Screening and design of COF-based mixed-matrix membrane for CH4/N2 separation

Tongan Yan ,Dahuan Liu,*,Qingyuan Yang,*,Chongli Zhong

1 State Key Laboratory of Organic-Inorganic Composites,Beijing University of Chemical Technology,Beijing 100029,China

2 State Key Laboratory of Separation Membranes and Membrane Processes,Tiangong University,Tianjin 300387,China

Keywords:Covalent organic frameworks Methane Molecular simulations Mixed-matrix membrane Nitrogen Separation

ABSTRACT Membrane separation is a high-efficiency,energy-saving,and environment-friendly separation technology.Covalent organic framework(COF)-based mixed-matrix membranes(MMMs)have broad application prospects in gas separation and are expected to provide new solutions for coal-bed methane purification.Herein,a high-throughput screening method is used to calculate and evaluate COF-based MMMs for CH4/N2 separation.General design rules are proposed from thermodynamic and kinetic points of view using the computation-ready,experimental COFs.From our database containing 471,671 generated COFs,5 COF membrane materials were screened with excellent membrane selectivities,which were then used as the filler of MMMs for separation performance evaluation.Among them,BAR-NAP-Benzene_CF3 combined with polydimethylsiloxane and styrene-b-butadiene-b-styrene show high CH4 permeability of 4.43 × 10-13 mol·m·s-1·Pa-1·m-2 and high CH4/N2 selectivity of 9.54,respectively.The obtained results may provide reasonable information for the design of COF-based membranes for the efficient separation of CH4/N2.

1.Introduction

Coal-bed methane(CBM)is an unconventional natural gas with abundant reserves and environmental friendliness,which is considered as a potential energy resource [1-3].At present,the most widely used traditional method for CH4/N2separation is cryogenic distillation[4].However,this process is energy-intensive with high operating costs.In contrast,membrane separation technology can effectively reduce the environmental impact of industrial processes and reduce operating costs due to its high energy efficiency and environmental sustainability [5-7].Unfortunately,less than 10 kinds of membrane materials can be made into commercial membranes [8],which highlights the importance of developing new membrane materials with high performance in gas separation applications.Compared to other membranes,mixed matrix membranes(MMMs)with excellent separation performance fillers have great potentials in selectivity and permeability.In addition,the flexibility of polymer can reduce the vulnerability of the membrane [9].

As a new kind of crystal porous materials with periodic expansion and covalent bonding network structure[10],covalent organic frameworks(COFs)have attracted more and more attentions in the field of membrane separation due to their advantages of low density,large surface area,adjustable pore size and structure,and easy-to-cut functionality [11].For example,in 2017,MMMs synthesized by polyether-b-amide (PEBA) polymer and 1% (mass)loading of COFs exhibited a CO2/N2selectivity as high as 64.0[12].Fanet al.[13] reported the ACOF-1 membrane prepared by continuous two-dimensional azide connection on porous α-Al2O3support for the separation of CO2/CH4.Due to the effective CH4molecular sieve synergy and the CO2adsorption capacity of ACOF-1’s laminated pores,the membrane has a high selectivity of 86.3 for CO2/CH4mixture and a good CO2permeability of about 9.9 × 10-9mol·m-2·s-1·Pa-1.Wuet al.[14] prepared a COF-based MMMs for CO2/N2separation using SNW-1 as a filler and intrinsic microporosity(PIMs)composite by experiment.Its CO2permeability and CO2/N2selectivity are 2.5 × 10-10mol·m-2·s-1·Pa-1and 22.5.

Similar to MOFs,the number of novels COFs synthesized in current experiments is increasing sharply in recent several years[15].Usually,these materials are synthesized under consideration of a specific application,and the experimental data is limited to that application.But for all possible applications of new material,it is obviously impractical to test one by one only through experiments.Therefore,it is valuable to first use computational screening to determine the most promising candidate materials.For example,Keskinet al.[16] performed calculations on the selectivity of COF-5,COF-6 and COF-10 membranes for CH4/H2mixtures,and found that they are higher than that of zeolite,which also proved the reliability of calculations for predicting the mixed adsorption and diffusion of gases in COFs.In 2016,our group carried out a systematic computational study on a multilayer two-dimensional COF[17] membrane to explore its ability to separate CO2/N2.It is revealed that there are narrow interlaminar pores between the stacked nanosheets,which can produce a ‘‘gate-closing” effect on the selective transport of molecules.By adjusting the accumulation method of COFs,it is possible to create a specific energy microenvironment,thereby achieving high CO2permeability and selectivity,which has been confirmed by our following experiments[18,19].However,to the best of our knowledge,separation of CH4/N2mixture using COF membranes is unexploited using the computational method for the moment.

Herein,the separation performance of the computation-ready,experimental (CoRE) COF-based MMMs for CH4/N2mixtures was evaluated at the first step.On the basis of the calculated results,the relationship between the separation performance of pure membrane and mixed matrix membrane was discussed,as well as the influence of geometric properties on membrane separation performance.The thermodynamic design strategy of LCD in the range of 0.4-0.6 nm was proposed,as well as the kinetic design strategy of PLD/LCD ratio in the range of 0.8-0.9.Thus,5 kinds of COFs were selected with high membrane selectivities,and 5 COF@polymer MMMs were calculated for the separation of CH4/N2.It is observed that BAR-NAP-Benzene_CF3@polydimethylsiloxane (PDMS) has high CH4permeability (4.43 × 10-13mol·m·s-1·Pa-1·m-2) and BAR-NAP-Benzene_CF3@styrene-b-butadiene-b-styrene(SBS)exhibits high selectivity(9.54).These results not only revealed promising candidates for efficient CH4/N2separation using COF@polymer membranes,but also provides useful information for the design of best MMMs for the specific gas separations.

2.Materials and Methods

2.1.COF structures

309 COFs in the simulations were taken from the CoRE COF database constructed in our previous work [20],which have been synthesized in experiments.Structural properties were calculated by Zeo++software[21],including pore limit diameter(PLD),largest cavity diameter(LCD),porosity(φ),free volume(Vfree)and surface area (Sacc).A probe with a diameter equal to the kinetic diameter(0.364 nm) of N2was used to calculateSacc.Vfreewere calculated by using a probe with a diameter equal to 0 nm.To ensure that molecules can enter the pores,only 296 CoRE COFs with PLD greater than 0.364 nm were simulated,considering the kinetic diameters of guest molecules (CH4,0.380 nm;N2,0.364 nm).

2.2.Force fields

The intermolecular interactions between adsorbate and adsorbate and between adsorbate and COFs were calculated by combining the site-site Lennard-Jones (LJ) and Coulombic potentials.Potential parameters of CH4and N2molecules are taken from the TraPPE force field [22].CH4molecule adopts LJ 12-6 potential single-site spherical model.N2is a three-point charged LJ model,where two sites are located on the N atom and one site is located at the center of mass (COM).In addition to the LJ interaction,the electrostatic interaction of adsorbate is also considered by Coulomb potential and evaluated by the Ewald summation technique[23].In order to consider the electrostatic interaction between molecules and COFs,the charge equilibration method (QEq) [24]was used to distribute partial point charges to the framework.All the parameters of LJ cross potential energy are described by the Lorentz-Berthelot mixing rule.

Force field is the key to describe the framework atom accurately.Before the CH4/N2membrane separation simulations of 296 CoRE COFs,the DREIDING force field [25] and the universal force field (UFF) [26] need to be evaluated.As shown in Fig.S1 and S2(in Supplementary Material),the single-component adsorption isotherms obtained by grand canonical Monte Carlo (GCMC)simulations are compared with the experimental data.The results show that for the adsorption behavior of CH4and N2in CoRE COFs,the DREIDING force field can reproduce the experimental data more accurately than UFF.Therefore,DREIDING force field is used in all calculations in this work.

2.3.Simulation details

The data of mixed adsorption and diffusion were used to investigate the separation performance of the CoRE COF membrane.At 298 K and 100 kPa,the adsorption of an equimolar mixture of CH4and N2in COFs was simulated by GCMC.The simulation was first balanced by 2.5 × 107steps,and then 2.5 × 107steps were used for sampling.Throughout the GCMC process,five experiments were carried out,including random replacement,random regeneration,new creation,deletion and exchange of molecules.The atoms of the COF framework were frozen in the crystallographic position to ensure rigidity.The cut-off radius was set to be 1.40 nm to eliminate the finite size effect.Corresponding to different COFs,the number of units in the simulation frame was different,ranging from 1 × 1 × 1 to 3 × 3 × 8.The conversion between pressure and fugacity was accomplished through the Peng-Robinson equation of state [27].

According to the molecular load obtained by GCMC,molecular dynamic(MD)simulations of the canonical ensemble were carried out at 298 K and 100 kPa.Each MD was simulated for 6 ns in a time step of 1 fs and then balanced for 3 ns.Nosé-Hoover chain [28]thermostat was used to maintain constant temperature conditions,and velocity Verlet algorithm was used to integrate Newton’s equation of motion.The self-diffusion coefficient can be obtained by averaging 10 independent trajectories.In order to ensure the statistical accuracy of MD simulation,the simulation box was expanded for COFs with high CH4/N2adsorption selectivity to increase the number of N2molecules.All simulations were performed using our in-house code HT-CADSS.

2.4.Membrane performance evaluation metrics

The adsorption selectivity of CH4relative to N2in the mixture is defined as:

wherexrepresents the mole fraction of the adsorbed phase,andyrepresents the mole fraction of the bulk phase components.

Through Einstein equation [29],the self-diffusivities of each substance in the adsorption mixture are related to the mean square displacement (MSD) of the tagged particles,which can be calculated by taking the slope for a long time:

where 〈···〉 is the ensemble average,Nis the number of molecules,andri(t) is the position vector of the COM of the moleculeidescribed when the diffusion time ist.drepresents the size of the inspected system:for COFs with three-dimensional pores,d=3,and COFs with one-dimensional pores,d=1.

Self-diffusivities of CH4and N2computed from MD simulations can be used to calculate the diffusion selectivity:

Membrane selectivity of COFs is obtained by multiplying adsorption and diffusion selectivity [30]:

wherePis the permeability of the component.φ,candfrepresent the porosity of the COFs,the corresponding concentration of component at the feed side of the membrane,and the bulk phase fugacity of component,respectively [31].

Maxwell model [32] is used to predict the gas permeability of MMMs.This model is suitable for low filling loads (0 ＜φ ＜0.2),and it assumes that the streamlines around spherical particles are not affected by nearby particles:

wherePMMM,PpolymerandPCOFrepresent the permeability of MMMs,polymer and COF.The permeability of polymer membrane and COF membrane are obtained from experimental data[33,34]in the literature and simulations in this work.φ is the volume fraction of dispersed COF particles.In the following simulations,the volume fraction of all MMMs is 20%.The membrane selectivity was calculated as the ratio of the permeabilities of the two gas components.

3.Results and Discussion

3.1.Verification of membrane calculation methods

First,the membrane calculation method was evaluated.When using the Maxwell model to evaluate the membrane separation performance of MMMs,it is necessary to provide the performance parameters of COF membranes and polymer membranes.For polymer membranes,data can be easily obtained from the literature.However,considering the huge challenge of experimental preparation,it is usually difficult to obtain the required data of COF membranes [35].It is more efficient and convenient to obtain the performance parameters of the COF membrane by calculations.Therefore,the evaluation of the reliability of the calculation method is particularly important.

The permeability of different membranes obtained by simulation and experiment are compared and the results are shown in Fig.1.The reference line ofx=yin the figure helps to judge the degree of agreement more intuitively between the calculated and experimental values.It can be seen that the deviation of all data points from the dotted line is not large,indicating that the simulations can reproduce the experimental permeability well,and proving the reliability of the simulation method.From Fig.1,it is worth noting that pure COF membranes have outstanding performance in CH4permeability compared with COF-based mixed matrix membranes.However,due to the difficulty of preparing pure COF membranes,it is difficult for us to obtain more CH4/N2separation data for comparison of results,while COF-based MMMs are relatively easy.This also illustrates the feasibility of MMMs in practical applications and is expected to bring a more effective solution for COF membrane separation for CH4/N2.

3.2.CoRE COF-based MMMs for CH4/N2 separation

The introduction of COFs into polymers to prepare MMMs is a practical way to improve the separation performance of polymer membranes.Therefore,we prefer to select MMMs prepared with 296 CoRE COFs as fillers to investigate the performance of CH4/N2separation.The membrane separation performance of MMMs is affected not only by the filler,but also by the choice of polymer.Three kinds of polymers with different properties were selected to compound with COFs (Table 1).PDMS [43] had the highest CH4permeability reported in the literature,up to 2.55 × 10-13mol·m·s-1·Pa-1·m-2.The selectivity of CH4/N2separation by SBS[44]was the highest(7.20).Pebax?2533[45]has been successfully commercialized and mass-produced.

Table 1Data of 3 polymers used for CH4/N2 separation

Fig.1.Comparison the permeavility data of simulations and experiments for membranes:(a) pure ACOF-1 [36],COF-LZU1 [36],ZIF-69 [37],ZIF-8 [38] and Bio-MOF-1 [39]membranes;(b) ACOF-1@Matrimid? [40],CTPP@Pebax?1657 [41] and COF-5@Pebax?1657 [42].

Fig.2.CH4 permeability and selectivity correlation diagram of COF based MMMs for CH4/N2 separation.

In Fig.2,888 CoRE COF-based MMMs used for CH4/N2separation were calculated under the conditions of 298 K and 100 kPa.Compared with pure polymer membranes,MMMs have a significant improvement in CH4permeability.On the other hand,the aggregation of data points in the figure indicates that COF fillers have a certain ‘‘ceiling” for the membrane selectivity of MMMs.Therefore,it is necessary to further explore the internal factors to obtain COF fillers that can break this limitation.

As shown in Fig.3,the membrane selectivity of CoRE COF membranes and CoRE COF-based MMMs were correlated.With the improvement of the selectivity of pure COF membrane,the selectivity of COF-based MMMs increases.This has been proved in the separation of other gas mixtures using MMMs (such as O2/N2[46],H2/N2[47],CO2/N2[48]).Although the increment is not evident,it inspires us to design MMMs using COFs with high pure membrane selectivity of CH4/N2.Specifically,when the selectivity of pure CoRE COF membrane exceeds 100,the selectivity of COFbased MMMs can be greatly increased.For example,using AEMCOF-2 with a pure membrane selectivity of 282 as the filler,AEM-COF-2@PDMS,AEM-COF-2@Pebax?2533 and AEM-COF-2@SBS exhibit membrane selectivities of 4.47,4.21 and 7.34 respectively.Therefore,the key for MMMs with excellent separation performance of CH4/N2is screening and design COF materials with high selectivities.

It is well known that pore size plays an important role in the separation performance of adsorbents.In order to obtain specific material design rules,it is necessary to explore the relationship between material structure and performance.Both thermodynamics and kinetic factors play an important role in membrane separation.Therefore,the relationship with pore size (PLD,LCD) is discussed separately.From Fig.4(a),with the increase of LCD,the selectivity of COFs for CH4/N2adsorption separation increases rapidly at first,and then decreases slowly.When the pore size of the COFs is small,the adsorbate is more susceptible to the strong interaction of the adsorbent.With the increase of the pore size,the weak interaction between guest molecules is obvious.It can be seen that when the LCD is in the range of 0.4-0.6 nm,the COFs have the highest adsorption selectivity.For example,the LCD of CCOF-MPC with the highest adsorption selectivity (7.09) is 0.544 nm.The LCDs of TpMA and 3D-COOH-COF are 0.473 nm and 0.477 nm,respectively.The former has a selectivity of 6.79 and the latter has a selectivity of 6.49.

Fig.3.Selective correlation diagram between COF membrane and COF@polymer membrane for CH4/N2 separation.

Fig.4.Correlation diagram between COFs pore size and CH4/N2 adsorption and diffusion selectivity.

Since molecular diffusion mainly occurs in the pores of the material and the PLD/LCD ratio describes the shape of the channel[49],a correlation was further made between the PLD/LCD ratio and the diffusion selectivity of the CoRE COFs (Fig.4(b)).When the PLD/LCD ratio is large (for example,at the range of 0.8-0.9),the CH4/N2diffusion selectivity of CoRE COFs tends to be high.For example,for 3D-Por-COF-0P with a PLD/LCD ratio of 0.859,the diffusion selectivity is 45.15,and the corresponding selfdiffusion coefficient of CH4is 7.53 × 10-8m2·s-1.The diffusion selectivity of Ph-AnCD-COF was 37.96,the PLD/LCD ratio and the diffusion coefficient of CH4are 0.837 and 5.41 × 10-8m2·s-1,respectively.In addition,it is observed that when the pores of COFs are columnar,the diffusion of CH4guest molecules is favorable.

3.3.Design of COF-based MMMs for CH4/N2 separation

Based on the above structural information obtained from the CoRE COF membranes,367 COFs were selected from a large database containing 471,671 generated COFs to satisfy LCD is 0.4-0.6 nm and PLD/LCD is 0.8-0.9.In our previous work [50],this COF database was constructed in batches by imitating the natural growth process of COFs with the method of genetic structural units(GSU).It contains a large number of COFs with unique structures,and the structural characteristics span a wide range,providing options for enriching the existing COF material library.

The calculations of CH4/N2separation are performed again on these 367 COFs to obtain the necessary membrane performance parameters.Top 5 generated COFs with high membrane selectivity are listed in Table 2.It can be seen that the adsorptive and diffusion selectivity of these generated COFs are well balanced compared with the CoRE COFs,which leads to excellent performances in membrane separation.For example,BAR-NAP-Benzene_CF3(Fig.5(a)) has the best membrane separation performance among generated COFs.Its LCD and PLD/LCD are 0.542 nm and 0.81 respectively,and the corresponding adsorptive and diffusion selectivities are 6.03 and 411.48 respectively.In comparison,BARBenzene-Ether has a PLD of 0.475 nm,resulting in a higher adsorption selectivity (15.12).However,due to the restriction of the strong van der Waals force on the CH4molecule,the diffusion selectivity (32.08) of CH4/N2is further weakened.Hence,the change of effective contact area or the number of interaction sites endow the pore structure with an important role in CH4/N2separation.Due to the selection of a suitable material design strategy,the final membrane separation has a good performance.

Table 2Geometric characteristics and membrane separation performance of top 5 generated COFs with the highest membrane selectivities

Furthermore,5 top-performing generated COFs were computationally evaluated as fillers in PDMS,Pebax?2533 and SBS,respectively.The properties of these three polymers are represented by a five-pointed star in Fig.5(b),and the CH4permeability and membrane selectivity are listed in parentheses.Obviously,COFs as fillers are favorable for improving the performance of MMMs.Compared with several common materials such as MOFs,zeolites and graphene oxide,they have great advantages in permeability and selectivity.Intuitively,for PDMS with low selectivity but high permeability,the addition of 5 generated COFs improves membrane selectivity significantly.For Pebax?2533 with low selectivity and low permeability,the membrane separation performance is also improved to a certain extent.For the selectivity and permeability well balanced SBS,all these COFs can effectively improve CH4permeability and membrane selectivity.

Fig.5.(a) Schematic diagram of BAR-NAP-Benzene_CF3@polymers;(b) Membrane performance of generated COF@polymers and other MMMs [45,51-54].

4.Conclusions

In this work,a high-throughput computational screening method was used to systematically study COF-based MMMs for CH4/N2separation.It is found that designing COFs with high membrane selectivities is the key to the development of COF-based MMMs with good separation performances.The thermodynamic design strategy with PLD of 0.4-0.6 nm and the kinetic design strategy with PLD/LCD ratio of 0.8-0.9 was proposed.Thus,5 generated COFs with high CH4/N2membrane separation selectivity were screened from a large-scale material database,which were then used as fillers for MMMs.Among them,BAR-NAPBenzene_CF3@PDMS has a CH4permeability as high as 4.43 × 10-13mol·m·s-1·Pa-1·m-2,and BAR-NAPBenzene_CF3@SBS has a separation selectivity as high as 9.54.Therefore,this work provides useful information for the design of new COF membranes for CH4/N2separation,as well as the selection of suitable COF fillers in different polymers.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was financially supported by the National Key Research &Development Program of China (2021YFB3802200)and the National Natural Science Foundation of China (Nos.22078004 and 21978005).

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2021.09.003.