of approximately 16000 Barrer, while for polymers located near the 2008 Robeson upper bound,9 it is equal to 1 for P(H₂) of approximately 30000 Barrer. For highly permeable polyacetylenes, such hydrogen permeability values are unusual, but, nevertheless, known.17,74 Hence, like in the case of separation of other hydrogen-containing gases, the use of highly permeable polymers is unfavourable, and in this case, too, highly selective polyimides or polysulfones are used to control the synthesis gas composition (see Table 1).

Generally, if the polymer has a favourable selectivity for the H₂/N₂ pair of gases, it will also be applicable for the H₂/­CO pair, although it may be located below the upper bound of the permeability-selectivity diagram.

The H₂/CO₂ pair of gases is most challenging for the separation on polymer membranes. However, this pair is simultaneously one of the most important, because hydrogen produced from synthesis gas always contains a large amount of CO₂ (up to 45%).96

For the H₂/CO₂ pair of gases, d(H₂)<<d(CO₂) (see Table 2) and, consequently, d²(CO₂) is 2 times greater than d²(H₂); hence, the H₂ diffusion coefficient is much greater than that of CO₂. However, the ε/k(H₂) value is 3.4 times lower than ε/k(CO₂) (see Table 2). The solubility of H₂ in polymers is lower than the CO₂ solubility to an extent such that the H₂ and CO₂ permeability coefficients for many polymers are comparable: for most polymers, the H₂/CO₂ selectivity does not exceed 2-4 and the Robeson plot passes through the selectivity inversion line α=1 (Fig. 9). For the polymers located near the Robeson upper bound of 1991,8 the H₂/CO₂ selectivity can be equal to 1 for P(H₂) of approximately 1200 Barrer, while for polymers located near the upper bound of 2008,⁹ it is equal to 1 for P(H₂) of approximately 4500 Barrer. Naturally, there are many polymers for which the CO₂ permeability is higher than hydrogen permeability: rubbery polymers,74,81 highly permeable glassy polymers, e.g., polyacetylenes,74--76,97 polynorbornenes98--106 or semiladder PIM polymers.12,40,41,47 For these highly permeable polymers, the target component of the mixture, hydrogen, is concentrated in the retentate, while the permeate becomes enriched in CO₂. The recovery of hydrogen, like the enrichment of air in oxygen, requires high CO₂/H₂ selectivity; however, the CO₂/H₂ selectivity for these polymers usually does not exceed 4-5 [α(H₂/­CO₂)>0.2]17 (see Fig. 9). The recovery of hydrogen into the permeate in the case where α(H₂/CO₂)>1, as for other hydrogen-containing mixtures, also requires high selectivity, but even the highest H₂/CO₂ selectivities known for polymers do not exceed 20, while the P(H₂) values for such polymers are much lower than 10 Barrer17 (see Fig. 9), which sharply reduces the performance of membrane ­processes.

Fig. 9

Robeson plot for H₂/CO₂. The plot shows the upper bounds of 1991⁸ and 2008⁹ and polymers studied after 2018 that contain triptycene units,^{12,13,21,32,36-38} spiro moieties^13,21,39-48 and Tröger's bases,^13,21,49-52 TR polymers,^33,37,53-63 CANAL polymers,^52,64,65 PNBIs,⁶⁶ PBIs^111,119 and commercial polymers^67-72 currently used in membranes for H₂/CH₄ separation (see Table 6).

Thus, two strategies are used to address the H₂/CO₂ mixture separation: hydrogen recovery in the permeate by the diffusion mechanism and CO₂ recovery in the permeate owing to high CO₂ solubility. According to the former strategy, high-temperature gas separation at 200-300 °C on thermally stable membranes is currently considered to be promising. The principle of this separation is that the temperature factor of the permeability coefficient is significantly higher for H₂ than for CO₂. If a polymer is stable to be used at temperatures above 200 °C, it is expedient to consider this polymer for the development of high-temperature polymer membranes. Polymers proposed today for processes of this type include polyimides,69 polybenzimidazoles (PBIs)4,96,107 and polynaphthoylenebenzimidazoles.66 While choosing polymers from this series, it should be borne in mind that the use of PIs, which are hydrolyzed under drastic conditions, is unreasonable, because hydrogen-containing high-temperature mixtures contain, most often, residual amounts of water; therefore, the main efforts of researchers are now concentrated on PBIs.107 For example, commercial m-PBI called Celazole (see Fig. 1), which is used to manufacture thermally stable and heat and fire resistant plastics and fibers and proton-conducting membrane matrices for high-temperature hydrogen fuel cells,108 has barrier propertes at room temperature107 [P(H₂)<1 Barrer].7 However, at temperatures of 200-250 °C, the permeability coefficient of hydrogen sharply increases to 14 (Ref. 7) and 23 (Ref. 109) Barrer, while the H₂/CO₂ selectivity reaches 20 (Ref. 7)-24 (Ref. 109). The hollow fibers based on m-PBI at temperatures of 200-250 °C have a hydrogen permeability of 200-400 GPU for the H₂/CO₂ selectivity of 20--40.107 Recent publications describe modification of m-PBI by doping with phosphoric acid110 or cross-linking.111

The data obtained at 150-200 °C are also far above the upper bound in the H₂/CO₂ plot (see Fig. 9). Other chemical structures of PBI107,109,112 and TR polymers mixed with m-PBI 107,113 are no less promising. These polymers and mixtures are much more permeable than m-PBI and are also above the upper bound in the H₂/CO₂ plot (see Fig. 9). Finally, a planar composite membrane Proteus107,114 was developed and characterized by Q(H₂)≈300 GPU and α(H₂/CO₂)≈32 at 200 °C.107 The membrane material is not disclosed, but judging from the position above the upper bound of the H₂/CO₂ plot (see Fig. 9),107,114 this may also be PBI.

If the latter strategy is used, polymers should have high CO₂/H₂ selectivities, which are, unfortunately, unattainable for common polymers. Therefore, research in this area is focused on polymers and materials that specifically interact with CO₂.96,115,116 Thus, due to the high solubility of CO₂ in these materials, the membrane selectivity can exceed 50 at a high performance.96,117 Materials of this type characterized by specific interactions with CO₂ are discussed below. The main drawback of these materials is operating temperature, which does not exceed 100 °C; therefore, the gas mixture must be cooled before the separation. Nevertheless, both separation strategies are used today:114 in the first, high-temperature stage, H₂-selective Proteus membranes are used,107,114 while in the second, low-temperature stage, CO₂ is recovered from the mixture on CO₂-selective Polaris membranes.118

An interesting exception to the general rule are CANAL polymers containing rigid cycloaliphatic motifs.65 Films of these polymers are characterized by P(H₂) from 2800 to 5200 Barrer at a H₂/CO₂ selectivity close to 1. However, during physical ageing, the CO₂ permeability decreases to a substantially higher extent than hydrogen permeability. Therefore, the points corresponding to these polymers cross the selectivity inversion line, and at P(H₂) from 900 to 2400 Barrer, the H₂/CO₂ selectivity is 4 to 9. This effect may also be attributed to an increase in the diffusion selectivity and ordering of chain packing in the polymer matrix during physical ageing,32,73 which requires further thorough investigation. Nevertheless, these selectivities of CANAL polymers containing rigid cycloaliphatic motifs65 in combination with high hydrogen permeability indicate that these polymers are evidently promising for the separation of the H₂/CO₂ pair.

In Table 6, the Δα values were calculated by Eqn (10) where α(1991) was found from known P(H₂) using the upper bound equations proposed by Robeson8 (see Table 2) for the corresponding pairs of gases. Comparison of the data shown in Figs 4-6 and in Table 5 indicates that only perfluorinated AF2400 for the H₂/CH₄ and H₂/CO₂ pairs is above the upper bound of 1991, but its application is unreasonable due to low selectivity. All other commercial polymers are far below the upper bound of 1991. Among commercial polymers, only PI P84 is located close to the upper bound of 1991 for the H₂/N₂ pair (Δα=12%). That is why Sepuran hollow fibers are best suited for solving this problem, while the Proteus membrane is optimal for high-temperature recovery of hydrogen.

The problem of nitrogen and methane gas separation is also important for increasing the calorific value of natural gas, which contains, as a rule, 4 to 10% of nitrogen and, in some cases, even 30% and more,120 and for methane enrichment of biogas containing 5-15% of nitrogen.96 The gas sent to a pipeline should contain less than 4% of nitrogen; the product containing 30-50% of nitrogen can be used as a compressor fuel; and the product with nitrogen content of 50-85% is suitable only as a flare gas.120

For the N₂/CH₄ pair of gases, d(N₂) is smaller than d(CH₄) (see Table 2), but d²(CH₄) is only 9% greater than d²(N₂); hence, the diffusion coefficient of N₂ is higher than the diffusion coefficient of CH₄, but the N₂/CH₄ diffusion selectivity depends most appreciably on K₂.18,19 Hence, for rubbery polymers74,81 and for highly permeable glassy polyacetylenes,74--76,97 α^D(N₂/CH₄) is moderate: 1.2 for PDMS 81 and 1.1-1.3 for polyacetylenes.17 According to Teplyakov et al.,18,19 the diffusion selectivity varies from 1.2 to 6.6. However, the ε/k(CH₄) value is also 1.9 times higher than ε/k(N₂) (see Table 2). Therefore, the N₂/CH₄ solubility selectivity is always less than 1 (from 0.28 to 0.09 according to Teplyakov et al.18,19). Since the diffusion and solubility selectivities are oppositely directed and comparable in magnitude, not only the Robeson plot for the N₂/CH₄ pair of gases passes through the selectivity inversion line α=1 (Fig. 10), but also the numbers of polymer located on both sides of the inversion line are approximately equal.9 Moreover, the nitrogen/methane separation selectivity does not exceed 7, while the methane/nitrogen selectivity does not exceed 8;17 therefore, the separation of a nitrogen--methane mixture is quite a complicated task for polymer membranes.

Fig. 10

Robeson plot for N₂/CH₄. The plot shows the upper bounds of 2008⁹ and 2019¹¹ and polymers studied after 2018 that contain triptycene moieties,^{12,13,21,32,36-38} spiro moieties^13,21,39-48 and Tröger's bases,^13,21,49-52 TR polymers,^33,37,53-63 perfluorinated polymers^84,89-92 and commercial polymers.^67-72

Feasibility calculations show that nitrogen separation from natural gas is inexpedient if the nitrogen content is more than 30%.120 As applied to the problem of nitrogen/methane separation, the whole array of polymeric materials is divided into nitrogen-selective (nitrogen-enriched stream in the permeate) and methane-selective materials (methane-enriched stream in the permeate).120 Thus, nitrogen-selective polymers are advantageous for separating small amounts of nitrogen from natural gas or biogas, while methane-selective polymers are advisable for mixtures with high nitrogen contents. Methane-selective materials are usually rubbery polymers, some block copolymers, glassy polynorbornenes and highly permeable polyacetylenes.

In the Robeson plots9,11 for the N₂/CH₄ pair, the upper bound position of 2008 was defined by PTMSP and its copolymers, fluorinated polypyrrolone and polyimide and, mainly, perfluorinated amorphous polymers.9 As in the case of helium--methane pair, the special role of perfluorinated polymers is attributed to a decrease in the methane solubility and, hence, increase in the selectivity.82 The beneficial effect of fluorinated groups on the selectivity is explained in a similar way.83 In 2019,11 a separate upper bound for perfluorinated polymers was proposed for the N₂/CH₄ pair (see Fig. 10). Thus, amorphous Teflon AF 2400,71 perfluorinated methyl ethyl dioxole82,84 and amorphous PHFP82,85 are located at approximately the upper bound of 2008 (see Fig. 10). Meanwhile, PHFP and its copolymers with tetrafluoroethylene annealed above the glass transition temperature lie above the upper bound of 2008,82,85 with annealed PHFP being located even somewhat higher than the 2019 upper bound for perfluorinated polymers11 [Δα(2019) is approximately 7%] (see Fig. 10). Although the use of perfluorinated polymers for nitrogen recovery from natural gas is questionable because of their high cost, they have been investigated as nitrogen-selective membranes on a pilot scale.120 Apparently, in view of high gas-separation characteristics of perfluorinated polymers, their application for the separation of nitrogen and methane is quite promising. A less expensive method for the fabrication of nitrogen-selective membranes is surface fluorination, which provides high N₂/CH₄ selectivity with some loss of permeability for a number of highly permeable polymers.86--88 Nevertheless, because of the difficulties in the design of modification process for large-area membranes, requiring a thorough selection of process conditions for the use of fluorine as a hazardous chemical, the need for special equipment stable in harsh environments, difficulty of disposal of used fluorine and so on,86 this method of polymer membrane modification has not yet found application in practice.

Currently, pilot projects using methane-selective membranes have been developed and are being implemented to address the task of separation of nitrogen-methane mixtures. In particular, high-performance PDMS membranes are used in this process,120 in spite of their low selectivity — α(CH₄/N₂)≈3. Other commercial membranes are inapplicable for this purpose, as their N₂/­CH₄ selectivity is close to 1.^67-72,121

The removal of acid gases from natural gas is one of the major large-scale membrane processes (see Table 1). The key trouble with this process is the release of carbon dioxide. The CO₂ content of natural gas is usually 20--40%,96,115 and, in some cases, it is up to 70%.96,115 Thus, the main pair of gases that served as the target for the selection of membrane materials is CO₂/CH₄.

Like in the case of the O₂/N₂ pair, d(CO₂)<d(CH₄) (see Table 2) and, hence, the diffusion coefficient of CO₂ is greater than that of CH₄. Also, ε/k(CO₂) considerably exceeds ε/k(CH₄) (see Table 2); therefore, the solubility coefficient is higher for CO₂ than for CH₄. Finally, the permeability coefficient is also much higher for CO₂ than for CH₄, and the separation selectivity of CO₂/CH₄ pair is determined by both the diffusion and solubility selectivities. In the membrane separation of the carbon dioxide-methane mixture, the permeate is enriched in the more permeable CO₂, while CH₄ is concentrated in the retentate. This is fairly advantageous, as in the case of obtaining technical-grade nitrogen from air. Therefore, the removal of acid gases from natural gas was expectedly among the first membrane gas separation processes to be implemented and to employ, since 1980s, asymmetric planar membranes (Separex) based on cellulose acetate, a cheap polymer produced on a large scale,3--5 despite the fact that P(CO₂) for cellulose acetate does not exceed 6 Barrer.17 When the CO₂ content in natural gas is high, multistage separation processes are of course necessary, which makes the separation more expensive.

One more problem requiring the separation of a CO₂/­CH₄ mixture is the separation of biogas components, which has been especially important in recent decades with the advent of microbiological techniques (see Table 1). Biogas also contains 30-40% of CO₂;96 therefore, the recovery is performed using the same membrane materials, as treatment of natural gas. One more biogas component is nitrogen (5 to 15%).96 However, for cellulose acetate membranes, nitrogen permeability is close to methane permeability and, hence, nitrogen is also concentrated in the retentate; generally, this does not prevent the use of recovered methane for fuel, together with nitrogen impurity.96

In the Robeson diagram8,9,12,13 for the carbon dioxide-methane pair (Fig. 11), like for other pairs of gases, the upper bound position has also significantly changed as new classes of polymers were studied. The upper bound of 1991 was mainly defined by highly permeable polyacetylenes, in particular PTMSP, fluorinated polyimides and poly(methyl methacrylate).8 The 2008 upper bound was defined by polyacetylenes, fluorinated polyimides and highly permeable ladder polymers with intrinsic microporosity (PIM-1 and PIM-7).⁹ Some polyimides with bulky side groups are also located near the upper bound of 2008.^34,35 Finally, according to the latest data of 2019-2020, the upper bound position is defined by highly permeable semiladder polymers, including those containing triptycene units in the backbone12 and TR polymers with similar units13 (see Fig. 11). As for the oxygen--nitrogen pair, this location in the plot for semiladder polymers with rigid kinks in the backbone is determined by not only the increased free volume and, hence, high permeability,13,31,32 but also by the increased diffusion selectivity,32 which is combined with high CO2 solubility and thus leads to high separation selectivity.

Fig. 11

Robeson plot for CO₂/CH₄.The plot shows the upper bounds of 1991,⁸ 2008⁹ and 2019,¹² some perfluorinated polymers and polymers studied after 2018 that contain triptycene units,^{12,13,21,32,36-38} spiro moieties^13,21,39-48 and Tröger's bases,^13,21,49-52 including TR polymers with respective moieties^33,37,53-63 and commercial polymers^67-72 currentlyused in membranes for separation of natural gas and biogas (Table 8).

CANAL polymers52,64,65,94 are located near the 2008 upper bound.9 And only physically aged CANAL polymers with rigid cycloaliphatic motifs65 are above the upper bound of 2008,⁹ although they still do not reach the upper bound of 2019.¹² Apparently, this can also be attributed to a sharp increase in the selectivity (from 5 to 11 within 55 days)65 and to possible ordering of the chain packing in the polymer matrix during physical ageing.32,73 Similar increase in the diffusion selectivity during physical ageing is observed for semiladder polymers with triptycene moieties in the backbone12 in which α^D(CO₂/CH₄) increases 2-2.5-fold within 300-700 days.

Perfluorinated amorphous polymers are also considered to be promising materials for separation of CO₂/CH₄ pair.11,116 Nevertheless, amorphous Teflons AF71 and other perfluorodioxoles82,84 (see Fig. 6) do not reach the upper bound of 1991. Meanwhile, the deviation Δα from the 1991 upper bound of amorphous PHFP is approximately 6%;82,85 its copolymers with tetrafluoroethylene annealed above the glass transition temperature are located above the upper bound of 1991,82,85 while annealed PHFP approaches the 2008 upper bound82,85 (the deviation Δα from the upper bound of 2008 is also approximately 6%) (see Fig. 11). These effects are, most often, attributed by the authors to a decrease in the methane solubility in perfluorinated polymers and, hence, increase in the selectivity.82 It is of interest that PNBI containing a hexafluoroisopropylidene bridge in the backbone66 is also above the 1991 upper bound and approaches the 2008 upper bound. The effect of fluorinated groups on the gas separation selectivity83 is also explained by decreasing methane solubility.82 The application of fluorinated and perfluorinated polymers for large-scale recovery of CO₂ from natural gas is unlikely, because of their high cost; however, this can be cost-effective for the separation of biogas.

The kinetic diameters of gas molecules in the CO₂/N₂ pair, which is the major gas mixture in the separation of flue gases (see Table 1), are roughly equal (see Table 2); therefore, the d²(CO₂)-d²(N₂) difference is close to zero, the diffusion selectivity is low, differing only slightly from unity.14 The ε/k(CO₂) value is 2.6 times greater than ε/­k(N₂) (see Table 2); therefore, the selectivity of separation of these gases is determined by the selectivity of solubility. Like in the case of CO₂/CH₄ pair of gases, the permeate should be enriched in CO₂, while N₂ should be concentrated in the retentate. The CO₂ content in flue gases is relatively low, ranging from 8 to 15%, while the nitrogen content is 60 to 70%;96 therefore, as in the case of production of oxygen-enriched air, it is necessary not only to increase the CO₂ permeability of membranes but also to considerably increase the selectivity; this can be attained only by increasing the CO₂ solubility in the membrane material. However, flue gases have to be cooled down before membrane separation; furthermore, they contain water vapour, sulfur oxides or nitrogen oxides, which requires additional purification. The need to include more stages retards the implementation of the membrane gas separation for the CO₂/N₂ pair: only pilot units now exist. The Robeson upper bounds (Fig. 12) for the CO₂/N₂ gas pair are generally quite arbitrary, because the point cloud is actually extended along the permeability axis.14 Nevertheless, the upper bound of 2008 is defined by polyacetylenes, including PTMSP, highly permeable ladder polymers with intrinsic microporosity (PIM-1 and PIM-7) and rubbery polysiloxanes and polyphosphazenes with methoxy and ethoxy groups.9 According to the data of 2019, the upper bound position is defined by the same groups of polymers as that for the CO₂/CH₄ pair, namely, highly permeable semiladder polymers, including the polymers featuring triptycene units in the backbone12,116 and TR polymers with the same units13,116 (see Fig. 12). Nevertheless, materials in which CO₂ is readily soluble based on nitrogen-containing polymers, ionic liquids and polymers containing aliphatic polyether blocks have been considered in recent years particularly for the CO₂/N₂ pair.96,115,116 High solubility of CO₂ in these polymers is determined by specific interactions between the quadrupole CO₂ molecule and charged or dipole groups of the polymer chain.96,116 Since the mechanism of CO₂ recovery from mixtures on these membranes is equally applicable to separation of CO₂/N₂ mixtures and CO₂/H₂ mixtures, they will be considered separately.

Fig. 12

Robeson plot for CO₂/N₂. The plot shows the upper bounds of 2008⁹ and 2019,¹² perfluorinated polymers and polymers studied after 2018 that contain triptycene units,^{12,13,21,32,36-38} spiro moieties^13,21,39-48 and Tröger's bases,^13,21,49-52 including TR polymers,^33,37,53-63 polymers with ether blocks,^{105,106,122-131} materials based on nitrogen-containing polymers and ionic liquids^50,132-141 and commercial polymers^{67-72,142,143} (see Table 8)

In Table 8, Δα is calculated by Eqn (10), where α(1991) and α (2008) are found from known P(CO₂) using the upper bound equations proposed by Robeson8,9 (see Table 2) for the corresponding gas pairs. Comparison of the data shown in Fig. 11 and Fig. 12 and Table 8 indicates that none of the commercial materials reaches the 1991 and 2008 upper bounds. Only polymer membranes characterized by specific interaction with CO₂ occupy top positions.

Table 8

\[ \]

Modern commercial membranes for carbon dioxide recovery and selective layer materials

(8)

Polymers and polymeric materials in which CO₂ is readily soluble, in particular those functioning according to active (facilitated) transport principles have been actively studied in recent years for the separation of CO₂/N₂ and CO₂/H₂ gas mixtures. Most of these materials can be regarded as polymers with stationary sites of complex formation with CO₂. Quite a few models for the transport in these systems have been developed to date;144 however, the simplest and most useful model has been proposed by Alentiev et al.96 and Rea et al.144 and is based on the dual mode sorption in glassy polymers.2,4,6,144

According to this model, the total permeability coefficient P at low pressures is defined as the sum of contributions from the passive and active transport

(13)

where P_D is the permeability coefficient for the passive transport, k_D is the solubility coefficient for the Henry population of the sorbate molecules in the polymer matrix, D_D is the diffusion coefficient for the passive transport in the matrix corresponding to this population, P_C is the permeability coefficient for facilitated transport, D_C is the effective diffusion coefficient for the population of the specifically interacting sorbate molecules, k_C is the solubility coefficient for the specifically interacting sorbate molecules. For non-interacting gases such as N₂ and H₂, the P value is determined only by the first term of Eqn (13), while in the case of CO₂, the specific interaction can markedly increase the total solubility coefficient and, hence, the permeability; as a result, the selectivity of separation of CO₂-containing gas mixtures increases.

For example, CO₂ reacts with amino groups –NH₂, –NHR and -NR₂ present in polymers such as polyvinylamine, polyallylamine, polyethyleneimine, chitosan or PAMAM (polyamidoamine dendrimer) (Fig. 13).117 Primary and secondary amines react with CO₂ to form zwitter-ions and thus they act as binding sites.145 If a membrane contains water, CO₂ is converted to carbonate or hydrogen carbonate ion, as in the standard amine treatment.116 In this case, k_C is determined by the concentration of nitrogen-containing groups and by the equilibrium constant for the reaction of carbon dioxide with nitrogen-containing groups.115 However, separation processes on these membranes depend not only on the concentration of binding sites, but also on the pressure, temperature and humidity, which in some case sharply decrease the gas separation characteristics.146,147 Nevertheless, the permeability and selectivity values for such membranes reported in original publications and reviews may be very high.96,115,117,148 For example, poly-N-methylvinylamine-based membranes provide separation selectivity of up to 160 for CO₂/H₂ and up to 350 for CO₂/N₂ at P(CO₂) of 6800 Barrer,149 while poly-N-isopropylallylamine-based membranes148 demonstrate a selectivity of 300 for CO₂/H₂ and 650 for CO₂/N₂ at P(CO₂) of 6500 Barrer.

Fig. 13

Polyamines and polymeric ionic liquids

An interesting approach is modification of polymers, e.g., poly(ether ether ketones), with polyethyleneimine,139 although the permeability level observed for polyamines cannot be attained in this way. A considerable drawback of these membranes is the presence of water; this requires moistening of gas streams to preserve the separation properties of the membranes, and the applicability of the membranes is restricted to temperatures not exceeding 100 °C. As a result, such membranes are now used only on a laboratory scale.150 Meanwhile, the obtained characteristics are suitable for recommending these membranes for fuel cell applications.151

A synergistic effect was noted for CO₂ reactions with amino groups and quaternary ammonium bases. Indeed, membranes based on vinylamine copolymers with ­poly(diallyldimethylammonium salts)148 demonstrating high CO₂ permeability (more than 1800 GPU) provide a CO₂/H₂ selectivity of about 30 and CO₂/N₂ selectivity of about 160. High CO₂/H₂ selectivity was found for membranes made of poly(diallyldimethylammonium chloride) doped with low-molecular-weight quaternary ammonium bases:133 the CO₂/H₂ selectivity is about 100 with the CO₂ permeability being above 100 GPU.96,148

Polymeric ionic liquids (PILs) with nitrogen-containing cations and various counter-ions are also considered as CO₂ transporting materials.96,116,152,153 The reactions of ionic liquid moieties with CO₂, like reactions of other nitrogen-containing groups, is associated with the formation of zwitter-ions or with nucleophilic addition.152 The selectivity for CO₂/N₂ pair attained in composite membranes with PILs can reach 2000, with the permeability exceeding 5000 GPU.154 However, many PILs, although readily dissolve CO₂, still show moderate gas separation characteristics.96,135,138,153,155 Nevertheless, some of them reach the upper bound of 2008 for the CO₂/N₂ pair.137,141 Highly permeable PILs based on polyacetylenes are also close to the 2008 upper bound for CO₂/N₂.156,157 For PILs, the presence of water in the membrane is not necessary; this forms an advantage for PILs over polyamines and accounts for high practical interest in the synthesis of new PILs.

The specific dipole--quadrupole interactions of CO₂ with the membrane material also provide for the ready solubility of CO₂ in the polymers.96,116 Thermoplastic PEBAX copolymers, that is, block copolymers of PA-6 or PA-12 polyamides with polyethylene oxide or polytetramethylene oxide96,116,158,159 (see Fig. 1) were among the first materials to demonstrate this effect. It was found that the mobile dipoles of aliphatic polyether units of these polymers can interact with CO₂ quadrupoles or with other polar molecules at room temperature.158 In principle, each dipole can be considered as a specific binding site. The polyether blocks should not be too long, because linear aliphatic polyethers are easily crystallized, which reduces the gas permeability.159

The PolyActive membrane developed on the basis of linear copolymers of terephhalic acid polyesters with short poly(ethylene glycol) blocks of various lengths143 (see Fig. 1) proved to be efficient for the separation of CO₂-containing mixtures [up to 50 for α(CO₂/N₂) and up to 8 for α(CO₂/H₂) depending on temperature]. In recent years, the main research efforts in this field have been concentrated on the design of cross-linked aliphatic polyethers,122,160 network copolymers of aliphatic polyethers with, for example, polynorbornenes (PNBs) and PDMS 123,124 and network copolymers with polyethylene glycol and diethylene glycol methacrylates,125,161 particularly those containing nitrogen-containing groups126,162 (Fig. 14), or polymer matrices filled with ionic liquids.163,164 Most efficient are comb-like copolymers of poly(1,3-dioxolane)116,127,129,153 (see Fig. 14), which are located above the upper bounds in the CO₂/N₂ and CO₂/H₂ plots127 and, in terms of selectivity values, they are close to the CO₂-selective Polaris membranes.118 Quantum chemical calculations127 demonstrated that the complex with CO₂ is most energetically favourable for these polymers.116,127,129,153

Fig. 14

Polymers with ethylene glycol groups (examples)

The crucial role of the mobility of ether dipoles in the appearance of specific interaction with CO₂ is indirectly evidenced by the results of studying glassy polymers with side groups also containing aliphatic ether groups. The introduction of aliphatic ether groups into ­rigid-­chain addition PNBs and polytricyclononenes (PTCNs)106,128,130,165 (see Fig. 14) also resulted in increasing solubility of CO₂, and some of the polymers reach the Robeson upper bound of 2008. However, for rigid-chain polymers, these effects are not as unambiguous as for flexible-chain polymers. For example, upon the successive replacement of the triethoxysilyl side group Si(OEt)₃ in additive PNB by Si(OC₂H₄OMe)₃ (Refs 128, 165), only the additive PNB-Si(OC₂H₄OMe)₃ homopolymer (see Fig. 11) approach the Robeson upper bound for CO₂/N₂. In the case of alkoxysilyl-substituted addition PTCNs106 (see Fig. 11), an increase in the length of the alkyl substituent at the Si–O bond leads only to a decrease in the CO₂/N₂ selectivity; meanwhile, the simplest addition PTCN-Si(OMe)₃ is located at the upper bound of the Robeson plot for CO₂/N₂. Finally, an increase in the length of alkyl group R in the –CH₂OC₂H₄OR side group of addition PNB 130 (see Fig. 14) decreases the selectivity, and only PNB-CH₂OC₂H₄OMe approaches the upper bound. Nevertheless, Alentiev et al.130 estimated the specific interactions by quantum chemical calculations and experimentally by Eqn (13), using separation of the contribution of passive transport for non-interacting gases at low pressures, and demonstrated that these interactions are most pronounced for R=Me.

Thus, analysis of published data indicates that the best characteristics for the separation of CO₂/N₂ and CO₂/H₂ mixtures are now inherent in polymers capable of specific interactions with CO₂; the synthesis and study of these polymers have been recently addressed in numerous publications. PolyActive and Polaris planar composite membranes and pilot units for the isolation of CO₂ from gas mixtures were developed on the basis of polymers of this class.

Thus, despite the fact that each of the indicated separation problems has already been solved either on an industrial scale or on a pilot scale, the gas transport and separation parameters of commercially manufactured membranes are, most often, far from being optimal. This considerably retards the implementation of membrane technologies for solving a variety of problems., e.g., application of membranes for high-temperature separation of hydrogen-containing mixtures or for separation of nitrogen-methane mixtures. The use of membranes not only purifies gas streams from contaminating components that decrease the yield of reaction products, but also solves a variety of environmental problems, for example, reduces the carbon dioxide emission to the atmosphere. In addition, the use of membrane gas separation technologies is relevant if the conventional cryogenic or adsorption techniques cannot be used or are economically unviable. Therefore, it is still necessary to synthesize new polymers and to explore new methods for improving performance of existing membrane materials; this is confirmed by the large number of publications in these fields. The attention is paid to not only the production of materials with high permeability--selectivity characteristics, but also improvement of important parameters such as thermal and chemical stability, structure stability with time, mechanical strength and so on. As demonstrated by the example of PTMSP, research along this line obviously gives beneficial results, for example, it makes it possible to find new efficient ways for increasing the durability of gas separation properties of polymer matrices with retention of the initial level of permeability for chemically diverse polymers. An important role for the prospects of application of a particular new polymer as a membrane material belongs to not only the properties of the material itself, but also the scalability of the synthesis of a new polymer to commercial or pilot production in order to manufacture large-area membranes with stable mechanical characteristics.

The numerous studies related to the application of polymeric materials and gas separation membranes are usually focus either on certain groups of polymers10--­13,31,32,34,35,80,88,89 or on attainment of very important, but specific goals, for example, production of hydrogen99,111,113 or CO2 recovery and utilization.102,120--­122,154,156,159 Analysis of the broad range of polymers and separation problems in Robeson's studies8,9 did not consider the possibility of using the accumulated data set for various practical applications of these materials. In the present review, the choice of the most promising materials is based on the correlation approach supplemented by additional analysis of the properties of polymers such as stability of characteristics over time and mechanical properties. The criteria for selection of polymers for gas separation membranes considered in this review do not exhaust the currently existing approaches, but expand their capabilities and thus make the choice more accurate and enable evaluation of not only commercial polymer membranes already existing on the market, but also other both existing and potential polymers and polymer systems. For example, PTMSP stable over time is promising for the production of technical-grade nitrogen from air. A good promise of the recovery of hydrogen from hydrogen-containing mixtures is held by not only highly selective and highly permeable polymers with high ordering of chain packing (triptycene and CANAL polymers), but also thermally stable polymers such as polybenzimidazoles and polynaphthoylbenzimidazoles that can function at temperatures above 200 °C. Perfluorinated and surface-fluorinated polymers are of most interest for the separation of methane-containing mixtures as regards further prospects for the development of membrane technology. The recovery of carbon dioxide from various gas mixtures by polymer membranes is best implemented using polymers capable of specific interactions with CO₂ molecules.

The separation of nitrogen-methane mixtures is of special interest for the membrane technology, in particular, for the use of non-porous polymer membranes. Analysis of the literature shows that this problem can be solved using both nitrogen- and methane-selective polymeric materials, depending on the composition of the mixture.

It is important to note that highly permeable and highly selectivity polymers are both of interest, depending on the composition of the initial gas mixture, the required flux and the purity of the final product. Furthermore, the relevant goals include both polymers that can be efficiently applied for solving quite a number of separation problems, for example, the use of membranes with thin selective layers based on polyimides for the separation of air components, recovery of helium from natural gas and separation of biogas components and polymers that are meant for solving specific problems, e.g., the use of thermally stable polymers for the separation of hydrogen-containing mixtures at elevated temperatures.

With obvious necessity and fundamental and practical importance of scientific research in particular fields of polymer synthesis and manufacture of polymer gas separation membranes for solving specific problems, which widely occur in the literature, this integrating review using a number of fundamental approaches made it possible to evaluate various trends of development, prospects and competitiveness of polymer membranes for solving gas separation problems.

This work was carried out within the State Program of TIPS RAS.

The following designations are used in the review:

α — permeation selectivity of gases,

α^D — diffusion selectivity of gases,

α^S — solubility selectivity of gases,

Δα — deviations of the selectivity values from the upper bound of the permeability--selectivity plots,

ε/k — effective Lennard--Jones gas--gas interaction potential,

AF2400 — amorphous Teflon AF2400,

Δc — gas concentration gradient across the membrane,

D — diffusion coefficient of a gas,

d — effective kinetic diameter of a gas molecule,

J — gas flux through the membrane,

K₁ - K₄ — linear correlation parameters for diffusion and solubility coefficients,

k — factor in the Robeson upper bound equation,

n — exponent in the Robeson upper bound equation,

l — thickness of the membrane selective layer,

Q — gas permeability of the membrane,

P — gas permeability coefficient,

Δp — pressure drop across the membrane,

S — gas solubility coefficients,

TR — thermally rearranged polymers,

Barrer — gas permeability unit, ­1 Barrer=10^–10cm³ (STP) cm (cm² s cm Hg)^–1,

CA — cellulose acetate,

PAMAM — polyamidoamine dendrimer,

PBI — polybenzimidazole,

PDMS — polydimethylsiloxane,

PEBAX — block copolymers of polyamides with polyethylene oxide,

PHFP — polyhexafluoropropylene,

PILs — polymeric ionic liquids,

PIM-1, PIM-7 — polymers with intrinsic microporosity,

PIs — polyimides,

PNB — polynorbornene,

PNBI — polynaphthoylenebenzimidazole,

PPO — polyphenylene oxide,

PSF — polysulfone,

PTCN — polytricyclononene,

PTMSP — polytrimethylsilylpropyne,

PVTMS — polyvinyltrimethylsilane,

TBPC — tetrabromo-polycarbonate.