Porous Organic Cages for Sulfur Hexafluoride Separation

A series of porous organic cages is examined for the selective adsorption of sulfur hexafluoride (SF6) over nitrogen. Despite lacking any metal sites, a porous cage, CC3, shows the highest SF6/N2 selectivity reported for any material at ambient temperature and pressure, which translates to real separations in a gas breakthrough column. The SF6 uptake of these materials is considerably higher than would be expected from the static pore structures. The location of SF6 within these materials is elucidated by X-ray crystallography, and it is shown that cooperative diffusion and structural rearrangements in these molecular crystals can rationalize their superior SF6/N2 selectivity.

θ to improve powder averaging. Gas was dosed into the system, initially to 2.7 bar and then 3 bar.
Samples were allowed to equilibrate at both pressures for approximately of 45 minutes after gas was dosed into the cell. PXRD data were collected during this time to monitor equilibration. The sample was then evacuated at 373 K under dynamic vacuum and the powder profile collected to confirm removal of the guest from the pore structure.

Single crystal data
Evacuated prism shaped single crystals of CC3α were exposed to dry SF 6 at 1 bar pressure (BOC, CAS number: 2551-62-4, material number: 112049-BC, minimum purity 99.9 %). The crystals were transferred to a sample vial and stored in air for 28 hours before a single crystal data collection was recorded.
For CC3-S•(SF 6 ) 2.5 •(H 2 O) 3 there are two complete crystallographically distinct CC3-S molecules in the asymmetric unit. Well-ordered, fully occupied SF 6 molecules, were found in the intrinsic cavity of each of these cages. In CC3-S•(SF 6 ) 2.5 •(H 2 O) 3 the crystal packing of CC3-S is isostructural with CC3α, the change in crystallographic symmetry arises due to the ordered positioning of SF 6 molecules in the crystal lattice. Electron density, located in the four crystallographically distinct cage windows, was poorly resolved. Electron density in these four regions was modelled as partially occupied SF 6 molecules, with a tentative site occupancies of between 11 -13 % determined using free variables. For these four partially occupied SF 6 molecules bond length restraints were used during refinement (DFIX and SADI in SHELX), and these molecules were refined isotropically with constrained displacement parameters (EADP in SHELX). Addition electron density located in the cage windows, and in close proximity to the imine N-atoms (~ 2.9 Å), was modelled as partially occupied H 2 O molecules. These H 2 O molecules, that have comparable N-O distances to those determined in a previous study for a water loaded CC3 crystal structure, 6 were absorbed from air. For CC3-S, two cyclohexyl rings were refined with rigid-body restraints (RIGU in SHELX). For a displacement ellipsoid plot of the asymmetric unit, see Figure S4.

Metadynamics simulation details
A 100 ns well-tempered metadynamics simulation was performed with DL_POLY2.20 8 and PLUMED2. 9 The input files for DL_POLY2.20 have been generated with DL_FIELD3.3. 10 The OPLS-AA force field parameters, 11 the Leapfrog Verlet algorithm 12 with a timestep of 0.5 fs was used. The Nose-Hoover thermostat 13 was used to keep the temperature fixed at 300 K and no interactions were applied between periodic images in a cubic system with cell length 39 Å. A timestep of 0.5 fs with sampling step of 1 ps was chosen and full molecular motion was allowed throughout the simulation. The collective variable along which the metadynamics bias was accumulated measured the distance between center of mass of the CC3 and the sulfur atom of the SF 6 . Gaussian hills with a width of 0.15 nm and an initial height of 1.2 kJ mol -1 were added every 500 MD steps and the so-called well-tempered factor was set equal to 10. The free energy surface was calculated using the 'sum_hills' utility of PLUMED2 with the minimum shifted to zero.
An addition well-tempered metadynamics using two collective variables (the distance and a torsion angle) was performed to analyse the mechanism further. The calculation of the torsion angle is complicated in this case because of the symmetries of the SF 6 and cage molecules so a new collective variable (CV), SF6ANGLE was written for PLUMED. When evaluating this variable we first calculate the vector, V, connecting the center of mass of the cage to the sulfur atom. The projections of the vectors connecting the centers of mass of the cage to each of the centers of mass of the six pendant cyclohexane molecules were then evaluated. For the majority of configurations only three of these projections should be positive. Furthermore, the three cyclohexanes for which the projections are positive surround the face of octahedral cage through which the SF 6 would escape if it were to continue to move away from the center of the cage along the vector V. We thus identify the three cyclohexane groups with the largest projections and calculate three angles. These measure the angle between the plane containing each of the identified cyclohexanes, the center of mass of the three identified cyclohexanes and the sulfur atom and the plane containing the sulfur atom, the center of mass of the three identified cyclohexanes and the fluorine atom that is furthest from the center of the cage. The final collective variable is the angle whose absolute value is the smallest. As illustrated in S4 Figure 2 of the main paper we can think of this quantity as the angular offset between the triangle of fluorine atoms that escape the cage first and the triangular window through which the SF 6 is escaping. The free energy surface shown in Figure 2 was obtained from a 10ns well-tempered metadynamics simulation with the same molecular dynamics parameters as described previously and the PLUMED2 input file shown below. In this input the Actions labelled ch* calculate the positions of the centers of mass of each of the 6 pendant cyclohexane groups. The atom numbers from 1-168 are the atoms that form the CC3 molecule, 169 is the sulfur atom and 170-175 are the fluorine atoms. The free energy surface shown in the paper was generated using the 'sum_hills' of PLUMED2 and the minimum was shifted to zero. The additional code SF6ANGLE required for PLUMED2 is supplied as a supplementary file.

Window size analysis
The pore envelopes shown in Figure 3e represent the dynamical change of the cage windows' diameter throughout the simulation. The reference values (black) were calculated for an MD simulation of an isolated and empty CC3 molecule. The resulting trajectory is further analysed with an in-house python script that recognises the three carbon atoms circumscribing each window (method as described by Holden et al.). 14 These dimensions are calculated at every step of the MD simulation and then a window histogram generated. Next, the trajectory from the CC3/SF 6 metadynamics simulations was analysed with the same method, but only using those sampled configurations where the SF 6 was in the following locations. The first pore envelope (green) has been calculated for the SF 6 positioned in the S5 centre of the cage, defined as the distance range of 0 -2.0 Å between the sulphur atom of the SF 6 and the centre of mass of the cage. The resulting pore envelope is a set of contributions of all four cage window diameters for any configurations where this condition is satisfied. Finally, the pore envelope for the SF 6 positioned at the window of the cage is a set of diameters when SF 6 is within 2.0 -3.5 Å from the centre of mass of the cage; the mean distance between their centre of masses throughout the simulation equals ~2.7 Å. Only the diameter of the individual window that SF 6 is occupying contributes to this pore envelope (red).

Ideal Adsorbed Solution Theory (IAST)
Mixture adsorption equilibria were predicted by ideal adsorbed solution theory (IAST) 15 using single-component adsorption data, measured experimentally. A detailed description of the approach used to obtain the results reported here can be found in the literature. 16 To apply IAST, single-component adsorption isotherms were specified by fitting an isotherm equation to the discrete, experimental adsorption measurements. Specifically, the SF 6 isotherms were fitted using an expression proposed by Jensen and Seaton, 17  showing that crystallinity is maintained (right). Figure S2. Gas sorption isotherms for the uptake of SF 6 , and N 2 , into CC3α, with adsorption curves shown as solid symbols, and desorption curves as hollow symbols.

Movie Caption
Movie S1: An example of the mechanism via which the SF 6 molecule diffuses through one of the four CC3 windows from the internal cavity of CC3 to the exterior. The three fluorine atoms that pass the window first and the three that follow are coloured red and green, respectively. Sulfur atoms are shown in yellow nitrogens in blue, carbons in gray and hydrogens in white. The mechanism we observed requires that three fluorine atoms shown in red align with the triangular window first. Then, as the SF 6 molecule moves along the vector perpendicular to the window's face, a rotation of 60 degrees is observed in order for the three following fluorine atoms (green) to align themself so that they can pass through the triangular window. The movie duration is equivalent to 3.1 ps with a time step between frames of 0.1 ps.

Breakthrough Experiments
The CC3 for the breakthrough experiments was prepared in a similar manner to as previously described. 19 To minimise pressure drop and to prevent potential contamination of the main gas pipelines, the column was packed with small pellets of CC3. The pellets were made as follows; first, a powder sample was pressed into a disk under 9 MPa for 3 min. The disk was then carefully broken up using a pestle and mortar and the fragments were sieved for 25-35 mesh (500-700 μm) pellets which were packed into the column.
Zeolite 13X molecular sieve pellets was also packed in a column and the same experiments were performed as a comparison as zeolite 13X is a benchmark adsorbent. The zeolite 13X was purchased from Sigma Aldrich and used as received.
All gases used were high purity. The gas lines were purged with the correct gas mixture before each experiment.
The breakthrough curves were measured using an automated breakthrough analyser (manufactured by Hiden Isochema, Warrington, U.K.). The gases were introduced through the bottom inlet of the adsorption bed. The adsorption bed was held between two layers of quartz wool and two sample holders, with frit gaskets installed at both the top and bottom ends of the adsorption bed to further prevent any potential powder contamination of the pipelines.
The m/z values used for detecting the gases were 28 for N 2 and 127 for SF 6 . The reason for not using the molecular mass ion of SF 6 is that m/z 146 gave no signal. It is known that the SF 6 + ion is very unstable and its abundance is estimated to be less than 2/10000 of the abundance of the SF 5 + ion. 20 The flow rate of each gas was controlled by individual mass flow controllers. The system was controlled by the software supplied by Hiden.
The samples are activated in situ by heating and flowing helium through the column. This involved heating CC3 to 373 K and zeolite 13X to 523 K for 10 hours. The gases of interest were desorbed from the column by flowing helium through at the same rate as the gases of interest in the corresponding breakthrough experiment.
Breakthrough and desorption curves for CC3 and zeolite 13X are shown below. Only SF 6 is shown and therefore C/C 0 is based on the inlet and outlet SF 6 concentration, not total gas concentration. In all cases N 2 breaks through within 1 minute and is predominantly (>95 %) desorbed in the same length of time. Breakthrough and desorption times of SF 6 match closely for CC3 for each flow rate, however desorption of SF 6 for zeolite 13X at 25 ml minute -1 was slow and approximately 2.5 times the breakthrough time. Figure S5. SF 6 breakthrough and desorption curves for CC3 for a N 2 /SF 6 (90:10) mixture at 298 K and 1 bar. N 2 is not shown as in all cases it breaks through or is predominantly desorbed within one minute. The breakthrough curves are shown with unbroken lines; desorption curves dashed lines. Total gas flow rates are 25 ml minute -1 (blue); 50 ml minute -1 (red) and 100 ml minute -1 (green). Figure S6. SF 6 breakthrough and desorption curves for zeolite 13X for a N 2 /SF 6 (90:10) mixture at 298 K and 1 bar. N 2 is not shown as in all cases it breaks through or is predominantly desorbed within one minute. The breakthrough curves are shown with unbroken lines; desorption curves dashed lines. Total gas flow rates are 25 ml minute -1 (blue); 50 ml minute -1 (red) and 100 ml minute -1 (green).
The N 2 and SF 6 capacity of CC3 at 298 K was calculated for the breakthrough experiment at a total flow rate of 25 ml minute -1 . This was done using equation 1 and the method described