Adsorption separation of heavier isotope gases in subnanometer carbon pores

Isotopes of heavier gases including carbon (13C/14C), nitrogen (13N), and oxygen (18O) are highly important because they can be substituted for naturally occurring atoms without significantly perturbing the biochemical properties of the radiolabelled parent molecules. These labelled molecules are employed in clinical radiopharmaceuticals, in studies of brain disease and as imaging probes for advanced medical imaging techniques such as positron-emission tomography (PET). Established distillation-based isotope gas separation methods have a separation factor (S) below 1.05 and incur very high operating costs due to high energy consumption and long processing times, highlighting the need for new separation technologies. Here, we show a rapid and highly selective adsorption-based separation of 18O2 from 16O2 with S above 60 using nanoporous adsorbents operating near the boiling point of methane (112 K), which is accessible through cryogenic liquefied-natural-gas technology. A collective-nuclear-quantum effect difference between the ordered 18O2 and 16O2 molecular assemblies confined in subnanometer pores can explain the observed equilibrium separation and is applicable to other isotopic gases.

S table isotope technologies have attracted increasing interest over the last decade due to their indispensable role in plant, aquatic, and animal life [1][2][3][4] . They are widely used as radiolabelled probes in isotopic analysis methods [5][6][7][8] , therapeutic cancer drugs 9,10 , and environmental studies 11,12 . Naturally occurring heavier gas isotopes including carbon ( 13 C and other isotopes), nitrogen ( 13 N), and oxygen ( 18 O) are extensively used for such radiolabeling because their molecular weight difference from their main isotope is quite minor compared to the lighter hydrogen ( 1 H)-deuterium ( 2 H) molecules, resulting in a lower isotopic effect and hence only a minor perturbation to the biochemical behavior 1,2,13 . The positron (β + )-emitting isotopes, including 15 C/ 11 C, 13 N, and 18 F, can be used as imaging probes in the radionuclide-based molecular imaging positron emission tomography (PET) technique and other useful clinical radiopharmaceuticals 2 . In particular, 18 O 2 acts as a target in cyclotrons for producing [ 18 F]-labeled 2-deoxyglucose (FDG) as a β + -emitting radioisotope for PET biomedical imaging. Of all of the β + emitters employed in PET, the 18 F isotope is the preferred probe in radiopharmaceuticals because of its relatively long half-life (110 min), which allows its use in clinical PET imaging centers that lack radiochemistry facilities, and its low positron energy (0.64 MeV) that enhances the spatial resolution to produce optimal physical characteristics 2 . Other β + emitters involving 11 C or 13 N exhibit short half-lives and can only be utilized at imaging centers with a cyclotron and radiochemistry facility 2 . PET imaging can show abnormalities that cannot be detected by other techniques, resulting in the early and more accurate diagnosis of infected or cancerous tissues 14 . Furthermore, 18 O 2 can be introduced into the body by simple inhalation to study the function of the brain for the treatment of patients with diseases, such as schizophrenia, manic depression 2,10,15,16 . Therefore, enhanced production of 18 O is indispensable for achieving improvements in healthcare, environmental protection, and basic sciences.
The natural abundance of oxygen isotope 18 O is very low and is only 0.204 at.% compared to the principal 16 O isotope (99.76 at. %). Isotopic separation is currently only possible with a limited number of techniques, such as cryogenic distillation of oxygen/ nitric oxide/water 17,18 , membrane distillation 19,20 , isotope exchange reaction 21 , and thermal diffusion 22 . These methods require complex equipment and are time and energy-intensive. Consequently, alternative technologies are needed to meet the high demand for 18 O in healthcare and environmental science fields.
Recently, low-temperature adsorption-based separation enabled by the differences in isotope adsorption in nanopores due to the higher zero-point energy of translational motion of light isotope molecules (so-called quantum molecular sieving, QMS) has been demonstrated 23,24 . Consequently, QMS is the most promising alternative to the currently used methods for the separation of light isotopes such as hydrogen or helium 25,26 . However, the effective size differences for heavier gas isotopes such as 18 O 2 and 16 O 2 or 13 CH 4 and 12 CH 4 at 112 K, as estimated from the thermal de Broglie wavelength for the QMS effect, are only 0.0017 nm and 0.0012 nm, respectively. In addition, the Feynman-Hibbs potential calculation shows a difference of only 0.07 K for both isotope gases (Supplementary Fig. 1 and Supplementary Note 1), showing that QMS is ineffective for heavier gas isotopes. Therefore, we cannot expect that efficient separation of oxygen, methane, or other heavier gas isotopes can be achieved with nanoporous materials through the QMS mechanism.
The O 2 or CH 4 molecule has other vibrational and rotational degrees of freedom that depend on the molecular weight. The vibrational states are essentially the same in the gas and adsorbed phases and cannot lead to the selective adsorption of 18 O 2 or 13 CH 4 . By contrast, the rotational degrees of freedom of the molecules adsorbed in the nanopores are highly restricted below 130 K, unlike those of gaseous molecules 27 . Nevertheless, a very small difference in the rotational energies of these isotope molecules coupled with translational motion 28 is not sufficient to induce the selective adsorption of 18 O 2 or 13 CH 4 . However, when O 2 or CH 4 molecules are densely packed at quasi-solid densities in nanopores at low temperature, collective quantum motion associated with vibrational and rotational modes can give rise to a sufficiently large adsorption-energy difference for oxygen and methane isotope molecules to enable the selective separation, as described in this article.
In this work, we report an industrially applicable adsorptionseparation route of 18 O 2 from a 16 O 2 -18 O 2 mixture using nanoporous solids at~112 K, utilizing the cryogenic facilities of liquefied natural gas industries to save energy. The observed dynamic selectivity or separation factor S( 18 O 2 / 16 O 2 ) exceeds 60, depending on the nanoporous adsorbent, as is further confirmed by breakthrough curve experiments. We also demonstrate an equally successful separation of 13 CH 4 / 12 CH 4 under similar conditions.

Results
Dynamic adsorption separation of CDC. The dynamic adsorption-based separation was measured at different temperatures using a custom-made flow-type mixed gas adsorption apparatus coupled to a quadrupole mass spectrometer (MS) (Supplementary Figs. 2 and 3; Supplementary Notes 2 and 3) 29 . High purity 16 O 2 (99.99995%) and 18 O 2 (≥98%) gases were mixed to achieve different compositions ( 18 O 2 % varied from 4.8 to 70 at. %) and then were introduced into the sample cell at a constant temperature. Similarly, 12 CH 4 (99.9999%) and 13 CH 4 (99%) were used to prepare isotopic mixtures. The adsorbents employed were carbide-derived carbon (CDC) produced by the chlorination of TiC 30 and activated carbon fibers (ACFs) with slit-shaped pores. The effective pore widths determined from the N 2 adsorption isotherms at 77 K are 0.7 nm for CDC and ACF5 and 0.8 nm and 1.1 nm for ACF10 and ACF20, respectively (Supplementary  Figs. 4-6 and Supplementary Table 1). For theoretical calculations, the pore widths were also converted into the effective pore widths by subtracting 0.334 nm (the average graphite interlayer spacing) from the actual diameters 31 . We also considered open single-walled carbon nanotubes (SWCNT ox ) with cylindrical 1.5nm and 1.0-nm wide pores and zeolites MS4A, MS5A, MFI, and BEA with interconnected cylindrical pores with the widths 0.40, 0.50, 0.55, and 0.66 nm, respectively; these materials were preevacuated prior to the dynamic and equilibrium adsorption measurements.
The adsorption selectivity S for 18 O 2 against 16 O 2 is defined as: where (  ) (ads-g) hereafter will be denoted as S. Figure 1 illustrates that our cryogenic adsorption separation is much simpler, more energy-efficient, and compact than traditional cryogenic distillation involving sophisticated equipment with a distillation column with a height of tens of meters. For the selectivity observed from the present adsorption separation, only three adsorption stages are estimated to be required to obtain >95% purity of 18 (Fig. 2a) is greater than 60 at the initial stage, irrespective of the 18 O 2 concentration, and decreases to 1.6-1.2 after 40 min (Fig. 2a, inset). Supplementary Fig. 9 shows the reproducibility of the selectivity. This decrease in the selectivity may be due to the decreased availability of the adsorption sites over time. CDC preferentially adsorbs 18 O 2 even from the mixed gas with a very low content of 18 18 O 2 is preferentially adsorbed from the beginning, creating a concentration difference of 20 µmol g −1 over 120 min, resulting in high adsorption selectivity. Notably, the difference in the adsorption amounts of 18 O 2 and 16 O 2 can be observed from the beginning of the experiment; however, the selectivity can only be analyzed when the pore volumes of CDC are sufficiently crowded to allow few 18 O 2 molecules to reach the MS, as shown in Supplementary Fig. 7 (Supplementary Note 4). Here, the pore volume filling, which is the ratio of the adsorbed O 2 volume derived from the liquid density of O 2 compared with the measured nanopore volume, is 2% for 18 O 2 ; the expression for the adsorption by the pore filling is convenient for adsorption in nanopores. Moreover, the pore volume filling of the CDC depends on various factors, such as the amount of mixture gas introduced, dosing rate of introduction, and temperature. If an adsorption experiment is performed with more mixed gas at a higher dosing rate, then the pore volume filling % will be higher, as demonstrated in Supplementary Fig. 12. The high selectivity trend in the initial stage is retained in the temperature range of 100-150 K, as shown in Fig. 2c. However, the S at 1% pore volume filling and the time period for which S > 2.5 both decrease with increasing temperature (Fig. 2d). In addition, the pore volume filling of the mixed gas is larger at lower temperatures, and at 90 min, it decreases from 2.5% to 0.25% as the temperature increases from 100 K to 140 K ( Supplementary Fig. 13). Consequently, the highly selective separation of 18 O 2 from the mixed gas ( 18 O 2 + 16 O 2 ) with a CDC of~112 K is highly promising for the design of an efficient separation process.
The cryogenic adsorption separation demonstrates that S > 60 in the initial stage of adsorption (~1 min) arises from the selective adsorption of 18 O 2 in the narrow sites of the pores (<0.4 nm) present in the CDC structure 32 . In our previous work, atomistic models of CDCs were generated via molecular dynamics simulation and validated by experimental adsorption measurements 33 . A slice with a depth of 3.5 nm and a side of 10.4 nm of a representative CDC model containing realistic slit-shaped pores is shown in Fig. 2e, left panel. The CDC porosity was evaluated by filling the structure with nonoverlapping spheres according to the Gubbins method 34 . Rendering of the spheres within the CDC structure aids the visualization of the pores, as shown in the right panel, where each sphere is colored according to its diameter. Narrow pores with diameters <0.4 nm are identified by dashed white ovals, confirming the presence of preferential adsorption sites for the 18 O 2 molecules in CDCs. Figure 2f shows the experimental S values of CDC at 100 K and 112 K compared with those of the other separation methods reported in the literature. The high selectivity S = 116 ± 14 at 100 K or S = 60 ± 15 at 112 K is ascribed to the preferential adsorption of 18 O 2 Fig. 1 Cryogenic distillation vs. Cryogenic adsorption-based selective separation of oxygen isotopes using carbide-derived carbon (CDC). The illustrative model quantitatively comparing the cryogenic distillation separation setup with the cryogenic adsorption-separation method. While distillation towers must be oriented vertically, adsorption beds can be configured in many different orientations. The nanoporous adsorbent bed in the adsorption column preferentially adsorbs 18 O 2 according to the ratio determined by the adsorbent selectivity. The plausible adsorption-separation tower size was estimated for future consideration assuming the ideal conditions with the selectivity remaining at 60 and the adsorption capacity of 15 mmol/g. The assumption of the adsorbent density of 500 kg/m 3 and space velocity = 10 min −1 leads to three separation towers with the capacity of 3 m (diameter) × 1 m (height) producing 18 O 2 of >95%. NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-20744-6 ARTICLE molecules at the narrow pore sites (left inset in Fig. 2f). Even after 30 min, the CDC pores are filled with S > 2 (right inset in Fig. 2f), which is still twice that of the other separation methods. To further ascertain the observed high selectivity trends, adsorption-separation experiments are performed using CDC adsorbent for only 10, 15, and 20 min at 112 K. The mole fractions of the feed and adsorbed mixture isotope gas are monitored using the time evolution of mass intensity. The molar ratio for the feed gas 18 Fig. 14). This shows that ∼8% higher adsorption of 18 O 2 occurs during the 10-min  (16,17), membrane distillation (18,19), and isotope exchange (20). g S( 13 CH 4 / 12 CH 4 ) (written as S( 13 C/ 12 C) in the figure) of CDC at 112 K for feed gas mixture ( 13 CH 4 + 12 CH 4 ) under similar dosing rate (~1 mL min −1 ). The inset shows an enlarged view of the dotted regions. The error bar represented by the red dashed line is the standard deviations derived from three measurements. selective adsorption experiment compared to the experiment carried out for 20 min, corresponding to a maximum difference of 1.33 mg/g between 18 O 2 and 16 O 2 . These results confirmed that the initial high selectivity tends to decrease over time.
In addition, we have verified that this method is applicable to other gaseous heavy isotope pairs involving 13 CH 4 and 12 CH 4 . The CDC demonstrates selective separation of 13 CH 4 from the mixed gas ( 13 CH 4 + 12 CH 4 ) at 112 K with S( 13 C/ 12 C) = 56 ± 6 initially and maintains S > 2.5 for more than 40 min (Fig. 2g).
Dynamic adsorption separation of different nanoporous adsorbents. Other nanoporous materials with different pore geometries show similar selectivity trends even though their selective absorptivities are slightly inferior to that of CDC, as shown in Fig. 3a, b. The equilibration time depends on the pore aperture. ACF5 (slit pore width: 0.7 nm) shows high selectivity for an extended time interval with S > 1.2 up to 120 min (complete experiment time, see inset Fig. 3a). SWCNT ox with 1 nm cylindrical pore maintains S > 1.2 for more than 60 min, while zeolite MFI (pore width 0.55 nm) shows S > 1.2 for only 30 min (inset Fig. 3a, b). We have also measured the selectivity in AFC10, AFC20, SWCNT ox (1.5 nm), and zeolites BEA and MS5A, all of which exhibit lower selectivity. In addition, the adsorbents with pore widths of < 0.4 nm do not demonstrate significant selective separation performance ( Supplementary Figs. 15 and 16). A significant difference in the adsorbed amounts of 18 O 2 and 16 O 2 can be observed in Fig. 3c, d. For ACF5, the adsorbed gas amount increases gradually, reaching a maximum adsorption difference of 13 µmol g −1 , while the corresponding values for SWCNT ox (1 nm) and zeolite MFI after 120 min are 10 µmol g −1 and 16 µmol g −1 , respectively. The pore volume filling percent after 120 min varies from 0.6% for ACF20 (pore volume of 0.81 ml g −1 ) to 5.2% for zeolite MFI (pore volume of 0.16 ml g −1 ) ( Supplementary Fig. 17). Figure 3e summarizes the S values for all the nanoporous adsorbents at a pore volume filling of 1%, demonstrating the best selective adsorption behavior of CDC. This implies that the observed selectivity depends strongly on the pore size and the pore geometry (shape). The narrow pores present in the CDC structure have a 2D structure, while SWCNT ox (cylindrical pores) or zeolites (interconnected channeled cylindrical pores) have 1D channels and inferior selectivity compared to CDC. The observed maximum adsorption difference of 1.33 mg/g between 18 O 2 and 16 O 2 under the present experimental setup during only 10 min of adsorption separation appears to be highly promising for dynamic separation. If we increase the sample amount to 1 kg of adsorbent, the available adsorption system can give rise to a preferential 18 O 2 adsorption of 0.8 L(STP) and will be quite useful. A new type of adsorption-separation system with a large sample holder and mixed gas reservoir can be constructed that utilizes the initial large selective adsorption of 18 O 2 ; this will enable human society to obtain a promising isotope separation technology, considering that the present 18 O 2 separation technology using distillation requires 10 months.
Breakthrough measurements. Furthermore, we confirmed this by performing breakthrough measurements with an adsorption column packed with a comparatively large amount of commercially available ACFs to evaluate the separation performance. We used ACFs because the breakthrough experiments required larger sample sizes than the amount of the lab-synthesized CDC available. The experimental conditions and the selectivities for the breakthrough experiments are listed in Supplementary  Table 2. A custom-made apparatus for measuring the breakthrough curves is schematically shown in Supplementary Fig. 18  (Supplementary Note 5). The breakthrough curves for ACF5 and ACF10 are shown in Fig. 4a, b. The concentration C/C 0 of 16 O 2 at the outlet in the initial stage is much larger than that of 18 O 2 for both ACFs, clearly indicating the preferential adsorption of 18 O 2 under continuous flow conditions using He as the carrier gas. The high S values of 1.5 and 3.0 for ACF5 and ACF10, respectively, in the initial stage qualitatively correspond to the results from mixed gas adsorption experiments, as pictorially described in Fig. 4c. This reflects that the adsorbed molecules can mostly occupy the pore entrance sites during the initial stage of high selectivity and then diffuse to the inner pore region. The selectivity decreases with time as 18 O 2 reaches full breakthrough and the flow approaches a stationary state. These selectivity values from the breakthrough measurement are much larger than the S ∼1.04 of the current separation methods (Fig. 2f). However, the selectivity from the breakthrough experiment is smaller than that obtained from the mixed gas adsorption method discussed above.
Theoretical selectivity of oxygen isotope adsorption. Above, we have presented experimental results demonstrating 18 O 2 / 16 O 2 selectivity but did not provide a clear explanation of the origin of these results. It is known that nuclear-quantum effects (NQEs) in the vibrational, rotational and translational motion of the condensed phase can each contribute to isotope selectivity [35][36][37] . O 2 molecules in the nanopores at low temperature form an ordered solid-like assembly in the nanopores due to the strong O 2 -nanopore and O 2 -O 2 interactions. We have performed simulations of 18 O 2 and 16 O 2 isotopes in MFI and SWCNTs using the path-integral formalism 35 to explicitly account for the NQEs in each of the degrees of freedom to identify the origin of the observed isotope selectivity. We note that isotopic selectivity is an inherently quantum mechanical phenomenon; we, therefore, employed path-integral molecular dynamics methods to compute the free energy differences for the gas and adsorbed phases of the different isotopes. In addition, adsorption selectivity is a thermodynamic equilibrium property, so that it is appropriate to use equilibrium path integral methods. In addition, we note that tunneling does not contribute in any way to the thermodynamic properties, and therefore does not need to be considered here. The experimental results give kinetic selectivity as a function of time. This quantity is not the true equilibrium selectivity but rather is related to a breakthrough process of dynamic adsorption. This process cannot be modeled using atomistic path integral methods because it would require detailed knowledge of the time-dependent pore filling process, including diffusion barriers through the irregularities in the adsorbent materials. Thus, it is only possible to model equilibrium selectivity. However, this modeling does provide a proof-of-concept that collective NQEs are responsible for the long-term (near-equilibrium) selectivity observed in the experiments. Details of the calculations are given in Supplementary Methods 1. We chose MFI and SWCNT because their atomistic structures are known precisely and therefore, these materials are amenable to accurate modeling. We note that these calculations represent equilibria and cannot account for the kinetic (time-dependent) selectivities observed in Fig. 3a, b but do explain the long-term (equilibrated) experimental results. We carried out simulations at both zero-loading (one O 2 per simulation cell) and at the loadings corresponding to the equilibrium amounts of O 2 adsorbed at a relative pressure P/P 0 of 0.12 at the temperatures of 90.2, 112, and 130 K to account for the effects of the adsorbate-adsorbate interactions on selectivity.
Path-integral calculations in the low O 2 coverage limit were carried out for SWCNTs having atom-center-to-atom-center tube diameters ranging from 0.54 to 1.35 nm (effective diameters of 0.21-1.02 nm) to obtain the relationship between the selectivity and tube diameter; the results are shown in Fig. 5a and Supplementary Table 3. The (4,4) and (5,5) SWCNTs with extremely narrow diameters of 0.54 nm (0.21 nm effective diameter) and 0.69 nm (0.36 nm effective diameter), respectively, give high selectivity values at zero loadings through strong O 2 -SWCNT interactions, resulting in mass-dependent NQEs in the rotational, vibrational, and translational degrees of freedom. However, these pores are too small to induce the observable O 2 adsorption experimentally. In contrast, adsorption in the (7,7) and (10,10) SWCNTs at zero loading shows very low selectivities (1.004 ± 0.002 and 1.006 ± 0.0037, respectively), indicating that the experimentally observed results cannot be explained by simulations at low coverages.
We, therefore, simulated O 2 adsorbed in (7,8) and (10,10) SWCNTs with the actual diameters of 1.02 (0.7 nm effective diameter) and 1.36 nm (1.03 nm effective diameter), respectively, at 90.2 K using amounts of adsorbate close to that reported for SWCNT ox (1 nm) at P/P 0 = 0.12 ( Supplementary Fig. 19). The selectivities obtained from the finite loading simulation were 1.164 ± 0.024 for the (7,8) SWCNT and 1.02 ± 0.007 for the (10,10) SWCNT, similar to the long-time experimental value for the SWCNT ox (1 nm) of 1.09, as shown in the inset of Fig. 3a. The origin of the significant increase in selectivity with finite loading relative to the low coverage limit can be found in the highly ordered state of the O 2 molecules observed in the simulations. The initial random configuration shown on the left of inset Fig. 5a transforms to a highly ordered state (right) during the PIMD simulation. This highly ordered state gives rise to a collective NQE not obtained at low coverage, resulting in higher selectivity.
Our simulation results indicate that (1) narrow pores give higher selectivity and (2) the observed selectivity is a result of both pore confinement and the cooperative or collective NQEs due to the ordering of the O 2 molecules when a high amount of O 2 molecules is adsorbed in the preferable pores (close to saturation). These observations are consistent with our hypothesis that narrow pore sites give rise to higher selectivities because they have higher confinement and are more likely to produce ordered O 2 -adsorbed phases than the larger nanopores within CDC. Furthermore, we measured the difference in the activation energy (E a ads ) for the overall adsorption rates of 18 O 2 and 16 O 2 on CDC at 112 K using the linear driving force model described in Supplementary Fig. 22 (Supplementary Methods 2). The E a ads values obtained for 18 O 2 and 16 O 2 are 9.1 ± 0.1 kJ mol −1 and 9.4 ± 0.1 kJ mol −1 , respectively. This small activation energy difference of 0.3 ± 0.1 kJ mol −1 between 18 O 2 and 16 O 2 may be associated with the potential energy difference in the transition state for adsorption.
Adsorption isotherms and energetics. Figure 5c shows the experimental adsorption isotherms for 18 O 2 and 16 O 2 on CDC at 90.2, 112, and 130 K. All of the adsorption isotherms exhibit Type I behavior in the IUPAC classification, indicating the filling of oxygen molecules in highly uniform nanopores 38 . The 18 O 2 uptake is essentially the same as the 16 O 2 uptake below P/P 0 = 10 −4 (Fig. 5d). However, the 18 O 2 uptake is slightly higher than that of 16 O 2 at higher relative pressures ( Supplementary  Fig. 23). The isosteric heat of adsorption (q st ) was evaluated from the Clausius-Clapeyron equation using the adsorption isotherms at different temperatures ( Supplementary Fig. 14 and Fig. 3 Pore geometry effect on oxygen isotope adsorption separation. a, b Time evolution of S for ACF5 and SWCNT ox (1 nm) and zeolite MFI (solid lines), respectively, during the initial few minutes at 112 K. Red dashed lines represent standard deviations derived from four measurements. Insets show S for the full duration of the experiment. c, d Time evolution of the amount of adsorbed 18 O 2 and 16 O 2 on ACF5 and SWCNT ox (1 nm) and zeolite MFI. The adsorption amount is calculated from the difference of feed mixed gas and the unadsorbed mixed gas. Insets show the enlarged view of the circled initial region. e Pore geometry-dependent selectivity S at 1% pore volume filling at 112 K. Slit pore (green rectangles) materials include carbide-derived carbon (CDC) and ACFs, cylindrical pore (blue triangles) materials are SWCNT ox (1 nm) and SWCNT ox (1.5 nm) and MS5A, MFI and BEA have channel cylindrical pores (red circle). An equimolar mixed gas ( 18 O 2 + 16 O 2 ) is used in all experiments performed at 112 K. The accessibility of oxygen molecules for each pore is schematically shown at the bottom.  (Fig. 5e), and is much larger than the heat of condensation of bulk O 2~6 .8 kJ mol −1 39 due to the favorable interactions with the pores. The absolute adsorption amount difference of 18 O 2 and 16 O 2 is not sufficiently large to obtain an evident difference in the q st of the oxygen isotope molecules in the low fractional filling range. It is noteworthy that q st for 18 O 2 is larger than that of 16 O 2 above the fractional filling of 0.1, giving a difference of 0.2 ± 0. 005 kJ mol −1 for CDC (inset in Fig. 5e). Similarly, the q st difference between 18 O 2 and 16 O 2 for SWCNT ox (1 nm) is 0.7 ± 0. 04 kJ mol −1 at the filling of 0.3 ( Fig. 5f) but much smaller differences are obtained at low coverage, consistent with our calculations. On the other hand, the q st of MFI gradually increases with fractional filling with no clear difference in the q st between 18 O 2 and 16 O 2 (Fig. 5f).
Since CDC gives the highest selectivity, we discuss the relationship between the pore shape and q st results. The large q st for CDC at the initial stage arises from the highly confined state of the oxygen molecules in the narrow pore sites with very deep interaction potential wells, forming the ordered molecular solids, as mentioned above. The q st gradually decreases with fractional filling due to the changes to the adsorption sites of the shallower interaction potential wells. To evaluate the contribution of the narrowest pore sites toward the total adsorption, we simulated N 2 adsorption on our CDC model as shown in Fig. 2e left. The geometrical cumulative pore volume using nitrogen as a probe atom was calculated using Poreblazer 40 . It is noted that the pore highlighted within the small cyan circle contains spheres of diameter <0.4 nm and that space is not accessible to nitrogen ( Supplementary Fig. 25). The cumulative pore volume of such narrow spaces is V narrow-pore (d < 0.4 nm) = 0.021 cm 3 g −1 , contributing to 3.5% of the total pore volume. These narrow sites exhibit 2D accessibility and this may facilitate the preferential adsorption of 18 O 2 as pictorially demonstrated in Fig. 5g. The 18 O 2 molecules strongly confined at the narrow spaces in the pores of CDC can form an ordered molecular solidlike assembly that leads to a collective NQE. Furthermore, 1D pores of SWCNTs and zeolites display less accessibility and weaker interaction potentials than the 2D narrow pores of CDC. Consequently, the collective NQE in SWCNTs and zeolites is not as remarkable as that in CDC. The interaction potential of ACFs is weaker than that of the narrow pore sites of CDC, even though ACF has well-accessible slit-shaped pores.

Discussion
We have demonstrated very high 18 O 2 adsorption selectivity of nanoporous materials that increases with decreasing temperature and has a strong dependence on the pore geometry of nanoporous materials. In particular, at approximately the boiling temperature of methane (112 K) CDC shows S( 18 O 2 / 16 O 2 ) exceeding 60 ± 15 for the initial stage of adsorption because 18 O 2 molecules are kinetically and thermodynamically preferentially adsorbed over 16 O 2 . Such high adsorption selectivity was also evident for the separation of 13 CH 4 with S( 13 C/ 12 C) = 56 ± 6. The highly efficient separation of 18 O 2 or 13 CH 4 evidenced in this study can be implemented in the industry by designing a rapid adsorption-separation instrument and will facilitate medical and other applications of these O and C isotopes. The CDC with highly accessible 0.4 nm wide pore spaces has a strong interaction potential for O 2 and gives the highest adsorption selectivity compared with activated carbon fibers, single-walled carbon nanotubes, and zeolites. Nanoporous materials consisting of graphitic walls and having an abundance of very narrow open pores are promising for achieving high separation selectivity and high separation capacity. The collective nuclear-quantum effect (NQE), which is different from the well-known translational motion-based QMS effect, can explain the equilibrium selective adsorptive separation of 18 O 2 or 13 CH 4 by subnanometer pores.

Methods
Synthesis and characterizations. Pitch-based activated carbon fibers (ACF20, ACF10 and ACF5) were procured from Ad'all Co., Ltd. The CDC sample derived from TiC was synthesized by following the previously reported method 41,42 . Singlewalled carbon nanotubes (SWCNT) grown by the CVD method were obtained from MEIJO NANO CARBON Co., Ltd. The samples were oxidized under dried air at 823 K for 10 min with the heating rate 1 K/minute. A typical steam-assisted crystallization synthetic method has been used for the synthesis of pure silica zeolite BEA 43 . Silicalite-1 or zeolite MFI was synthesized by following the seed surface crystallization mechanism discussed by Ren et al. 44 . Molecular sieves MS5A and MS4A were purchased from Nakarai Tesque. High purity 16  Data availability