as a Tool for the Design of Metal-Organic Framework Materials Supporting Information

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1 Evaluation of Ideal Adsorbed Solution Theory as a Tool for the Design of Metal-Organic Framework Materials Supporting Information Naomi F. Cessford, Tina Düren,, and Nigel A. Seaton Institute for Materials and Processes, School of Engineering, The University of Edinburgh, King s Buildings, Mayfield Road, Edinburgh, EH9 3JL, United Kingdom University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom Details of definition of distinct sites for application of Heterogeneous Ideal Adsorbed Solution Theory (HIAST) In order to account for the large-scale heterogeneities in the structures of MIL-68 and Cu-BTC which contain more than one pore type, HIAST can be applied. Implementation of HIAST requires that individual sites corresponding to different pore types in the metalorganic framework (MOF) are defined. This can be achieved by creating a sitemap S1

2 which takes the form of a three-dimensional grid with 0.1 Å spacing. Since different pore types represent distinct sites, by assigning each site a different number, the pores in the MOF can be allocated a site number. By defining mathematical inequalities relating to the boundaries of the pores, each grid point on the sitemap can be assigned a number corresponding to the site (e.g. type of pore) within which it is positioned. Thus, for MIL- 68, where the smaller, triangular pores constitute one site and the larger, hexagonal pores represent a second site, using inequalities to distinguish between pores, a sitemap can be produced detailing the locations of the individual sites. When the adsorption simulation data are processed, the sitemap can be incorporated to obtain isotherms which describe the adsorption on separate sites. Sites in Cu-BTC can be defined using the same method, with the tetrahedral side pockets representing one site, and the two main cavities forming a second site. Figure S1. MIL-68 unit cell showing the adsorption sites available to a methane molecule where all areas colored red represent one site (larger, hexagonal pores) and all areas colored green represent a second site (smaller, triangular pores). The positions occupied by the framework atoms (i.e. where adsorption is not possible for methane) are colored white. S2

3 Table S1. Lennard-Jones parameters for atoms in the adsorbents studied, where ε is the LJ well depth, k B is the Boltzmann constant, and σ is the atomic diameter. Parameters were taken from the Universal Force Field. 1 Framework Atom σ (Å) ε/k B (K) H C O Zn Cu V Table S2. Partial charges on framework atoms in the MOFs studied. Framework Atom IRMOF-1 Cu-BTC MIL-68 MIL-47 C C C O O H Zn Cu V S3

4 Figure S2. Selectivity for methane from an equimolar mixture of methane and hydrogen as a function of pressure in Cu-BTC at 300 K. Figure S3. Comparison of adsorption selectivity values for CH 4 from an equimolar mixture of CH 4 and H 2 and for CF 4 from an equimolar mixture of CF 4 and CH 4 in the respective pores in Cu-BTC as calculated from GCMC simulations. S4

5 Figure S4. Selectivity for from an equimolar mixture of and CF 4 as a function of pressure in IRMOF-1, Cu-BTC, MIL-68, MOF-69A and MIL-47 at 300 K. S5

6 Fitting Parameters for Single-Component Isotherms c KP n( P) = KP 1+ (1 P) α + κ denotes piece-wise fitting used to accurately represent entire pressure range. Parameters given fit the data in the highest pressure piece. Table S3. Fitting parameters for IRMOF-1 1/ c K α κ c H 2 /CH 4 CH 4 /CF 4 CH 4 / CF 4 / CH 4 / H E CH E CH E-09 2 CF E CH E E CF E As for CH 4 / mixture CH E C 2 H E CH E C 3 H E /C 3 H 8 C 3 H E As C 3 H 8 for mixture CO E H E CO E (CO 2-CO 2 electrostatics off) H 2 As H 2 for mixture S6

7 Table S4. Piece-wise fitting parameters for IRMOF-1 A 1 A 2 A 3 A 4 A 5 Pressure Limit (kpa) CH 4 / CH 4 / /C 3 H 8 (a) (a) (a) C 3 H 8 C 3 H 8 (a) CO 2 (a) E E E E E (a) A2 A4 n ( P) = A1 P + A3 P n( P) = A1 P 1+ A 2 A1 P (1 A3 P) + A 4 1/ A 4 S7

8 Table S5. Fitting parameters for Cu-BTC K α κ c H 2 /CH 4 CH 4 /CF 4 CH 4 / CF 4 / CH 4 / H E CH E CH E CF E CH E E-06 1 CF E SF E CH E C 2 H E CH E C 3 H E /C 3 H 8 C 3 H E As C 3 H 8 for mixture CO E H E CO E (CO 2-CO 2 electrostatics off) H 2 As H 2 for mixture S8

9 Table S6. Piece-wise fitting parameters for Cu-BTC A 1 A 2 A 3 A 4 A 5 Pressure Limit (kpa) H 2 /CH 4 CH 4 /CF 4 CH 4 / CF 4 / CH 4 / /C 3 H 8 (CO 2-CO 2 electrostatics off) (c) CH 4 CH 4 CF 4 CH 4 (d) CH 4 (a) (a) C 3 H 8 CO 2 CO E E E E E E E E E (c) A1 A2 P n( P) = (1+ A P) 2 A 3 (d) n ( P) = A1 P+ A2 P + A3 P + A4 P + A5 P S9

10 Table S7. Fitting parameters for MIL-68 K α κ c H 2 /CH 4 CH 4 /CF 4 CH 4 / CF 4 / CH 4 / H E CH E CH E CF E CH E E CF E As for CH 4 / mixture CH E C 2 H E CH E C 3 H E /C 3 H 8 C 3 H E As C 3 H 8 for mixture CO E H E E CO E (CO 2-CO 2 electrostatics off) H 2 As H 2 for mixture S10

11 Table S8. Piece-wise fitting parameters for MIL-68 A 1 A 2 A 3 A 4 A 5 Pressure Limit (kpa) CH 4 / CH 4 / /C 3 H 8 (CO 2-CO 2 electrostatics off) CH 4 CH 4 (e) C 3 H 8 CO 2 CO E E E E E E (e) n ( P) = A1 + A2 P+ A3 P + A4 P + A5 P S11

12 Table S9. Fitting parameters for MOF-69A K α κ c H 2 /CH 4 CH 4 /CF 4 CH 4 / CF 4 / CH 4 / H E E CH E CH E CF E CH E E CF E As for CH 4 / mixture CH E C 2 H E CH E C 3 H E /C 3 H 8 C 3 H E As C 3 H 8 for mixture S12

13 Table S10. Piece-wise fitting parameters for MOF-69A A 1 A 2 A 3 A 4 A 5 Pressure Limit (kpa) CH 4 /CF 4 CH 4 / CH 4 / /C 3 H 8 CF 4 C 3 H E E E E E S13

14 Table S11. Fitting parameters for MIL-47 K α κ c H 2 /CH 4 CH 4 /CF 4 CH 4 / CF 4 / CH 4 / H 2 5.6E E CH E CH E CF E CH E E CF E As for CH 4 / mixture CH E C 2 H E CH E C 3 H E /C 3 H 8 C 3 H E As C 3 H 8 for mixture CO E H 2 5.7E E CO E (CO 2-CO 2 electrostatics off) H 2 As H 2 for mixture S14

15 Table S12. Piece-wise fitting parameters for MIL-47 A 1 A 2 A 3 A 4 A 5 Pressure Limit (kpa) CH 4 / CH 4 / /C 3 H 8 C 3 H 8 CO E E E E E References (1) Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A.; Skiff, W. M. Uff, A Full Periodic-Table Force-Field For Molecular Mechanics And Molecular-Dynamics Simulations. J. Am. Chem. Soc. 1992, 114, S15