Molecular dynamics simulations of metal-organic frameworks as membranes for gas mixtures separation

Journal of Membrane Science 428 (2013) 241–250

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Molecular dynamics simulations of metal-organic frameworks as membranes for gas mixtures separation Fredy A. Cabrales-Navarro a, Jose L. Go´mez-Ballesteros a, Perla B. Balbuena a,b,n a b

Artie McFerrin Department of Chemical Engineering, Texas A&M University, 3122 TAMU, College Station, TX 77843-3122, USA Materials Science and Engineering Program, Texas A&M University, 3122 TAMU, College Station, TX 77843-3122, USA

a r t i c l e i n f o

abstract

Article history: Received 6 August 2012 Received in revised form 20 October 2012 Accepted 27 October 2012 Available online 17 November 2012

We use molecular dynamics simulations to analyze the dynamic behavior of the CO2/N2 and CO2/CH4 gas mixtures through IRMOF-1 and Cu-BTC metal-organic frameworks-based membranes. Two approaches are considered to simulate the membrane system: permeation at constant pressure gradient and permeation at variable pressure gradient. The results show that both materials would work similarly to separate CO2/N2 and that Cu-BTC is the most acceptable to separate CO2/CH4 gas mixtures. The roles of diffusion and adsorption are clearly elucidated from the simulations. These simulation results also demonstrate how metal-organic framework properties influence the separation ability of the membrane and help to understand the dynamic mechanism of the process at a molecular level thus providing orientations that may guide experimental work. & 2012 Elsevier B.V. All rights reserved.

Keywords: Molecular dynamics Membrane simulations Metal-organic frameworks Permselectivity

1. Introduction Metal-organic frameworks (MOFs) are porous materials that are extensively investigated for gas [1–3] and liquid separations [4,5]. The structure consists of metal centers connected by organic ligands and depending on the specific chemistry a variety of porous ranges can be obtained, which makes them attractive not only for physical but also for chemical separations. Due to their potential industrial significance, a great deal of research has been committed to their synthesis, characterization, evaluation of adsorption and selectivity properties, and to their chemical and thermal stability, using modern theoretical and experimental tools [1–3]. Most interesting applications of these materials such as gas storage, gas separation, filtration, and catalytic separations would require the deposition of the porous materials as supported thin films or their use as free standing membranes [6]. The microscopic mechanisms of adsorption and diffusion in MOFs resultant from their intrinsic molecular nature make them especially suited to be investigated with first principles methods. For this reason a variety of theoretical methods ranging from ab initio density functional theory (DFT), Grand Canonical Monte Carlo (GCMC) simulations, and classical molecular dynamics (MD), are routinely used for evaluation of adsorption and dynamic properties [7–13]. From these studies, it is possible to obtain accurate binding energies of species to active sites in the framework, adsorption isotherms of

n Corresponding author at: Artie McFerrin Department of Chemical Engineering, Texas A&M University 3122 TAMU, College Station, TX 77843-3122, USA. Tel.: þ1 979 845 3375; fax: þ 1 979 845 6446. E-mail address: [email protected] (P.B. Balbuena).

0376-7388/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.memsci.2012.10.058

single components and mixtures, diffusion coefficients, and screening of possible new candidate materials for given separations. In comparison, probably because of the non-equilibrium character of the process, much less work has been dedicated to simulate membrane performance using atomistic models. Mizukami et al. [14] introduced a method to evaluate membrane performance using MD simulations of a mixture flowing through a few nanometer-thick zeolite-based membrane film. Others have also utilized classical MD to determine permeation properties in microporous Al2O3 membranes [15], and nanoporous silica [16]. More recently, MD simulations have also been used to characterize reverse osmosis processes in polymeric membranes [17,18]. In this work, we examine two mixtures: CO2/N2 and CO2/CH4 and two MOF materials: IRMOF-1 and Cu-BTC, modeling membrane behavior under variable pressure and constant pressure approaches. The second model is similar to that presented by Mizukami et al. [14] Cu-BTC, also known as HKUST-1 [19], is composed of Cu2(COO)4 paddle wheels and benzene-1,3,5-tricarboxylate (BTC), whereas IRMOF-1 [20] has eight Zn4O clusters linked by 24 1,4-benzene dicarboxylates linker molecules. Our objective is to investigate the roles of diffusion and adsorption inside the MOFs membranes to assess their capability as a potential material for separation purposes.

2. Simulation method 2.1. Variable pressure gradient approach The dynamic diffusion behavior of CO2/N2 and CO2/CH4 gas mixtures through the metal organic frameworks IRMOF-1 and

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Fig. 1. Membrane model used in molecular dynamics simulations. The figure illustrates an initial configuration for an IRMOF1 membrane to separate a CO2/N2 gas mixture. Color code for the gas molecules: C (CO2), orange; O (CO2), red; N, blue. For the framework atoms, Zn, magenta; Cu, cyan; C, gray; O, ocher. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

Cu-BTC was simulated using the MD software DL_POLY 2.21. [21]. The system used to emulate the membrane performance is shown in Fig. 1 for the IRMOF-1 case. A similar system was created for the Cu-BTC simulations. In this approach, we utilized a 2  2  2 MOF unit cell stack as the membrane material. The membrane phase has a thickness corresponding to 2 unit cells for IRMOF-1 ˚ respectively). The feed region and Cu-BTC (51.190 A˚ and 52.686 A, was built of equal volume and filled up with a 50/50 CO2/N2 mixture or a 50/50 CO2/CH4 with the molecules being randomly distributed. This feed region contains a total of 200 gas molecules for each system initially at a pressure P. The region underneath the membrane, which is also of the same volume as the other two regions, is the permeate phase which is initially empty. We use the Dreiding force field [22] to represent the inter- and intramolecular interactions for all atoms, except for He, for which we used the Universal force field [23]. The framework atoms are kept fixed in their crystal positions. The three-site Trappe model was used for CO2 [24] and the single-site Trappe model for CH4 [25]. A three-site model was used for N2 as well in order to represent its molecular quadrupole [24]. MD simulations were carried out in the NVT ensemble (constant number of molecules N, volume V, and temperature T), at 298 K. The temperature was regulated

using the Berendsen thermostat [26]. The equations of motion were integrated using the velocity Verlet integration algorithm [27]. Periodic boundary conditions were applied in the three directions and a wall was used at the bottom of the permeate phase to avoid molecules passing to the feed phase due to the periodicity of the simulation along the z axis. The wall is composed by 400 (20  20) He atoms, which have a weak interaction with the other atoms in the system, guaranteeing that the wall does not influence the results [15]. The total simulation time was 3 ns and the number of molecules of each type was monitored at all times in the permeate, membrane, and feed regions. The simulations were set making the volumes of the three phases: feed, membrane, and permeate, equal to each other. If the thickness of the membrane changes, the other volumes also would change accordingly. Thus, we expect the geometrical parameters not to affect dramatically the results. The crystal structure coordinates of each MOF were obtained from published data [19,28]. To build the unit cells of Cu-BTC and IRMOF-1, structural properties and unit cell lattice constants obtained from original data are shown in Table 1. To account for molecular interactions between adsorbates and adsorbents, Lennard Jones (LJ) and electrostatic interactions were used. The LJ potential parameters for the atoms in the selected MOFs were obtained from the Dreiding force field [29]. For the O and C atoms in CO2, and those for the N atoms in N2 the LJ parameters were taken from the transferable potentials for phase equilibria (TraPPE) force field model [29], whereas for the O and H atoms in water they were taken from the simple point charge/ extended (SPC/E) model [30]. The single site TraPPE model was used for the CH4 molecule [25]. To determine the LJ parameters between the atoms in the MOFs and the adsorbate sites, the Lorentz–Berthelot mixing rules [31] were applied. The charges of the atoms in Cu-BTC and IRMOF-1 were obtained from the literature [32]. The partial point charges of each atom site in N2 and CO2 were taken from the Trappe force field model [29]. To account for the quadrupole of the N2 molecule a partial point charge of þ0.964e is assigned for the center of mass site in nitrogen, while a partial point charge of –0.482e is assigned to each of the N atoms. Partial point charges centered at each LJ site in CO2 were qO ¼–0.35e and qC ¼ þ0.70e. 2.2. Approach at constant pressure gradient In this approach the number of gas molecules in the feed phase is kept constant, intending to emulate a breakthrough experiment commonly used to evaluate membrane performance [33]. We consider the following experimental settings in order to carry out the simulations: (a) a constant flow of gas is fed to the equipment as permeation through the membrane takes place; (b) the gas that passes to the vacuum phase is removed using an inert gas; and (c) the concentrations are monitored through time. Consequently, in the simulations, the following actions were implemented: (a) every 50 ps, molecules that pass to the vacuum phase are removed, whereas a number of molecules according to the same initial composition are added to the top keeping a constant pressure gradient. The tasks of removing and completing were Table 1 Unit cell geometry for IRMOF-1 and Cu-BTC. MOF

˚ Lattice parameters (A)

Cell angle (Degree)

Cu-BTC IRMOF-1

a¼ b¼ c¼ 26.343 a¼ b¼ c¼ 25.832

a ¼ b ¼ g ¼90 a ¼ b ¼ g ¼90

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carried out using a FORTRAN code. (b) The number of molecules in the membrane and the number of molecules that passes to the permeate phase are monitored against time for a total time of 2 ns. A similar approach was used before by Mizukami et al. [14] to evaluate the flow of CO2/N2 gas mixture through a zeolite membrane. Statistical variations may be expected for different initial configurations of the set of molecules in the feed phase. In this work, we have a developed a simple program that adds the necessary amount of molecules every time the simulation is interrupted (every 50 ps) to keep the pressure gradient constant. These molecules are initially arranged in a random distribution, just keeping the necessary distances to avoid hot spots. However, we have not determined the error bars which may be evaluated based on variations of these initial configurations. The simulation was set making the volumes of the three phases: feed, membrane, and permeate, equal to each other. If the thickness of the membrane changes, the other volumes also would change accordingly. Thus, we expect the geometrical parameters not to affect dramatically the results.

The evaluation was done in the membrane phase, where the distribution of angular velocities determined at different times as shown in Fig. 2. The graphs illustrate that the average angular velocity of the N2 molecules is approximately double the value of that for CO2 molecules. The distribution is practically independent of time and for CO2 peaks at about 2.5 ps  1 (with 30% of the molecules in that maximum angular velocity), whereas for N2 peaks between 5 and 6 ps  1 showing a slightly wider distribution. Due to this slow diffusion, but also due to its enhanced affinity toward the MOF sites, CO2 stays longer, and adsorbs strongly in both IRMOF-1 and Cu-BTC cages, whereas N2 and CH4 move more easily among cages. Based on their relative mobilities, one may think that these membrane structures should carry out a gas separation process by trapping CO2 and letting the other gases to flow towards the permeate region of the membrane. However, both solubility and diffusivity are factors that determine permeability. This topic is further discussed in a later section, on the basis of the simulation results.

3.2. Variable pressure gradient

3. Results and discussion 3.1. Diffusion mechanism A common factor visually observed in all the simulated systems is that the diffusion mechanism of the gases through the membrane is dominated by rotational motion for all molecules, though some translational motion is presented as well; however, N2 rotation and translation is much faster than CO2 rotation. To quantify these effects, rotational motion was assessed by calculation of the time evolution of the angular velocity for each of the molecules. The calculation was based on the characterization of the magnitude and direction of the velocity vectors corresponding to each of the sites in the molecules: for CO2 the relevant sites are the two oxygen atoms, and both nitrogen atoms in N2; the velocities of these sites are computed relative to that of the center of mass. Since both CO2 and N2 are modeled as rigid linear three-site molecules, rotation of any of these molecules occurs when the velocity vectors of the end sites have the same magnitude and opposite direction to each other, which is assessed by evaluation of the dot product. The magnitude of the rotation is calculated according to ! 9v 9

o¼ ! 9r 9 ! where o is angular velocity (in ps  1), v is the velocity of an end! site atom relative to that of the center of mass, and r is the position of an end-site atom relative to the center of mass.

Fig. 3 shows the final configurations obtained using the variable pressure gradient approach, and it illustrates in a schematic way the distribution of each gas in the three regions of the system (permeate, membrane and feed). The most marked difference in concentration that can be seen in these snapshots is for the Cu-BTC simulations, where there is a very high amount of CO2 inside the membrane and a very small amount reaches the permeate phase, where the other component is predominant. Fig. 3d illustrates that for the CO2/CH4 gas mixture in the Cu-BTC membrane, at 3 ns the majority of the permeate region is filled with CH4 molecules, and the few CO2 molecules in this region are not evenly distributed throughout it, but they are selectively located at the closest possible to the membrane due to the strong interaction between this MOF structure and the gas. For a more quantitative representation, we plotted the number of molecules in the permeate region as a function of time for all the study cases; these results are displayed in Fig. 3. In these cases, permeation occurs until the system reaches an equilibrium between the permeate phase and the feed phase, since at that condition there is no longer a pressure gradient that forces the gases to flow through the membrane. Fig. 4 reveals that the relative concentration of CO2, expressed in terms of the number of molecules, is lower than the concentrations of N2 and CH4 for the majority of the monitoring points in their corresponding simulation. This is because CO2 is captured by the IRMOF-1 and Cu-BTC membranes, as their affinity of this compound for the membrane material is higher than those of N2 and CH4.

0.3

0.3 CO2

0.25

Fraction of molecules

Fraction of molecules

243

500 ps

0.2

1000 ps

0.15

1500 ps 2000 ps

0.1 0.05

N2 500 ps

0.25

1000 ps

0.2

1500 ps

0.15

2000 ps

0.1 0.05 0

0 0

2

4

6

ω, ps-1

8

10

0

5

10

15

20

ω, ps-1

Fig. 2. Distribution of angular velocities for CO2 and N2 molecules diffusing through the Cu-BTC membrane, evaluated at 500, 1000, 1500, and 2000 ps, respectively.

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Fig. 3. Snapshots of final configuration (at 3 ns) for the variable pressure approach at 298 K. (a) IRMOF-1 and CO2/N2, (b) IRMOF-1 and CO2/CH4, (c) Cu-BTC and CO2/N2, and (d) Cu-BTC and CO2/CH4. Color code for the gas molecules: C (CO2), orange; O (CO2), red; N, blue; CH4, green. For the framework atoms: Zn, magenta; Cu, cyan; C, gray; O, ocher. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

IRMOF-1 Membrane 30 Number of Molecules

Number of Molecules

30 25 20 15 10 5 0

0

1000 2000 Time [ps] CO2

25 20 15 10 5 0

3000

0

1000 2000 Time [ps]

N2

CO2

3000

CH4

30

Number of Molecules

Number of Molecules

Cu-BTC Membrane 25 20 15 10 5 0

0

1000

2000

25 20 15 10 5 0

0

1000

2000

3000

Time [ps]

Time [ps] CO2

3000

30

N2

CO2

CH4

Fig. 4. Gas monitoring in the permeate region for the variable pressure approach simulations: (a) IRMOF-1 and CO2/N2, (b) IRMOF-1 and CO2/CH4 Cu-BTC, (c) Cu-BTC CO2/N2, and (d) Cu-BTC and CO2/N2 membranes simulated at 298 K.

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3.3. Constant pressure gradient

900

IRMOF-1

800 700

CO2

600

N2

500 400 300 200 100 0

0

500

1000

1500

where the membrane does not seem to capture a significant excess of CO2 compared to methane (Fig. 5b). This result suggests that the affinity of IRMOF-1 towards CO2 and CH4 is very similar. Since permeability is the product of solubility and diffusivity, we first use the simulation results in order to estimate solubilities, and then diffusivities for CO2, N2, and CH4 in the two MOFs. To determine the relative affinity of the two mixtures, we have calculated the adsorption isotherms at 298 K for IRMOF-1 and CuBTC for the two mixtures using GCMC simulations with the same force fields. The differences in affinities observed in Fig. 4 can be

Number of Molecules

Number of Molecules

Results for the separation of CO2 from N2 and CO2 from CH4 on IRMOF-1 and Cu-BTC at 298 K keeping a constant pressure gradient are shown in Fig. 5. The reported simulations correspond to a pressure gradient of 5.62 MPa for the Cu-BTC membrane and 5.99 MPa for the IRMOF-1 membrane. At this pressure, it is found that the membrane starts filling up approximately after 250 ps with a higher amount of CO2 compared to the other gases for all the cases, except for the separation of CO2 from CH4 in IRMOF-1,

900 700

CO2

600

CH4

500 400 300 200 100 0

2000

IRMOF-1

800

0

500

1000

Time [ps]

2000

2500

3000

900

CuBTC

800 700 600

CO2

500

N2

Number of Molecules

Number of Molecules

1500

Time [ps]

900

400 300 200 100 0

245

0

500

1000

1500

2000

800

CuBTC

700 600 500

CO2

400

CH4

300 200 100 0

0

500

1000

1500

2000

Time [ps]

Time [ps]

16 14 12 10 8

CO2

6

N2

4 2

Excess adsorbed amount [mmol/cm3]

Excess adsorbed amount [mmol/cm3]

Fig. 5. Membrane gas uptake under a constant pressure gradient at 298 K: (a) IRMOF-1 membrane with CO2/N2, (b) IRMOF-1 membrane with CO2/CH4, (c) Cu-BTC membrane withCO2/N2, and (d) Cu-BTC membrane with CO2/N2.

0

16

CO2

14

CH4

12 10 8 6 4 2 0

0

20

40

60

80

0

20

16 14 12 10 8

CO2

6

N2

4 2 0

0

20

40

P[bar]

40

60

80

P[bar]

Excess adsorbed amount [mmol/cm3]

Excess adsorbed amount [mmol/cm3]

P[bar]

60

80

16 14 12 10 8

CO2

6

CH4

4 2 0

0

20

4

60

80

P[bar]

Fig. 6. Adsorption isotherms of the individual gases in 50/50 CO2/N2 and CO2/CH4 mixtures at 298 K calculated with GCMC simulations. Top row: on IRMOF-1; bottom row: on Cu-BTC.

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directly obtained from the analysis of the adsorption isotherms. As observed in Fig. 6 (top row), there is a clear difference in affinities between CO2 and N2 in IRMOF-1, whereas CO2 and CH4 are adsorbed in practically the same amounts up to 10 bar (  1 MPa) where the loading starts to be higher for CO2 than for CH4. At 3.75 MPa, the pressure used in our membrane calculation, the ratio of the excess loadings of CO2 to N2 species in IRMOF-1 is 52, while the ratio of CO2 to CH4 is 1.8. This difference in affinities partially explains the differences observed in the membrane behavior shown in Fig. 5, although the differences in diffusivities also play a role, as discussed in a later section. On the other hand, the two mixtures show very similar relative affinities in Cu-BTC (Fig. 6, bottom panel), in agreement with the similar behavior observed in the membrane process (Fig. 5). We note that our calculated isotherms are in good agreement with experimental reports of CO2/CH4 mixtures in Cu-BTC [34]. However, there are not too many reports of direct measurements of mixture isotherms [2,3]. Instead, mixture isotherms are computed using Ideal Adsorbed Solution Theory (IAST) [35] simulations, which are based on experimental data for pure component isotherms, and have proved to yield very good agreement with experimental results[2,3]. Karra and Walton [36] have reported calculated selectivities for our systems of study and our calculated isotherms are in agreement with those reports for the CO2/N2 system in IRMOF-1 and Cu-BTC. Assuming that the solubility of the gases in the membrane follows Henry’s law, the concentration of a given gas in the membrane may be considered as proportional to the product of the solubility coefficient (S) and the partial pressure of the gas (p) C membrane ¼ Sp

ð1Þ

However, Henry’s law would be only a rough approximation at the high pressure used in the simulations. Therefore we have calculated the solubilities based on the adsorption isotherms in Fig. 6, as shown in Table 2. To illustrate the differences, we also used the concentrations of the gases when the membrane is saturated taken from Fig. 5 to estimate the solubilities of the gases in the two MOFs, as shown by the values in parenthesis of Table 2. Table 2 clearly shows the higher affinities of the two membranes by CO2. However, the geometric differences between the two gases may influence the diffusion mechanism, and consequently the permeabilities. To verify this, a useful method is the analysis of the time lag observed by plotting the cumulative amount of molecules (Qt) computed in the permeate region as a function of time. This type of time lag analysis was first proposed by Daynes [37] and then refined by Barrer [38], and is widely used experimentally to obtain diffusivities and permeabilities [39,40]. The corresponding time-lag experiment is very similar to our constant-pressure gradient simulation: the feed face of the membrane is maintained at constant concentration C1 and that of the permeant phase at another constant concentration C2, Table 2 Solubilities (S) of the gases in IRMOF-1 and Cu-BTC calculated from the slope of the adsorption isotherms (Fig. 6). Values in parenthesis were calculated using Eq. (1). Adsorbate

Solubility [mol/Pa*m3] Cu-BTC

CO2 CH4 CO2 N2

3.49 5.51 3.40 3.28

E-4 E-5 E-4 E-5

IRMOF-1 (2.09E-03) (5.69E-04) (2.13E-03) (5.05E-04)

6.23 9.71 1.25 9.05

E-4 E-5 E-3 E-5

(3.46E-03) (3.34E-03) (2.41E-03) (5.09E-04)

Table 3 Diffusivities of gases in the MOF membranes calculated from Fig. 5 and Eq. (2). MOF

Adsorbate

D*109 m2/s

IRMOF-1

CH4 CO2 N2 CO2 CH4 CO2 N2 CO2

18.76 6.40 17.10 6.05 7.88 5.09 13.12 6.11

IRMOF-1 Cu-BTC Cu-BTC

Table 4 Calculated perm-selectivities of CO2 relative to CH4, and CO2 relative to N2 in the two model membranes. Mixture

CO2/CH4 CO2/N2

Solubility ratio

Diffusivity ratio

Permselectivity

Cu-BTC

IRMOF-1

Cu-BTC

IRMOF-1

Cu-BTC

IRMOF-1

6.33 10.37

6.41 13.81

0.64 0.47

0.34 0.35

4.05 4.87

2.18 4.83

where C1 4C2, and the increase in concentration of the effluent gas is followed in a collecting volume on the downstream side of the membrane [39]. The increase is kept small compared with the upstream concentration, therefore the driving force for permeation can be essentially considered constant. A graph of the cumulative amount of gas collected in the permeate phase vs. time yields an initial time-lag, after which the amount rises approximately linearly (steady state) as a function of time. The time-lag (y) is determined as the intercept of the extrapolated linear part on the time axis, and it is related to the diffusion coefficient D of the gas species by 2

y¼

l 6D

ð2Þ

where l is the membrane thickness. Reading the time lag in each case from the graphs in Fig. 5, we can estimate the diffusivities of each species using Eq. (2). The results are shown in Table 3. The results in Table 3 indicate that N2 diffuses much faster than CO2 in both membranes, and CH4 diffuses much faster than CO2 in IRMOF-1 and only slightly faster than CO2 in Cu-BTC. Combining the results in Tables 2 and 3 we calculate selectivities to permeation of adsorbate A1 to adsorbate A2 (permselectivities, PA1/A2) defined as the product of the ratio of solubilities (SA1/SA2) and the ratio of diffusivities (DA1/DA2), as shown in Table 4. It is found that both membranes are selective to CO2 in both mixtures; with the separation CO2/N2 being more favorable than that of CO2/CH4. Cu-BTC is slightly more effective (  17%) to separate CO2 from N2 than CO2 from CH4, but in IRMOF-1 the difference is larger (  55%). This can be explained observing that the perm-selectivity difference in IRMOF-1 is practically determined by the solubility ratio, since the diffusivity ratios in the two mixtures are practically the same. Instead, in Cu-BTC the solubility ratio and the diffusivity ratio follow opposite trends: the affinity difference is larger in CO2/N2 than in CO2/CH4, but the relative mobility of CO2 to N2 is lower than that of CO2 to CH4, which makes the permselectivity difference between the two mixtures to become smaller in this material than in IRMOF-1. Density profiles in the vertical z direction, parallel to the gas flow, were computed inside the membrane region from the MD simulation trajectories at various times, and they are shown in Fig. 6 for the 50/50 CO2/N2 mixture in Cu-BTC. The z-density

F.A. Cabrales-Navarro et al. / Journal of Membrane Science 428 (2013) 241–250

Qt [number of molecules]

400

N2

350 300

y =0.1731x -44.894 R²=0.9848

250

CO2

200 150

y =0.1571x -115.15 R² =0.9193

100 50 0

IRMOF-1 0

500

1000

1500

2000

2500

Our results are in qualitative agreement with those reported by Keskin and Sholl [12,13] for IRMOF-1 and Cu-BTC membranes in CO2/N2 separations, however, these authors predicted permeselectivities greater than 1 for the CO2/CH4 mixture in IRMOF-1. Finally, we also investigated the effect of overall mixture concentration on membrane performance. Fig. 10 illustrates that these MOFs materials are able to enrich the CO2 flow from 15 to 40% molecular fraction in both IRMOF-1 and Cu-BTC. On the other hand, the same materials enrich the CO2 flow from 50 to 83% in IRMOF-1 and to 81% in Cu-BTC. Defining membrane efficiency Z ¼(final CO2 concentration in the membrane feed CO2 concentration)/(100 feed CO2 concentration)  100, we get efficiencies of 29% for CO2/N2 separation

Qt [number of molecules]

profiles r (z) are computed by evaluating the number of molecules in a thin film perpendicular to the z direction, divided by the overall number of gas molecules that would occupy such volume at the conditions of the system. Fig. 6 illustrates how CO2 is preferentially filling the membrane from the feed to the downstream side, whereas the amount of N2 in the membrane is small at all times. Similar observations were found in the case of the CO2/CH4 mixture (not shown). The concentration of the two gases in the membrane can be visualized from snapshots taken at various times. Fig. 7 shows how the saturation of the IRMOF-1 and Cu-BTC membranes takes place, as a function of time, for the simulations corresponding to the separation of CO2 from N2.

400 350

y=0.1279x -30.234 R²=0.9834

300 250 200

y =0.1464x -101.46 R² =0.9642

CH4

150 100

CO2 IRMOF-1

50 0

0

500

1000

1500

400 y =0.1982x -69.906 R²=0.9918

300 250

y =0.2567x -194.51 R²=0.9853

200 150

N2

100

CO2

50 0

Cu-BTC 0

500

1000

1500

2000

2500

3000

3500

Time[ps]

2000

2500

Qt [number of molecules]

Qt [number of molecules]

Time[ps]

350

247

400 350 300

y =0.2061x -120.93 R²=0.9859

250 200 150

y =0.22x -200.07 R²=0.992

CH4

100

CO2 Cu-BTC

50 0

0

500

1000

Time[ps]

1500

2000

2500

Time[ps]

Fig. 7. Cumulative number of molecules (Qt) in the permeate region as a function of time in 50/50 mixtures. (a) CO2/N2 in IRMOF-1, (b) CO2/CH4 in IRMOF-1, (c) CO2/N2 in Cu-BTC, and (d) CO2/CH4 in Cu-BTC. A time lag is determined as the intercept of the fitted straight line with the time axis, and related to the diffusivity of the respective species through Eq. (2). Simulations are at 298 K.

4.00E-03

500ps

3.00E-03 2.00E-03

N2

2.00E-03 1.00E-03

1.00E-03 0.00E+00 -30

-20

-10

0

10

20

0.00E+00 -30

30

-20

-10

z[Å]

1500ps

CO2

20

30

N2

1.00E-03

2000ps

CO2

4.00E-03

ρ(z)

ρ(z)

10

z[Å]

2.00E-03

0.00E+00 -30

0

5.00E-03

4.00E-03 3.00E-03

1000ps

CO2

3.00E-03

N2

ρ(z)

ρ(z)

4.00E-03

CO2

N2

3.00E-03 2.00E-03 1.00E-03

-20

-10

0

z[Å]

10

20

30

0.00E+00 -30

-20

-10

0

10

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30

z[Å]

Fig. 8. Density profiles in the z direction parallel to the membrane flow. The zero is located in the center of the membrane region. The entrance to the membrane from the ˚ and the base of the membrane, which connects to the permeate region is located in  26 A. ˚ Simulations are at 298 K. feed side is located at approximately 26 A,

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IRMOF-1

Cu-BTC Time = 0ps

Time = 500ps

Time = 1000ps

Time = 1500ps

Time = 2000ps

Fig. 9. Snapshots of the IRMOF-1 and Cu-BTC membrane saturation for CO2/N2 gas mixture at 298 K as a function of time from the constant pressure gradient approach MD simulations. Color code for the gas molecules: C (CO2), orange; O (CO2), red; N, blue; CH4, green. For the framework atoms: Zn, magenta; Cu, cyan; C, gray; O, ocher. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

in IRMOF-1 starting from a 15% feed concentration of CO2, and 66% if the feed CO2 concentration is 50%. In Cu-BTC, the corresponding efficiencies according to the results in Fig. 8 are 29% and 62%, respectively. Of course these results reflect an ideal membrane that does not possess any defects Fig. 9.

4. Conclusions We used a molecular dynamics simulation model to study the separation processes of CO2/N2 and CO2/CH4 in IRMOF-1 and CuBTC metal-organic framework membranes at 298 K. Two approaches were used that represent two different physical conditions; the first one at variable pressure and the second one using a constant pressure gradient. Our analyses allow us to elucidate contributions to perm-selectivity due to adsorption and diffusion, independently. It is found that the diffusion mechanism of the gases through the membrane is dominated by rotational motion for all molecules, though some translational motion is

presented as well; however, N2 rotation and translation is much faster than CO2 rotation. As determined from the solubilities calculated in the respective binary CO2/N2 and CO2/CH4 mixtures, both membranes have clearly much higher affinities for CO2 than for N2 and CH4, respectively. On the other hand, analysis of the time lag observed by plotting the cumulative amount of molecules computed in the permeate region as a function of time allows us to extract diffusivities for each gas component. It is found that N2 diffuses much faster than CO2 in both membranes, and CH4 diffuses much faster than CO2 in IRMOF-1 and only slightly faster than CO2 in Cu-BTC. From the solubility and mobility results, we conclude that this type of materials do have a satisfactory capacity of gas separation when used as membranes, with both materials proved to be equally efficient to separate the CO2/N2 mixture. On the other hand, Cu-BTC showed to be the most selective to separate CO2 from CH4. This behavior may change if either the pressure or the temperature of the system is altered, since IRMOF-1 could tolerate more pressures due to its larger storage capacity, leading probably to a change in the separation mechanism that could

1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00

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IRMOF - 1 (15/85 mixture)

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Fig. 10. Permeation of 15/85 (top) and 50/50 (bottom) CO2/N2 mixtures in IRMOF-1 and Cu-BTC membranes at 298 K. The figures display the computed fraction of molecules of each species in the membrane region as a function of time.

increase or even decrease its performance. Simulations are in progress to determine such effect.

Acknowledgments This work is supported by the U.S. Department of Energy, ARPA-E, through the IMPACCT program (AR0000073). The authors of this article acknowledge computational support from Texas A&M University Supercomputing Facility. References [1] J.R. Li, R.J. Kuppler, H.C. Zhou, Selective gas adsorption and separation in metal-organic frameworks, Chem. Soc. Rev. 38 (2009) 1477–1504. [2] J.R. Li, Y.G. Ma, M.C. McCarthy, J. Sculley, J.M. Yu, H.K. Jeong, P.B. Balbuena, H.C. Zhou, Carbon dioxide capture-related gas adsorption and separation in metal-organic frameworks, Coord. Chem. Rev. 255 (2011) 1791–1823. [3] J.R. Li, J. Sculley, H.C. Zhou, Metal-Organic Frameworks for Separations, Chem. Rev. 112 (2012) 869–932. [4] K.A. Cychosz, R. Ahmad, A.J. Matzger, Liquid phase separations by crystalline microporous coordination polymers, Chem. Sci. 1 (2010) 293–302. [5] K.A. Cychosz, A.J. Matzger, Water stability of microporous coordination polymers and the adsorption of pharmaceuticals from water, Langmuir 26 (2010) 17198–17202. [6] O. Shekhah, J. Liu, R.A. Fischer, C. Woll, MOF thin films: existing and future applications, Chem. Soc. Rev. 40 (2011) 1081–1106. [7] L.A. Clark, G.T. Ye, R.Q. Snurr, Molecular traffic control in a nanoscale system, Phys. Rev. Lett. 84 (2000) 2893–2896. [8] D. Dubbeldam, R.Q. Snurr, Recent developments in the molecular modeling of diffusion in nanoporous materials, Mol. Simul. 33 (2007) 305–325. [9] A.O. Yazaydin, R.Q. Snurr, T.H. Park, K. Koh, J. Liu, M.D. LeVan, A.I. Benin, P. Jakubczak, M. Lanuza, D.B. Galloway, J.J. Low, R.R. Willis, Screening of metal-organic frameworks for carbon dioxide capture from flue gas using a combined experimental and modeling approach, J. Am. Chem. Soc. 131 (2009) 18198. [10] E. Haldoupis, S. Nair, D.S. Sholl, Efficient calculation of diffusion limitations in metal organic framework materials: a tool for identifying materials for kinetic separations, J. Am. Chem. Soc. 132 (2010) 7528–7539. [11] S. Keskin, J.C. Liu, J.K. Johnson, D.S. Sholl, Atomically detailed models of gas mixture diffusion through CuBTC membranes, Micro. Meso. Mat. 125 (2009) 101–106. [12] S. Keskin, D.S. Sholl, Efficient methods for screening of metal organic framework membranes for gas separations using atomically detailed models, Langmuir 25 (2009) 11786–11795. [13] S. Keskin, D.S. Sholl, Assessment of a metal-organic framework membrane for gas separations using atomically detailed calculations: CO2, CH4, N-2, H-2 mixtures in MOF-5, Ind. Eng. Chem. Res. 48 (2009) 914–922.

[14] K. Mizukami, H. Takaba, Y. Kobayashi, Y. Oumi, R.V. Belosludov, S. Takami, M. Kubo, A. Miyamoto, Molecular dynamics calculations of CO2/N-2 mixture through the NaY type zeolite membrane, J. Membr. Sci. 188 (2001) 21–28. [15] K.L. Yin, D.J. Xu, Study on permeation of acetone/nitrogen mixed gas through Al2O3 microporous membranes: molecular dynamics, Chem. Eng. Commun. 193 (2006) 1678–1688. [16] M.V. Kozachok, Equilibrium molecular dynamics and mean first passage time analysis of the separation of exhaust gases at high temperatures by silica nanoporous membranes, Model. Simul. Mater. Sci. Eng. 18 (2010). [17] E. Harder, D.E. Walters, Y.D. Bodnar, R.S. Faibish, B. Roux, Molecular dynamics study of a polymeric reverse osmosis membrane, J. Phys. Chem. B 113 (2009) 10177–10182. [18] Y. Luo, E. Harder, R.S. Faibish, B. Roux, Computer simulations of water flux and salt permeability of the reverse osmosis FT-30 aromatic polyamide membrane, J. Membr. Sci. 384 (2011) 1–9. [19] S.S.Y. Chui, S.M.F. Lo, J.P.H. Charmant, A.G. Orpen, I.D. Williams, A chemically functionalizable nanoporous material Cu-3(TMA)(2)(H2O)(3)(n), Science 283 (1999) 1148–1150. [20] H. Li, M. Eddaoudi, M. O’Keeffe, O.M. Yaghi, Design and synthesis of an exceptionally stable and highly porous metal-organic framework, Nature 402 (1999) 276–279. [21] W. Smith, T.R. Forester, DL_POLY_2.0: A general-purpose parallel molecular dynamics simulation package, J. Mol. Graphics 14 (1996) 136–141. [22] S.L. Mayo, B.D. Olafson, W.A. Goddard, Dreiding: A generic force field for molecular simulations, J. Phys. Chem. 94 (1990) 8897–8909. [23] A.K. Rappe, C.J. Casewit, K.S. Colwell, W.A. Goddard, W.M. Skiff, UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations, J. Am. Chem. Soc. 114 (1992) 10024–10035. [24] J.J. Potoff, J.I. Siepmann, Vapor–liquid equilibria of mixtures containing alkanes, carbon dioxide, and nitrogen, Aiche J. 47 (2001) 1676–1682. [25] M.G. Martin, J.I. Siepmann, Transferable potentials for phase equilibria. 1. United-atom description of n-alkanes, J. Phys. Chem. B 102 (1998) 2569–2577. [26] H.J.C. Berendsen, J.P.M. Postma, W.F.v. Gunsteren, A.D. Nola, J.R. Haak, Molecular dynamics with coupling to an external bath, J. Chem. Phys. 81 (1984) 3684–3690. [27] L. Verlet, Phys. Rev. 159 (1967) 98. [28] M. Eddaoudi, J. Kim, N. Rosi, D. Vodak, J. Wachter, M. O’Keeffe, O.M. Yaghi, Systematic design of pore size and functionality in isoreticular MOFs and their application in methane storage, Science 295 (2002) 469–472. [29] J.J. Potoff, J.I. S, Vapor–liquid equilibria of mixtures containing alkanes, carbon dioxide, and nitrogen, AIChe 47 (2007) 1676–1682. [30] H.J.C. Berendsen, J.R. Grigera, T.P. Straatsma, The missing term in effective pair potential, J. Phys. Chem. 91 (1987) 6269–6271. [31] A.K. Al-Matar, D.A. Rockstraw, A generating equation for mixing rules and two new mixing rules for interatomic potential energy parameters, J. Comp. Chem. 25 (2003) 660–668. [32] D. Farrusseng, C. Daniel, C. Gaudillere, U. Ravon, Y. Schuurman, C. Mirodatos, D. Dubbeldam, H. Frost, R.Q. Snurr, Heats of adsorption for seven gases in three metal-organic frameworks: systematic comparison of experiment and simulation, Langmuir 25 (2009) 7383–7388.

250

F.A. Cabrales-Navarro et al. / Journal of Membrane Science 428 (2013) 241–250

[33] I. Park, K.S. Knaebel, Adsorption breakthrough behavior – unusual effects and possible causes, Aiche J. 38 (1992) 660–670. [34] L. Hamon, E. Jolimaitre, G.D. Pirngruber, CO2 and CH4 separation by adsorption using Cu-BTC metal-organic framework, Ind. Eng. Chem. Res. 49 (2010) 7497–7503. [35] J.A. O’Brien, A.L. Myers, Rapid calculations of multicomponent adsorption equilibria from pure isotherm data, Ind. Eng. Chem. Process Des. Dev. 24 (1985) 1188–1191. [36] J.R. Karra, K.S. Walton, Molecular simulations and experimental studies of CO2, CO, and N-2 Adsorption in metal-organic frameworks, J. Phys. Chem. C 114 (2010) 15735–15740.

[37] H.A. Daynes, The process of diffusion through a rubber membrane, Proc. R. soc. Lond. Ser. A-Contain. Pap. Math. Phys. Character 97 (1920) 286–306. [38] R.M. Barrer, Permeation, diffusion and solution of gases in organic polymers, Trans. Faraday Soc. 35 (1939) 0628–0643. [39] W.R. Vieth, J.M. Howell, J.H. Hsieh, Dual sorption theory, J. Membr. Sci. 1 (1976) 177–220. [40] R. Adams, C. Carson, J. Ward, R. Tannenbaum, W. Koros, Metal organic framework mixed matrix membranes for gas separations, Micro. Meso. Mat. 131 (2010) 13–20.