Does Mixed Linker-Induced Surface Heterogeneity Impact the Accuracy of IAST Predictions in UiO-66-NH2?

To move toward more energy-efficient adsorption-based processes, there is a need for accurate multicomponent data under realistic conditions. While the Ideal Adsorbed Solution Theory (IAST) has been established as the preferred prediction method due to its simplicity, limitations and inaccuracies for less ideal adsorption systems have been reported. Here, we use amine-functionalized derivatives of the UiO-66 structure to change the extent of homogeneity of the internal surface toward the adsorption of the two probe molecules carbon dioxide and ethylene. Although it might seem plausible that more functional groups lead to more heterogeneity and, thus, less accurate predictions by IAST, we find a mixed-linker system with increased heterogeneity in terms of added adsorption sites where IAST predictions and experimental loadings agree exceptionally well. We show that incorporating uncertainty analysis into predictions with IAST is important for assessing the accuracy of these predictions. Energetic investigations combined with Grand Canonical Monte Carlo simulations reveal almost homogeneous carbon dioxide but heterogeneous ethylene adsorption in the mixed-linker material, resulting in local, almost pure phases of the individual components.


S.1.1 Defect quantification based on thermogravimetric analysis
The procedure to quantify the amount of defects in the five UiO-66 derivatives used in this study follows an approach introduced by Shearer et al. for the defect generation in UiO-66 suing modulators. 1 It is based on the following general reaction for the complete combustion of dehydroxylated mixed-linker UiO-66-NH 2 under an oxidizing atmosphere.The coefficient y is the fraction of BDC-amine as determined from Here, the molar mass of each of the mixed-linker materials can be determined as Since the starting temperature of the lattice collapse decreases with increasing amounts of BDCamine linkers, the corresponding weight decrease starts overlapping with the weight loss attributed to solvent and water desorption (Figure S16).Thus, a constant temperature to determine the start weight W ex,Pl of 300 °C was selected based on the results from Shearer et al. 1 since no capping agent was used. 2 The equations derived by Shearer et al. were used to determine the theoretical weight of the plateu W theo,Pl , the theoretical weight contribution of each linker W t,Pl,theo , and the experimentallydetermined number of missing linkers X per Zr 6 unit.All these values are tabulated in Table S3.

S2.1 GCMC Simulations
The pressure space for both adsorbates of interest, carbon dioxide and ethylene, was explored using GCMC simulations in all five generated UiO-66 derivative structures to obtain single-component isotherms at 298 K (Figure S17).A comparison of these computed isotherms to experimentally measured isotherms is shown in Figure S18.The isotherms for both adsorbates show qualitative agreement between simulations and experiments in terms of isotherm type, shape, and saturation loadings.Quantitative discrepancies can be observed since the GCMC simulated isotherms seem to be compressed along the pressure axis.These differences can be attributed to force-field differences during the simulations and differences in the defective synthesized structures compared to the defect-free, ideal simulation structure.4] This work does not aim to optimize the simulation approach and structures to find a quantitative match between experiments and simulations.It rather uses the simulations to generate a visualization to illustrate and understand the underlying adsorption mechanism.Thus, specific loadings of interest concluded from experiments were simulated and visualized using the GCMC simulations.

Figure S2 .
Figure S1.PXRD pattern for the main peak around a 2θ of 7.5 for all five materials.Inset shows the linear relationship between the peak position and the amount of BDC-amine linker in the structure as determine by 1 H NMR with the coefficient of determination for the linear relationship (peak position = 7.5195 -0.0007 Amount BDC-amine[%])

Figure S9 .
Figure S9.Comparison of the two experimentally measured carbon dioxide isotherms at 298 K (gravimetric and volumetric measurements) to the consensus isotherm for carbon dioxide adsorption in UiO-66 at 298 ± 5 K from literature meta-analysis 3 .

Figure S11 .
Figure S11.Loading dependent isosteric heats of adsorption for (A) ethylene and (B) carbon dioxide in the pristine UiO-66, the mixed-linker UiO-66-NH 2 50:50, and the fully functionalized UiO-66-NH 2 determined using the Clausius-Clapeyron equation based on isotherms measured at 288, 298, and 308 K. Uncertainty intervals were determined by adding a normally distributed error to each data point in the isotherms, refitting the data, and then calculating maximum and minimum values.

Figure S12 .
Figure S12.The radial distribution function of the carbon atom in ethylene with respect to Zr and N in the mixed-linker UiO-66-NH 2 50:50.100,000 configurations are used to calculate the distribution.

Figure S15 .
Figure S15.Visualization of the experimentally-determined loadings of ethylene and carbon dioxide using an equimolar mixture at a total, carrier-free pressure of 0.667 bar in (A) UiO-66 and (B) UiO-66-NH 2 from GCMC simulations.

Figure S16 .
Figure S16.Thermogravimetric analysis curves for five UiO-66-NH 2 mixed-linker derivatives under oxidizing atmosphere from air flow using a heating rate of 2 °C/min.All weights are normalized using the plateau after full decomposition assuming a complete oxidation to zirconium dioxide.

Figure S18 .
Figure S18.Comparison of GCMC simulated single-component isotherms as symbols to fits of experimentally measured isotherms as dashed lines for (A) ethylene and (B) carbon dioxide at 298 K.The pressure axis is plotted on a logarithmic scale.

Table S1 .
Suppliers and purities of chemicals and gases used in this study

Table S2 .
Lennard-Jones parameters used for the GCMC simulations in this study.The simulation inputs derived based on these parameters are available as Supporting Information usable with RASPA.

Table S3 .
Results of defect quantification based on TGA curves

Table S4 .
Fitting parameter for carbon dioxide adsorption isotherms tabulated in TableS23-S31 and plotted in FigureS10D-F using the Langmuir-Freundlich isotherm model.

Table S16 .
Fitting parameter for isotherms listen in TableS6-S15 used for IAST calculations.