Quantification of gas-accessible microporosity in metal-organic framework glasses

Metal-organic framework (MOF) glasses are a new class of glass materials with immense potential for applications ranging from gas separation to optics and solid electrolytes. Due to the inherent difficulty to determine the atomistic structure of amorphous glasses, the intrinsic structural porosity of MOF glasses is only poorly understood. Here, we investigate the porosity features (pore size and pore limiting diameter) of a series of prototypical MOF glass formers from the family of zeolitic imidazolate frameworks (ZIFs) and their corresponding glasses. CO2 sorption at 195 K allows quantifying the microporosity of these materials in their crystalline and glassy states, also providing excess to the micropore volume and the apparent density of the ZIF glasses. Additional hydrocarbon sorption data together with X-ray total scattering experiments prove that the porosity features of the ZIF glasses depend on the types of organic linkers. This allows formulating design principles for a targeted tuning of the intrinsic microporosity of MOF glasses. These principles are counterintuitive and contrary to those established for crystalline MOFs but show similarities to strategies previously developed for porous polymers.

Supplementary Figure 12. Overlay of the XRPD patterns of agZIF-zni' and agZIF-4' which were obtained by attempting to prepare the desired glasses without an isothermal segment in the TGA/DSC program (see Section S5.2). The black tick marks indicate the allowed Bragg peak positions for ZIF-zni (CCDC code IMIDZB).

Supplementary Methods 3 -Fourier-transform infrared (FTIR) spectroscopy data
The activation of all materials is demonstrated by the absence of the carbonyl stretching band of DMF at 1675 cm -1 . DMF is found in the as-synthesized materials as the template for the porous channels (except for ZIF-zni). 1,2 For ZIF-4 and the amorphous phases derived thereof, a broadening of the vibrational band at 835 cm -1 ascribed to the out-of-plane ring deformation of the imidazolate linker 3 is observed (see Supplementary Figure 13). For the zni phases (ZIF-zni and zniTZIF-4) a much sharper band is observed which may be caused by the higher density of the material corresponding to fewer degrees of freedom for this vibration.

Supplementary Methods 4 -1 H NMR spectroscopy data
The activation of all materials is demonstrated by the absence of signals ascribed to DMF. 1,2 For TIF-4, ZIF-62 and their corresponding glasses the ratio between the implemented linkers has been determined by the integral corresponding to the proton attached to the carbon atom between the two nitrogen atoms in the imidazolate type linkers. The corresponding signals are integrated in the spectra below. A deeper inspection of the 1 H NMR spectroscopy data unveiled additional small signals in the range of 9.0 ppm -9.5 ppm and 7.5 ppm -8.5 ppm for agZIF-4 and agZIF-zni which are ascribed to aromatic or polyaromatic compounds formed as the result of partial framework decomposition during high temperature treatment under inert atmosphere (see Figure 2c for a zoom into the aromatic region). For agZIF-4 this has been already observed in the literature. 4 However, as shown by the intensity of the 13 C satellite signals assigned to the protons of imidazole, the amount of decomposition is rather low.   For all DSC measurements a heating rate of +10 °C min -1 was applied. Samples of ZIF-4 and ZIF-zni were heated to a maximum temperature of 600 °C. Samples of ZIF-62, TIF-4 and their corresponding glasses were heated to a maximum temperature of 485 °C. Data analysis was performed with the TRIOS (v5.1.0.46403) software from TA Instruments. The melting temperatures (Tm) are determined as the peak offset, the glass transition temperatures (Tg) as the peak onset, whereas all other derived temperatures are defined as the peak temperature. The enthalpies are determined from the integral of the corresponding signal.

Supplementary Methods 5.2 -Simultaneous thermogravimetric analysis / differential scanning calorimetry (TGA/DSC)
Several different temperature programs were utilized for the preparation of the thermal products of the investigated ZIFs starting with material of the solvothermally synthesized corresponding crystalline precursor (see Supplementary Table 4).

Supplementary Methods 8 -X-ray total scattering data
X-ray total scattering data have been collected for all investigated materials. From these data, pair distribution functions in the form D(r) have been calculated showing long range order correlations (up to at least 50 Å) for all crystalline materials (ZIF-4, ZIF-zni, zniTZIF-4, ZIF-62 and TIF-4) whereas the last intense peak is found at approx. 5.9 Å for all amorphous materials (aTZIF-4, agZIF-4, agZIF-zni, agZIF-62, agTIF-4; see Figure 2e and Supplementary Figure 42). This peak equals the Zn-Zn distance in the materials. The data are in accordance with previously reported total scattering data.  Intensity / a.u.

Supplementary Methods 8.1 -Fitting of the first sharp diffraction peak (FSDP)
The FSDP of the total scattering data in the form S(Q) (see Supplementary Figure 44) has been fitted to a pseudo-Voigt function for all investigated amorphous materials. From these fits we obtained the position of the FSDP (QFSDP) and the peak width at half maximum (∆QFSDP) (see Supplementary Table 5    The absolute CO2 uptake recorded at 298 K and 4130 kPa amounts to 2.55 mmol g -1 . By considering the molar mass of CO2 (44.009 g mol -1 ) and the saturated liquid phase density of CO2 at 298 K (0.7128 g cm -3 ), we determine a pore volume of ZIF-62 of 0.16 cm 3 g -1 . This is the same value as the one determined from the CO2 sorption isotherms recorded at 195 K (applying the density of the supercooled liquid of CO2 extrapolated to 195 K, see Supplementary Figure 62). Hence, the high-pressure CO2 sorption data verify the robustness of our data analysis of the CO2 sorption data recorded at 195 K.    Supplementary Methods 9.2 -Surface area and pore volume analysis BET 21 surface areas were determined with the Quantachrome ASIQwin version 5.2 software. The applied relative pressure ranges and quality factors are given in Supplementary Table 8. We again note that the BET model is not applicable to microporous materials. Hence, the BET areas must be taken with great care and cannot be considered as absolute physical values. We provide the values of the BET areas for comparison purposes only.
The specific micropore volumes (Vpore) were calculated according to: with *+, -*. the specific molar amount of gas adsorbed (mmol of gas/g material) at 195 K and 95 kPa, /01 the molar mass of CO2, and ,2 the density of the supercooled liquid at 195 K (that is 1.258 g cm -3 ). In analogy to previous reports 23 , 234 is obtained from the linear extrapolation of the tabulated liquid phase density of CO2 from its triple point temperature (216.592 K) to 195 K (Supplementary Figure 62). Reference data for the liquid phase density of CO2 as a function of temperature are taken from the NIST Chemistry Webbook (https://webbook.nist.gov/cgi/cbook.cgi?ID=C124389). The obtained values are summarized in Supplementary Table 8  The experimental void fractions (eVF) were calculated according to: with the density of the solid, either obtained from the crystallographic data (crystalline ZIFs) or obtained from the apparent density approximation (glassy ZIFs, see Section 9.4).  Table 9. Comparison of the specific micropore volumes (Vpore) of agZIF-62 and agTIF-4 obtained from gas sorption isotherms of n-butane (@273 K) and CO2 (@195 K).

Supplementary Methods 9.3 -Pore size distribution analysis
In analogy to previous studies 1, 19 , experimental pore size distributions (PSDs) were derived from CO2 isotherms at 273 K with the nonlocal density functional theory (NLDFT 28 , carbon equilibrium transition kernel at 273 K based on a slit pore model 29 ) using the Quantachrome ASIQwin version 5.2 software. This is the only NLDFT kernel implemented in the software packages of commercial gas physisorption analysers and thus often used in the MOF literature to derive PSDs. Theoretical PSDs were calculated with the Zeo++ 30 software package using the default CCDC radii (-ha 'high accuracy' flag 31 ) and the implemented routine for pore size distributions. The probe size was 0.1 Å and 5000 Monte Carlo samples per unit cell were averaged. The structures for the calculations were taken from the CSD database (ZIF-4: CCDC code IMIDZB11; ZIF-zni: CCDC code IMIDZB). In both structures, missing hydrogen atoms have been added geometrically with Olex2 32 .
Supplementary Figure 63. Theoretical pore size distribution calculated with Zeo++ for crystalline ZIF-4 and ZIFzni in comparison to experimental pore size distributions calculated from the CO2 isotherms recorded at 273 K using the NLDFT method for the crystalline and glassy phases of these materials.
Supplementary Figure 63 demonstrates that the PSDs derived from experimental CO2 sorption isotherms of crystalline ZIF-4 and ZIF-zni recorded at 273 K by the NLDFT model (carbon, slit pore) are inconsistent with the theoretical PSDs derived from their crystal structures. It is evident that the NLDFT model for carbon materials with slit pore geometry is inappropriate for the calculation of PSDs of ZIF materials. This must be ascribed to the very different surface electrostatics (non-polar carbon vs. appreciably polar ZIFs) and the different pore geometries of the ZIFs. Since the PSDs of the crystalline ZIFs is not described accurately by the utilized NLDFT model, we conclude that also the PSDs previously derived for ZIF glasses via the same method 1, 19 do not represent a meaningful description of their pore structure.
relative amount / arb. units

Supplementary Methods 9.4 -Density approximation
The apparent densities of the glasses were determined from the correlation of the density to the specific pore volumes determined by CO2 adsorption isotherms at 195 K.
Feasibility test First, the feasibility of the correlation was proven with theoretical and experimental considerations for ZIF-4 and ZIF-zni. Therefore, the theoretical and experimental void fractions were calculated. The theoretical void fractions (tVFs) -based on the crystal structures for both materials -were calculated with the implemented routine in Olex2 32 applying a probe radius of 1.6 Å and grid spacing of 0.2 Å. The structures were taken from the CSD database. In both structures, missing hydrogen atoms have been added geometrically with Olex2. The theoretical accessible pore space for ZIF-4 (CCDC code IMIDZB11) amounts to 28.7% and for ZIF-zni (CCDC code IMIDZB) to 7.5%. a The experimental void fractions (eVFs) were calculated from the specific micropore volumes (Vpore) derived from the CO2 adsorption isotherms at 195 K given in cm 3 g -1 (see Supplementary Table 8 and Supporting Information Section S9.2) multiplied by the crystallographic densities b (rcryst) of the materials (eVF = Vpore · rcryst, see Supporting Information Section S9.2 for further details). The densities are 1.22 g cm -3 (ZIF-4) and 1.56 g cm -3 (ZIF-zni). The corresponding eVFs amount to 30.6% and 6.2% for ZIF-4 and ZIF-zni, respectively, which are in very good agreement with the tVFs, demonstrating the feasibility of the methodology.

Exponential fit
The Vpore vs. rcryst data for the crystalline compounds ZIF-4, ZIF-zni were completed with the corresponding values for ZIF-62 and TIF-4 and fitted with an exponential fitting function (see Figure 3; R 2 -value = 0.998).
a The same calculation has also been performed for ZIF-62 (CCDC code SIWJAM) and TIF-4 (CCDC code QOSYAZ). Before the calculation, some disordered groups were resolved and solvent molecules were removed where present. tVF values are given in Figure 1. We note that the comparison of these values to the corresponding eVFs is not applicable, because of some unresolvable residual disorder leading to partially occupied secondary linkers (bimor mbim -).
b All densities for crystalline materials have been calculated from the mass of atoms in one unit cell and the unit cell volume determined via profile fits of XRPD data (see Supplementary Table 1).