ZIF-67 Framework: A Promising New Candidate for Propylene

Subscriber access provided by GAZI UNIV

Article

ZIF-67 Framework: A Promising New Candidate for Propylene / Propane Separations - Experimental Data and Molecular Simulations Panagiotis Krokidas, Marcelo Castier, Salvador Moncho, Dusan N Sredojevic, Edward N. Brothers, Hyuk Taek Kwon, Hae-Kwon Jeong, Jong Suk Lee, and Ioannis George Economou J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b00305 • Publication Date (Web): 24 Mar 2016 Downloaded from http://pubs.acs.org on March 25, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 32

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

The Journal of Physical Chemistry

ZIF-67 Framework: a Promising New Candidate for Propylene / Propane

Separation

-

Experimental

Data

and

Molecular

Simulations Panagiotis Krokidas,1 Marcelo Castier,1 Salvador Moncho,2 Dusan Sredojevic,2 Edward Brothers,2 Hyuk Taek Kwon,3 Hae-Kwon Jeong,3,4 Jong Suk Lee5 and Ioannis G. Economou1,* 1

Chemical Engineering Program, Texas A&M University at Qatar, P.O. Box 23874, Education City,

Doha, Qatar 2

Science Program, Texas A&M University at Qatar, P.O. Box 23844, Education City, Doha, Qatar

3

Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station,

TX 77843-3122, USA 4

Department of Materials Science and Engineering, Texas A&M University, College Station, TX

77843-3003, USA 5

Center for Environment, Health and Welfare Research, Korea Institute of Science and Technology,

Hwarang-ro 14-gil, Seongbuk-gu, Seoul 136-791, Republic of Korea *Corresponding author at [email protected]

1 Environment ACS Paragon Plus


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

Page 2 of 32

Abstract ZIF-67, a Co-substituted ZIF-8 structure, is investigated as a candidate for the industrially highly demanding propylene / propane separation, with the use of computational techniques for the first time. A new force field for the ZIF-67 framework based on DFT calculations is reported along with a recently developed force field for ZIF-8. The new force field is validated through comparison with structural data for ZIF-67 from literature. Molecular dynamics simulations are reported for ZIF-67, showing a dramatic increase of propylene / propane corrected diffusivities ratio when compared to ZIF-8, implying a huge improvement in the separation of the mixture. The sieving mechanism of ZIF frameworks is investigated and the results yield a dependency of the swelling motion of the gates from the bonding of the metal atom with its surrounding atoms. The presence of Co in the modified framework results in a tighter structure, with a smaller oscillation of the gate opening, which leads to a narrower aperture. The results from the simulations and experiments in ZIF-67 place this new structure at the top of the candidates for propylene / propane separation.


Page 3 of 32

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


Introduction ZIF-8 (ZIF: Zeolitic imidazolate framework) is one of the most investigated Metal Organic Frameworks (MOFs) for separation of gas mixtures because of its excellent thermal and chemical stability.1,2 Experimental data from literature revealed that gas molecules with size larger than the aperture accessing the main pores can diffuse in ZIF-8. 3,4,5 The mechanism has yet to be fully understood, but this behavior is attributed to the elastic behavior of the ligands forming the aperture, whose size fluctuates. Recent experiments on the industrially important propylene / propane separation show a favorable diffusion of propylene against propane through ZIF-8, due to its slightly smaller effective diameter. 6,7,8,9,1011,12,13,14 Kwon et al. 15 improved this separation by replacing the Zn metal atoms in the ZIF-8 framework with Co metal atoms, resulting in a structure known as ZIF-67. The goal of this work is to compare the performances of ZIF-8 and ZIF-67 for the propylene / propane separation. Molecular simulations provide important insight in the sorption and diffusion of gases in ZIF-8 and kinetic data which compare successfully with experiments.16,17,18,19,20,21,22,23,24,25 However, no computational work has been conducted for ZIF-67,26 to the authors’ knowledge. Since there is no force field for the ZIF-67 framework in literature, new parameters were developed from Density Functional Theory (DFT) calculations, following the same approach that we reported recently27 for the development of a ZIF-8 force field. These newly derived force fields are essential for the very demanding and delicate calculations needed to predict propylene / propane separation in ZIF-67. A recent publication by Verploegh et al. raises a similar point.28 The proposed model is initially validated by reproducing the structure of ZIF-8 and ZIF-67 and comparing major structural properties of their frameworks, such as bond lengths and angles, with literature experimental values. Subsequently, the model is applied to predict the corrected 3 Environment ACS Paragon Plus


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

Page 4 of 32

diffusivity of propane and propylene through both ZIF-8 and ZIF-67. The improvement of the separation is investigated and new findings concerning the role of aperture flexibility are discussed. We conclude upon the new clearly improved propylene / propane separation in ZIF-67 and the capabilities of our approach to lead to further improvement of the material performance by proper modification of the ZIF structure.

Methodology Computational reconstruction of unit cell The unit cells of ZIF-8 and ZIF-67 were reconstructed according to the experiments conducted by Park et al1 and Banderjee et al.,26 respectively. The resulted Zn/Co-(N-mIM)4 tetrahedra shown in Figure 1(a) form the basis of the ZIF-8/-67 unit cells that are shown in Figure 1(b).

Figure 1. (a) The basic tetrahedral unit of ZIF-8 and ZIF-67 framework and (b) the reconstructed super cell of the simulations for ZIF-8.


Page 5 of 32

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


Force fields for ZIF structure and gas molecules The force field development of the ZIF-67 framework followed the procedure reported in our recent work on gas separation in ZIF-8 framework.27 We used the Gaussian 09 suite of programs,29 with the implementation of DFT to obtain the parameters. The hybrid B3LYP density functional30,31 with the 6-311g++(2d,2p) basis set was the same as the one used for ZIF-8 and was selected based on previous success with related MOFs.32 A very dense grid (“ultrafine”) was used for numerical integration. A dianionic model complex with one central metal atom, [M(N-mIM)4]2-, (M=Zn, Co), was used for the ab-initio calculation of the parameters (Figure 1(a)). The geometric parameters correspond to the most stable conformers considered of the DFToptimized [M(N-mIM)4]2- model geometries. Force constants (bonds and angles) were calculated from the Cartesian Hessian matrix, using the procedure proposed by Seminario.33 The parameters for the torsion potential were based in the default AMBER parameter set for rotation of internal bonds in the ligands. Partial charges were calculated using the RESP procedure within the Antechamber program, 34 , 35 in which charges were fitted to the electrostatic potential. The electrostatic potential was calculated and sampled using the Merz-Singh-Kollman procedure,36,37 2-

with UFF radii. The fitted charges for the ML4 model were corrected to neutralize the ML2 fragment (consistently with the neutral extended MOF). The excess charge of the ML2 fragment was reduced by the same amount for all atoms in the ligands, but the metal charge was not modified. Partial charges in the force-field were obtained by averaging the values for different fullyoptimized conformers of the complex with relative energies within 10 kJ/mol. This average value provides a description of how charge redistributes dynamically around the metal center. The bonded terms of framework of ZIF-8 and ZIF-67 as implemented in our newly developed force fields are the following:



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

Page 6 of 32

Bond stretching term: ( − ) 2

(1)

( − ) 2

(2)

( ) = Angle bending term: () = Torsional potential term:

() = 1 + cos(! − ) ]]

(3)

Values of the parameters for each term, as developed in our previous work27 and in this work, can be found in Tables 1 and 2 for ZIF-8, and 3 and 4 for ZIF-67, respectively. The non-bonded interactions are a sum of Lennard-Jones and Coulombic interactions and are described by the expression: +

)$ (#$ ) = 4&$ '( * #$

,

)$ 1 0 0$ −( * -+ #$ 4.& #$

(4)

The values of the terms for the LJ potential are based on the AMBER force field38 and can be found in the work of Hertag et al.39 The partial charges for ZIF-67 and ZIF-8 frameworks are shown in Table 5.


Page 7 of 32

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 1. New structure force-field parameters for bond stretching and bond angle bending for ZIF8.27 Bond Zn-N N-C2 N-C1 C1-C1 C1-H1 C2-C3 C3-H2

l0 (Å) 2.048 1.360 1.376 1.375 1.077 1.498 1.091

kl (kJ/mol/nm2) 52802.1 257818.1 253048.3 339991.8 327690.9 203760.8 286855.0

Angle N-Zn-N Zn-N-C2 Zn-N-C1 C1-N-C2 C1-C1-N C1-C1-H1 C2-C3-H2 H2-C3-H2 N-C2-N N-C2-C3 N-C1-H1

θ0 (degrees) 109.5 130.3 125.1 104.5 107.9 130.6 110.8 108.1 113.8 123.1 121.5

kθ (kJ/mol/rad2) 296.23 462.75 475.30 1077.80 909.61 552.29 565.68 317.98 955.63 958.97 549.78

Table 2. New structure force-field parameters for the torsional potential of ZIF-8 using the AMBER potential.

Dihedral N-C1-C1-N N-C1-C1-H1 C1-C1-N-Zn C1-C1-N-C2 C3-C2-N-Zn C3-C2-N-C1

φ0 (degrees)

m

kφ (kJ/mol)

Source

180 180 180 180 180 180

2 2 2 2 2 2

90.0 90.0 25.1 25.1 41.8 41.8

AMBER AMBER AMBER AMBER AMBER AMBER



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

Page 8 of 32

Table 3. New structure force-field parameters for bond stretching and bond angle bending for ZIF67.

Bond Co-N N-C2 N-C1 C1-C1 C1-H1 C2-C3 C3-H2

l0 (Å) 2.044 1.361 1.377 1.375 1.077 1.498 1.091

kl (kJ/mol/nm2) 58910.7 253383.0 249952.2 340242.9 327774.6 286101.9 286101.0

Angle N-Co-N Co-N-C2 Co-N-C1 C1-N-C2 C1-C1-N C1-C1-H1 C2-C3-H2 H2-C3-H2 N-C2-N N-C2-C3 N-C1-H1

θ0 (degrees) 109.5 130.8 124.7 104.4 107.9 130.6 110.8 108.1 113.9 123.1 121.5

kθ (kJ/mol/rad2) 924.66 534.72 537.23 1074.45 920.48 551.45 564.84 317.98 964.83 974.87 550.61

Table 4. New structure force-field parameters for the torsional potential of ZIF-67 using the AMBER potential.

Dihedral N-C1-C1-N N-C1-C1-H1 C1-C1-N-Zn C1-C1-N-C2 C3-C2-N-Zn C3-C2-N-C1

φ0 (degrees) 180 180 180 180 180 180

m 2 2 2 2 2 2

kφ (kJ/mol) 90.0 90.0 25.1 25.1 41.8 41.8

Source AMBER AMBER AMBER AMBER AMBER AMBER


Page 9 of 32

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 5. Partial charges for ZIF-8 and ZIF-67.

Atom type Zn Co N C1 C2 H1 C3 H2

Partial charge (e) ZIF-8 ZIF-67 1.3429 1.3497 -0.6822 -0.6956 -0.0622 -0.0581 0.7551 0.7846 0.0912 0.0910 -0.2697 -0.3094 0.0499 0.0584

The interactions of all diffusing species were described by the Transferable Potential for Phase Equilibria (TraPPE) force-field, which is accurate for thermodynamic and transport properties of hydrocarbons in mixtures40,41 and ZIFs.23 In TraPPE, the length of C-C single bonds is 1.54 Å, while the length of C=C double bonds is 1.33 Å. Harmonic potentials describe the change in angles between three interconnected atoms according to Eq. (2), while Lennard-Jones interactions account for the non-bonded inter- and intra-molecular interactions, according to Eq (4). The values for all the parameters of the TraPPE force-field for the guest molecules used in this work can be found in Tables 6 and 7. The Lorentz-Berthelot combining rules were used for the non-bonded interactions between different hydrocarbon atoms, as well as for the cross-interactions between guest and host atoms.

Table 6. Lennard-Jones parameters for propane and propylene in the TraPPE force field. Molecule Propane

Propylene

UA

σ (Å)

ε (kJ/mol)

CH3

3.750

0.8142

CH2 CH3 CH2 CH

3.950 3.750 3.675 3.730

0.3820 0.8142 0.7058 0.3904



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

Page 10 of 32

Table 7. Parameters of the TraPPE force field for the harmonic angle potential of propane and propylene. Molecule

θ0 (degrees)

kθ (kJ/mol)

Propane

114.0

519.2895

Propylene

119.7

585.0906

In our calculations, all the van der Waals interactions were subject to a 13Å cut-off, while the particle mesh Ewald method (PME) was used for the electrostatic interactions. We followed the 1-4 convention for the interactions between bonded atoms, which is a common choice for these systems in the literature.42

Methodology for the calculation of corrected diffusivities Propagation of diffusing species is characterized based on the corrected diffusivity, D0, of the species which connects the transport diffusivity with the so-called thermodynamic correction factor in the Darken equation43 through the expression:

1 (2) = 1 (2) 3

4 ln 7 8 4 ln 2 9

(5)

where 1 (2) is the transport diffusivity, f and c are the fugacity and concentration of adsorbed species, respectively. D0 describes the displacement of center of mass of the swarm of diffusing molecules. Being subject to larger error than the mean square displacement (MSD) of molecules, 10 Environment ACS Paragon Plus

Page 11 of 32

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


much larger simulation time is needed for the proper extraction of meaningful values for D0 compared to the self-diffusivity calculations. D0 for propane and propylene was calculated with the use of a methodology developed by Theodorou et al.,44 which has provided satisfactory results in simulations of gas diffusion in zeolites in the past:45

E

1 1 1 = lim 〈BC(#D (@) − #D (@ ))B 〉 6; →? @ F+

(6)

Estimation of corrected diffusivities using the Maxwell-Stefan model When the Langmuir adsorption model is applied, the Maxwell-Stefan model enables to estimate the single gas permeance through a microporous membrane using the following equation:9

H=

1 + PMN IJ1 K ln ( * L(MN − MO ) 1 + PMO

(7)

where H is the gas permeance, I is the constant accounting for the geometrical factor of a

membrane material, which is the ratio between material porosity (&) and tortuosity (Q), J is the density of the membrane material, 1 is the corrected diffusivity of gas species diffusing through

the membranes, K and P are the Langmuir isotherm constants, L is the membrane thickness, and MN

and MO are the feed and permeate side pressures of the membrane, respectively. Since the

permeating side of the membranes is constantly swept by an inert carrier gas to collect the gas permeation data (Wicke-Kallenbach technique, MO ~0), Eq. (7) is further simplified to: H=

IJ1 K lnT1 + PMN U LMN


(8)


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

Page 12 of 32

With knowledge of the constants and membrane permeation data, one can easily estimate the corrected diffusivities (1 ). The required values for the various properties are summarized in Table 8. In Figure 2, the Langmuir fit to collected adsorption isotherms of propane and propylene in ZIF67 is shown. It should be noted that binary gas permeation data were used to approximate the corrected diffusivities. The usage of the binary permeation data in conjunction with Eq. (8) is rationalized because the presence of a second gas rarely influences the diffusion of one gas in nanoporous materials with larger cages connected through smaller windows. Indeed, Krishna recently showed that the binary permeances of propylene and propane in ZIF-8 membranes can be accurately predicted even after neglecting correlations between two gases (i.e., based on single gas permeances).46


Page 13 of 32

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


Table 8. Summary of structural parameters and propylene and propane Langmuir adsorption constants (at 35oC) of ZIF-8 and ZIF-67, and propylene and propane gas permeation data through polycrystalline ZIF-8 and ZIF-67 membranes. Framework

ZIF-8

ZIF-67

&

0.58847

0.588a

K d

Pd

MN

L

(mmol/g)

(1/bar)

(bar)

(µm)

J

Q

(g/cm3)

1.7329

1.732a

0.94347

0.912b

C3=

C3

C3=

C3

6.368

5.5612

1.7212

2.5912

6.72c

6.06c

2.23c

3.67c

H

(x10-10 mol/m2·Pa·s) C3=

C3

Measured temperature (oC)

Ref.

0.5

1.5

207.88 ± 6.54

5.46 ± 1.45

25

12

0.5

1.5

212.66 ± 29.47

4.38 ± 0.57

25

10

0.5

0.8

268.52 ± 2.03

3.97 ± 0.79

25

13

0.5

1.5

308.96 ± 10.85

1.98 ± 0.40

25

15

a: Due to the structural similarities between ZIF-8 and ZIF-67, the & and Q values for ZIF-8 were adopted for ZIF-67. b: The density of ZIF-67 was calculated based on the number of atoms in a unit cell (Co: 12, C: 96, N:48, H: 120) and the cubic unit cell dimension of ZIF-67 (16.908 Å).8 c: Propylene and propane adsorption isotherms on ZIF-67 were collected at 35 oC as shown in Figure 2 and fitted based on the Langmuir adsorption model to extract the constants. d: The Langmuir adsorption constants obtained from the isotherms at 35 oC for both ZIF-8 and ZIF-67 were used as approximated values to

calculate

the

corrected

diffusivities

from

the

gas

permeation


data

collected

at

25

o

C.


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

Page 14 of 32

Figure 2. Propylene and propane adsorption isotherms of ZIF-67 at 35 oC.

Results and discussion The super cell used in the simulations was a 2×2×2 extension of the unit cell shown in Figure 1(b). This approach was used in order to achieve better statistics in the simulations. Structure visualization was done with the Discovery Studio Visualizer. 48 The Molecular Dynamics (MD) simulations were carried out with cubic boundary conditions applied in all three directions, in the NVT ensemble, with the Nosé-Hoover thermostat, employing a step of 1.0 fs.49,50 5 ns of simulation runs were used for the structural validation and multiple runs of 100 ns for the production of


Page 15 of 32

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


trajectories of the diffusing gases. The data were processed for the calculation of the corrected diffusivity, D0, and the results were compared with estimated corrected diffusivities from experiments carried out by our group. MD simulations were carried out using the GROMACS opensource molecular simulation platform (version 4.6.5).51 MD simulations in the NVT ensemble were conducted in empty ZIF-8 and ZIF-67 supercells (2×2×2 unit cells) using the newly derived force-fields, and structural parameters were measured. Two sets of simulations were done for each framework: the first was at 258 K for ZIF-8 and 153 K for ZIF-67 for a full structural comparison at the experimental temperature; the second set was at 295 K for both frameworks, which corresponds to the room temperature in which most diffusion experiments are carried out. Comparison of MD predictions with the experimental structure shows a very good agreement for all the representative bonds and angles, as can be seen in Table 9. Table 9. Comparison of representative bond lengths and bond angles of the ZIF-8 and ZIF-67 as extracted by MD simulations from [27] and this work, and experiments reported in literature.1,26

M* stands for metal atom; Zn in ZIF-8 and Co in ZIF-67, respectively.



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

Page 16 of 32

ZIF-8 and ZIF-67 have similar frames but ZIF-67’s aperture (3.31 Å) is smaller than ZIF-8’s (3.42 Å). This difference of approximately 0.1 Å, which agrees with experiments,1,26 persists at 295 K, as the results of Table 10 show. The smaller aperture size of ZIF-67 is expected to favor the propylene / propane sieving.

Table 10. Aperture size of ZIF-8 and ZIF-67 from experiments and MD simulations.

dZIF-8 (Å)

dZIF-67 (Å)

Experiments from [1] and [26] MD simulations corresponding to experimental temperature (258K for ZIF-8; 153K for ZIF-67)

~3.4

~3.3

3.42

3.31

MD simulations at 295K

3.44

3.35

For the calculation of corrected diffusivities in both frameworks, the reconstructed super cells of ZIF-8 and ZIF-67 were loaded with 80 propane and 72 propylene molecules, which corresponds to the loading of the experiments (about 10 and 9 molecules/u.c., respectively) carried by Kwon et al.15 Achieving low diffusivities such as those of propane at room temperature is a task that cannot be handled by conventional equilibrium MD calculations. An interesting approach developed by Verploegh et al.28 that measures hopping rates using dynamically corrected transition theory gives an accurate description of diffusion of hydrocarbon molecules (including propylene / propane) in ZIF-8. In this work, we calculated the corrected diffusivity, D0, of propane at elevated temperatures and derived the D0 at room temperature by extrapolation. Multiple MD runs were carried out at elevated temperatures, ranging from 400 K to 550 K. The whole process is computationally very demanding and time consuming since in order to achieve proper statistic for each value of D0 long runs are needed (multiple runs of 100 ns). The two Arrhenius plots for propane and propylene D0 in ZIF-8 16 Environment ACS Paragon Plus

Page 17 of 32

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


and ZIF-67 are shown in Figure 3(a) and 3(b), respectively. All D0 values of the plots are summarized in Table 11.

Figure 3. Arrhenius plot for D0 of propane (□) and propylene (■) in (a) ZIF-8 and (b) ZIF-67.

Table 11. D0 values of propane and propylene in ZIF-8 and ZIF-67 at various temperatures, as used in the Arrhenius plots of Figures 3(a) and (b).

T (K) 400 450 470 530 550

D0,C3H8 (m2/sec) ZIF-8 ZIF-67 -12 (1.0±0.3) × 10 (2.6±0.8) × 10-12 (3.0±0.3) × 10-13 (4.0±0.8) × 10-12 (5.0±0.3) × 10-13 (1±0.1) × 10-11 (1.2±0.3) × 10-12 (1.5±0.3) × 10-12

T (K) 295 330 350 370 430 470

D0,C3H6 (m2/sec) ZIF-8 ZIF-67 -12 (1.9±0.5) × 10 (2.8±0.1) × 10-13 (5.3±0.9) × 10-12 (6.0±0.5) × 10-13 (1.0±0.3) × 10-12 (8.0±0.8) × 10-12 (1.8±0.4) × 10-11 (4.0±1.0) × 10-12 (3.5±0.9) × 10-11 (7.0±2.0) × 10-12

The calculation of corrected diffusivities is subject to higher uncertainty than the calculation of self-diffusivities - a fact reflected in the results of Table 11. In Table 12, estimated D0 based on previously reported membrane permeation data for both ZIF-8 and ZIF-67 by Kwon et al12,15 are provided, following the procedure presented in the previous section (Maxwell-Stefan Model). The experimental and simulation results for ZIF-8 agree with each other. Our results show that propane 17 Environment ACS Paragon Plus


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

Page 18 of 32

and propylene diffuse in both ZIF frameworks in spite of having size larger (>4.0 Å) than the aperture accessing the pores. These results suggest that our force fields and model are reliable for these demanding calculations and predict framework flexibility satisfactorily. Simulations and experiments agree that, in ZIF-8, propane’s diffusion is 30 to 60 times slower than propylene’s. Moreover, our propylene / propane D0 values in ZIF-8 compare well with propylene / propane selfdiffusivities (Ds) from molecular simulations by Verploegh et al. 28 (D0 and Ds are expected to be of the same order of magnitude and, at very low loadings, be equal44). The ratio of propylene / propane D0 in ZIF-67 is larger, on the order of 190, as propane has hindered motion in the tighter environment of the modified frame. This result agrees with our experimentally estimated D0 values on membranes, placing ZIF-67 at the top of the existing candidates for propylene / propane separation. Table 12. Corrected diffusivities, D0, of C3H8 and C3H6 from this work (MD simulations and experimental data) and comparison with experiments from literature (all values correspond to room temperature). D0 (m2/sec)

Simulations ZIF-8 This work

Expt. data*

C 3H 8

C 3H 6

D0, C3H6 / D0, C3H8

(4.0±1.5)×10-14

(1.8±0.1) ×10-12

45±3

(2.22±0.29)×10-14

(1.26±0.17)×10-12

57±5

(2.77±0.74)×10-14

(1.23±0.04)×10-12

46±10

(1.07±0.21)×10-15

(0.85±0.04)×10-13

80±13

ZIF-8

[9]

3.70×10-14

1.21×10-12

32.7

Literature expt.

[14]

1.1×10-14

1.2×10-12

109

ZIF-67

Simulations

(1.5±0.5)×10-15

(2.8±0.1) ×10-13

190±5


Page 19 of 32

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


This work *

Expt. data*

(0.76±0.15)×10-15

(1.49±0.05)×10-12

200±38

The estimations were based on ZIF-8 ([10] [12] [13]) and ZIF-67 [15] reported data.

Simulations at elevated temperatures were extended in the same manner for the diffusion of propylene in both ZIF-8 and ZIF-67 and corrected diffusivities were calculated as shown in Table 11. The activation energies of diffusion of both species were extracted from the Arrhenius plots. The comparison of the activation energies of propane and propylene in ZIF-8 with experimental findings9,10 in Table 13 shows a very good agreement: propane has more restricted motion than propylene, and has to overcome higher energy barriers (appproximately 31 kJ/mol) when propagating in ZIF-8. Similar findings hold for ZIF-67, where propane’s activation energy (approx. 39 kJ/mol) is higher than propylene’s (approximately 20 kJ/mol). Table 13. Activation energies of diffusion as-calculated by simulations from this work, along with experimentally reported values*

ZIF-8

ZIF-67

EC3H8 (kJ/mol)

EC3H6 (kJ/mol)

Experiments [9]

38.8

12.7

Experiments [10]

26.6

15.1

MD simulations

31±2

17±2

MD simulations

39±4

20±1

*

available only for ZIF-8

In order to infer the separation mechanism of this mixture, the sorption affinity of the two species was estimated. The Widom test particle insertion method52 was employed for the calculation of the Henry constant, K, of propane and propylene in both ZIF-8 and ZIF-67. The calculations were extended over a wide range of temperatures and the logarithmic values, lnK, were plotted against 1/T separately for ZIF-8 and ZIF-67 cases, in Figures 4(a) and 4(b), respectively. The 19 Environment ACS Paragon Plus


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

Page 20 of 32

isosteric heats of adsorption were extracted from the slope of the Arrhenius plot. The results for ZIF-8 show that propane and propylene demonstrate equal affinity with the framework, yielding a similar soprtion behavior. These results agree with findings from literature,10, 53 which report equivalent isosteric heats of adsorption for propane and propylene in ZIF-8 (Table 14). The same behavior is observed in ZIF-67; the similar isosteric heats of adsorption (Table 14) and adsorption isotherms (Figure 2) reveal an equivalent adsorption behavior of the two species in ZIF-67. It should be noticed that the slight increased sorption of propane against propylene at low pressure agrees with the slightly higher calculated propane isosteric heat, which reflects slightly higher guest-host interaction for propane against propylene. Overall, the big differences in propane/propylene activation energies, which are accompanied by a similar sorption affinity, define their separation in ZIF-8/ZIF-67 as kinetic-driven. The excellent overall agreement of the calculations with the various experimental data reported shows the efficieny of our model in reproducing the proper flexible behavior of the studied ZIF materials.

Figure 4. Arrhenius plot for of Henry constants of propane (□) and propylene (■) in (a) ZIF-8 and (b) ZIF-67, calculated from molecular simulation.


Page 21 of 32

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 14. Isosteric heats of adsorption as calculated by simulations from this work, along with experimentally reported values.*

ZIF-8

ZIF-67

EC3H8 (kJ/mol)

EC3H6 (kJ/mol)

Experiment [10]

18.9

18.4

Experiment [53]

30

34

Molecular simulation

25.9

26.3

Molecular simulation

26.4

25.0

*

available only for ZIF-8

Figure 5. Distribution of the aperture sizes observed in MD runs of 10 ns. The vertical axis is normalized and corresponds to an area of unity: (a) ZIF-67 (filled black line) and ZIF-8 (openspaced line at 295 K), (b) ZIF-8 aperture and (c) ZIF-67 aperture response upon heating (blue line: 295 K, orange line: 530 K). An investigation of the aperture behavior of the empty cells of ZIF-8 and ZIF-67 was carried out during the molecular simulations by measuring the size of the aperture that connects adjacent cages and recording the frequency. Figure 5 shows that the aperture of the framework fluctuates with a



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

Page 22 of 32

swelling-like motion, giving a mean value that matches the experiments. This behavior agrees with the findings of Haldoupis et al.54 ZIF-67 exhibits a sharper distribution with the fluctuation shifting to lower aperture values, resulting in a smaller diameter (Figure 5(a)). The limiting molecular size and the sieving abilities of the ZIFs should be connected to the maximum value observed of the oscillation and not to the mean value observed in experimental XRD measurements. The difference observed between the tails of the two distributions explains the favored diffusion of the slightly smaller propylene against propane. No dependency of the aperture size was observed upon the presence of sorbed molecules. On the other hand, a strong dependency on temperature is observed. Although the mean size remains nearly constant upon heating, the fluctuation width increases for both ZIF-8 and ZIF-67 (Figure 5 (b) and (c)). This finding agrees with the recent experiments by Kolokov et al., whose 2H NMR results for ZIF-8 show a clear oscillation of the ligands (described as “saloon door” motion), with pronounced increasing amplitude upon temperature increase. 55 Another comparison yields a sound agreement: the maximum aperture size of ZIF-8 at 530 K observed in our simulations is approx. 4.6 Å; Kolokov et al. report a maximum aperture of approx. 4.7 Å at approx. 550 K. The factor that governs the aperture stiffness and the gate fluctuation/opening is the bonding of Zn/Co atoms with the N atoms shown in Figure 6. This is reflected in the parameters of the potential for the bond Zn/Co-N and angle N-Zn/Co-N, which in the case of Co are higher. Especially the K constant of the harmonic angle in the case of Co-ZIF takes a value almost 3 times higher than in the case of Zn-ZIF (see Tables 1 and 3), making this angle much stiffer. This observation is in agreement with spectroscopic evidences (i.e., IR and NMR spectra) by Kwon et al.14, who pointed out that the separation enhancement in ZIF-67 occurs because of the restricted ligand flipping motion in ZIF-67 when compared to ZIF-8, due to the stiffer Co-N bonds.


Page 23 of 32

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


Figure 6. Aperture leading to the cage of ZIF-8/67. The N-Zn/Co-N angle flexibility governs the aperture size response in the model that we propose. Conclusions A new force-field for the ZIF-67 structure has been developed following a methodology presented recently for the development of a ZIF-8 force field. The force field is used to provide for the first time simulations results for the ZIF-67 framework. Important structural parameters (bond lengths and angles) were predicted with high accuracy for both ZIF-8 and ZIF-67 frameworks, using the two force fields. The critical aperture size of the two frameworks has a difference of approx. 0.1 Å from each other, which agrees with experimental measurements from the literature. Furthermore, the computational and experimental results reported here show a dramatic increase of the propylene / propane separation in the ZIF-67, which places it on the top of the existing candidates for this highly demanding separation. The fluctuation of the aperture size covers a range whose maximum value is temperature dependent, and which determines the maximum molecule size that can pass through the pores. Our model shows that this maximum aperture value can be tailored by metal atom replacement, because the bonding of the metal atom (Zn/Co) with the



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

Page 24 of 32

neighboring N atoms controls it. The significance of the Metal-N bonding agrees with recent experimental findings by Kwon et al.14 Additionally, the model we propose reproduces an oscillatory motion of the ligands that agrees with recently reported experiments.55

ACKNOWLEDGMENT This publication was made possible by NPRP grant number 7–042–2–021 from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the authors. We are grateful to the High Performance Computing Center of Texas A&M University at Qatar for generous resource allocation. H.-K.J. acknowledges the financial support from the National Science Foundation (CBET-1132157, CBET-1510530). H.-K.J. and J.S.L. would like to acknowledge the financial support from the R&D Convergence Program of MSIP (Ministry of Science, ICT and Future Planning) and NST (National Research Council of Science & Technology) of Republic of Korea (CRC-14-1-KRICT). H.-K.J. and H.K. are grateful to Mr. He Seong An at Korea University for his support on the measurements of adsorption isotherms.


Page 25 of 32

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


References (1) Park, K. S.; Ni Z.; Cote A. P.; Choi J. Y.; Huang R.; Uribe-Romo, F. J.; Chae, H. K.; O’Keeffe, M.; Yaghi, O. M. Exceptional Chemical and Thermal Stability of Zeolitic Imidazolate Frameworks. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 10186-10911. (2) Li, J. R.; Ma, Y.; McCarthy, M. C.; Sculley, J.; Yu, J.; Jeong, H. K.; Balbuena, P. B.; Zhou, H. C. Exceptional Chemical and Thermal Stability of Zeolitic Imidazolate Frameworks. Chem. Rev. 2011, 255, 1791-1823. (3) Bux, H.; Chmelik, C.; Krishna, R.; Caro, J. Ethene/Ethane Separation by the MOF Membrane ZIF-8: Molecular Correlation of Permeation, Adsorption, Diffusion. J. Membr. Sci. 2011, 369, 284289. (4) Gücüyener, C.; Van Den Bergh, J.; Gascon, J.; Kapteijn, F. Ethane/Ethene Separation Turned on Its Head: Selective Ethane Adsorption on the Metal−Organic Framework ZIF-7 through a GateOpening Mechanism. J. Am. Chem. Soc. 2010, 132, 17704-17706. (5) Diestel, L.; Bux, H.; Wachsmuth, D.; Caro, J. Pervaporation Studies of n-hexane, Benzene, Mesitylene and their Mixtures on Zeoolitic Imidazolate Framework-8 Membranes. Micropor. Mesopor. Mater. 2012, 164, 288-293. (6) Ma, X. L.; Lin, B. K.; Wei, X. T.; Kniep, J; Lin, Y. S. Gamma-Alumina Supported Carbon Molecular Sieve Membrane for Propylene/Propane Separation. Ind. Eng. Chem. Res. 2013, 52, 4297-4305. (7) Bernardo, P.; Drioli, E.; Golemme, G. Membrane Gas Separation: A Review/State of the Art. Ind. Eng. Chem. Res. 2009, 48, 4638-4663.



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

Page 26 of 32

(8) Zhang, C.; Lively, R. P.; Zhang, K.; Johnson, J. R.; Karvan, O.; Koros, W. Unexpected Molecular Sieving Properties of Zeolitic Imidazolate Framework-8. J. Phys. Chem. Lett. 2012, 3, 2130-2134. (9) Liu, D.; Xiaoli, M.; Hongxia X.; Lin, Y. S. Gas Transport Properties and Propylene/Propane Separation Characteristics of ZIF-8 Membranes. J. Membr. Sci. 2014, 451, 85-93. (10) Hara, N.; Yoshimune, M.; Hideyki, N.; Haraya, K.; Hara, S.; Yamaguchi, T. Diffusive Separation of Propylene/Propane with ZIF-8 Membranes. J. Membr. Sci. 2014, 450, 215-223. (11) Kwon, H. T.; Jeong, H.-K. In Situ Synthesis of Thin Zeolitic-Imidazolate Framework ZIF-8 Membranes Exhibiting Exceptionally High Propylene/Propane Separation. J. Amer. Chem. Soc. 2013, 135, 10763-10768. ( 12 ) Kwon, H. T.; Jeong, H.-K.; Highly Propylene-selective Supported Zeolite-imidazolate Framework (ZIF-8) Membranes Synthesized by Rapid Microwave-assisted Seeding and Secondary Growth. Chem. Comm. 2013, 49, 3854-3856. (13) Kwon, H. T.; Jeong, H.-K. Improving propylene/propane separation performance of ZeoliticImidazolate framework ZIF-8 Membranes. Chem. Eng. Sci. 2015, 124, 20-26. (14 ) Pan, Y.; Liu, W.; Zhao, Y.; Wang, C.; Lai, Z. Improved ZIF-8 Membrane: Effect of Activation Procedure and Determination of Diffusivities of Light Hydrocarbons. J. Membr. Sci. 2015, 493, 88-96. (15) Kwon, H. T.; Jeong, H.K.; Lee, A. S.; An, H. S.; Lee, J. S. Heteroepitaxially Grown Zeolitic Imidazolate

Framework

Membranes

with

Unprecedented

Performances. J. Am. Chem. Soc. 2015, 137, 12304-12311.


Propylene/Propane

Separation

Page 27 of 32

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


(16) Seehamart, K.; Nanok, T.; Krishna, R.; van Baten, J. M.; Remsungnen, T.; Fritzsche, S. A Molecular Dynamics Investigation of the Influence of Framework Flexibility on Self-diffusivity of Ethane in Zn(tbip) Frameworks. Microporous Mesoporous Mater. 2009, 125, 97-100. (17) Hertag, L.; Bux, H.; Caro, J.; Chmelik, C.; Remsungen, T.; Knauth, M.; Fritzsche, S. Diffusion of CH4 and H2 in ZIF-8. J. Membr. Sci. 2011, 377, 36-41. (18) Battisti, A.; Taioli, S.; Garberoglio, G. Zeolitic Imidazolate Frameworks for Separation of Binary Mixtures of CO2, CH4, N2 and H2: A Computer Simulation Investigation. Microporous Mesoporous Mater. 2011, 143, 46-53. (19) Mayo, S. L.; Olafson, B. D.; Goddard, W. A. DREIDING: a Generic Force Field for Molecular Simulations. J. Phys. Chem. 1990, 94, 8897-8909. (20) Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A., III; 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. (21) Pantatosaki, E; Megariotis, G.; Pusch, A. K.; Chmelik, C.; Stallmach, F; Papadopoulos, G. K. On the Impact of Sorbent Mobility on the Sorbed Phase Equilibria and Dynamics: A Study of Methane and Carbon Dioxide within the Zeolite Imidazolate Framework-8. J. Phys. Chem. C 2012, 116, 201-207. (22) Zheng, B.; Sant, M; Demontis, P.; Suffritti, G. B. Force Field for Molecular Dynamics Computations in Flexible ZIF-8 Framework. J. Phys. Chem. C 2012, 116, 933-938. (23) Chokbunpiam, T.; Chanajaree, R.; Saengsawang, O; Reimann S.; Chmelik. C.; Fritzsche S.; Caro, J.; Remsungnen, T.; Hannongbua, S. The Importance of Lattice Flexibility for the Migration 27 Environment ACS Paragon Plus


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

Page 28 of 32

of Ethane in ZIF-8: Molecular Dynamics Simulations. Microporous Mesoporous Mater. 2013, 174, 126-134. (24) Wu, X.; Huang, J.; Cai, W.; Jaroniec, M. Force field for ZIF-8 Flexible Frameworks: Atomistic Simulation of Adsorption, Diffusion of Pure Gases as CH4, H2, CO2 and N2. RSC Adv. 2014, 4, 16503-16511. (25) Zheng, B.; Pan, Y.; Lai, Z.; Huang, K. W. Molecular Dynamics Simulations on Gate Opening in ZIF-8: Identification of Factors for Ethane and Propane Separation. Langmuir 2013, 29, 8865-8872. (26) Banerjee, R.; Phan, A.; Wang, B; Knobler, C.; Furukawa, H.; O’Keefee, M.; Yaghi, O. M. High-throughput Synthesis of Zeolitic Imidazolate Frameworks and Application to CO2 capture. Nature 2008, 319, 939-943. (27) Krokidas. P.; Castier, M.; Moncho, S.; Brothers, E.; Economou, I. G. Molecular Simulation Studies of the Diffusion of Methane, Ethane, Propane, and Propylene in ZIF-8. J. Phys. Chem. C 2015, 119, 27028-27037. (28) Verploegh, R. J.; Nair, S.; Sholl, D. S. Temperature and Loading-Dependent Diffusion of Light Hydrocarbons in ZIF-8 as Predicted Through Fully Flexible Molecular Simulations. J. Am. Chem. Soc. 2015, 137, 15760-15771. (29) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A. Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A., et al. Gaussian 09, Revision D.01; Gaussian Inc.: Wallingford CT, 2013. (30) Becke, A. D. Density-functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648-5652.


Page 29 of 32

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


( 31 ) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-energy Formula into a Functional of the Electron-density. Phys. Rev. B 1988, 37, 785-789. (32) Lin, F.; Wang, R. Systematic Derivation of AMBER Force Field Parameters Applicable to Zinc-Containing Systems. J. Chem. Theory Comput. 2010, 6, 1852-1870. ( 33 ) Seminario, J. M. I. Calculation of Intramolecular Force Fields from Second-derivative Tensors. J. Quantum Chem. 1996, 60, 1271-1227. (34) Wang, J.; Wang, W.; Kollman P. A.; Case, D. A. Automatic Atom Type and Bond Type Perception in Molecular Mechanical Calculations. J. Mol. Graph. Model. 2006, 25, 247-260. (35) Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and Testing of a General Amber Force Field. J. Comput. Chem. 2004, 25, 1157-1174. ( 36 ) Singh, U. C.; Kollman, P. A. An Approach to Computing Electrostatic Charges for Molecules. J. Comp. Chem. 1984, 5, 129-145. (37) Besler, B. H.; Merz, K. M. Jr.; Kollman, P. A. Atomic Charges Derived from Semiempirical Methods. J. Comp. Chem. 1990, 11, 431-439. (38) Duan, Y.; Wu, C.; Chowdhury, S.; Lee, M. C.; Xiong, G.; Zhang, W.; Yang, R.; Cieplak, P.; Luo, R.; Lee, T.; et al. A Point-charge Force Field for Molecular Mechanics Simulations of Proteins Based on Condensed-phase Quantum Mechanical Calculations. J. Comput. Chem. 2003, 24, 19992012. (39) Hertag, L.; Bux, H.; Caro, J.; Chmelik, C.; Remsungen, T.; Knauth, M.; Fritzsche, S. Diffusion of CH4 and H2 in ZIF-8. J. Membr. Sci. 2011, 377, 36-41.



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

Page 30 of 32

(40) Michalis, V. K., Moultos, O. A., Tsimpanogiannis, I. N. and Economou, I. G. Molecular Dynamics Simulations of the Diffusion Coefficients of Light n-Alkanes in Water Over a Wide Range of Temperature and Pressure. Fluid Phase Equilib. 2016, 407, 236-242. ( 41 ) Makrodimitri, Z. A.; Unruh. D. J. M.; Economou, I. G. Molecular Simulation and Macroscopic Modeling of the Diffusion of Hydrogen, Carbon Monoxide and Water in Heavy nAlkane Mixtures. Phys. Chem. Chem. Phys. 2012, 14, 4133-4141. (42) Zheng, B.; Sant, M; Demontis, P.; Suffritti, G. B. Force Field for Molecular Dynamics Computations in Flexible ZIF-8 Framework. J. Phys. Chem. C 2012, 116, 933-938. (43) Darken, L. S. Diffusion, Mobility and their Interrelation through Free Energy in Binary Metallic Systems, Trans. AIME 1948, 175, 184-201. (44) Theodorou, D. N.; Snurr, R. Q.; Bell, A. T. Comprehensive Supramolecular Chemistry; Pergamon Press: New York, 1996. (45) Skoulidas, A. I.; Sholl, D. S. Transport Diffusivities of CH4, CF4, He, Ne, Ar, Xe, and SF6 in Silicalite from Atomistic Simulations. J. Phys. Chem. B 2002, 106, 5058-5067. (46) Krishna, R. The Maxwell-Stefan Description of Mixture Diffusion in Nanoporous Crystalline Materials. Microporous and Mesoporous Materials 2014, 185, 30-50. (47) Tan, J. C.; Bennett, T. D.; Cheetham, A. K. Chemical Structure, Network Topology, and Porosity Effects on the Mechanical Properties of Zeolitic Imidazolate Frameworks. Proc. Nat. Acad. Sci. USA 2010, 107, 9938-9943. (48) Discovery Studio Modeling Environment, Release 4.5, San Diego: Dassault Systèmes, 2015.


Page 31 of 32

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


(49) Nosé, S. A Molecular Dynamics Method for Simulations in the Canonical Ensemble. Mol. Phys. 1984, 52, 255-268. (50) Hoover, W. G. Canonical Dynamics: Equilibrium Phase-space Distributions. Phys. Rev. A 1985, 31, 1695-1697. (51) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theor. Comput. 2008, 4, 435-447. (52) Widom, B. Some Topics in the Theory of Fluids. J. Chem. Phys. 1963, 39, 2808-2812. (53) Li, K.; Olson, H. D.; Seidel, J.; Emge, J. T.; Gong, H.; Zeng, H.; Li, J. Zeolitic Imidazolate Frameworks for Kinetic Separation of Propane and Propene. J. Am. Chem. Soc. 2009, 131, 1036810369. (54) Haldoupis, E.; Watanabe, T.; Nair, S.; Sholl, D. S. Quantifying Large Effects of Framework Flexibility on Diffusion on MOFs: CH4 and CO2 in ZIF-8. Chem. Phys. Chem. 2012, 13, 34493452. (55) Kolokov, D. I.; Stepanov, A. G.; Jobic, H. Mobility of the 2-Methylimidazolate Linkers in ZIF-8 Probed by 2H NMR: Saloon Doors for the Guests. J. Phys. Chem. C 2015, 119, 27512-27520.



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


Page 32 of 32

ZIF-67 Framework: A Promising New Candidate for Propylene

Recommend Documents