Structural dynamics of a metal–organic framework induced by CO2 migration in its non-uniform porous structure

Stimuli-responsive behaviors of flexible metal–organic frameworks (MOFs) make these materials promising in a wide variety of applications such as gas separation, drug delivery, and molecular sensing. Considerable efforts have been made over the last decade to understand the structural changes of flexible MOFs in response to external stimuli. Uniform pore deformation has been used as the general description. However, recent advances in synthesizing MOFs with non-uniform porous structures, i.e. with multiple types of pores which vary in size, shape, and environment, challenge the adequacy of this description. Here, we demonstrate that the CO2-adsorption-stimulated structural change of a flexible MOF, ZIF-7, is induced by CO2 migration in its non-uniform porous structure rather than by the proactive opening of one type of its guest-hosting pores. Structural dynamics induced by guest migration in non-uniform porous structures is rare among the enormous number of MOFs discovered and detailed characterization is very limited in the literature. The concept presented in this work provides new insights into MOF flexibility.


Quasi-elastic neutron scattering (QENS)
QENS data were collected using the IRIS indirect geometry time-of-flight (TOF) spectrometer at ISIS Neutron and Muon Source, Rutherford Appleton Laboratory, Harwell, UK. At IRIS, the sample first got a white beam of neutrons containing a band of energy. After scattering, the crystal analyzer (the (002) plane of pyrolithic graphite) chose a single final energy (1.84 meV) to send to detectors. Scattered neutrons were detected over an angular range of 2θ = 25-160 o . The instrumental resolution and detector efficiencies were calibrated by fitting the spectrum of a vanadium standard. The elastic energy resolution was 17.5 μeV. The energy transfer range was -0.4-0.4 meV and the Q range was 0.42-1.85 Å -1 . IRIS was also built with long-wavelength diffraction capability. The d range was 1-12 Å with Δd/d = 2.5 × 10 -3 .
The as-synthesized sample was first activated at 400 K in air for 24 h. The activated sample (ca. 4.6 g) was then wrapped into two pieces of aluminum foil to make a sample lining fitted into the annular space of an aluminum cylinder sample cell (∅ 24/28 mm × h 65.6 mm). The thickness of the sample lining was about 2 mm. Glass wool was placed in the top of the sample cell. The sample cell was then sealed with indium and connected to a custom-made gas loading system. During data collection, the temperature of the sample was controlled by a helium cryostat and thermocouples. QENS spectra were first recorded when the sample was under vacuum. At 15 and 225 K, the accumulated proton current was 600 μA for good statistics. At 298 K, the accumulated proton current was 1146.8 μA. CO 2 was then loaded into the sample cell at 298 K to enable ZIF-7 to reach a CO 2 uptake of 1.3 mmol·g -1 . For QENS data of the loaded sample collected at 15, 225 and 298 K, the accumulated proton current was 600 μA. Diffraction data were collected simultaneously with QENS data collection. CO 2 loading was measured using the method employed in the literature [4][5][6] . A gas handling system shown in Supplementary Fig. 3 was used for gas loading. The volume of the system without the sample cell (i.e. to the valve on top of the cell) (V1) was measured using N 2 . A certain amount of N 2 (n0) was loaded into the vacuumed system at room temperature so that a pressure of p0 was reached (shown on the barometer). According to the ideal gas law, we can obtain the value of V1: The volume of the system including the sample cell (V2) was also measured using the same method. ZIF-7 has almost no N 2 adsorption capacity at 298 K 7 , so V2 is the actual volume of the system. After the sample was evacuated to 10 -5 Pa at room temperature for 16 h to remove any remaining trace guest molecules, the valve on top of the sample cell was closed. CO 2 was then loaded into the system to reach a pressure of p1. The amount of CO 2 in the system (n1) can be calculated: Then the valve on top of the sample cell was open, CO 2 pressure will stabilize at p2. The amount of CO 2 left in the system (n2) can also be calculated: The amount of CO 2 adsorbed (n) by ZIF-7 is: As we know the amount of sample used in each experiment (ca. 4.6 g), we can precisely control the CO 2 loading to be 1.3 mmol·g -1 .

Inelastic neutron scattering (INS)
INS data were collected using the TOSCA TOF spectrometer at ISIS Neutron and Muon Source, Rutherford Appleton Laboratory, Harwell, UK. TOSCA has a wide energy transfer range of -2.5-1000 meV (-20-8050 cm -1 ) and a high energy resolution of ca. 1.25% ΔE/E.
The sample environment at TOSCA was similar to that at IRIS. Before data collection, the as-synthesized sample was first activated at 400 K in air for 24 h. The activated sample (ca. 4.6 g) was then wrapped into two pieces of aluminum foil to make a sample lining for a stainless steel cylinder sample cell (∅ 16 mm × h 76 mm). Glass wool was placed in the top of the sample cell to prevent any sample spillage during the experiment. The sample cell was then sealed with a copper O-ring and connected to a custom-made gas loading system. The sample chamber was evacuated to 10 -5 Pa at room temperature for 16 h to remove any remaining trace guest molecules from the sample. During data collection, the temperature of the sample was controlled by a closed cycle refrigerator (CCR) and was kept below 10 K to minimize the thermal motion of CO 2 molecules and the host framework which influences the accuracy of the measurement. Namely, at higher temperatures the increase in Debye-Waller factor causes broadening of the spectral peaks, i.e. decrease in peak intensity or spectral resolution. INS spectra were first recorded when the sample was under vacuum. The accumulated proton current was 3604 μA for good statistics. CO 2 was then loaded into the sample cell at 298 K to enable ZIF-7 to reach a CO 2 uptake of 1.3 mmol·g -1 . CO 2 loading was measured using the same method as that in the QENS experiment. During data collection of the loaded sample, the accumulated proton current was 3558.6 μA.

Density functional theory (DFT) calculation
Models for the DFT calculations were built based on the crystal structures from the literature 8,9 . One ZIF-7 unit cell was used with a chemical formula of Zn 18 C 252 N 72 H 180 . Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) 10 implemented in the VASP package 11 was used. The projector augmented wave (PAW) 12 pseudopotential method was employed. Due to the large unit cell of ZIF-7, only Gamma point was sampled. The cutoff energy was 400 eV. The shape of the unit cell and atomic positions were allowed fully relaxed during the optimization. The energy convergence for the self-consistent electronic relaxation was set to be 10  eV and the force convergence was set to be 0.01 eV·Å -1 . To count in the weak dispersive interaction, van der Waals interactions (as implemented in the DFT-D2 scheme 13,14 ) were considered during the calculations. We included a typical input file of our DFT calculations as a supporting file (Supplementary Data 1). Details of the calculation can be found in this file.

Grand canonical Monte Carlo (GCMC) molecular simulations
CO 2 adsorption isotherms in ZIF-7 were investigated using grand canonical Monte Carlo (GCMC) simulations performed in the multi-purpose code RASPA 15 . ZIF-7-I and ZIF-7-II models were built based on the crystal structures from the literature 8,9 . Framework atoms were kept fixed at the crystallographic positions. In order to correctly describe the absence of CO 2 molecules in pores A before the ZIF-7-II to ZIF-7-I phase transition, pores A were all blocked in ZIF-7-II during the simulation. We used the standard Lennard-Jones (LJ) 12-6 potential to model the interactions between the framework and fluid atoms. In addition, a Coulomb potential was used for fluid-fluid interactions. The parameters for framework atoms were derived from the Universal Force Field 16 and those previously developed for ZIF-8 17 . CO 2 molecules were modeled using the TraPPE potential with charges placed on each atom and at the center of mass (Supplementary Table 5) 18 . EQeq was used to assign the partial charges of the framework. The Lorentz-Berthelot mixing rules were employed to calculate fluid-solid LJ parameters, and LJ interactions beyond 12.8 Å were neglected. The Ewald summations method was used to compute the electrostatic interactions. Up to 50,000 Monte Carlo cycles were performed, the first 50% of which were used for equilibration, and the remaining steps were used to calculate the ensemble averages. Monte Carlo moves consisted of insertions, deletions, displacements, and rotations. In a cycle, N Monte Carlo moves are attempted, where N is defined as the maximum of 20 or the number of adsorbates in the system. To calculate the gas-phase fugacity we used the Peng-Robinson equation of state 19 . The isosteric heat of adsorption (Q st ) was calculates using the fluctuation theory 20 . Input files are included in Supplementary Data 2.

QENS data analysis
TOF data were converted to energy transfer using the Mantid software 21 . In each measurement, 50 QENS spectra were recorded over the energy transfer range (-0.4-0.4 meV, 0.42-1.85 Å -1 in Q). To fit each QENS spectrum, a delta function and a Lorentzian function were used to describe the elastic and coherent quasi-elastic scattering from the sample, respectively ( Supplementary Fig. 4). They were convolved by the scattering function of the vanadium standard, which is close to a Lorentzian function. The baseline was regarded as a straight line. Sequential fitting was conducted. The QENS spectrum collected at Q = 0.44 Å -1 was first manually fitted. The starting functions used for fitting each following spectrum at Q = 0.48-1.85 Å -1 were the calculated results from the previous spectrum in the sequence.
No coherent quasi-elastic scattering signal can be found in the QENS spectra of ZIF-7 under vacuum. This indicates that the dynamics of ZIF-7 do not contribute to the QENS spectra of CO 2 -loaded ZIF-7, regardless of the ZIF-7-II to ZIF-7-I phase transition observed by simultaneous neutron powder diffraction. No coherent quasi-elastic scattering signal can be found in the QENS spectra of CO 2 -loaded ZIF-7 at 15 K. This suggests that CO 2 was frozen in ZIF-7 at 15 K.
Thus the coherent quasi-elastic scattering signal in the QENS spectra of CO 2 -loaded ZIF-7 at 225 and 298 K predominantly reflects the collective motion of CO 2 molecules in ZIF-7 at these temperatures. The contribution from the vibrational and rotational motions of CO 2 molecules is negligible: the vibrational motion only affects the measured intensity through a Debye-Waller factor; for a linear and symmetrical molecule like CO 2 , the influence of the rotational motion is very small in the QENS domain 22 . We can say that the coherent quasi-elastic scattering signal in the QENS spectra of CO 2 -loaded ZIF-7 at 225 and 298 K predominantly reflects the collective translational motion of CO 2 molecules, i.e. CO 2 transport diffusion at these temperatures.
Over a small Q range (i.e. large length scales), assuming CO 2 transport diffusion is isotropic, the coherent quasi-elastic scattering function has the form 22 : where D(Q) is CO 2 transport diffusion coefficient and L corresponds to a Lorentzian function. The half-width at half-maximum (HWHM) of L is the product of D(Q) and Q 2 : where HWHM is in s -1 , Q is in m -1 and D t is in m 2 ·s -1 . At larger Q values (i.e. over smaller length scales), the relationship between HWHM and Q 2 is no longer linear due to CO 2 elementary jumps between adsorption sites ( Supplementary Fig. 5). Since we are simply interested in CO 2 long-range diffusion (i.e. small Q range), the calculation of D(Q) can be based on Supplementary Equation 6. Fitting the QENS spectra of CO 2 -loaded ZIF-7 at 225 and 298 K allows the calculation of D(Q) over the whole Q range. By fitting D(Q) with a polynomial function, D(0), i.e. macroscopic CO 2 transport diffusivity D t , can be determined 22 . CO 2 transport diffusivity in zeolites usually ranges from 10 -10 to 10 -8 m 2 ·s -1 23,24 . CO 2 transport diffusivities in ZIF-7 at 225 and 298 K (6.3(7) × 10 -9 m 2 ·s -1 and 4(2) × 10 -11 m 2 ·s -1 , respectively) are comparable with those in zeolites.
While transport diffusion reflects the collective motion of CO 2 molecules caused by local concentration gradients, self-diffusion often describes the displacement of individual CO 2 molecules, i.e. elementary jumps between adsorption sites. In zeolites, D t has a close relationship with self-diffusivity D s 22 : ) ln where ∂ lnp/ ∂ lnc is the thermodynamic correction factor and can be calculated directly from the CO 2 adsorption isotherm. p is CO 2 pressure in kPa and c is CO 2 uptake at p in mmol·g -1 .

INS data analysis
The INS spectrum of ZIF-7 at a CO 2 loading of 1.3 mmol·g -1 was compared with that of ZIF-7 without CO 2 loaded (ZIF-7-II) (Supplementary Fig. 7A). Peaks were assigned based on previous works [25][26][27] (Supplementary Table 4). In the ZIF-7-II spectrum, a doublet at 230−245 cm -1 represents the out-of-plane bending motion of bIm linkers at the bridge of the imidazole ring (Im) and the benzene ring (Bz) (Supplementary Fig. 7B). The ratio between peak areas at 242 cm -1 and 234 cm -1 is 1:2.3. As shown in Fig. 1d, linkers in ZIF-7-II are distributed in two types of pore B. The ratio between the number of type I and II pore B is 1:2, thus the INS peak at 242 cm -1 corresponds to the out-of-plane bending motion of the linkers in type I pore B. After CO 2 loading, the 242 cm -1 peak merges into the 234 cm -1 peak, this peak shift matches well with what is expected when 0.5 CO 2 molecule is adsorbed per linker in type I pore B, as predicted by neutron powder diffraction results 9 . According to Hooke's Law,

Supplementary Equation 8
where ω is wavenumber, k is the elastic constant, m is mass. Thus, where ω 0 is the wavenumber when the linker is without CO 2 adsorbed, ω f is the wavenumber when the linker is adsorbed with CO 2 , m 0 is the mass of one bIm linker, ∆m is mass of one CO 2 molecule, N is the number of CO 2 molecules adsorbed per linker. When N = 0.5, ω 0 = 242 cm -1 and ω f = 234 cm -1 ,

Supplementary Equation 10
Thus we can conclude that the linkers of type I pore B are mainly responsible for the initial CO 2 adsorption, rather than those of type II pore B.
A higher-frequency peak occurs after CO 2 loading in the energy ranges corresponding to Im torsion (644 cm -1 ) and the out-of-plane bending motion of Im C-H (843 cm -1 ) ( Supplementary Fig. 7D). The occurrence of higher-frequency peaks could be due to the formation of hydrogen bonds between CO 2 and Im C-H. The ratio between peak areas at two frequencies is approximately 1:1. This is because only half of the linkers can adsorb CO 2 on its Im (Supplementary Fig. 7E).
Admittedly, ZIF-7-II to ZIF-7-I phase transition can also induce peak shift and affect that induced by CO 2 adsorption. For the torsion motion of Bz (415-435 cm -1 , Supplementary  Fig. 7C), the ratio between peak areas at 419 cm -1 and 429 cm -1 is 1:1.6. Bz in type I pore B is more relaxed since they are further away from each other when compared with those in type II pore B. After CO 2 loading, two peaks merge into one, indicating type I and II pore B became one structure (Fig. 1d). The narrowing of 898 cm -1 peak (the out-of-plane bending motion of Bz C-H) is also due to the same reason. Figure 1 Pore size distribution of ZIF-7-I, ZIF-7-II, and ZIF-8, measured by CrystalMaker 10.3 software using their crystal structures 1,8 . The probe radius was 1.55 Å, the same as the van der Waals radius of a N 2 molecule. SOD: sodalite cage, 4M: four-memberring pore. Values of pore sizes are listed in Supplementary Table 1. From the analysis results, it is clear that there is only one type of pores in ZIF-8 (7.1 Å), which corresponds to the sodalite cage of ZIF-8. This indicates that ZIF-8 has a uniform porous structure. In ZIF-7-I, four types of pores with distinct radius were found: pore A (4.0 Å), sodalite cage (3.8 Å), pore B (3.2 Å), and four-member-ring pore (2.4 Å). The pore distribution in ZIF-7-II is very different from that in ZIF-7-I. During ZIF-7-II to ZIF-7-I phase transition, the radius of pore B decrease from 3.5 -4.7 Å to 3.2 Å, whereas the radii of pore A and sodalite cage increase from 2.3 -2.5 Å and 2.8 -3.1 Å to 4.0 Å and 3.8 Å, respectively. The radius of four-member-ring pore remains unchanged (2.5 -2.9 Å to 2.4 Å).

Supplementary
As ZIF-7-II to ZIF-7-I phase transition is induced by CO 2 adsorption, it can be said that with the filling of CO 2 , pore B decreases in size whereas pore A increases in size. This strengthens our proposed mechanism on the sequential CO 2 filling of pore B (first) and pore A (last). The filling of pore A with CO 2 requires pore deformation which is induced by the interaction between CO 2 and pore B. The adsorption behaviors of flexible MOFs are recently found to strongly depend on their crystal sizes. For DUT-49 and ZIF-8 mentioned in the main text, it has been demonstrated that the adsorption-induced flexibility of samples with nanometer-scaled crystal sizes is suppressed or the transition pressure is significantly higher than that for those with micrometer-scaled crystal sizes [28][29][30][31] . Our activated ZIF-7 sample contains micrometer-scaled crystals, which allows it well exhibiting adsorption-induced flexibility under our experimental conditions. The crystal sizes of all activated samples analyzed by various techniques in this manuscript are the same, so the crystal size effect is not discussed in the main text.