Fractionation of Isotopic Methanes with MetalâOrganic Frameworks

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C: Physical Processes in Nanomaterials and Nanostructures

Fractionation of Isotopic Methanes with Metal-Organic Frameworks Musen Zhou, Yun Tian, Weiyang Fei, and Jianzhong Wu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11393 • Publication Date (Web): 26 Feb 2019 Downloaded from http://pubs.acs.org on February 27, 2019

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The Journal of Physical Chemistry

Fractionation of Isotopic Methanes with Metal-Organic Frameworks Musen Zhou1, Yun Tian1, Weiyang Fei2 and Jianzhong Wu1* 1

Department of Chemical and Environmental Engineering, University of California, Riverside, CA 92521, United States 2

Department of Chemical Engineering, Tsinghua University, Beijing 100084, China ABSTRACT The need of isotopic compounds has been rising in recent years for both medical

applications and scientific research. Existing technologies (e.g. cryogenic distillation, Girdler sulfide process, supersonic beam diffraction etc.) have difficulties to meet the growing global demand for enriching pure isotopic compounds because of low separation capacity, poor selectivity, and large energy consumptions. Metal-organic frameworks (MOFs) have been demonstrated promising for separation of isotopic compounds due to their tunable pore sizes and chemical affinities. In this work, we theoretically investigate 4764 experimentally synthesized MOFs for their potential applications to separation of three representative isotopic methane pairs selected on the basis of their differences in molecular size, in interaction energy, and in a combination of both size and energy characteristics. Top MOF candidates have been identified with highest adsorption performance scores (APS), highest adsorption selectivity, and highest membrane selectivity. The theoretical results suggest that MOF adsorption provides the selectivity of isotopic methanes significantly larger than conventional separation methods. While isotopic separation by adsorption alone is compromised by a small working capacity, utilization

*

To whom correspondence should be addressed. Email: [email protected] 1 ACS Paragon Plus Environment

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of MOFs as a porous membrane facilitates efficient separation of isotopic methanes with both high working capacity (permeability) and large selectivity. 1. INTRODUCTION Recent years have witnessed a rising interest in separation and purification of radioactive isotopes of different elements for biomedical and analytical applications. For example, high purity 13C isotope can be used as a tracer in chemical and biological analysis, in early diagnosis of human diseases, and in determining chemical reaction mechanisms1-9. Besides, the increasing energy demand leads to construction of more nuclear power plants and, subsequently, generation of more nuclear waste10. Isotope separation is often a prerequisite to store and post-treat radioactive nuclear materials. Fractionation of isotopic compounds (e.g., 1H2O, 2H2O and 3H2O) is challenging because they have virtually identical molecular characteristics and chemical properties11-13. As discussed in our previous work14, the single-stage selectivity is below 1.01 for chromatography and cryogenic distillation, while metal-organic frameworks (MOFs) may result in selectivity as high as 1.06 at similar conditions. Most importantly, MOF promises efficient separation of isotopic methanes at ambient temperature (300 K). Typically, a MOF material may have an ultra-large specific surface area and its properties (e.g., aperture, chemical affinity and mechanic strength) can be easily tailored for specific applications by changing the metal nodes or organic links15-16. A large number of MOF structures could be constructed by combining different building blocks (organic linkers and metal nodes).17 The existence of such a large database makes it possible to design MOF materials with excellent mechanic strength, working capacity and selectivity that can be tailored for specific applications. For example, the MOF database could be firstly screened with simulation methods, and the promising candidates are then further investigated by 2 ACS Paragon Plus Environment

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experiment. The procedure has been widely used to identify promising materials for methane storage17, CO2 capture and separation18-19, separation of CH4/H220, to mention but a few applications. A number of experimental studies have been reported in recent years in applying MOFs for separating isotopic compounds11-13,

21-23.

Several mechanisms have been identified from

quantum- mechanical calculations such as kinetic quantum sieving (KQS) and chemical affinity quantum sieving (CAQS). KQS is possible only for the separation of very light isotopes (H2/D2) because it needs the pore size (~3.0-3.4 Å for rigid structures below 77 K23) close to the thermal de Broglie wavelength, which is inversely proportional to the molecular mass. For compounds with larger molecular weights, isotopic separation could hardly take place even if MOFs with the pore size close to the thermal de Broglie wavelength could be identified. Similar to traditional isotopic separation by adsorption processes, CAQS hinges on the difference in adsorption enthalpy to separate isotopic compounds11. It is challenging to maximize the quantum effect in CAQS by precise design and control MOF structures. In a previous work14, we investigated the potential of MOFs for separation of isotopic methanes with carbon isotopes (12C,

13C

and

14C)

using the classical density functional theory

(cDFT) in combination with excess-entropy scaling and the transition-state theory24-25. Considering both carbon and hydrogen substituted methane isotopologues are abundant in nature, we investigate in this work most promising MOFs for fractionation of an isotopic methane pairs via gas adsorption and membrane separation (Figure 1). Special attention is given to three representative isotopic pairs, 12CHD3/12CD4, 12CH3D/13CH3D and 12CH2D2/13CH2D2, selected on the basis of size difference, energy difference, and overall similarity, respectively. To stimulate experimental investigations in the future, our theoretical study is focused on a computation-ready, 3 ACS Paragon Plus Environment


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experimental (CoRE) MOF database for MOF candidates, i.e., all 4764 MOF structures from this database have already been synthesized experimentally. 2. THEORETICAL METHODS 2.1 Molecular model A number of semi-empirical models, ranging from the single-site Lennard-Jones (LJ) model to fully atomistic representations, have been proposed to describe the pair potential between methane molecules26-27. In addition to two-body interactions, analytical expressions are also available to represent effective many-body forces, which make significant contributions to the macroscopic properties of bulk fluids28-29. Because experimental results for different isotopic methanes are scarce and their behavior in a confined geometry depends not only on the molecular model for methane but also on the crystalline structure and the force-field parameters for the underlying porous material, we adopt the simple one-site LJ model to represent the effective pair interaction between various isotopic methane molecules. As discussed in our previous work14, the energy and size parameters for the pairwise additive potential are customized such that the model can best reproduce existing experimental data. 2.2 Classical density functional theory Application of cDFT to gas adsorption in nanoporous materials has been reported in our previous publications24,

30.

Here we recapitulate only the key equations. More extensive

discussion of the different versions of cDFT functionals, their comparisons with simulation results, and the numerical procedure for solving the density profiles can be found in our earlier work30.

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Within the framework of the one-site LJ model, cDFT predicts that the local number density of methane molecules in a nanostructured material is determined by bulk density  b , one-body ext ex external potential V (r) , and excess local chemical potential  (r) :

 (r)  b exp   V ext (r)   ex (r) 

(2)

where r stands for position,   1 / (k BT ) , k B is the Boltzmann constant and T is absolute temperature. The external potential accounts for the interaction of each gas molecule with the adsorbent, i.e., the potential energy arising from interaction of each gas molecule with all atoms from the porous material. The last term on the right side of Eq.(2) is defined as

 ex (r)   ex (r)  bex , which represents deviation of the local excess chemical potential,  ex (r) , from that corresponding to the bulk phase, bex . The thermodynamic properties of the bulk system, including bulk density  b and excess chemical potential bex as functions of T and P , can be determined from the modified Benedict-Webb-Rubin (MBWR) equation of state31. Intuitively, Eq.(2) may be understood as the Boltzmann distribution for gas molecules in the porous material. While this equation is formally exact within the thermodynamic framework, ex approximations are inevitable in calculation of the local excess chemical potential,  (r) .

Formally, the local excess chemical potential can be derived from the functional derivative of the intrinsic excess Helmholtz energy, F ex (r) ,  ex (r)   F ex (r) /  (r) .

(3)

Similar to typical excess properties in classical thermodynamics, F ex (r) accounts for the thermodynamic non-ideality due to intermolecular interactions. It is an intrinsic property of the gas molecules, independent of the external potential or specific properties of the adsorbent. At 5 ACS Paragon Plus Environment


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low density or bulk pressure, the interaction between gas molecules is negligible. In that case, we may neglect the intrinsic excess Helmholtz energy, and Eq.(2) reduces to the distribution of ideal-gas molecules inside the porous material as predicted by Henry’s law. To determine the distribution of gas molecules inside the porous material, we need a ex quantitative relationship between local chemical potential  (r) and local density profile  (r) .

Highly accurate expressions are available to compute F ex (r) for LJ systems32-33. However, little is known about the performance of various functionals at conditions most relevant to industrial processes. In a previous work30, we examined four versions of cDFT for predicting hydrogen adsorption in various MOF materials. These functionals are all based on the modified fundamental measure theory (MFMT)34 to describe molecular excluded volume effects. The attractive part of the intrinsic excess Helmholtz energy functional is represented by the meanfield approximation (MFA)35, the first-order mean-spherical approximation (FMSA)33, and two slightly different forms of weighted density approximation (WDA-Y36 and WDA-L37). The WDA methods were found most accurate at 77 K, a temperature typically used for characterization of porous materials with nitrogen gas. In the present work, all cDFT calculations are based on the WDA-Y functional36. The force field parameter for MOFs are from the UFF force field38 with the cutoff of 12.9 Å and grid size of 0.5 Å. From the excess Helmholtz energy functional, we can readily calculate the excess entropy from the thermodynamic relation

 F ex  S    T  ex

.

(4)

 ,V

The excess entropy is used as an input to evaluate the self-diffusivity of gas molecules in MOFs at finite loadings. The quantity can also be utilized to calculate the isosteric heat of adsorption25. 6 ACS Paragon Plus Environment

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2.3 Transition-state theory We use the transition-state theory (TST) to describe the hopping kinetics of individual gas molecules in a nanoporous material at infinite dilution. The self-diffusion coefficient is related to the transmission from one cage to another by

1 D0   a 2 2

(5)

where a is the distance between the equilibrium positions of the gas molecule in two neighboring cages (the initial and final states of the transmission), and  stands for the hopping rate. The latter can be calculated from39

k BT  2 m

exp   V ext (s* ) / k B T 



1

0

exp   V ext (s) / k B T  ds

(6)

where m denotes the molecular mass, the integral is performed along the reaction coordinate of gas hopping, and superscript * represents the transition state for the hoping of gas molecules between neighboring cages. It is noted that MOF materials of our interests in this work consist of micropores ranging in 10~20 Å with relatively less confined channels. One major advantage in application of TST at infinite dilution is that the energy landscape ext can be directly calculated from external potential V (r) . To identify a multidimensional

minimum-energy path, we use a simplified string method40, which allows us to identify the diffusion pathway for a gas molecule hopping between neighboring pores without the geometrical analysis25. Specifically, we define s as a normalized reaction coordinate, i.e.,

0  s  1 , and p(s) as a minimum energy pathway that connects the initial ( s  0 ) and final ( s  1) states of the gas molecule hopping between neighboring cages. The saddle point, which has a maximum energy along the diffusion pathway, corresponds to the transition state of gas 7 ACS Paragon Plus Environment


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hopping. In our earlier work25, we constructed the initial strings by connecting the lowest energy points at different facets of the simulation box with a straight line. To avoid high energy due to penetration of the initial string through the atoms, a straight channel with a small cross section area was used to construct the initial string such that it passes through the lowest energy points at each grid point. The curved string such constructed makes string optimization numerically much more robust. 2.4 Excess entropy scaling For gas adsorption at finite loadings, we need to account for the effect of gas-gas interactions on diffusivity. In our previous publications24, 41, we have demonstrated that the self-diffusivity can be predicted by a linear combination of the corresponding result at the infinite dilution and the excess due to interaction between gas molecules:   3   3 ln D  ln Ds   1 ln DE  0 v free  v free 

(7)

where subscript s represents self-diffusivity. The single molecule diffusivity D0 is calculated from TST. In Eq.(7), parameter  is related to the maximum molecular packing density, and

v free represents the total accessible volume per gas molecule in the porous material. As discussed in our previous work24, 41, we assume that   2 / 2 3 , where  stands for the diameter of the gas molecule. The accessible volume was calculated from the total accessible volume of the material divided by the number of confined gas molecules. The mixing parameter,  3 / v free , accounts for the relative contribution of gas-gas interactions to the self-diffusivity. While this parameter changes slightly for different systems, it is independent of pressure and temperature41.


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The contribution to self-diffusivity due to gas-gas interactions, DE , is calculated from the excess entropy scaling method41: DE 

where 



0.585 kBT exp 0.788S ex / Nk B 1/3 m 



(8)

is the average number density of gas molecules inside the porous material, and

N  V is the total number of gas molecules. 2.5 Selectivity Adsorption selectivity and membrane selectivity are commonly taken as benchmarks to compare the effectiveness of different porous materials for gas separations7. The former is most relevant to gas separation by pressure swing adsorption (PSA) or temperature swing adsorption (TSA) processes, and the latter is used for gas permeation through a membrane. In this work, we consider the potential of MOFs for the separation of isotopic methanes using both adsorptionand membrane-based processes, as shown schematically in Fig. 1A and Fig. 1B. The adsorption selectivity is defined as the ratio of the adsorption amounts of different species in the porous material normalized by the corresponding concentration ratio in the bulk phase42. For a binary mixture of components 1=light methane and 2=heavy methane, the adsorption selectivity is defined as



 2 / y2 1 / y1

(9)

where  i is the total adsorption amount for component i

i 

1  (r) dr V i

(10)



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and yi is the corresponding mole fraction in the bulk phase. Throughout this work, all binary gas mixtures are assumed to have equal molecular fraction in the bulk. Accordingly,   1 means preferential adsorption of the heavy methane, and the greater deviation of the selectivity from unity, the easier separation of the mixture by gas adsorption. At low pressure, we can predict the local density or the distribution of gas molecules in the porous material from the Boltzmann law. In that case, the adsorption selectivity can be calculated from the ratio of Henry’s constants:

 IM 

 

exp    Vext ,2 (r)  dr y2 K h,2 /  y K h,1   exp   V (r) dr 1 b,1 ext ,1  

b,2

(11)

where superscript IM stands for an ideal mixture, b,i denotes the bulk density, and K h stands for Henry’s constant

Kh 

1 exp    Vext (r)  dr RTV 

(12)

where R is the gas constant, and V is the system volume. For comparison with conventional separation methods, the adsorption selectivity amounts to the relative partition coefficient in chromatography or the relative volatility in distillation. The thermodynamic quantity reflects the degree of enrichment in separation of different compounds. With the assumption of Raoults’ law for vapor-liquid equilibrium, the relative volatility is related to the compositions of liquid and vapor phases as x2 / y2 P1sat   x1 / y1 P2sat

(13)

where xi and yi represent the mole fractions of component i in the coexisting liquid and vapor phases, respectively. 10 ACS Paragon Plus Environment

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For membrane-based processes, the effectiveness of separation is often discussed in terms of the permeation or membrane selectivity. Conventionally, the membrane selectivity is defined as the ratio of self-diffusivity DS multiplied by the adsorption selectivity42-43:  D  / y  k   s,2   2 2   Ds,1   1 / y1 

(14)

The higher the membrane selectivity, the easier is the separation of different compounds by membrane permeation. In Henry’s law region (viz., at low pressure), the membrane selectivity can be written as the ratio of Henry’s constants multiplied by the ratio of the self-diffusivity at infinite dilution42, 44: k IM 

K h,2 D0,2 K h,1 D0,1



P2 P1

(15)

Within Henry’s region, the permeability equals to the product of Henry’s constant and selfdiffusivity at infinite dilution44. Unlike adsorption selectivity, membrane selectivity depends on both equilibrium and transport properties of individual compounds. 3. RESULTS AND DISCUSSIONS 3.1 Isotopic methane pairs As discussed in our previous work14, we use the corresponding-state theory45 to extract the LJ parameters for different isotopic methanes from the saturation pressure data46-48. For systems without the vapor pressure data, a dual-parameter model is used to extrapolate the LJ parameters from existing data. The detail procedure is given in Supporting Materials. Figure 2 shows the LJ parameters for all isotopic methanes. Table 1 summarizes the LJ parameters for isotopic methanes used in this work.



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Mathematically, the similarity between two isotopic methanes, i and j , can be measured in terms of a dimensionless parameter:

di , j

 i  j     CH 4 

2

  i   j       CH 4

  

2

(16)

where  and  are the size and energy parameters of the methane molecules, respectively. In this work, we choose

12CHD /12CD 3 4

pair to illustrate the size effect on isotopic separation

because they have the smallest energy difference and relatively large size difference. 12CH

13CH

3D/

3D

pair has relatively close size parameters but small energy difference so that they

are used as the pair to illustrate the energy effect on isotopic separation. Finally, 12CH

13 2D2/ CH2D2

pair is considered the most similar overall isotopic methanes because they

have the smallest di , j value. 3.2 Isotopic separation by gas adsorption As discussed above, the ideal adsorption selectivity reflects the separation efficiency at infinite dilution. It provides a simple measure of the potential of MOF candidates for isotopic separation at low pressure. Figure 3 shows theoretical predictions for the ideal adsorption selectivity of 4764 MOFs from the CoRE database for separation of the three isotopic pairs at 150 K (Figure 3A) and at 300 K (Figure 3B). We selected 300 K to present room temperature, and 150 K was chosen as a representative temperature for cryogenic distillation. Here the selectivity is plotted against the separation capacity, measured in terms of the adsorption amount of the methane with a heavier isotope at 300 K and 1 atm. Ideal adsorption selectivity of most MOF candidates is around one for all three isotopic methane pairs. As discussed in our previous work14, heavier isotopic methanes have smaller size parameters or/and stronger attraction with the substrate. As a result, they would have larger Henry’s constants in comparison with the 12 ACS Paragon Plus Environment

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lighter ones except at conditions when the surface repulsion plays a major role. In other words, the ideal adsorption selectivity is above one when the adsorption loading is relatively low. Unsurprisingly, all MOF candidates perform the worst in separating

13CH

12 2D2/ CH2D2

because this pair of isotopic methanes has the most similar molecular parameters. Comparing 12CD /12CHD 4 3

and 13CH3D/12CH3D pairs, Figure 3 indicates that the ideal adsorption selectivity

is most sensitive to the difference in molecular size, implying that this parameter is most critical for separation of isotopes by MOF adsorption at low pressure. When the temperature increases from 150 K to 300 K, over 90% of MOF candidates have ideal adsorption selectivity closer to one for all three isotopic methane pairs, indicating that a lower temperature would favor adsorption separation. For MOFs with increased ideal adsorption selectivity at higher temperature, we find that, in those MOFs, Henry’s constant for the lighter isotope decreases much faster than the heavier isotope. Intuitively, one may expect that ideal adsorption selectivity fall when temperature increases. After screening the MOF candidates from the CoRE database for the separation of isotopic methanes, we find that the temperature effect on selectivity is actually specific to each porous material. In Figure S2, column (A) shows how Henry’s constants, the ideal adsorption selectivity, and the relative difference between Henry’s constants of

12CD

4

and

12CHD

3

change

with temperature for a representative MOF material (MOF: ABEMIF). While the results are intuitively expected, opposite trends are observed in column (B) for CAWDOU01, a different type of MOF. In the latter case, Henry’s constants still decrease with increasing temperature, but Henry’s constant of the lighter isotopic methane

12CHD

3

declines slower than the heavier

isotopic methane 12CD4. As a result, the ideal adsorption selectivity increases with temperature. To verify this counterintuitive phenomenon, we repeat the calculation using a much smaller grid 13 ACS Paragon Plus Environment


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size (0.1 Å instead of 0.5 Å, which is even smaller than the difference between the LJ diameters of 12CHD3 and 12CD4). While the results are slightly different in terms of the absolute numbers, we observe similar trends and believe that the opposite temperature effects are not due to the numerical noise. As Henry’s constant is calculated from an integration of the Boltzmann factor over the simulation cell, its dependence on temperature reflects a balance between the effects of molecular size and adsorption energy. While in general Henry’s constant falls as temperature increases, the lighter isotope has larger Henry’s constant for methane adsorption in relatively large pores. However, the trend is opposite for small pores. In the latter case, the methane with a heavier isotope tends to give rise a larger Henry’s constant. Figure 4(A) and (B) show how the adsorption selectivity, as defined by Eq.(9), changes with the adsorption amount of the heavier isotope at 300 K, 1 atm and 5 atm, respectively. Here we assume that the composition ratio of all isotopic methane pair is 1:1 in the bulk phase. Similar to ideal adsorption selectivity, adsorption selectivity decreases with the increase of adsorption amount among all MOF candidates. In general, pressure swing from low pressure to high pressure reduces the adsorption selectivity because the adsorbate-adsorbate interaction is typically more sensitive to the gas pressure than adsorbate-adsorbent interactions. Regrettably, those MOF candidates with high adsorption selectivity are often compromised by small adsorption amount, meaning low separation capacity. 3.3 Membrane separation In addition to being used as adsorbents, MOF materials can also be utilized as the membrane for permeation processes. Figure 5 shows the ideal membrane selectivity with respect to the permeability of the heavier isotope for the 4764 MOFs from the CoRE database. Following the 14 ACS Paragon Plus Environment

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definition discussed above, here we present the ideal membrane selectivity in terms of the heavier methane over the light methane. The solid line in each panel is known as the Robeson boundary, which sets the upper limit for membrane separations. Details on the Robeson boundary parameters are discussed in Supporting Materials. The Robeson boundary predicts that, in logarithm scales, the ideal membrane selectivity falls linearly with the permeability, suggesting a tradeoff between the separation capacity and selectivity. While the ideal membrane selectivity for most MOFs is close to root square of the mass ratio and confined by the Robeson boundary, we are able to identify a few candidates with good permeability and selectivity at the same time. It is worth noting that the permeability depends not only on the molecular weight but also on the LJ parameters for gas-gas and gas-MOF interactions. Although the diffusivity coefficient is inversely proportional to the root square of molecular mass, heavier isotopic methane typically has a smaller size and stronger attraction energy than lighter methane, leading to a lower energy barrier for gas diffusion between pores. As a result, it depends on the specific MOF material whether or not the ratio of diffusivity coefficient is over or below one. Those MOF candidates lying outside the Robeson boundary are definitely most promising for application to isotropic methane separation. Nevertheless, candidates, having high permeability and deviating further away from unit, may also be promising for practical applications. In Figure 5, MOFs with top membrane separation performance are marked with star signs and will be further discussed in next section. For the Robeson boundary, the slope is determined by the difference in molecular size while the intercept is mainly influenced by the molecular energy parameters. Compared with the energy difference, the size difference has a more significant impact on the Robeson boundary. From Figure 5, we see that the slope for

12CD /12CHD 4 3

is

much larger than those for the other two pairs, whereas the intercepts for different pairs of 15 ACS Paragon Plus Environment


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isotopic methanes do not differ too much. MOF candidates are not able to overcome the Robeson boundary for 12CD4/12CHD3 even though they have much higher ideal membrane selectivity than that for other pairs. For all three pairs of isotopic methanes, we can identify only few MOF candidates with performance at 300 K beyond the Robeson boundary. When temperature drops to 200 K, more MOFs are able to surpass the Robeson boundary for all three pairs of isotopic methanes (Figure S3). The separation is more efficient at lower temperature because the energy effects are magnified. In particular, lowering temperature enhances the difference between the diffusivity of different isotopic species. Figure 6A and 6B show respectively the membrane selectivity versus the adsorption amount at 1 atm and at 5 atm for those MOF materials shown in Figure 5. As discussed above, the difference between membrane selectivity and adsorption selectivity is that membrane selectivity has an additional term depending on the ratio of the self-diffusion coefficients (Eq.(14)). Although the membrane selectivity is lower than the adsorption selectivity for most MOF candidates, exceptions can be identified that yield high membrane selectivity and high capacity at the same time. Consistent with our previous work14, the difference in the diffusivity coefficients of isotopic methanes becomes smaller when pressure increases. In addition, the adsorption selectivity gets closer to one at higher pressure. As a result, the membrane selectivity falls as the high pressure increases. 3.4 Top MOFs for isotopic separations We have ranked MOF candidates for adsorption separation based on three different criteria: adsorption performance score (APS), ideal adsorption selectivity, and adsorption selectivity. The corresponding results are given in Table 2, Table 3, Table 4, respectively. In each table, three columns represent the top MOF candidates for separating

12CD /12CHD , 13CH D/12CH D, 4 3 3 3

and 16

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13CH

12 2D2/ CH2D2,

respectively. Because adsorption selectivity is close to one for all three

isotopic methane pairs, the larger deviation of adsorption selectivity from one, the better the separation performance. In this work, APS is defined according to

APS=|Sads (1/2)  1| ( N ads ,1  N des ,1 )

(17)

where S ads (1/2) stands for the adsorption selectivity at 300 K and 5 atm, N ads ,1 is the adsorption amount (adsorbent mass based) of the heavier isotope at the adsorption condition (300 K and 5 atm), and N des ,1 (adsorbent mass based) is the adsorption amount of heavier isotope at desorption condition (300 K and 1 atm). Based on the APS formula, achieving a high APS value requires a MOF material to have either high mass-based net adsorption amount or high adsorption selectivity at the working condition. For separation of isotopic methanes, the difference among the adsorption selectivity of all MOF candidates is relatively small in comparison to the difference in the working capacity. Therefore, the APS ranking is dominated by the mass-based net adsorption amount. MOF candidates with low mass density have advantage because they usually yield a large amount of gas adsorption (adsorbent mass based). As shown in Table S2, the APS ranking follows a decreasing trend in the MOF density. More details on the APS ranking are discussed in Supporting Information (Table S2). In Table 2, we highlight the top MOFs for separation of different pairs of isotopic methanes. After screening 4764 materials from the CoRE database, we find five MOF candidates yielding the top performance in terms of the ideal adsorption selectivity for all three isotopic pairs of methane. The ranking appears independent of the identities of the methane pairs. The low adsorption amount is attributed to small pores of the top MOF candidates in terms of selectivity, and the confined structure makes the results extremely sensitive to the changes in the 17 ACS Paragon Plus Environment


Page 18 of 36

molecular size or the energy parameters. Interestingly, ranking according to the adsorption selectivity (Table 4) yields MOF candidates to have low adsorption amounts as well. Based on the three types of adsorption performance rankings, it is clear that adsorption separation can hardly achieve both high selectivity and large working capacity at the same time. To further investigate the relation between adsorption and the characteristics of the promising porous materials, we present in Figure S4 the dependence of ideal adsorption selectivity on the void fraction and the largest cavity diameter (LCD). All geometry calculations (e.g., largest cavity diameter, pore limiting diameter and void fraction) are based on the Zeo++ software with the UFF force field49 . For the three pairs of isotopic methanes considered in this work, the ideal adsorption selectivity is significantly decreased as the void fraction or LCD of the material increases, suggesting that small pores favor more efficient isotope separation. In Figure S5, columns A and B show respectively the LCD distribution and the void fraction distributions for the MOF candidates with top 10% ideal adsorption selectivity. The results for the three pairs of methane isotopes share similar ranges of void fraction and LCD distributions. The materials with the best separation factors have void fractions in the range between 0 to 0.2 and LCD between 1 Å and 5 Å. Unlike adsorption separation, membrane separation depends not only on the difference in solubility but also on the difference in diffusivity. As a result, high selectivity and large working capacity could be achieved at the same time. With help of the Robeson boundary, we can identify MOF candidates with top performance for membrane-based separation and their names are listed in Table 5. More detailed information on the ranking is given in Supporting Materials. At infinite dilution, the diffusion coefficient is mainly determined by the energy barrier of gas hopping, which is strongly correlated with the pore limiting diameter (PLD). To illustrate, Figure 18 ACS Paragon Plus Environment

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S6 shows the diffusivity coefficient of 12CD4 versus PLD for a large number of porous materials. When PLD is extremely small (viz., smaller than 2 Å), a decimal change of PLD may result in diffusion coefficient change by several orders of magnitude. The diffusion coefficient increases rapidly with the increase of PLD and gradually reaches a plateau when PLD has little influence on the diffusivity44. For membrane separation, we need to consider not only the absolute value of diffusivity but the ratio as well. As shown in Supporting Materials (Figure S7), the diffusivity ratio can be approximated by the root square of the mass ratio owing to the fact that most MOF candidates do not have a particular aperture or chemical affinity to magnify the small difference in the energy barrier for different isotopic methanes. Figure S8 shows the pore size distribution for those MOF candidates with a diffusivity ratio larger than one. Although the range of PLD slightly differs, the PLD distribution is still mainly clustered around the LJ diameters of different isotopic methanes (2 Å to 4 Å). Table 6 presents the top 5 MOF candidates with the highest membrane selectivity at 300 K and 1 atm. In both Table 5 and Table 6, three columns represent the top MOF candidates for separating 12CHD3/12CD4, 12CH3D/13CH3D, and 12CH2D2/13CH2D2, respectively. From Table S3, we see that the ideal membrane selectivity is mainly determined by the ratio of diffusivity coefficients. Meanwhile, the permeability depends on both the diffusivity coefficient and Henry’s constant. Although heavier isotopic methane has a smaller size and a higher attractive energy, lighter isotopic methane typically has a higher diffusion coefficient in most MOF candidates. As a result, the membrane selectivity is smaller than one for most MOF candidates in Table 5 and Table 6. Unlike adsorption separation, membrane separation can be operated to have high working capacity and large selectivity at the same time. 4. CONCLUSIONS 19 ACS Paragon Plus Environment


Page 20 of 36

In this work, we have investigated 4764 metal-organic frameworks (MOFs) from the computation-ready, experimental (CoRE) MOF database for their potential applications to both adsorption and membrane separation of three isotopic methane pairs. The performance of these MOFs was evaluated under different conditions (viz., temperature and pressure) using a theoretical procedure established in our earlier work14. We identified top MOF candidates based on different ranking categories for the separation performance. For both adsorption- and membrane-based separation processes, isotopic methane pair differs in molecular size, is subjected to higher selectivity than

12CD /12CHD , 4 3 12CH

13CH

3D/

3D,

which mainly which mainly

differs in the molecular energy parameter. The theoretical results indicate that MOFs are more suitable for separation of isotopic methanes that have a large size difference than those with a large energy difference. Although adsorption separation can achieve high separation performance, it often suffers from low working capacity. By contrast, the separation capacity and selectivity can be well balanced for membrane-based separation processes. High-throughput screening allows us to identify promising candidates for separating chemical species with similar physical properties like isotopic mixtures that are much more efficient than conventional separation methods (e.g. cryogenic distillation and MAGIS). Supporting Information Technical details for predicting of the Lennard-Jones parameters for all isotopic methanes and the Robeson boundary, lists of top performance metal-organic frameworks, and figures illustrating the effects of structural features on separation performance. Acknowledgement The authors are grateful to the U.S. National Science Foundation (NSF-CBET-1404046) for the financial support. The simulation work was performed at the National Energy Research 20 ACS Paragon Plus Environment

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Scientific Computing Center (NERSC), supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. REFERENCES 1. de Vries, R. A.; de Bruin, M.; Marx, J. J.; Van de Wiel, A., Radioisotopic Labels for Blood Cell Survival Studies: A Review. Nucl. Med. Biol. 1993, 20, 809-817. 2. Van Eyk, J. E.; Dunn, M. J., Clinical Proteomics, 2007. 3. Ciais, P.; Tans, P. P.; Trolier, M.; White, J. W.; Francey, R. J., A Large Northern Hemisphere Terrestrial Co2 Sink Indicated by the 13c/12c Ratio of Atmospheric Co2. Science 1995, 269, 1098-1102. 4. Matucha, M.; Jockisch, W.; Verner, P.; Anders, G., Isotope Effect in Gas—Liquid Chromatography of Labelled Compounds. J. Chromatogr. A 1991, 588, 251-258. 5. Berger, G.; Prenant, C.; Sastre, J.; Comar, D., Separation of Isotopic Methanes by Capillary Gas Chromatography. Application to the Improvement of 11ch4 Specific Radioactivity. Appl. Radiat. Isot. 1983, 34, 1525-1530. 6. Cloete, C. E.; De Clerk, K., Distillation Vs. Chromatography: A Comparison Based on the Purity Index. Sep. Sci. 1972, 7, 449-455. 7. Yang, Q.; Liu, D.; Zhong, C.; Li, J. R., Development of Computational Methodologies for Metal-Organic Frameworks and Their Application in Gas Separations. Chem. Rev. 2013, 113, 8261-8323. 8. Oziashvili, E. D.; Egiazarov, A. S., The Separation of Stable Isotopes of Carbon. Russ. Chem. Rev. 1989, 58, 325-336. 9. Takeshita, K.; Nakano, Y.; Shimizu, M.; Fujii, Y., Recovery Of14c from Graphite Moderator of Gas-Cooled Reactor (Gcr). J. Nucl. Sci. Technol. (Abingdon, U. K.) 2002, 39, 1207-1212. 10. Yim, M. S.; Caron, F., Life Cycle and Management of Carbon-14 from Nuclear Power Generation. Prog. Nucl. Energy 2006, 48, 2-36. 11. Oh, H.; Hirscher, M., Quantum Sieving for Separation of Hydrogen Isotopes Using Mofs. Eur. J. Inorg. Chem. 2016, 2016, 4278-4289. 12. Kim, J. Y.; Balderas-Xicohtencatl, R.; Zhang, L.; Kang, S. G.; Hirscher, M.; Oh, H.; Moon, H. R., Exploiting Diffusion Barrier and Chemical Affinity of Metal-Organic Frameworks for Efficient Hydrogen Isotope Separation. J. Am. Chem. Soc. 2017, 139, 15135-15141. 13. Oh, H.; Savchenko, I.; Mavrandonakis, A.; Heine, T.; Hirscher, M., Highly Effective Hydrogen Isotope Separation in Nanoporous Metal-Organic Frameworks with Open Metal Sites: Direct Measurement and Theoretical Analysis. ACS Nano 2014, 8, 761-770. 14. Tian, Y.; Fei, W. Y.; Wu, J. Z., Separation of Carbon Isotopes in Methane with Nanoporous Materials. Industrial & Engineering Chemistry Research 2018, 57, 5151-5160. 15. Li, J. R.; Kuppler, R. J.; Zhou, H. C., Selective Gas Adsorption and Separation in MetalOrganic Frameworks. Chem. Soc. Rev. 2009, 38, 1477-1504. 16. Getman, R. B.; Bae, Y. S.; Wilmer, C. E.; Snurr, R. Q., Review and Analysis of Molecular Simulations of Methane, Hydrogen, and Acetylene Storage in Metal-Organic Frameworks. Chem. Rev. 2012, 112, 703-723. 17. Wilmer, C. E.; Leaf, M.; Lee, C. Y.; Farha, O. K.; Hauser, B. G.; Hupp, J. T.; Snurr, R. Q., Large-Scale Screening of Hypothetical Metal–Organic Frameworks. Nat. Chem. 2011, 4, 83. 21 ACS Paragon Plus Environment


Page 22 of 36

18. Qiao, Z.; Zhang, K.; Jiang, J., In Silico Screening of 4764 Computation-Ready, Experimental Metal–Organic Frameworks for Co2 Separation. J. Mater. Chem. A 2016, 4, 21052114. 19. Chung, Y. G.; Gomez-Gualdron, D. A.; Li, P.; Leperi, K. T.; Deria, P.; Zhang, H.; Vermeulen, N. A.; Stoddart, J. F.; You, F.; Hupp, J. T., et al., In Silico Discovery of MetalOrganic Frameworks for Precombustion Co2 Capture Using a Genetic Algorithm. Sci. Adv. 2016, 2, e1600909. 20. Altintas, C.; Erucar, I.; Keskin, S., High-Throughput Computational Screening of the Metal Organic Framework Database for Ch4/H2 Separations. ACS Appl. Mater. Interfaces 2018, 10, 3668-3679. 21. Jiao, Y.; Du, A.; Hankel, M.; Smith, S. C., Modelling Carbon Membranes for Gas and Isotope Separation. PCCP 2013, 15, 4832-4843. 22. Cai, J.; Xing, Y.; Zhao, X., Quantum Sieving: Feasibility and Challenges for the Separation of Hydrogen Isotopes in Nanoporous Materials. RSC Adv. 2012, 2. 23. Oh, H.; Park, K. S.; Kalidindi, S. B.; Fischer, R. A.; Hirscher, M., Quantum Cryo-Sieving for Hydrogen Isotope Separation in Microporous Frameworks: An Experimental Study on the Correlation between Effective Quantum Sieving and Pore Size. J. Mater. Chem. A 2013, 1, 32443248. 24. Fu, J.; Tian, Y.; Wu, J. Z., Classical Density Functional Theory for Methane Adsorption in Metal-Organic Framework Materials. AlChE J. 2015, 61, 3012-3021. 25. Tian, Y.; Xu, X.; Wu, J., Thermodynamic Route to Efficient Prediction of Gas Diffusivity in Nanoporous Materials. Langmuir 2017, 33, 11797-11803. 26. Aimoli, C. G.; Maginn, E. J.; Abreu, C. R., Transport Properties of Carbon Dioxide and Methane from Molecular Dynamics Simulations. J. Chem. Phys. 2014, 141, 134101. 27. Jiang, C. T.; Ouyang, J.; Zhuang, X.; Wang, L. H.; Li, W. M., An Efficient Fully Atomistic Potential Model for Dense Fluid Methane. J. Mol. Struct. 2016, 1117, 192-200. 28. Hauschild, T.; Prausnitz, J. M., Monte-Carlo Calculations for Methane and Argon over a Wide-Range of Density and Temperature, Including the 2-Phase Vapor-Liquid Region. Mol. Simul. 1993, 11, 177-185. 29. Abbaspour, M., Computation of Some Thermodynamics, Transport, Structural Properties, and New Equation of State for Fluid Methane Using Two-Body and Three-Body Intermolecular Potentials from Molecular Dynamics Simulation. J. Mol. Liq. 2011, 161, 30-35. 30. Fu, J.; Liu, Y.; Tian, Y.; Wu, J. Z., Density Functional Methods for Fast Screening of Metal Organic Frameworks for Hydrogen Storage. J. Phys. Chem. C 2015, 119, 5374-5385. 31. Johnson, J. K.; John, A. Z.; Keith, E. G. D.-L. D., The Lennard-Jones Equation of State Revisited. Mol. Phys. 1992, 78, 591-618. 32. Tang, Y. P.; Wu, J. Z., A Density-Functional Theory for Bulk and Inhomogeneous Lennard-Jones Fluids from the Energy Route. J. Chem. Phys. 2003, 119, 7388-7397. 33. Tang, Y.; Wu, J., Modeling Inhomogeneous Van Der Waals Fluids Using an Analytical Direct Correlation Function. Phys. Rev. E 2004, 70, 011201. 34. Yu, Y. X.; Wu, J. Z., Structures of Hard-Sphere Fluids from a Modified FundamentalMeasure Theory. J. Chem. Phys. 2002, 117, 10156-10164. 35. Ravikovitch, P. I.; Neimark, A. V., Density Functional Theory Model of Adsorption on Amorphous and Microporous Silica Materials. Langmuir 2006, 22, 11171-11179.


Page 23 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


36. Yu, Y. X., A Novel Weighted Density Functional Theory for Adsorption, Fluid-Solid Interfacial Tension, and Disjoining Properties of Simple Liquid Films on Planar Solid Surfaces. J. Chem. Phys. 2009, 131, 024704. 37. Liu, Y.; Liu, H.; Hu, Y.; Jiang, J., Development of a Density Functional Theory in ThreeDimensional Nanoconfined Space: H2 Storage in Metal-Organic Frameworks. J. Phys. Chem. B 2009, 113, 12326-12331. 38. Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A.; Skiff, W. M., Uff, a Full Periodic-Table Force-Field for Molecular Mechanics and Molecular-Dynamics Simulations. J. Am. Chem. Soc. 1992, 114, 10024-10035. 39. Frenkel, D.; Smit, B., Understanding Molecular Simulation: From Algorithms to Applications, 2nd ed.; Academic Press: San Diego, 2002, p 638. 40. E, W.; Ren, W.; Vanden-Eijnden, E., Simplified and Improved String Method for Computing the Minimum Energy Paths in Barrier-Crossing Events. J. Chem. Phys. 2007, 126, 164103. 41. Liu, Y.; Fu, J.; Wu, J., Excess-Entropy Scaling for Gas Diffusivity in Nanoporous Materials. Langmuir 2013, 29, 12997-13002. 42. Keskin, S.; Sholl, D. S., Efficient Methods for Screening of Metal Organic Framework Membranes for Gas Separations Using Atomically Detailed Models. Langmuir 2009, 25, 1178611795. 43. Li, J. R.; Sculley, J.; Zhou, H. C., Metal-Organic Frameworks for Separations. Chem. Rev. 2012, 112, 869-932. 44. Haldoupis, E.; Nair, S.; Sholl, D. S., Efficient Calculation of Diffusion Limitations in Metal Organic Framework Materials: A Tool for Identifying Materials for Kinetic Separations. J. Am. Chem. Soc. 2010, 132, 7528-7539. 45. Lotfi, A.; Vrabec, J.; Fischer, J., Vapour Liquid Equilibria of the Lennard-Jones Fluid from Thenptplus Test Particle Method. Mol. Phys. 1992, 76, 1319-1333. 46. Bigeleisen, J.; Cragg, C. B.; Jeevanandam, M., Vapor Pressures of Isotopic Methanes— Evidence for Hindered Rotation. Journal of Chemical Physics 1967, 47, 4335-4346. 47. Van Hook, W. A.; Rebelo, L. P. N.; Wolfsberg, M., An Interpretation of the Vapor Phase Second Virial Coefficient Isotope Effect: Correlation of Virial Coefficient and Vapor Pressure Isotope Effects. J. Phys. Chem. A 2001, 105, 9284-9297. 48. Setzmann, U.; Wagner, W., A New Equation of State and Tables of Thermodynamic Properties for Methane Covering the Range from the Melting Line to 625 K at Pressures up to 100 Mpa. J. Phys. Chem. Ref. Data 1991, 20, 1061-1155. 49. Willems, T. F.; Rycroft, C.; Kazi, M.; Meza, J. C.; Haranczyk, M., Algorithms and Tools for High-Throughput Geometry-Based Analysis of Crystalline Porous Materials. Microporous Mesoporous Mater. 2012, 149, 134-141.



Page 24 of 36

Table 1. The Lennard-Jones parameters for several isotopic methanes

Pair 1 12CHD 12CD

4

3

σ/Å

(ε/kB)/K

Pair 2

3.6430

150.3390

12CH

3.6309

150.3411

13CH

σ/Å

(ε/kB)/K

Pair 3

3D

3.6754

150.1229

12CH

3D

3.6718

150.2776

13CH

σ/Å

(ε/kB)/K

2D2

3.6587

150.2601

2D2

3.6558

150.391


Page 25 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. Top ranking MOFs for the separation of different methane pairs according to the adsorption performance score (APS). Materials applicable to all three pairs are highlighted with the bold font. 12CD /12CHD 4 3

13CH

3D/

12CH

3D

13CH

12 2D2/ CH2D2

MOFs

APS

MOFs

APS

MOFs

APS

SETTAO

0.7738

SETTAO

0.1329

SETTAO

0.1015

UDEPIE

0.7220

UDEPIE

0.1245

UDEPIE

0.0792

NEXXEV

0.5070

NEXXEV

0.0785

NEXXEV

0.0643

YICREI

0.4803

YICREI

0.0662

YICREI

0.0563

HAFVUH 0.3317

HAFVUH

0.0506

HAFVUH

0.0375

FAHGAY 0.1350

FAHGAY

0.0256

HIHNUJ

0.0202

EXEQII

0.1250

VAGTAA

0.0220

FAHGAY

0.0201

VAGTAA

0.1131

EXEQII

0.0197

SUKYON

0.0185

EKOPOK

0.1004

TONQOD

0.0178

VEJYIT

0.0156

TONQOD

0.0992

KEWZOD

0.0163

EXEQII

0.0142


The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 26 of 36

Table 3. Top ranking MOFs for the separation of different methane pairs according to the ideal adsorption selectivity at 300 K 12CD /12CHD 4 3

13CH

3D/

12CH

3D

13CH

12 2D2/ CH2D2

MOFs

KH/(mol·m-3·Pa-1)

αIM

MOFs

KH/(mol·m-3·Pa-1)

αIM

MOFs

KH/(mol·m-3·Pa-1)

αIM

QEYWUN

1.15×10-8

1.537

QEYWUN

2.57×10-9

1.143

QEYWUN

4.69×10-9

1.111

CUGLTM02

2.03×10-7

1.374 CUGLTM02

6.69×10-8

1.105 CUGLTM02

1.05×10-7

1.082

ZNGLUD

2.78×10-6

1.279

ZNGLUD

1.18×10-6

1.082

ZNGLUD

1.66×10-6

1.064

DEBNUU

1.56×10-4

1.183

DEBNUU

8.64×10-5

1.058

DEBNUU

1.10×10-4

1.045

IDAZEU

2.28×10-5

1.180

IDAZEU

1.28×10-5

1.055

IDAZEU

1.61×10-5

1.043


Page 27 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Table 4. Top ranking MOFs for the separation of different methane pairs according to adsorption selectivity at 1 atm 12CD /12CHD 4 3

13CH

MOFs

Γ(mol/L)

α

QEYWUN

2.30×10-5

1.438

CUGLTM02 2.00×10-5

1.429

ZNGLUD

2.97×10-4

DEBNUU

MOFs

3D/

12CH

3D

Γ(mol/L)

13CH

α

CUGLTM02 7.00×10-6

1.167

QEYWUN

7.00×10-6

1.167

1.280

ZNGLUD

1.26×10-4

1.16×10-2

1.192

DEBNUU

IDAZEU

2.36×10-3

1.182

LIBJAJ

6.50×10-3

1.168

MOFs

12 2D2/ CH2D2

Γ(mol/L)

α

CUGLTM02 1.10×10-5

1.111

QEYWUN

1.00×10-5

1.100

1.086

ZNGLUD

1.78×10-4

1.066

6.30×10-3

1.060

DEBNUU

8.08×10-3

1.049

IDAZEU

1.32×10-3

1.055

IDAZEU

1.66×10-3

1.043

LIBJAJ

3.70×10-3

1.053

LIBJAJ

4.70×10-3

1.041


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Page 28 of 36

Table 5. Top ranking MOFs for the separation of different methane pairs according to the ideal membrane selectivity at 300K 12CD /12CHD 4 3

13CH

3D/

12CH

3D

13CH

12 2D2/ CH2D2

MOFs

P(barrer)

kIM

MOFs

P(barrer)

kIM

MOFs

P(barrer)

kIM

XICYEP

879.8

1.2796

NETHOJ

22704.1

1.0773

XICYEP

513.0

1.0384

GUWDUY

9337.7

1.2676

CERMIV

386.8

1.0528

GUWDUY

5539.9

1.0384

XICYIT

1329.3

1.2617

XICYIT

570.7

1.0523

TAPXOZ

2382987.1

0.9635

CERMIV

905.6

1.2524

GUWDUY

3939.0

1.0476

XUTQEI

648985.7

0.9647

VAGTAA

4378.9

1.2252

XICYEP

363.5

1.0473

AWEJIW

3393097.8

0.9648


Page 29 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Table 6. Top ranking MOFs according to the membrane selectivity at 300 K and 1 atm 12CD /12CHD 4 3

13CH

3D/

12CH

3D

13CH

12 2D2/ CH2D2

MOFs

Γ(mol/L)

k

MOFs

Γ(mol/L)

k

MOFs

Γ(mol/L)

k

XICYEP

0.9520

1.2274

NETHOJ

0.9468

1.0599

XUTQEI

0.4129

0.9652

XICYIT

0.9179

1.2164

UKIQIP

0.6148

1.0418

SONTUL

0.8918

0.9664

GOJFAN

0.1570

1.2151

GOJFAN

0.1624

1.0392

CETGOY

0.6588

0.9667

YENLUA

0.2131

1.2101

CEKHIL

0.5115

0.9626

WEHJOK

0.6165

0.9671

UKIQIP

0.5784

1.2081

XICYIT

0.9784

1.0384

QOZFUG

0.7473

0.9676



Page 30 of 36

Figure 1. Schematic diagram of gas separation by adsorption (A) and membrane (B)


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Figure 2. The Lennard-Jones parameters for different isotropic methanes obtained from vaporpressure data (filled symbols) or by extrapolation (open symbols)



Page 32 of 36

Figure 3. Ideal adsorption selectivity at 150 K (A) and 300 K (B) versus adsorption amount of heavier isotope at 300 K and 1 atm for three isotopic methane pairs


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Figure 4. Adsorption selectivity versus adsorption amount of heavier isotope at 300 K and 1 atm (A) and 5 atm (B) for three isotopic methane pairs



Page 34 of 36

Figure 5. Ideal membrane selectivity verse permeability of heavier isotopic methanes for three isotopic methane pairs at 300 K. The Robeson boundary is shown as the solid lines.


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Figure 6. Membrane selectivity versus the adsorption amount of heavier isotope at 300 K and 1 atm (A) and 5 atm (B) for three isotopic methane pairs



Page 36 of 36

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