Temperature-regulated guest admission and release in microporous materials

While it has long been known that some highly adsorbing microporous materials suddenly become inaccessible to guest molecules below certain temperatures, previous attempts to explain this phenomenon have failed. Here we show that this anomalous sorption behaviour is a temperature-regulated guest admission process, where the pore-keeping group's thermal fluctuations are influenced by interactions with guest molecules. A physical model is presented to explain the atomic-level chemistry and structure of these thermally regulated micropores, which is crucial to systematic engineering of new functional materials such as tunable molecular sieves, gated membranes and controlled-release nanocontainers. The model was validated experimentally with H2, N2, Ar and CH4 on three classes of microporous materials: trapdoor zeolites, supramolecular host calixarenes and metal-organic frameworks. We demonstrate how temperature can be exploited to achieve appreciable hydrogen and methane storage in such materials without sustained pressure. These findings also open new avenues for gas sensing and isotope separation.

| Illustration of the 8MR pore framework and the pore-keeping cation at site SIII'. The dimension of the 8MR pore is characterized in three directions, namely D1 for the distance between (O1-O1), D2 for the distance between (O2-O2), and D3 for (O3-O3). Atomic size not in portion. The exact locations of each atoms and cation were determined by Rietveld refinement of the synchrotron PXRD data.

Supplementary Figure 3 | Comparison of isobars for normal physisorption and temperaturedependent admission.
Illustration of a "normal" physisorption isobar (blue dashed line) showing a monotonic increase in uptake with decreasing temperature (a), in comparison with an "abnormal" bellshaped isobar for temperature-dependent guest admission observed on typical molecular trapdoor zeolites, showing an abrupt drop of loading below a certain temperature (b). The bell-shaped isobar can be divided into three zones with decreasing temperature, namely pore-accessible, transitional, and pore-inaccessible, denoted as Zone I, II, and III, respectively. The distance from K cation at saddle point to K cation at site SIII' is ~2.95 Å. As the K cation at saddle point is along the 8MR passage, leaving a "room" of ~1.6 Å for guest molecule which is substantially smaller than the size of any gas molecule studied herein, the K cation has to pass the saddle point to allow for the entrance of the guest molecule. The distance from K cation at saddle point to K cation at site SIII' is ~3.7 Å. As the position at saddle point is well beyond the 8MR passage, it gives a completely unblocked doorway (distance between K cation at saddle point and the opposite oxygen of the 8MR is greater than 3.8 Å) thus permitting the entrance of the guest molecule without the need for K cation necessarily reaching the saddle point.     The gas used for demonstration was hydrogen but can be other gases appropriate for the selected microporous material. The sample cylinder constructed for the purpose of containing the r2KCHA whilst it undergoes activation, dosing, quenching and decapsulation procedures. The main cylinder is a Swagelok double-ended TPED-compliant sample cylinder rated to 124 bar with 1/4 inch female NPT ends and a volume of 50cm 3 . V-4 is a Swagelok stainless steel bonnet needle valve with 1/8 inch Swagelok tube fittings. Current valve positions show high pressure dosing step. At quenching step, the cylinder is immersed in a liquid nitrogen bath while keeping all valve positions unchanged and maintaining the gas pressure. At evacuation, the feed gas regulator is turned off and valve V1 is then opened for venting; after closing V1, valve V2 is opened to allow for evacuation of free space hydrogen from the dosed sample cylinder by the vacuum pump. The vacuum was maintained at a pressure below 1 mbar for approximately 10 min. The gas encapsulated inside the r2KCHA sample is then released by warming up the sample cylinder in ambient air; and the amount of gas evolved is quantified by measuring the pressure increase in the system.

Supplementary Figure 25 | Synchrotron PXRD data of the sublimed p-t-butylcalix[4]arene.
Data obtained at 293 K under vacuum with a X-ray wavelength of 0.77502 Å. High angle data were omitted for clarity purposes. Supplementary Table 2 | Diameter of the 8MR pore and distance between the pore-keeping cation and the pore framework as illustrated in Supplementary Fig. 2. Note the radii of the oxygen atom (1.35 Å) and potassium cation (1.33 Å) were subtracted to represent the effective distance available to a guest molecule.   Si/Al ratio of 5.5 whose BET surface area was measured to be 520 m 2 g -1 .

Supplementary
Supplementary To completely rule out the possibility that pore dilation governed the pore accessibility, we examined the diameter of the 8MR pore and the relative location of the pore keeping cation at the centre of the 8MR. As shown in Supplementary Fig. 2, we measured the distance between the framework oxygen atoms sitting opposite to each other in the 8MR, and the distance between the potassium cation at site SIII' and the surrounding oxygen atoms. The results are summarized in Supplementary Rate of adsorption measurements were carried out on r2KCHA with CH4 as the adsorptive gas at different temperatures from 195 K to 333 K. The dynamic CH4 uptake curves were recorded to show the adsorption capacity plateaued after a sufficiently long time. The rate of adsorption coefficient k was extracted from the curve based on the linear driving force model, 7 at 195 K, 279 K and 333 K representing the pore-inaccessible, transitional, and pore-accessible temperatures, respectively. The k values at 333 K and 279 K were found to be 7×10 -3 s -1 , and 2.6×10 -4 s -1 respectively, which is comparable to that of CH4 on CMS (carbon molecular sieves) or zeolite 4A, indicating the thermodynamic equilibrium was reached. 8,9 The rate of adsorption measured at 195 K was actually greater than at the higher temperatures with a k of 2×10 -2 s -1 In all three cases, the observed characteristic sorption times (1/k) are sufficiently short that the measured capacities could differ only slightly to those achieved after an arbitrarily long time. Furthermore, while the modest reduction in rate of adsorption resulting observed from 333 K to 279 K is expected from the standard theory of gas diffusivity, the increase in the observed sorption rate from 279 K to 195 K is not. This increase in sorption rate can be explained in terms the loss of access to internal adsorption sites and the rapidity with which external adsorption sites can be saturated. The fast rate of adsorption observed at 195 K then is characteristic of adsorption only onto the external surface sites and defects of the material. These results demonstrate that adsorption kinetics are not the determining factor governing the observed temperature-dependent pore accessibility.

Supplementary Note 3. Density functional theory (DFT) calculations
A rhombohedral lattice was used to construct the DFT model based on the Rietveld results from the synchrotron PXRD data. For all the DFT calculations, the cut-off energy of the plane wave basis-set was 405 eV. A gamma point only k-point mesh was used for one unit cell of chabazite (including three double six-ring prisms or one and a half supercavities). Such cut-off energy and k-point mesh have been tested to ensure the total energy value convergence within 1 meV/atom. The atomic positions were optimized with the conjugate gradient method until the forces acting on atoms were below 0.015 eV Å -1 , as suggested by Göltl and Hafner. 10 The DFT-D3 functional (with IVDW=11) was adopted to account for the van der Waals interactions, and the nudged-elastic-band (NEB) method for energy barrier calculations.

(1) Identification and justification of the pathway for cation deviation
We proposed that the door-keeping K cation has to move away from the 8MR aperture (site SIII') temporally and reversibly to allow for the admission of guest molecules, based on the fact that substantial gas adsorption occurs without permanent cation migration as observed in our in situ synchrotron PXRD of adsorption experiments (Fig. 1). We naturally considered that the K cation moves towards a secondary cation site, i.e., site II or site III 11,12 and determined using NEB calculations 13 the energy profile for both cation migration pathways under vacuum. The resulting cation migration profile suggests that the K cation would have to pass the saddle point to permit the entrance of any guest molecule in this study (H2, N2, Ar, or CH4) if the cation were to follow the SIII'to-SII pathway. This is because the opening of the pore will be not enough for the entrance of any molecule if the door-keeping K cation only reaches the saddle point ( Supplementary Fig. 5) , given the K cation at saddle point along the SIII'-to-SII pathway is along the 8MR passage. A successful admission of a H2 molecule necessitates the K cation relocation of at least 4.2 Å (diameter of H2 plus the radius of K cation) along the SIII'-to-SII pathway. If this is the case, we should have observed a permanent cation migration to site SII from PXRD results; but we did not.
On the other hand, if the cation follows the SIII'-to-SIII pathway, the distance between K cation at site SIII' and at the saddle point is ~3.7 Å (Supplementary Fig. 6). If the K cation reaches the saddle point, it will be beyond the 8MR passage, and will give a completely unblocked doorway (distance between K cation at saddle point and the opposite oxygen of the 8MR is greater than 3.8 Å, larger than the guest molecules studied in this work). Thus, the entrance of the guest molecule is permitted without the K cation passing the saddle point, requesting no permanent cation migration to a secondary stable site. Therefore, we excluded the SIII'-to-SII pathway and adopted the SIII'-to-SIII pathway for further study.

(2) Calculation of the energy barrier for gas admission
The cation deviation and the gas entrance should occur simultaneously but the state of the art DFT calculations are not capable of treating such scenario straightforwardly. To overcome this difficulty, we adopted an iteration method with three steps: Step one: we used NEB to determine the trajectory and corresponding energy profile for the cation moving from SIII' to the SIII under vacuum.
Step two: we used pseudo NEB to determine the energy profile for the cation movement following the trajectory determined in step one in presence of different gases, respectively. Thus, we determined a series of ΔEhost along the cation trajectory for each gas. Note that we did not only determine one ΔEhost at the saddle point because different gases may require the cation to move away (door open) to different extents before reaching the saddle point (door fully open). Therefore, for each gas, we plotted ΔEhost v.s. distance of cation movement (where the energy barrier value monotonically increases with distance till the saddle point since clearly the further the cation leaves away from SIII', the more energy toll paid by the cation).
Step three: we used NEB to determine ΔEguest for each gas moving from inside the supercavity to the 8MR doorway with the cation fixed at each location determined in step two, respectively. We plotted ΔEguest v.s. distance of cation movement (where the energy barrier value monotonically decreases with the distance since clearly the further the cation leaves away from SIII', the "wider opening" for the guest molecule and thus the less energy toll paid by the molecule).
ΔEtotal for the admission of each gas was thus obtained by the summation of ΔEhost and the corresponding ΔEguest at each point ( Supplementary Fig. 7). By fitting the curve of ΔEtotal vs distance of cation deviation and adopting the minimum, we determined ΔEtotal for each gas.

Supplementary Note 4. Grand Canonical Monte Carlo (GCMC) simulations
(1) K-CHA Structure used The experimentally determined lattice constants from PXRD for K-CHA, for example at 273K, are a = b = c = 9.35504 Å and α = β = γ = 91.9708°. These lattice parameters remain almost constant in the temperature range used in this study according to the Rietveld synchrotron PXRD experimental data. Also, the experimental structures at various temperatures obtained do not distinguish between Al and Si atoms. Hence, the required number of Al atoms need to be generated by randomly replacing Si with Al in the CHA framework following the Lowenstein's rule which dismisses Al-O-Al linkage. Note that for such a high aluminium density chabazite like r2KCHA, the 8MR pore structure at least consists of one Al in any possible random placement of Al in the framework and the dwelling of the porekeeping cation K + is ensured.
First, we generated a 3  3  3 supercell of the K-CHA framework and then replaced 101 Si atoms (out of 324) with Al atoms randomly to generate an aluminosilicate framework with Si:Al ~ 2.2. Then, 101 K ions (81 at SIII' and 20 at SII sites) were placed in the aluminosilicate framework. These K + cations may or may not be at equilibrated positions for the purpose of GCMC simulations and hence we used a parallel tempering procedure to equilibrate the K + positions. Obtaining good initial positions for the extra-framework cations (K + ) is essential to GCMC simulations. The details of the parallel tempering procedure can be found in the literature. [14][15][16] The single unit cell and the supercell of the CHA structure are shown in the Supplementary Fig. 8.

Adsorbate-adsorbate interactions
For the adsorbate CH4, 3 the spherical united atom model with zero net charge was used. This model uses only the dispersion interactions without any columbic interactions. For N2, we used a 3-site model with two N atoms separated by a distance of 1.10 Å and a pseudo atom (Ncom) at the centre of mass. The pseudo atom is used to create a quadrupole moment and can only be used with coulombic interactions and hence does not have dispersion interactions. The magnitude of the charge on each N atom is qN= -0.482. A point charge of magnitude -2qN (+0.964) is located on a pseudo atom so that the total molecule charge is zero. 4 The dispersion interactions for CH4-CH4 and N2-N2 were defined using Lennard-Jones (LJ) 12-6 force fields (FF) from the literature as given in the Supplementary Table 3 with their respective references.

K + -framework interactions
For K-framework interaction, we used the FF developed by Fang et al. 5 Here, K + as shown in Supplementary Fig. 8b interacts via two interactions: (i) Coulombic interactions with the framework atoms (Si, Al, , and ) using the charges given in the Supplementary Table 4 where Si, Al, stand for Silicon and Aluminium while is oxygen connected to two Si, and is oxygen connected to Si and Al, and (ii) dispersion interactions (modelled here as a Buckingham potential instead of a LJ-12-6 type potential) between K and Oz (both and ) atoms of a zeolite given by where, Aij, Bij, and Cij are the Buckingham parameters for cross species i (K) and j (Oz) given in Supplementary Table 4 for K-Oz. The Buckingham terms for K-Si, K-Al, and K-K interactions are not explicitly considered, but taken into account through the effective potential with the oxygen atoms. 5

Adsorbate-framework interactions
The force field parameters to model the interactions of CH4 and N2, with K-CHA in the GCMC simulations are not available in the literature. Hence, we developed our own force field for both the adsorbates with the K-CHA separately. The adsorbate-framework dispersion interactions were defined using Lennard-Jones (LJ) 12-6 force fields (FF). For columbic interactions, the charges used are already listed in the Supplementary Tables 3 and 4. In this work, we used our experimental data for the parametrization of the force field. Similar approaches have been used earlier, 3,17,18 where the force field parameters were fitted to adsorption isotherms data obtained from the experiments. The Lennard-Jones parameters of aluminium and silicon atoms with adsorbate molecules were excluded like many previous force fields. 3,18 This is because the polarizabilities of aluminium and silicon are lower than those of oxygen atoms resulting into shielding effect. Therefore, it is a reasonable assumption to ignore the LJ-12-6 terms for adsorbate-Si and adsorbate-Al interactions and thus include only adsorbate-Oz for simplicity.
First, we made an initial guess for the force field parameters for adsorbate-Oz ( and ) and adsorbate-K interactions by using the Lorentz-Berthelot mixing rule on adsorbate-adsorbate (from above section 2.1) and adsorbate-framework (CLAY FF for Oz-Oz and K-K) 19 interactions. Next, we selected a set of experimental adsorption isotherms at temperatures at which pores are not blocked by cations for the comparison. Then, we performed GCMC computations at five pressure points for each of the isotherms using the initial force field. We compared the calculated adsorption loading with the corresponding experimental data and if the deviation was large, then the LJ-12-6 (ε and σ) parameters were scaled one at a time for the adsorbate-Oz and adsorbate-K interactions till a reasonable fit of the adsorption isotherms was obtained. Also, while optimizing the parameters, care was taken to have a set of the force field parameters with reasonable physical meaning. In the initial stages of the iterative procedure, a coarse scaling of the LJ-12-6 parameters was done to make it computationally efficient, while in the later stages a fine scaling of the parameters was done to better fit the individual isotherms. The final parameters of the optimized FF are listed in the Supplementary Table 5.

(3) Blocking of the cavities
The number of cavities to be blocked at a given temperature for a given adsorbate was obtained from the percentage of accessible sites calculated from the regressed LJM-Langmuir models (see Fig. 4b).
In the GCMC calculations, any blocked cavities were simply simulated by excluding a spherical volume around the cavity centre. The radius required to block a particular cavity completely is equal to the sum of the distance from the centre to the nearest framework atom (oxygen in this case) and the radius of that oxygen atom (~1.35 Å). The addition of 1.35 Å was needed because the actual CHA cavity is oval shaped and not actually spherical as assumed. After extensive calculations and visualization of the cavities, it was confirmed that this method will block the cavities perfectly without spilling out of the cavity and also no volume in the cavity is available for adsorption.
To find the centre of the cavity, the simulation box consisting of 27 unit cells (3  3  3) (Supplementary Fig. 9) was divided into discrete grid points with 0.2 Å spacing along each coordinate axis. Cavities, in which molecules can be adsorbed, were identified using an in-house code written in Fortran. In this code, for every grid point, the distance from the nearest framework atom was calculated.
The grid point corresponding to the maximum of these distances is one of the focal points of the approximately oval shaped cavity. Similarly, other focal point of the same cavity was obtained by finding the grid point which (i) is not the next nearest neighbour of the first focal point and (ii) has the next maximum distance from the framework atom. The midpoint between the two focal points is considered as the centre of the cavity. Remaining cavity centres were obtained by continuing the same process after excluding all the grid points present in the cavities already obtained. In the supercell, there are 27 cavities as shown by the coordinates of their centres in the Supplementary Table 6.

(4) GCMC simulation details and results
All the adsorption isotherms in this section were computed by the Grand Canonical Monte Carlo (GCMC) method using the RASPA software. 20,21 The LJ-12-6 potentials used were cut and shifted using a cut-off radius of 12 Å. Periodic boundary conditions were employed. Other GCMC simulation details are described in previous publications. 3,22 We used a 3  3  3 simulation box so that the minimum length in each of the coordinate directions was larger than 24 Å (which is double the cutoff radius). In all the simulations, 2×10 4 Monte Carlo cycles were used for equilibration and 1×10 5 Monte Carlo cycles were used for production. The Ewald summation method was used to calculate the electrostatic part of the interaction. K + cations were allowed to move during the GCMC simulations and could be wiggling around their starting positions.
First, we have generated GCMC predicted adsorption isotherms for N2 and CH4 in r2KCHA (Si:Al=2.2), at pressures between 0 to 110 kPa (see Supplementary Fig. 10(a) for N2 and Supplementary Fig. 11(a) for CH4) at various high temperatures with accessible pores for respective gases (above 283 K and 303 K for N2 and CH4 respectively). Not all of the isotherms are shown here for the clarity purposes. Firstly, the predicted adsorption isotherms match well with the experimental adsorption isotherms at higher temperatures at which pores are fully accessible. They also agree with low temperature isotherms extrapolated from LJM-Langmuir model assuming zero pore blocking. Secondly, we obtained the adsorption isotherms from GCMC at lower temperatures by blocking the corresponding number of pores determined from the LJM-Langmuir models. The predicted GCMC capacities were then found to be in excellent agreement with the experimental adsorption isotherms measured at lower temperatures, as shown in Supplementary Fig. 10(b) for N2 and Supplementary Fig.  11(b) for CH4.

Supplementary Note 5. Implementation of LJM models (1) LJM for single component systems
The LJM-Toth model is given by substituting the standard Toth model into Q(T,P) in Equation (6): Here n∞ is the maximum monolayer adsorption capacity, b0 the gas-solid affinity coefficient, H the enthalpy of adsorption, R the gas constant, and m the surface heterogeneity coefficient. For homogeneous adsorption, m becomes unity and Supplementary Equation (2) reduces to the LJM-Langmuir model as follows: The Levenberg-Marquardt method was used to find the best-fit parameters resulting from the regression of Supplementary Equations (2) and (3) to the experimental data. The goodness of fit is characterized by the square of correlation coefficient (R 2 ) and the root-mean-square-error (RMSE).
In the r2KCHAgas system, we chose the LJM-Langmuir isotherm model to describe the complete experimental data sets, since adsorption isotherms of non-polar or inert gases on zeolites are normally of Langmuirian type. As demonstrated by the representative isobars shown in Fig. 3 and summarised in Supplementary Table 7, the LJM-Langmuir model achieved an excellent agreement of the experimental results for all four gases. The enthalpies of adsorption H obtained for CH4, N2, Ar, and H2 on r2KCHA (Supplementary Table 7), of 24.2, 19.4, 7.02, and 6.71 kJ mol -1 , respectively, are typical of similar adsorption on small pore zeolites. The fraction of external surface sites, ε, available for N2 on r2KCHA was determined via independent experiments by using the 77 K N2 BET surface area (SBET) of r2KCHA (21 m 2 g -1 ) divided by that of the closest non-trapdoor chabazite, i.e., r5.5KCHA (520 m 2 g -1 ) which gave ε = 0.043. The second closest analogue is r2NaCHA (a sodium exchanged non-trapdoor chabazite) 23 with a SBET of 490 m 2 g -1 . Using both values lead to very similar values of ε for r2KCHA. Given the size of a CH4 molecule is quite close to that of N2, the same ε was used for the analysis of CH4 adsorption data as well. For the case of hydrogen or argon adsorption on r2KCHA, the external surface parameter ε was found by regression to the primary data set due to the lack of experimental data for "H2 surface area" or "Ar surface area". We found a larger ε for H2 (i.e., 0.14) compared with that estimated for N2, suggesting hydrogen molecules with a much smaller size could access more external sites in the chabazite crystal facets and defects. Similarly, a value of ε = 0.065 was found for Ar which is in-between that of H2 and N2, and consistent with the order of their molecular sizes. Nevertheless, the model is relatively insensitive to ε and a variation of ε from 0.043 to 0.065 has an insignificant impact on the performance of the model.
It should be noted that the classical Toth/Langmuir parameters can be independently determined with a minimum of two adsorption isotherms if they were collected at temperatures well above T0 (illustrated as Zone I in Supplementary Fig. 3). That means the two new parameters T0 and β introduced by the LJM model are able to account for the transition behavior, i.e., the change of the pores from inaccessible to accessible (Zone II in Supplementary Fig. 3). For example, description of the eight N2 isotherms from 223 K to 273 K would be completely impossible without the two LJM parameters. The complementary parameter ε accounts for the almost negligible uptake of the gases at temperatures far below the corresponding threshold admission temperature T0 (Zone III in Supplementary Fig. 3).

(2) Extension of LJM model to multicomponent adsorption
It is a simple and straightforward method to apply the LJM model to the prediction of adsorption capacities of gas mixtures, because the multicomponent calculations require no experimental data for the mixture but only rely on LJM model parameters derived from pure component isotherm data. For example, to use the IAST model, 24 only the step in which spreading pressure is determined requires input from the parameters of the LJM model: Here the function of ni represents the pure component adsorption isotherm characterized by an LJM model as described by Equation (6).

(3) Model determined T0 vs T(nmax)
We also found the threshold temperature T0 for gas admission does not align with the peak of the isobar, although the temperature at the peak, denoted as T(nmax), was used as an arbitrary reference for the gas admission temperature in the past. 25 Comparing all the cases in this study, T0 is found to be always lower than T(nmax). On r2KCHA, this difference is around 10 -15 K. Furthermore, unlike T0, T(nmax) is not a fixed value and varies with the isobar pressure. This is because the peak of the bellshaped isobar is a trade-off between the LJM function for site accessibility (positive temperature derivative) and the Langmuir isotherm function for adsorption uptake (negative temperature derivative but positive pressure derivative) where higher pressures will result in an increase of T(nmax). This is evident from the isobars observed for the trapdoor chabazite (Fig. 3) and p-t-butylcalix [4]arene (Fig.  5a). Therefore, we suggest that T0 is a more appropriate parameter for characterizing the threshold admission temperature.
Supplementary Note 6. Procedures for H2 storage, determination of amount of H2 evolved and repeatability (1) Experimental setup The experimental setup and the procedure used for this experiment is described in Supplementary Fig.  20.
(2) Quantification of amount of hydrogen stored by encapsulation The calculation of the amount of H2 stored by encapsulation is presented as follows. Note that total amount of hydrogen stored (nrecorded) is the summation of three contributing terms: amount of desorbed (previously adsorbed on the internal surface of the zeolite), amount of decapsulated (molecules previously trapped in the zeolite intracrystal pore cavity), and residual amount (molecules re-adorbed after decapsulation). For the residual amount, it is a function of decapsulation pressure and temperature; if the release pressure is 1 bar and this term nresedual hydrogen is negligible.
Supplementary Equation (5) was validated by comparing with the experimental data as shown by Supplementary Fig. 21. Noting that the storage capacity above 60 bar becomes linearly proportional to the initial dosing pressure, suggesting the term of ndesorbed flats off due to saturation on internal surface sites which is consistent with the weak adsorption of hydrogen on zeolites. The linearly increasing part of nrecorded is predominantly the contribution of ndecapsulated, which is proportional to the volume of internal pores of the chabzite available from literature. Therefore, the amount of hydrogen stored with much higher initial dosing pressures can be reasonably predicated using the knowledge of pore volume and the density of hydrogen at various temperature and pressures.

(3) Repeatability and reversibility test
For r2KCHA to be a suitable hydrogen storage material, it must be possible to repeat the encapsulation procedure multiple times with ease. The amount of hydrogen released from r2KCHA after dosing it with hydrogen at a pressure of approximately 100 bar on 5 separate occasions is given in Supplementary Table 9. The average amount of hydrogen released was found to be 4.65mol kg -1 , but more importantly the standard deviation of this value is just 0.07mol kg -1 . This is less than the standard error associated calculating the amount of hydrogen released. Although only five repetitions have been completed in this project, the initial findings are encouraging, in that there is no observed correlation between number of repetitions and the hydrogen storage capabilities of the zeolite. It should be noted that these repetitions were undertaken without sample reactivation. Many adsorbents that have reportedly stored large gravimetric densities of hydrogen require reactivation (e.g. metal hydrides), in that they must be heated to a substantially high temperature to remove all hydrogen before hydrogen can be stored at high gravimetric densities once more 26 . The relatively constant amount of hydrogen released from r2KCHA after several repetitions of the encapsulation process means that the process is fully reversible, and as such this reactivation step is not required, giving the process a great advantage over other hydrogen storage mechanisms with comparable gravimetric densities of stored hydrogen.
Theoretically, adsorbents showing temperature-regulated admission for hydrogen can all be used for hydrogen storage without sustained pressure. Exploration of microporous materials with a higher threshold admission temperature T0 for hydrogen is currently investigated. One promising strategy is to use Rb + or Cs + exchanged trapdoor chabazites as heavier cations are known to increase the threshold admission temperature.

(4) Conceptual tank-in-tank design for light weight on-board storage
We propose an on-board hydrogen (or methane) storage via repeatable encapsulation/decapsulation process. The mechanism of hydrogen filling, storage, use and re-fuelling is described in Supplementary Fig. 22. The on-board tank is low pressure rated to save the weight and it contains the to-be-improved trapdoor zeolite with a hydrogen threshold admission temperature between 50 and 100°C. While refuelling, the on-board tank is taken 'off-board', opened, and placed in a dosing tank designed to withstand very high pressures. The on-board tank is then warmed above the threshold admission temperature and dosed with high pressure hydrogen before being cooled below the threshold admission temperature to encapsulate the hydrogen. After the high pressure hydrogen in the free space is removed from the high pressure dosing tank, the on-board tank (now filled with encapsulated hydrogen at atmospheric pressure) can be closed and returned to its on-board location. At this point, as long as the on-board tank's temperature is kept below the hydrogen threshold admission temperature, atmospheric pressure will be maintained within the tank without any loss of hydrogen. Once the hydrogen is required for its on-board application, the on-board tank is carefully warmed, slowly releasing the hydrogen from the zeolite. Finally, when all the hydrogen originally encapsulated within the zeolite is used up, the tank is taken 'off-board' once more and the mechanism is repeated.

(5) CH4 encapsulation in trapdoor zeolites and calix[4]arene, and ignition demonstration
In a similar setup, the encapsulation of methane was achieved at 195 K onto r2KCHA and p-tbutylcalix [4]arene with an initial doing pressure of 1 MPa and 2.2 MPa, respectively. We demonstrated a considerable amount of CH4 gas can be stored without sustained pressure in a glass bottle at dry ice temperatures by encapsulation in r2KCHA trapdoor zeolites and the p-tbutylcalix [4]arene superamolecular hosts. When the bottle was placed in an ambient environment for around 5 minutes, CH4 evolved gradually from the two materials, amounting to 7.4 ml g -1 and 25.9 ml g -1 , respectively. Interestingly, in the case of calixarene, the amount of CH4 encapsulated equals approximately 1 CH4 molecule for every two cages.
The methane was then ignited while being de-capsulated at ambient conditions for demonstration purposes (Supplementary Videos).