Macromolecular Design for Oxygen/Nitrogen Permselective Membranes—Top-Performing Polymers in 2020—

Oxygen/nitrogen permselective membranes play particularly important roles in fundamental scientific studies and in a number of applications in industrial chemistry, but have not yet fulfilled their full potential. Organic polymers are the main materials used for such membranes because of the possibility of using sophisticated techniques of precise molecular design and their ready processability for making thin and large self-supporting membranes. However, since the difference in the properties of oxygen and nitrogen gas molecules is quite small, for example, their kinetic diameters are 3.46 Å and 3.64 Å, respectively, the architectures of the membrane macromolecules should be designed precisely. It has been reported often that oxygen permeability (PO2) and oxygen permselectivity (α = PO2/PN2) have trade-off relationships for symmetric membranes made from pure polymers. Some empirical upper bound lines have been reported in (ln α − ln PO2) plots since Robeson reported an upper bound line in 1991 for the first time. The main purpose of this review is to discuss suitable macromolecular structures that produce excellent oxygen/nitrogen permselective membranes. For this purpose, we first searched extensively and intensively for papers which had reported α and PO2 values through symmetric dense membranes from pure polymers. Then, we examined the chemical structures of the polymers showing the top performances in (ln α − ln PO2) plots, using their aged performances. Furthermore, we also explored progress in the molecular design in this field by comparing the best polymers reported by 2013 and those subsequently found up to now (2020) because of the rapid outstanding growth in this period. Finally, we discussed how to improve α and PO2 simultaneously on the basis of reported results using not only symmetric membranes of pure organic polymers but also composite asymmetric membranes containing various additives.


Significance of Oxygen/Nitrogen Permselective Membranes
Gas separation membranes are very important and have a promising future not only because of their scientific interest to chemists and scientists but also for their practical applications such as removal of contaminants and purification of resources important to chemical and materials engineers [1][2][3][4][5][6][7][8]. Therefore, intensive and continuous studies on gas separation membranes have been carried out for many years that have resulted in some practical uses. In particular, oxygen/nitrogen permselective membranes are very important in both the industrial and medical fields. For example, they can be used to treat seriously ill patients with a pulmonary disease like COVID-19. However, the performances of gas separation membranes, especially for separating oxygen and nitrogen, are not as good as desired because their sizes and properties are very similar. For example, the kinetic diameters of an oxygen molecule and a nitrogen molecule are 3.46 Å and 3.64 Å, respectively, and this size difference is extremely small (0.18 Å). As materials for such membranes, soluble organic polymers are popular and useful because they can be fabricated very easily and economically as dense thin membranes without any void defects through which gas molecules can pass freely without any selectivity.

Requirements for Polymers as Oxygen/Nitrogen Permselective Membranes
There are mainly two requirements for polymers as permselective membranes for a gas mixture of oxygen/nitrogen as follows [1].
(1) high processability, mechanical strength, and stability (2) high oxygen permselectivity, that is, a high oxygen permeability coefficient (P O 2 (barrer)) and high oxygen separation factor (α = P O 2 /P N 2 ) The oxygen permeability coefficient (P O 2 (barrer)) is the quantity (volume: cc(STP)) of oxygen gas molecules permeated through a polymer membrane normalized by the membrane area (cm 2 ), membrane thickness (cm), permeation time (s), and pressure difference applied (driving force) (cmHg). The unit, barrer, is defined by 1 barrer = 1 × 10 −10 cc (STP) cm cm −2 s −1 cmHg −1 , where STP means a standard temperature (25 • C) and pressure (1 atm). Since this is a characteristic value for each polymer architecture, this value basically depends on the macromolecular structure. However, different P O 2 values for polymers with the same first-order structures (chemical structures) were often reported because they could have different high-ordered structures (solid-state structures or membranes structures) even if the polymers had the same macromolecular structures.
There are two main trade-off problems concerning the requirements for good oxygen separation membrane materials as follows.
(1) Polymers with higher regular structures which are needed for higher α values have lower processability because they are insoluble and vice versa. Because gas molecules are very small particles around 2.6-5.5 Å in kinetic diameter, membranes for gas separation should be dense (non-porous) or microporous and not have any defects whose sizes are more than several Å. Figure 1 summarizes three well-known permselective mechanisms useful for oxygen and nitrogen separation [1][2][3][4][5][6][7][8]. The details of the three are described below. (1) Solution-diffusion (SD) mechanism for dense (non-porous) membranes, (2) molecular-sieving (MS) mechanism for ultra-microporous membranes, (3) Knudsen (Kd) mechanism for microporous and mesoporous membranes.

Solution-Diffusion (SD) Mechanism for Dense (Non-Porous) Membranes
Dense (non-porous) membranes have no pores but gas molecules can permeate them. A popular and the simplest mechanism for gas permeation through dense membranes known as the solution-diffusion (SD) mechanism involves the following two-step process: (i) dissolution (or sorption) of permeating gas molecules on a membrane surface and then (ii) diffusion of the gas molecules across the membrane. In this simple model, the oxygen permeability coefficient (PO2: cc (STP) cm cm −2 s −1 cmHg −1 ) is the product of the oxygen solubility coefficient (SO2: cc(STP) cm −3 cmHg −1 ) and the oxygen diffusion coefficient (DO2: cm 2 s −1 ).

Molecular-Sieving (MS) Mechanism for Ultramicroporous and Microporous Membranes
When one of the authors (T.A.) published a review article on macromolecular design for permselective membranes in 1999 [1], the molecular-sieving (MS) mechanism was not popular and most oxygen permselective membranes were discussed on the basis of the (1) Solution-diffusion (SD) mechanism for dense (non-porous) membranes, (2) molecular-sieving (MS) mechanism for ultramicroporous membranes, (3) Knudsen (Kd) mechanism for microporous and mesoporous membranes.

Solution-Diffusion (SD) Mechanism for Dense (Non-Porous) Membranes
Dense (non-porous) membranes have no pores but gas molecules can permeate them. A popular and the simplest mechanism for gas permeation through dense membranes known as the solution-diffusion (SD) mechanism involves the following two-step process: (i) dissolution (or sorption) of permeating gas molecules on a membrane surface and then (ii) diffusion of the gas molecules across the membrane. In this simple model, the oxygen permeability coefficient (P O 2 : cc (STP) cm cm −2 s −1 cmHg −1 ) is the product of the oxygen solubility coefficient (S O 2 : cc(STP) cm −3 cmHg −1 ) and the oxygen diffusion coefficient (D O 2 : cm 2 s −1 ).
Therefore, oxygen separation of membranes based on the SD mechanism depends on the two factors, that is, dissolution (or sorption) selectivity α S (=S O 2 /S N 2 ) and diffusion selectivity α D (=D O 2 /D N 2 ). Although, in many of gas pairs, if α S > 1, α D < 1 and vice versa. However, in the case of oxygen/nitrogen, α S > 1 and α D > 1 generally.

Molecular-Sieving (MS) Mechanism for Ultramicroporous and Microporous Membranes
When one of the authors (T.A.) published a review article on macromolecular design for permselective membranes in 1999 [1], the molecular-sieving (MS) mechanism was not popular and most oxygen permselective membranes were discussed on the basis of the SD mechanism described above. Recently, it has been thought that this MS mechanism is important for realizing high performance for oxygen separation membranes. Because the sizes of an oxygen and a nitrogen molecule are 3.46 Å and 3.64 Å, respectively, it is ideally desired that static micropores whose sizes are smaller than around 5 Å are created in polymer membranes. However, for common polymers, since 5 Å is within the range of the thermal motion of their polymer backbones and polymer molecules can flex over this range, it is not easy to create static pores whose sizes are less than 5 Å suitable for oxygen separation based on the MS mechanism.
The MS separation mechanism for an oxygen/nitrogen mixture may be applied to permeations through membranes containing micropores whose sizes are less than around 5-10 Å (0.5-1 nm) because the pore sizes should be less than 2-3 times of the size of the permeating gas molecule (0.346 nm) The IUPAC defined the terms "ultra-micropores" and "micropores" as small pores with sizes of less than 0.7 nm and 2 nm, respectively. Therefore, for highly oxygen permselective membranes based on the MS mechanism, ultra-micropores are appropriate and micropores are too large.

Knudsen (Kd) Mechanism for Microporous and Mesoporous Membranes
When pore sizes in a membrane are smaller than the mean free path (λ) of a permeant gas, the diffusion of the gas follows the Knudsen (Kd) mechanism, where the permeability coefficient is inversely proportional to the square root of the molecular weight of the gas. In the case of oxygen, its λ value is about 60-100 nm. Therefore, when separating oxygen using the membranes with pores whose sizes are from 5-10 Å (0.5-1 nm) to 60-100 nm follows the Knudsen (Kd) mechanism. Its permeation (diffusion) selectivity is expressed by the following equation.
Because α S (S O 2 /S N 2 ) = 1, in this case, Therefore, in the case of oxygen/nitrogen mixtures, nitrogen permeates predominantly through Knudsen (Kd) membranes. In addition, because α S makes no contribution for this kind of membrane, separation by selective dissolution is not useful for the case of oxygen/nitrogen separation.

Transition
Range between the Solution-Diffusion (SD) Mechanism for Dense (Non-Porous) Membranes, the Molecular-Sieving (MS) Mechanism for Ultra-Microporous Membranes, and the Knudsen (Kd) Mechanism for Microporous and Mesoporous Membranes As described above, in the case of oxygen, permeation through membranes with pores whose sizes are less than 60-100 nm follows the Knudsen (Kd) mechanism, and separation based on the molecular-sieving (MS) mechanism for oxygen/nitrogen mixture requires micropores with sizes less than about 5-10 Å (0.5-1 nm). Baker also reported that the transition between the MS mechanism and the solution-diffusion (SD) mechanism is in the range of 0.5-1 nm [9]. In conclusion, the minimum and maximum sizes of actual pores in polymer membranes which can separate oxygen/nitrogen mixtures by the MS mechanism are around 5 Å and 10 Å, respectively. In order to compare oxygen permselectivity, that is, P O 2 and α (=P O 2 /P N 2 ) for various membranes, many researchers used a plot of ln α versus ln P O 2 . In general, trade-off relationships between P O 2 and α are well-known. Prof. Robeson plotted many experimental values obtained from the literature and drew an upper bound line in 1991 as shown in Figure 2 [10]. This is the original upper bound line. In the 1991 figure, substituted acetylene polymers (PAs) including poly(1-trimethylsilylpropyne) (PTMSP, see Figure 2) and polyimides (PIs) were plotted as very high P O 2 polymers, and as high α polymers, respectively. The figure also showed that in general, glassy polymers showed better performances than rubbery polymers. The details are described in Section 2.1. membranes, many researchers used a plot of ln α versus ln PO2. In general, trade-off rela-tionships between PO2 and α are well-known. Prof. Robeson plotted many experimental values obtained from the literature and drew an upper bound line in 1991 as shown in Figure 2 [10]. This is the original upper bound line. In the 1991 figure, substituted acetylene polymers (PAs) including poly(1-trimethylsilylpropyne) (PTMSP, see Figure 2) and polyimides (PIs) were plotted as very high PO2 polymers, and as high α polymers, respectively. The figure also showed that in general, glassy polymers showed better performances than rubbery polymers. The details are described in Section 2.1.

Meaning of the Upper Bound Lines-The Slope and Intercept
Although Robeson's 1991 upper bound line was drawn from empirical results, Prof. Freeman explained the theoretical meaning of the line in 1999 [11]. He constructed the following equation for the line: where A and B indicate the slope of the line and the intercept at ln PO2 = 0, respectively. He discussed the meaning of A and B in the following way.
where dO2 and dN2 are kinetic diameters for oxygen and nitrogen, respectively. Since the A value is determined by gas pairs as permeants, it has no relationship to the structures   [11]. He constructed the following equation for the line: where A and B indicate the slope of the line and the intercept at ln P O 2 = 0, respectively. He discussed the meaning of A and B in the following way.
where d O 2 and d N 2 are kinetic diameters for oxygen and nitrogen, respectively. Since the A value is determined by gas pairs as permeants, it has no relationship to the structures of the membrane polymers. Therefore, it cannot be improved by well-organized molecular design based on researchers' efforts. On the other hand, he proposed that the B value is affected by solubility selectivity and the structures of membrane polymers. Therefore, researchers can design new polymers showing good performances by controlling the B value. Furthermore, since the solubility selectivity is low in the case of oxygen/nitrogen, precise design of polymers to enhance α D is more important. In order to obtain good performance of polymer membranes, that is, to realize a simultaneous increase in selectivity and permeability, it is effective to increase chain stiffness (main chain rigidity) and interchain spacing (fractional free volume (FFV)).  [12] and Pinnau's 2015 upper bound line [13] were reported as shown in Figure 2. As Prof. Freeman predicted in 1999 [11], their slopes are the same as shown in Figure 2.
The advent of Robeson's 2008 upper bound line was caused by the emergence of a new type of polymer called PIM (polymers of intrinsic microporosity) such as PIM-1 as shown in Figure 2. This polymer backbone includes a rigid ladder structure consisting of alternating fused aromatic and aliphatic cycles with spiro-type carbons as kink points. In this review, we call this type of PIMs as Spiro-PIM. The details are described in Section 2.1.4.
Recently, Pinnau's 2015 upper bound line appeared. The new line was caused by the advent of another type of PIMs. Similar to a Spiro-PIM, these advanced new PIMs contain a rigid ladder structure consisting of alternating fused aromatic and aliphatic cycles. But instead of spiro-type carbons in Spiro-PIMs, they include triptycene groups as kink points (see Figure 2). In this review, we call this type of PIM the Trip-PIM. The details are described in Section 2.2.2.

Aging Problems for Ultrahigh Permeable Polymers
As described above, the ultramicropores which are needed for high performance of oxygen permselective membranes based on the molecular-sieving (MS) mechanism have a similar size to that of the thermal motion of the polymer backbone. In addition, because these pores are mainly present between macromolecules, they are usually unstable, particularly in the case of ultrahigh permeability polymers (P O 2 > 10 3 ) such as PTMSP (the details are described in Section 2.1.2). Therefore, they often showed an aging effect, whereby with increasing time their permeability significantly decreased. Because we think that the stable values after aging are the real and intrinsic values of polymers, we plotted separately the aged values by solid symbols and transient non-aged values by open symbols in all the figures in this review whenever aged values were reported.

Advantages and Disadvantages of Polymers as Materials for Oxygen/Nitrogen Permselective Membranes
As described in Section 1.1, soluble polymers are suitable for oxygen/nitrogen permselective membranes because they can be fabricated easily as dense thin membranes. This is the fundamental advantage of polymers. In addition, their chemical structures can be controlled with an accuracy of subnanometer order by organic and polymer synthesis. Therefore, it is possible to control precisely the size of the permeation path of oxygen and nitrogen. However, in the case of linear soluble polymers because permeation paths are mainly present between macromolecules, they are usually unstable (see Section 1.4.4) and it is difficult to control the size.

Purposes of This Review
The main aim of this review is to discuss how to design and obtain new good polymers with both high oxygen permeability (P O 2 ) and oxygen permselectivity (α (P O 2 /P N 2 )). For this purpose, we first extensively searched for papers reporting values of α and P O 2 for polymers with well-defined chemical structures. Then, we selected polymers showing the highest α at each P O 2 among them. Finally, we plotted them on a (ln α (P O 2 /P N 2 ) − ln P O 2 ) graph (see Section 2). As described above, if papers reported more than two values before and after aging for the same polymer, we plotted both values as open and solid symbols, respectively. In addition, in order to see the history of recent progress of the research for oxygen permeation polymers, results until 2013 and up to now (until 2020) are discussed separately in Sections 2.1 and 2.2, respectively. Furthermore, in Section 3, in order to discuss strategies for enhancing P O 2 and α (P O 2 /P N 2 ) simultaneously, we selected such examples from the literature although we found they were quite few. While we described the performance of only pure polymers in Section 2, we included modified polymers such as composite polymers in Section 3 because of the very rare examples for pure polymers (For the contents of this review, see Supplementary Materials S1). Finally, by using these collected data of pure membranes from these top-performing linear soluble polymers and composite membranes including insoluble polymers whose P O 2 and α (P O 2 /P N 2 ) were simultaneously enhanced, we will summarize the relationships between the chemical structures and performances and discuss how to obtain new good polymers with high values for both P O 2 and α.    Table 1, and for the chemical structures of the polymers in the plots, see Chart 1. In the milestone paper which reported Robeson's 1991 upper bound line [10], it was described that glassy polymers generally show better performances than rubbery polymers. For example, poly (substituted acetylene)s (PAs) are typical glassy polymers with very high glass transition temperatures (Tg) because of their very rigid chemical structures created by their conjugated backbones with bulky and crowded side groups. In fact, PAs reported until 2013 show relatively good performance in oxygen permselectivity as shown in Figure 4 and Table 2 [36][37][38][39][40][41][42][43]. They are plotted at very close to or on Robeson's 1991 upper bound line but do not exceed the 2008 line until 2013.

Macromolecular Design for Oxygen/Nitrogen
Among the best 20 PAs, polymers 7 and 28 show the best and second-best performances, as shown in Figure 4. Polymer 7 lying on the 1991 upper bound line shows ultrahigh PO2 around 10 3 with relatively high α [20]. This polymer has two trimethylsilyl and two phenyl groups. Polymers 9, 24, and 26 show lower PO2 with similar α values compared with polymer 7. All these three polymers have one or two trimethylsilyl and two phenyl groups. Among these four PA type polymers, the polymer 7 from the monomer with the greatest number of trimethylsilyl and phenyl groups is the best. These bulky  Table 1, and for the chemical structures of the polymers in the plots, see Chart 1. Table 1. Categorization and detailed data for membrane polymers in Figure 3 (All polymers until 2013).

Purposes of this Review
The main aim of this review is to discuss how to design and obtain new good polymers with both high oxygen permeability (PO2) and oxygen permselectivity (α (PO2/PN2)). For this purpose, we first extensively searched for papers reporting values of α and PO2 for polymers with well-defined chemical structures. Then, we selected polymers showing the highest α at each PO2 among them. Finally, we plotted them on a (ln α (PO2/PN2) − ln PO2) graph (see Section 2). As described above, if papers reported more than two values before and after aging for the same polymer, we plotted both values as open and solid symbols, respectively. In addition, in order to see the history of recent progress of the research for oxygen permeation polymers, results until 2013 and up to now (until 2020) are discussed separately in Sections 2.1 and 2.2, respectively. Furthermore, in Section 3, in order to discuss strategies for enhancing PO2 and α (PO2/PN2) simultaneously, we selected such examples from the literature although we found they were quite few. While we described the performance of only pure polymers in Section 2, we included modified polymers such as composite polymers in Section 3 because of the very rare examples for pure polymers (For the contents of this review, see Supplementary Materials S1).
Finally, by using these collected data of pure membranes from these top-performing linear soluble polymers and composite membranes including insoluble polymers whose PO2 and α (PO2/PN2) were simultaneously enhanced, we will summarize the relationships between the chemical structures and performances and discuss how to obtain new good polymers with high values for both PO2 and α.  In the milestone paper which reported Robeson's 1991 upper bound line [10], it was described that glassy polymers generally show better performances than rubbery polymers. For example, poly (substituted acetylene)s (PAs) are typical glassy polymers with very high glass transition temperatures (Tg) because of their very rigid chemical structures created by their conjugated backbones with bulky and crowded side groups. In fact, PAs reported until 2013 show relatively good performance in oxygen permselectivity as shown in Figure 4 and Table 2 Table  2, and for the chemical structures of the polymers in the plots, see Charts 1 and 2.   Table  2, and for the chemical structures of the polymers in the plots, see Charts 1 and 2.  Table 2, and for the chemical structures of the polymers in the plots, see Charts 1 and 2. Table 2. Categorization and detail data for the membrane polymers in Figure 4 (PAs until 2013).  [Note] For the codes, see Chart 2 and 1-9 are the same as those in Table 1. Data in parentheses are ones before aging.

Code
Among the best 20 PAs, polymers 7 and 28 show the best and second-best performances, as shown in Figure 4. Polymer 7 lying on the 1991 upper bound line shows ultrahigh P O 2 around 10 3 with relatively high α [20]. This polymer has two trimethylsilyl and two phenyl groups. Polymers 9, 24, and 26 show lower P O 2 with similar α values compared with polymer 7. All these three polymers have one or two trimethylsilyl and two phenyl groups. Among these four PA type polymers, the polymer 7 from the monomer with the greatest number of trimethylsilyl and phenyl groups is the best. These bulky groups may create large amounts of micropores and the high mobility of the trimethylsilyl groups may maintain a high P O 2 . Polymer 28 show the best performance among the best 20 PAs [39]. Only this polymer includes polar atoms, sulfurs. The other nineteen polymers consist of only non-polar atoms, i.e., carbon, silicon, and hydrogen which do not induce polarity in the molecule. Therefore, it is thought the polar structure might enhance the α S .

Poly(1-Trimethylsilylpropyne) (PTMSP) (an Ultrapermeable Polymer) (Polymer 8 in Figures 3 and 4)
Among the PAs in Figure 4 (1-9 in Chart 1 and 24-34 in Chart 2), only a few PAs (1-7) show very high P O 2 values of more than 10 3 . The highest value is more than 10 4 . Such polymers are called ultrapermeable polymers [44]. They are all poly(disubstituted acetylene)s (DPA). Poly(1-trimethylsilylpropyne) (PTMSP, polymer 8 in Chart 1) [45,46] reported by Prof. Masuda in 1983 is most meritorious among DPAs. The high P O 2 value (10 4 ) was much higher than that (10 2 ) for poly(dimethylsiloxane) (PDMS) which had been the highest value before his discovery. After this discovery, a great number of chemists, physicists, and materials scientists started new research projects concerning PTMSP in order to clarify the reason for the extremely high P O 2 value and to try to apply it to practical use. As a result, it was found that the extremely high P O 2 was caused by an unusually high fractional free volume (FFV, around 25-30%), which is also sometimes called ultrahigh FFV, or a large amount of very large micropores. The density is also the lowest (around 0.75). Therefore, the polymer is also called a super-glassy polymer. The sizes of the unusually large micropores in PTMSP have been reported in many papers as follows: 0.5-1.0 nm by Bakers [9], 0.9-1.2 nm by Robeson [12], 1.12 nm by Freeman [47], 1.24 nm by Lee [48], 1.1-1.5 nm by Pinnau [49], 0.45-0.55 nm by Yampolskii [50]. Judging from these reports, the sizes of the pores in PTMSP may be around 0.5-1.5 nm.
As described above, in order to separate oxygen (3.46 Å) and nitrogen (3.64 Å) based on the molecular sieving mechanism, pore sizes should be less than 1.0-0.5 nm. Since the sizes of the pores in PTMSP may be around 0.5-1.5 nm as described above, PTMSP is partially suitable for oxygen/nitrogen separation membranes on the basis of the MS mechanism. In fact, it was reported that the permselectivity α (P O 2 /P N 2 ) of PTMSP was mainly due to the diffusion selectivity, α D (D O 2 /D N 2 ) (=1.4) and no dissolution selectivity, α S (S O 2 /S N 2 ) (=1.1) was detected [9,51].
Although the P O 2 value of PTMSP is very high, the α value is extremely low, around 1.3. The pores in PTMSP whose sizes are around 0.5-1.5 nm are categorized both as micropores (<2.0 nm), useful for high P O 2 , and ultramicropores (<0.7 nm), useful for high α, but PTMSP contains mainly micropores and only a small amount of ultramicropores. Therefore, the P O 2 is very high and the α is very low. Another possible reason for the extremely low α value is the effect of partial permeation based on the Knudsen (Kd) mechanism. If the permeation was solely based on the Kd mechanism, no dissolution selectivity should be found. Therefore, its α should be α D = 0.93. If the contribution of possible dissolution selectivity values is considered, the α values are 1.5-2.1 [12]. Since it was reported that the oxygen permeation behavior through PTMSP is within the transition range from SD mechanism to Kd mechanism [12], this possible reason may be reasonable.
A search of papers for P O 2 values for PTMSPs results in scattered values from 10 4 to 10 2 . This is unusual. Because a P O 2 value generally and inherently is one of physical properties of a usual polymer, the P O 2 should depend on the chemical structure of the polymer. Therefore, a polymer has its own specific P O 2 value. However, in general, the same polymers do not always produce the same homogeneous dense membranes because their high-order structures such as crystallinity, and their membrane structures, such as an asymmetric structure, are not the same in each case. In the case of PTMSP membranes that have a variety of P O 2 values, they can have quite different pore sizes. One of the reasons why the reported values of the pore sizes for PTMSPs were scattered as described above is that the sizes depend on the membrane preparation method. This variation of the pore sizes suggests instability of the micropores. In fact, strong aging effects were reported for the P O 2 values. The pore sizes must have been also decreasing with time. This may be another reason for the scattered data for the pore sizes. In fact, the very high P O 2 decreased significantly from 10 4 to 10 2 over time. The change is shown in Figures 3 and 4 (•: after aging, : before aging).
Although PTMSP and PDMS similarly show very high P O 2 values, the physical properties of PTMSP and PDMS are completely different and therefore their permeations are based on different permeation mechanisms. While PTMSP is a very rigid super-glassy polymer (whose Tg is thought to be more than 200 • C) with the lowest density, PDMS is a very flexible polymer with the lowest Tg = −123 • C. PTMSP has static micropores but PDMS has no micropores. As a result, permeation through PTMSP mainly follows the MS mechanism and permeation through PDMS follows the SD mechanism, although their performances are similar. In Figure 4, there are some poly(substituted acetylene)s showing ultrapermeability, i.e., P O 2 of more than 10 3 even after aging (polymers 1-7), although PTMSP shows ultrapermeability only before aging. Most of them are poly(diphenylacetylene)s (PDPAs) (polymers 1-7, except for 3). PDPAs have a more rigid backbone than PAs in general because they have bulky substituted phenyl groups at every carbon of the main chain. Although they show very high P O 2 even after aging similar to non-aged PTMSP, their α values tend to be low and further from the upper line compared with other PAs. This may be caused by the permeation mechanism including not only the SD mechanism but also the Kd mechanism. In particular, the two PDPAs with indan groups (polymers 1 and 2) show extremely high P O 2 of more than 10 4 even after aging, similar to non-aged PTMSP. There are almost no aging effects on their performances, a situation quite different from PTMSP, as shown in  [29]. Although network amorphous polymers like carbon molecular sieve membranes (CMSMs) contain a large fractional free volume (FFV), they were insoluble and had no processability for their self-supporting membranes. Therefore, they designed a soluble non-network amorphous polymer containing a large FFV, called PIM-1 (no.11 in Figure 3). The new polymer is a linear macromolecule consisting of a very rigid fused rings backbone connected by spiro-carbons at contorted positions (In this review, this type of PIM is called Spiro-PIM). Because this is a linear (ladder) polymer, it is soluble and processable. In addition, the rigid ladder (fused rings) backbone with the kink points (spiro-carbons) can create relatively stable large micropores.
As a result, it shows good performance beyond the 1991 upper line. The α for non-aged PIM-1 (11 in Chart 1 and Figure 3) [25] is much higher than that for non-aged PTMSP (8 in Chart 1 and Figure 3) [14], although the P O 2 for non-aged PIM-1 is much lower than that of PTMSP. The plot for PIM-1 lies above the 2008 upper bound after aging, although the P O 2 is less than 10 3 . It was reported that the selectivity of permeation (α = 2.8) mainly depended on that of diffusion (α D = 2.8) and that of dissolution (α S = 1.0) was almost unity (no selectivity) suggesting it follows the MS mechanism [24]. This better α is because the size of pores, determined by nitrogen adsorption, in PIM-1 was much smaller (around 6.5 Å) than that (around 9 Å) in PTMSP [13].
(2) Improved Spiro-PIM (polymers 10 and 15 in Chart 1) In addition, to enhance the rigidity of the main chain of PIM-1, a bulky group (fluorene) was introduced around the spirocarbons (10) or the fused rings backbone was extended (15). Compared with PIM-1 (11 in Chart 1 and Figure 3) both the P O 2 and α increased for PIM 10. This is because the introduction of the additional fused benzene rings restricted motion around the spiro-center of the backbone. The selectivity of permeation (α = 3.4) mainly depended on that of diffusion (α D = 3.4) and that of dissolution (α S = 1.0) was almost unity (no selectivity) suggesting it follows the MS mechanism [24]. In the case of no.15 PIM, both the α and P O 2 decreased compared with no. 11. The lower ratio of the kink points may enhance the stacking of the backbones to reduce their micropores or FFV.
The two Spiro-PIMs (10 and 11 in Chart 1) described above showed strong aging effects as shown in Figure 3  They contain contorted backbones. Therefore, they are also categorized as Spiro-PIM-PI as mentioned above. Figure 5 shows plots of the best PIs until 2013. Table 3 lists the detailed data for the polymers in Figure 5 [52][53][54]. They are amorphous and have very high Tg values, that is, they are glassy polymers. Conventional PIs are known as insoluble polymers and, therefore, they have no direct processability and their membranes are prepared from their soluble precursor polymers called poly(amic acid)s [55]. However, by introducing bis(trifluoromethyl)methylene (-(CF 3 ) 2 C-) to the main chain of PIs, they became soluble and therefore direct fabrication to their membranes became possible. The bulky groups inhibit efficient packing of the polymer chains resulting in higher permeability. In fact, almost all the PIs showing the best performances here in Figure 5 include the fluorine-containing group (-(CF 3 ) 2 C-), except for polymers 40 and 43 and PIM-PIs (35, 36, 18, 20, and 21)) (Charts 1 and 3). The PIs can be classified into two groups. One group contains a lot of methyl groups (polymers 17, 19, 22, 37-44) and the other have contorted spiro carbons (polymers 18, 20, 21, 35, and 36; PIM-PI, the details are described above). The PIs with many methyl groups (39, 19, 41, 22) had relatively high densities around 1.3-1.4 and low FFVs of about 10-20%. However, they had relatively large spaces between macromolecules, because their d-spacing values from XRD were 0.46-0.57 nm [56] and their pore sizes by PALS [48] were 0.6-0.7 nm. In other words, these PIs may contain ultramicropores (<0.7 nm). It was reported that their selectivities of permeation (α) through these PIs mainly depended on those of diffusion (α D ) and those of dissolution (α S ) were almost unity (<1.2) [32,52]. Therefore, since the permeation may involve the MS mechanism, relatively high α values are shown. However, since they have no large micropores (0.7-1.0 nm), unlike PTMSP, their P O 2 values were low. uble precursor polymers called poly(amic acid)s [55]. However, by introducing bis(trifluoromethyl)methylene (-(CF3)2C-) to the main chain of PIs, they became soluble and therefore direct fabrication to their membranes became possible. The bulky groups inhibit efficient packing of the polymer chains resulting in higher permeability. In fact, almost all the PIs showing the best performances here in Figure 5 include the fluorine-containing group (-(CF3)2C-), except for polymers 40 and 43 and PIM-PIs (35, 36, 18, 20, and 21)) (Charts 1 and 3). The PIs can be classified into two groups. One group contains a lot of methyl groups (polymers 17, 19, 22, 37-44 [56] and their pore sizes by PALS [48] were 0.6-0.7 nm. In other words, these PIs may contain ultramicropores (<0.7 nm). It was reported that their selectivities of permeation (α) through these PIs mainly depended on those of diffusion (αD) and those of dissolution (αS) were almost unity (<1.2) [32,52]. Therefore, since the permeation may involve the MS mechanism, relatively high α values are shown. However, since they have no large micropores (0.7-1.0 nm), unlike PTMSP, their PO2 values were low.  Table 3, and for the chemical structures of the polymers in the plots, see Charts 1 and 3.  Table 3, and for the chemical structures of the polymers in the plots, see Charts 1 and 3. Table 3. Categorization and detail data for the membrane polymers in Figure 5 (PIs until 2013).

Top-Performing Polymers in 2020 as Oxygen/Nitrogen Permselective Membranes
After we had reviewed the data until 2013 and summarized them as described in 2.1, we then thoroughly searched for reports published from 2014 to the present and renewed the plots for top-performing polymers from the previous plots until 2013 (Figure 3) to the

Top-Performing Polymers in 2020 as Oxygen/Nitrogen Permselective Membranes
After we had reviewed the data until 2013 and summarized them as described in 2.1, we then thoroughly searched for reports published from 2014 to the present and renewed the plots for top-performing polymers from the previous plots until 2013 (Figure 3) to the latest plots ( Figure 6) of polymers showing the highest α at each P O 2 reported until 2020. The values and categorization are listed in Table 4 [57][58][59][60][61][62][63][64][65][66][67][68][69]. The chemical structures of these polymers showing the best performances are shown in Chart 4. It is very surprising that many high-performance polymers which are beyond the 2008 upper bound line appeared in this period of 2014-the present. It is very clear that the progress is very rapid by comparing the changes for six years in 2014-2020 in Figure 6 with those for the 22 years 1991-2013 in Figure 3 (The plots in Figure 3 are also shown by open small circles with thin lines in Figure 6).
(Chart 4) with the highest α and the lowest PO2 beyond the 2008 upper line and close to, or beyond, the 2015 upper bound line. Typical polymers categorized into Groups I, II, and III are poly (disubstituted acetylenes) such as poly (1-trimethylsilylpropyne) (PTMSP) and poly(diphenylacetylene)(PDPA), ladder polymers with side arylene groups without spirocarbons (Trip-PIM), and polyamides (PAm) or polyimide (PI) with bulky pendant groups, respectively. The details are described below.  Group I (see Table 1    Group I (see Table 1) Group Ⅱ In the plots of this region in Figure 6 (polymers 1-9 in Chart 1), the situation is similar to that until 2013 (Figure 3, polymers 1-9). Therefore, no noticeable improvements in this region have occurred in the period since 2014 to the present (for the discussion, see Section 2.1.3).
(2) Modified PAs (60-78 in Figure 7 and Chart 5;) Table 5. Categorization and detailed data for the membrane polymers in Figure 7 (PAs in 2020). [Note] For the codes, see Chart 5. The two polymers (3 and 6) are removed from the nine polymers (1-9) in Table 2, because the aged data for the two polymers were not reported until 2020. Data in parentheses are those before aging.
In the plots of this region in Figure 6 (polymers 1-9 in Chart 1), the situation is similar to that until 2013 (Figure 3, polymers 1-9). Therefore, no noticeable improvements in this region have occurred in the period since 2014 to the present (for the discussion, see Section 2.1.3).
(2) Modified PAs (60-78 in Figure 7 and Chart 5;)  Table 5, and for the chemical structures of the polymers in the plots, see Charts 1 and 5.  In category A, since cis-cisoid polyphenylacetylenes (c-c PAs) are more rigid than c-t PAs and similarly to PDPAs, some c-c PAs show better performance than c-t PAs. In particular, a combination of the rigid backbone and soft and short oligosiloxane grafts are suitable (66) [74]. Introduction of soft crosslinking and modification by SCAT reaction of these types of polymer enhanced their performances (61)(62)(63) [71]. In category B, introducing hyperbranched (73)(74)(75) [77] or soft network (71 and 72) [76] structures to c-t PAs enhanced their permselectivities. In category C, by embedding two-dimensional (2D) polymers created by SCAT reaction of c-c PAs to membranes, good performances were realized. The 2DP 70 [75] was synthesized by interfacial polycondensation at the solid-solid interface and 2DP 60 membrane [70] was prepared by blending with polymer 9. In summary, it was found that a rigid backbone based on c-c PAs, soft short side chains and network structures including hyperbranched and 2DP structures were effective for enhancement of α values. Rigidification of PA's main chain enhanced α and P O 2 simultaneously (66) [74]. However, network structures (69, 71, 72, and 77) including a multi-stranded structure (76) [78] caused a decrease of P O 2 compared with the precursor liner polymers, although α increased. Only   Figure 7 (PAs in 2020). For 1-9, see Chart 1.

Ladder Polymers with Side Arylene Groups without Spirocarbons and Other Ladder
Polymers (Group II; Polymers 44-56 in Figure 6 and Chart 4) (1) Ladder polymers with side arylene groups without spirocarbons (Trip-PIMs) As shown in Figure 6 for all the polymers until 2020, great developments are observed in the region between 10 2 and 10 3 (ultrapermeable region) of P O 2 compared with all the polymers until 2013 shown in Figure 3. They (44)(45)(46)(47)(48)(49)(50)(51)(52)(53)(54)(55)(56) [13], their P O 2 values were much less than 10 3 (ultrapermeable region) and lower than that for PTMSP (8 in Chart 1) (as described above, non-aged PTMSP has a large amount of micropores around 13 Å which is effective for the very high P O 2 .) These excellent performances of Trip-PIMs were caused by the effective size distribution of ultra-micropores (<7 Å) and micropores (<20 Å). For example, in the case of Trip-PIM 52, the sizes of ultramicropores [27] are smaller (around 5.3 Å) than those of Spiro-PIM (PIM-1) (around 6-7 Å) [13,27]. In addition, both the PIMs have similar amounts of a larger size of micropores (around 13 Å) useful for high permeability. Therefore, this Trip-PIM shows much better performance than the Spiro-PIM(PIM-1). Table 6 summarizes data of α (P O 2 /P N 2 ), α S (S O 2 /S N 2 ), and α D (D O 2 /D N 2 ) values for some of Trip-PIMs (46, 47, and 53) plotted in Figure 6. For these polymers, the high α values depend only on α D and their α S values were around unity.  Some substituent effects on the performances of Trip-PIMs were examined. The size of arylene groups as the side groups and the size or shape of alkyl groups at the bridge heads were changed. When the phenylenes (47 in Figure 6) [59] are changed to larger naphthylenes (46) [58], the P O 2 increases and α decreases. These α rely almost exclusively on α D as shown in Table 6. The spaces may be enlarged by enhancing the size of the substituents. The bulkier substituents may create micropores suitable for P O 2 enhancement. On the other hand, when the alkyl groups at the bridge heads are changed from hydrogen groups (=no substituent, 47) ( [59]) to bigger methyl groups (53), ref. [64] both P O 2 and α decrease at the same time. The small substituents may fill the original micropores. When the alkyl groups at the bridge heads were changed from n-propyl groups (P O 2 = 101, α = 5.7 [63] to iso-propyl groups (52), ref. [63] both P O 2 and α increased. These α values were almost exclusively on α D as shown in Table 6. The rigidity may be increased by enhancing the bulkiness of the substituents and, therefore, ultramicropores suitable for α enhancement may form. In fact, the pore sizes were found to become narrower based on NLDFT analysis.
Among Trip-PIMs 47, 49, and 54 ( Figure 6 and Chart 4) which are isomers to one another, and are all composed of triptycenes and Tröger's bases, polymer 54 shows the best α. The main chain of polymer 54 is relatively straight, while the others are not straight. Therefore, polymer 54 may create the smallest micropores among the three. Actually, polymer 54 has the highest density (0.931), lowest FFV (0.349), and smallest pore sizes (5.7 Å) [60].
Recently among Trip-PIMs, a new polymer (45) was reported to have extremely high P O 2 of more than 10 3 , i.e., ultrapermeability while maintaining their excellent α values (>4). This is the best performance up to the present [44]. This Trip-PIM has a totally complete ladder backbone having no Tröger's base units. In addition to the fact that Trip-PIMs have generally smaller ultramicropores than Spiro-PIMs as described above, this Trip-PIM also has a much higher population of larger micropores (7-10 Å) effective for enhancing P O 2 than a Spiro-PIM. Therefore, polymer 45 shows the best performance having both ultrahigh P O 2 and high α values. In fact, the FFV is very large (0.309), similar to PTMSP (Table 6).
(2) PIs with Trip Polymer 50 showing one of the best performances is a polyimide containing Trip units. Several Trip-PIM-PIs were synthesized from different diamines [53]. Among them, polymer 50 showed the best performance. Because it contains tetramethylphenylene units, the rigidity of the C-N bonds may be the highest.
(3) Other ladder polymers Two novel ladder polymers with no Trip groups and spiro carbons in their backbones (51 and 56) were reported as some of the best performance polymers. While Trip-PIMs are totally straight ladder structures with bulky side groups (1,2-phenylene groups), these new ladder polymers have no bulky side groups like a Trip. Since their ladder backbones are not straight instead, they may have micropores. However, their performances are inferior to Trip-PIMs. Similar to the Trip-PIMs containing Tröger's base units (47,49, and 54) mentioned above, the ladder polymer 51 containing Tröger's base units showed a similar tendency. The pure isomer polymer had a higher α and lower P O 2 .

(4) Modified Spiro-PIMs
The polymers 44 [57] and 48 [23] are modified Spiro-PIMs. The former polymer has a more rigid backbone made by introducing additional cyclic structure around the relatively flexible spirocarbons. In other words, this is a locked PIM-1 (11 in Chart 1). As a result, both P O 2 and α values are increased simultaneously. This may be caused by increasing the rigidity producing a longer interchain distance. The latter BenzoSpiro-PIM (48) with four methyl groups shows higher P O 2 and lower α than the original BenzoSpiro-PIM (10 in Chart 1 and Figure 3) without substituents. Figure 8 summarizes the performance and progress of all the PIMs, that is, Spiro-PIMs and Trip-PIMs. It shows clearly that both P O 2 and α values are improved by a change from Spiro-to Trip-PIMs. In addition, they show a large decrease in P O 2 by aging. As a consequence, most aged PIMs are not ultrapermeable, except for polymers 45-47. However, plots for most of Trip-PIMs are located on the 2015 upper bound line at the aged state. are not straight instead, they may have micropores. However, their performances are inferior to Trip-PIMs. Similar to the Trip-PIMs containing Tröger's base units (47,49, and 54) mentioned above, the ladder polymer 51 containing Tröger's base units showed a similar tendency. The pure isomer polymer had a higher α and lower PO2.

(4) Modified Spiro-PIMs
The polymers 44 [57] and 48 [23] are modified Spiro-PIMs. The former polymer has a more rigid backbone made by introducing additional cyclic structure around the relatively flexible spirocarbons. In other words, this is a locked PIM-1 (11 in Chart 1). As a result, both PO2 and α values are increased simultaneously. This may be caused by increasing the rigidity producing a longer interchain distance. The latter BenzoSpiro-PIM (48) with four methyl groups shows higher PO2 and lower α than the original BenzoSpiro-PIM (10 in Chart 1 and Figure 3) without substituents. Figure 8 summarizes the performance and progress of all the PIMs, that is, Spiro-PIMs and Trip-PIMs. It shows clearly that both PO2 and α values are improved by a change from Spiro-to Trip-PIMs. In addition, they show a large decrease in PO2 by aging. As a consequence, most aged PIMs are not ultrapermeable, except for polymers 45-47. However, plots for most of Trip-PIMs are located on the 2015 upper bound line at the aged state.  Figure 6 and Chart 4)

PI or Polyamides (PAms) with Bulky Side Groups (Group III, 57-59 in
As described in 2.1.5, the polyimide (PI) (20 reported in 2010 in Chart 1 and Figure 3 until 2013) shows an unusually high α value (10.8). In this case, kink points were introduced to a PI by spirocarbon structures in a similar way to Spiro-PIMs. In Figure 6 in 2020, some condensation polymers of not only PI (59 in Chart 4 and Figure 6) [69] but also polyamides (PAms) (57 and 58 in Chart 4 and Figure 6) [67,68] show extremely high α values from 10 to 20. The PI has spiro-carbons (fluorene) and bulky alkyl side groups and the PAms have bulky side groups (tris(tert-butyl)phenoxy and adamantyl groups). As a result, their d-spacing values (5.9-6.2 Å ) [67][68][69] determined by XRD were larger than those (4.6-5.7 Å ) [55] for conventional PIs.  (10.8). In this case, kink points were introduced to a PI by spirocarbon structures in a similar way to Spiro-PIMs. In Figure 6 in 2020, some condensation polymers of not only PI (59 in Chart 4 and Figure 6) [69] but also polyamides (PAms) (57 and 58 in Chart 4 and Figure 6) [67,68] show extremely high α values from 10 to 20. The PI has spiro-carbons (fluorene) and bulky alkyl side groups and the PAms have bulky side groups (tris(tert-butyl)phenoxy and adamantyl groups). As a result, their d-spacing values (5.9-6.2 Å) [67][68][69] determined by XRD were larger than those (4.6-5.7 Å) [55] for conventional PIs. Table 6 summarizes data of α (P O 2 /P N 2 ), α S (S O 2 /S N 2 ), and α D (D O 2 /D N 2 ) values from the literature for some of the polymers plotted in Figure 6. For these condensation polymers (57- 59 in Chart 4 and Table 6), the extremely high α values depend not only on α D but also on α S This is much different from Trip-PIMs whose α (P O 2 /P N 2 ) values depend only on α D values because the α S values are almost unity. Therefore, these extremely high α values could be realized by high α S values in addition to high α D values. It suggests the mechanism of this permeation partially involves the SD mechanism. Figure 9 shows the present situation for PIs. In the plots for PIs reported until the present, the situation is similar to those in Figure 5 and Table 7 [80] and only a few noticeable improvements were reported during the period (50 and 59). They possess kink points or bulky groups in their backbones.  Table 7, and for the chemical structures of the polymers in the plots, see Chart 6. Chart 6. Chemical structures of the membrane polymers in Figure 9 (PIs in 2020). Table 7. Categorization and detailed data for the membrane polymers in Figure 9 (PIs in 2020).

Tendency of Change in Oxygen Permeation Performances by Changing Chemical Structures of Polymers
As described above as shown in Figures 3-9, it was found that almost all the changes in the oxygen permeation performances by changing the polymer chemical structures are from lower-right positions to upper-left positions and vice versa in these α − PO2 plots. They moved parallel to the upper bound lines in the figures. In other words, whenever their permeability increased, their permselectivity decreased and vice versa. In the case of aging causing physical changes, they also moved parallel to the upper bound lines (for example, Figure 8). However, we found some welcome exceptions in which the permeability and permselectivity increased at the same time as described in this section (Section 2). Here we summarize the exceptions as follows.  Table 7, and for the chemical structures of the polymers in the plots, see Chart 6.
Chart 6. Chemical structures of the membrane polymers in Figure 9 (PIs in 2020).  Table 7, and for the chemical structures of the polymers in the plots, see Chart 6. Table 7. Categorization and detailed data for the membrane polymers in Figure 9 (PIs in 2020).

Tendency of Change in Oxygen Permeation Performances by Changing Chemical Structures of Polymers
As described above as shown in Figures 3-9, it was found that almost all the changes in the oxygen permeation performances by changing the polymer chemical structures are from lower-right positions to upper-left positions and vice versa in these α − P O 2 plots. They moved parallel to the upper bound lines in the figures. In other words, whenever their permeability increased, their permselectivity decreased and vice versa. In the case of aging causing physical changes, they also moved parallel to the upper bound lines (for example, Figure 8). However, we found some welcome exceptions in which the permeability and permselectivity increased at the same time as described in this section (Section 2). Here we summarize the exceptions as follows.

I.
Changing their backbone structures: (1) Linear polymers to ladder polymers (ex. Therefore, as can be seen in (1)- (6), it can be concluded that rigidification of main chains is very effective method for producing such simultaneous improvements. In addition to this, introducing contorted sites in the main chains is important. Therefore, as can be seen in (8)- (11), it can be concluded that bulkier side groups may create spaces suitable for simultaneously enhancing both P O 2 and α values. But sometimes small and flexible substituents can unfavorably occupy spaces between macromolecules. In such cases, the performances were lowered. In fact, such a case was observed in (12). The influence of side groups in polymers with high FFV on their performances is not simple.

Simultaneous Improvements of Selectivity and Permeability of Polymer Membranes
In Section 2, performances for pure membranes from mainly only pure polymers whose chemical structures are clear are plotted in Figures 3-9 except for Figure 7 because the main aim of this review is to discuss the relationships between macromolecular structures and their performances. However, the performances usually changed in upper-left directions or lower-right directions, that is, the changes were often parallel to the upper bound lines when chemical structures were changed. In other words, when P O 2 values increased, their α values decreased and vice versa. Although improvement of both P O 2 and α values at the same time is very desirable, observations of such improvements were very rare, especially in pure polymer membranes. Therefore, in order to discuss how both P O 2 and α values can be increased simultaneously, in this section we will discuss membranes made from physically-modified polymers whose structures are not clear and also composite membranes made from polymers containing porous additives.

Thermally Rearranged Polymers (TRs)
Thermal rearrangement is one of the effective methods for improving both P O 2 and α values simultaneously [81]. Typically, polyimides (PIs) with hydroxyl pendant groups can be thermally converted to poly(benzoxazole)(PBO) by heating around 400 • C (For example, 55 in Chart 4 and Figure 6) [65]. In general, thermally rearranged polymers (TRs) have much higher P O 2 values than the original polymers with similar or slightly higher α values. The TRs have both large (8-11 Å) and small (3-5 Å) pores, although the precursor hydroxyl PIs have only intermediate sized (6-7 Å) pores (these sizes were determined by the PALS method). The smaller pores (ultramicropores) are important for the high α values and the larger pores (micropores) are important for the high P O 2 values [48].

Carbon Molecular Sieve Membranes (CMSM)
Organic polymers are used as precursors of carbon molecular sieve membranes (CMSM). The precursor polymers are polyimides (PIs), polysulfones (PSfs), poly(phenylene oxide)s (PPOs) and so on. Figure 10 shows plots of oxygen permeation behaviors for CMSMs. Table 8 lists the detailed data . There are many plots for CMSMs above the 2015 upper bound line for organic polymers. Many CMSMs show the best performance among all the membranes and much better performance than organic polymers, although most of them do not show ultrapermeablity. CMSMs are generally prepared by pyrolysis by heating of the precursor polymers to more than about 550 • C. Although fabrication of CMSMs that are thin and large in area is generally more difficult and expensive than that of organic polymers, their performance is much better than those of organic polymers. In particular, CMSMs f, g, z, A, and B have very high α values of more than 20. Although the original P O 2 values of the precursor polymers seem to affect those of the resulting CMSMs, these α values for the CMSMs were not influenced by those of the precursor polymers (Chart 7). Since CMSMs z, A, B, and C showing high α values of more than 20 were prepared at higher temperatures (at 800 or 900 • C) than usual CMCMs, the temperature seems to be more important for α values than the chemical structures of the precursor polymers.
Although the original PO2 values of the precursor polymers seem to affect those of the resulting CMSMs, these α values for the CMSMs were not influenced by those of the precursor polymers (Chart 7). Since CMSMs z, A, B, and C showing high α values of more than 20 were prepared at higher temperatures (at 800 or 900 °C) than usual CMCMs, the temperature seems to be more important for α values than the chemical structures of the precursor polymers.  Table 8, and for the chemical structures of the precursor polymers of the plots, see Chart 7. Table 8. Categorization and detailed data for CMSMs in Figure 10 (CMSMs in 2020).  Since CMSMs are insoluble and amorphous materials which are composed of solely carbon atoms without any organic functional groups, it is difficult to discuss the relationships between macromolecular structures and their performance. Instead, this section focuses on pore sizes in CMSMs. Figure 11 shows change of performances from the precursor polymers to the resulting CMSMs showing excellent performance. They all change in the direction of upper-right significantly, that is, simultaneous enhancements of P O 2 and α values are observed. In particular, the changes of the performance from their precursors to the CMSMs f, g, z, A, and C are very large. These desirable changes come about because the CMSMs may have both ultramicropores contributing high α and micropores contributing high P O 2 , although the precursor polymers may have only intermediate-sized pores [101]. These high α values were caused by their high α D values. Their α S values were almost at unity because CMSMs had no functional groups which could selectively interact with gas molecules. CMSM A (in Figures 9 and 10) has performance (P O 2 = 10, α = 21) similar to a polyimide (P O 2 = 8.5, α = 20; Figure 6 and Chart 4, 59) with bulky pendant groups showing the highest α value among all the polymers described in Section 2.2.3. However, the α value of CMSM depends only on the α D value (=17), but the α value of the polyimide depended both on the α D (=7) and α S values (=3). (Table 6) Their separation mechanisms are different. Generally, both ultramicropores and micropores were created simultaneously by pyrolysis of precursor polymers such as polyimides. When the pyrolysis temperature was high, the size of the ultramicropores became smaller. Therefore, CMSMs prepared at higher temperatures showed higher α values and lower P O 2 values. In other words, by increasing the pyrolysis temperature, α values increase and P O 2 values decrease [101].  Figure 10. Plots of oxygen permselectivity through carbon molecular sieve membranes (CMSM), showing the highest α at each PO2 reported in the literature in 2020. For the data and categorization of the precursor polymers of the plots, see Table  8, and for the chemical structures of the precursor polymers of the plots, see Chart 7. depends only on the αD value (=17), but the α value of the polyimide depended both on the αD (=7) and αS values (=3). (Table 6) Their separation mechanisms are different. Generally, both ultramicropores and micropores were created simultaneously by pyrolysis of precursor polymers such as polyimides. When the pyrolysis temperature was high, the size of the ultramicropores became smaller. Therefore, CMSMs prepared at higher temperatures showed higher α values and lower PO2 values. In other words, by increasing the pyrolysis temperature, α values increase and PO2 values decrease [101]. Figure 11. Change in the α and PO2 from the precursor polymers to carbon molecular sieve membranes (CMSMs). For the codes, data and categorization of the precursor polymers of the plots, see Chart 7.

Polymer Membrane Modification by Blending with Microporous Additives-Mixed Matrix Membranes (MMMs)
As described in Section 3.1, in order to enhance PO2 and α values simultaneously for a membrane, both ultramicropores and micropores should be created in the membrane. Preparation of CMSMs by pyrolysis of polymers is a very suitable method. However, control of the membrane preparation process and the pore sizes are still challenging. As another methodology for preparation of membranes with good mechanical strength and micropores whose sizes are well-controlled, mixed matrix membranes (MMMs) have been recently developed [104][105][106][107]. Typically, an MMM consists of a soluble amorphous organic polymer which shows good membrane-forming ability as a matrix and insoluble crystalline inorganic porous compounds as an additive or a filler which has no membrane- Figure 11. Change in the α and P O 2 from the precursor polymers to carbon molecular sieve membranes (CMSMs). For the codes, data and categorization of the precursor polymers of the plots, see Chart 7.

Polymer Membrane Modification by Blending with Microporous Additives-Mixed Matrix Membranes (MMMs)
As described in Section 3.1, in order to enhance P O 2 and α values simultaneously for a membrane, both ultramicropores and micropores should be created in the membrane. Preparation of CMSMs by pyrolysis of polymers is a very suitable method. However, control of the membrane preparation process and the pore sizes are still challenging. As another methodology for preparation of membranes with good mechanical strength and micropores whose sizes are well-controlled, mixed matrix membranes (MMMs) have been recently developed [104][105][106][107]. Typically, an MMM consists of a soluble amorphous organic polymer which shows good membrane-forming ability as a matrix and insoluble crystalline inorganic porous compounds as an additive or a filler which has no membraneforming ability and well-defined micro-or ultramicropores. In this section, we will describe examples of the simultaneous increase in P O 2 and α values found in the studies on MMMs.
Because such examples are very rare, especially for separation of the mixture of O 2 and N 2 whose size is 3.46 Å and 3.64 Å, respectively (their size difference is 0.18 Å), here we will include results from studies on separation performances for the other mixtures. For example, the mixture of CO 2 and CH 4 whose size is 3.30 Å and 3.80 Å, respectively (their size difference is 0.50 Å) and the mixture of CO 2 and N 2 whose size is 3.30 Å and 3.64 Å, respectively (their size difference is 0.34 Å), are described.

Required Conditions for Simultaneous Improvements of Selectivity and Permeability by the MMM Method
In order to use effectively both the roles of matrix polymers and porous additives in MMMs, it is necessary that the two components do not interact negatively with each other and their boundaries produce no defects. To avoid forming such defects, compatibility of polymers with additives in MMMs is important.
(2) Metal organic frameworks (MOF) [105] Because metal organic frameworks (MOF) include organic ligands, the compatibility of MOFs with organic polymers should be higher than that of purely inorganic zeolites. In addition, to reduce the formation of defects between polymers and MOF fillers, introduction of functional groups such as amino or acid groups was effective. For example, MMMs of sulfonated MOFs with sulfonated polyimides showed higher P CO 2 and P CO 2 /P CH 4 than those of non-modified polyimides [110]. MMMs of an amine-functionalized MOF and a polyimide also showed higher P CO 2 and P CO 2 /P CH 4 than the polyimide itself [111,112]. Similarly, in the combination of a polyimide-grafted MOF and a polyimide, a simultaneous increase of P CO 2 and P CO 2 /P CH 4 values was observed [113].
(3) Microporous organic cages (POC) [107] Because microporous organic cages (POC) are purely organic compounds, the compatibility of POCs with organic polymers should be much higher than that of MOFs described above. For example, in an MMM consisting of an imine POC and PIM-1, by addition of the POC, P CO 2 and P CO 2 /P N 2 simultaneously increased [114]. In the case of the mixture of O 2 and N 2 , the addition of a β-cyclodextrin (the pore size is 6.0-6.4 Å) as a POC to a polyimide resulted in only a slight increase in α with a slight decrease in P O 2 [115].

Sizes (Nanocrystals), Shapes (Nanosheets), and Assembled Structures of Microporous Additives
The sizes of additives in MMMs showed large effects on performance. For example, when nanocrystals of a MOF were added to a polyimide, both the PC 2 H 2 and PC 2 H 2 /PC 2 H 4 values were enhanced, although when the bulk MOF was used the PC 2 H 2 increased but PC 2 H 2 /PC 2 H 4 decreased [116]. The nanosize crystals may avoid the production of defects. The shape of additives also had great effects. In the case of a nanosheet of a MOF accumulated on a macroporous support, by suppressing stackings of the nanosheets, P H 2 and P H 2 /P CO 2 increased simultaneously [117]. An MMM based on polybenzimidazole using a nanosheet of a MOF showed simultaneous increases in P H 2 and P H 2 /P CO 2 . On the other hand, when nanocrystals were used instead, P H 2 /P CO 2 increased but P H 2 decreased [118]. Similarly, only a nanosheet of a MOF was effective for enhancing P CO 2 /P CH 4 (although P CO 2 decreased), while nanocrystals of the MOF were not effective [119].

High Permeable Linear Polymers, PTMSP and PIMs
The ultrahigh P O 2 (>10 4 ) of very rigid polymers consisting of alternating double bonds with bulky substituents, that is, PTMSP (8 in Chart 1 and Figure 3), was reported by Prof. Masuda in 1983 [45] and it was confirmed that it contains micropores and its permeation is based on the MS mechanism. Then a new ladder polymer with spirocarbons as contorted points, that is, PIM-1 (11 in Chart 1 and Figure 3), was developed by Prof. Budd and McKeown in 2005 [29]. With the advent of this new polymer, the original Robeson's 1991 upper bound [10] was revised in 2008 [12]. Finally, Prof. Pinnau updated Robeson's 2008 upper bound in 2015 after several Trip-PIMs emerged (47,50, and 52 in Chart 4 and Figure 6) in 2014 [59,61,63]. Recently, the best PIM having higher ultrapermeability and a very high α was reported by Prof. McKeown in 2017 [44]. Furthermore, it was reported that a new polyimide (polymer 25 in Figure 6) having bulky substituents showed extremely high α (=20.3) by Prof. Banerjee in 2016 [69]. The rate of progress during 2014-2020 was much faster than that during 1991-2013, although the former term (7 years) is much shorter than the latter (23 years).
The separations of these high-performance polymers are based on mainly α D , particularly for polymers with high P O 2 values such as PTMSP and PIMs. (Although excellent research on oxygen permselective membranes based on α S using metal complexes as oxygen carriers has been carried out by Prof. Nishide, this review does not describe this work because it is outside its scope [120]) In other words, it depends on the MS mechanism. Therefore, the size distribution of their micro-and ultramicropores is decisive and the control of their sizes is important. However, since the micropores are created as spaces between macromolecules, the control of the size is not easy and in addition their stability is low. In fact, their P O 2 values decreased significantly with time (see Figure 8). This is a big problem for these polymers in terms of practical applications.

High Permselective Inorganic Membranes, CMSM and Graphene
When the chemical structure of a polymer was changed, their performances often changed in the direction of the upper-left or lower-right in the α − P O 2 graphs. In other words, their direction of change is parallel to the upper bound lines. The most desirable change of improvements of their performances is a movement in the direction of the upperright, i.e., a simultaneous increase in P O 2 and α. However, such examples were very rare, as described above. Treatment with physical factors such as heat [121] and light [122] resulted in an increase in α with a decrease in P O 2 and vice versa. However, we noticed extreme changes in the direction of the upper-right for the preparation of CMSMs from their precursor polymers by heating at 550-800 • C ( Figure 11). Although heat treatment of polymer membranes usually affects just high-ordered structures, in this case of formation of CMSMs, changes in chemical structures happened, that is, carbonization with evolution of organic vapers and gases. However, the resulting CMSMs were insoluble and amorphous and, therefore, it is not easy to prepare wide thin membranes of CMSMs like polymer membranes. In addition, it is difficult to know their precise chemical structures from NMR and XRD. The details of the chemical structures are not known but it was thought they may contain graphene sheets. Although graphene macromolecules themselves have no internal pores and, therefore, no filtration functions based on the MS mechanism, the 2D shape seems to be suitable for enhancing performances. (Although some graphenes were applied to gas separation membranes [123,124], their selective permeation occurred during permeation through spaces between graphene sheets or internal defects in graphene sheets.)

Promising Membranes from Regularly Networked Organic Polymers, 2DPs
Some researchers reported networked 2DPs or nanosheets which are similar to graphene but have micropores whose sizes are similar to those of gas molecules and tried to apply them for gas separation membranes. An example of synthetic 2DPs is a two-dimensional covalent framework (2DCOF) [125]. However, since COFs are crystalline and insoluble, reports of successful applications to oxygen separation membranes were almost zero. Instead we tried to use some kinds of networked polymers and the related polymers made from linear polymers described in Section 2.2.1 (2). By adding networked structures, α values often increased but P O 2 decreased. In the case of networks prepared by short flexible crosslinking, the decrease of P O 2 was suppressed [76]. In particular, when networked 2DPs was introduced in situ into linear polymers in the membrane state, both α and P O 2 increased [75]. Although application of 2D materials to separation membranes was reported recently, there have been very few studies on gas separation. In particular, to the best of our knowledge, there have been no reports on the application of 2DP to oxygen permselective membranes [126]. Judging from all these reports, membranes from organic polymers containing organic network 2DPs inside the membranes seem to be a very promising avenue to pursue.