**2. Results and Discussion**

Typical 1H CPMG relaxation decays of the pure solvents and their mixtures, acquired at room temperature, along with the corresponding inverse Laplace transform (ILT) analysis are exemplarily depicted in Figure 1 and Figure S1. The extracted values of effective spin– spin relaxation times *T*2eff for the pure solvents are reported in Table S1 along with literature values for the corresponding viscosity and self-diffusion coefficients. The *T*2eff generally increase with increasing number of carbons and are higher for the cyclic alkane than the linear one. The lower *T*2eff relaxation times for n-octane compared to cyclooctane are in agreement with reported spin–spin relaxation times *T*<sup>2</sup> data obtained in a much more homogeneous magnetic field [46]. Yet, the detected trends for the other solvents are contrary to the expected behavior due to the increase in the viscosity and the reported trends in literature for the relaxation times of alkanes for which has been shown that the *T*<sup>2</sup> relaxation times decrease with increasing the number of carbons [46,47]. Generally, the higher the viscosity, the shorter are the values of the *T*<sup>2</sup> relaxation times and the same trend can be usually observed also for the *T*2eff given that the echo-time used for the CPMG measurement is low enough to minimize the effect of self-diffusion on the CPMG decay [37,38,46,47]. The observed trend for our data can thus be explained by the impact of self-diffusion on the CPMG decays acquired using an echo-time of 70 μs in the presence of a strong static magnetic field gradient of around 20 T m−1. In this case, the higher the self-diffusion coefficient, the stronger is the impact of the static magnetic field gradient on the dephasing of the transverse magnetization and thus the lower the corresponding measured *T*2eff. A further effect comes from the used recycle delay of 4 s, which is for some of the investigated solvents of the same order as the corresponding *T*<sup>1</sup> value. Nevertheless, both effects pose no impediment on discriminating the various solvents based on their *T*2eff values. They can be even used to induce a higher relaxation contrast between the solvents to be investigated, another key advantage of the proposed methodology.

**Figure 1.** (**a**) Typical 1H CPMG NMR decays of two pure solvents and their mixtures at different mass ratios. The CPMG decays were recorded at room temperature. (**b**) The corresponding ILTs of the CPMG decays depicted in (**a**). The amplitudes are normalized to unity.

The 1H CPMG relaxation decays of the investigated binary solvent mixtures and the corresponding relaxation spectra as obtained by ILT are sensitive to the mass proportion of the two solvents within the mixture, as exemplarily shown by the results depicted in Figure 1. Single relaxation peaks are observed for the mixtures at positions in between those of the pure solvents (Figure 1b). Similar results were obtained for all investigated mixtures (Figure S1, in the Supplementary Materials). The ILT results enable the extraction of an averaged *T*2eff for a particular solvent mixture as an efficient parameter for further use.

The variation of the obtained *T*2eff of the mixtures with the mass content of the two solvents is exemplarily depicted in Figure 2 for a 1,3,5-triisopropylbenzene (TiPB)/2 pentanone mixture and in Figure S2 (in the Supplementary Materials) for all the other mixtures. All correlation curves could best be described by simple single exponential functions (Figure 2 and Figure S2). Once the correlation curves are established following the measurement and analysis of the CPMG decays, and the fit function for the correlation curve identified, a process which takes around 1 h for each mixture, the separation power of a particular MOF can be quantified within few minutes.

**Figure 2.** Correlation of the relaxation times with the solvent content in a binary mixture as exemplarily shown for TiPB/2-pentanone. The line depicts the fit result using the equation *T*2eff\_mixture = 3.72 × exp(content/30.3) + 12 with a correlation factor higher than 0.99. The relaxation times were measured at room temperature.

UiO-66(Zr) (Figure 3) was chosen as a model MOF to test our methodology in the view of its high thermal, mechanical, and chemical stability, well-controlled synthesis procedure, and great promise in the field of separation [23,48–54]. This MOF is built from Zr6O6(CO2)12 nodes connected via terephthalate linkers. Its pore system contains tetrahedral and octahedral cavities (free diameters of about 8 Å and 11 Å) [50]. Both cavities are connected by a small triangular window with a pore aperture of about 6.5 Å [50] which needs to be passed by any molecule entering the pores of UiO-66 acting thus as a sieve for larger molecules.

The separation efficiency of powdered UiO-66 due to selective adsorption was tested at room temperature under static conditions for different solvent mixtures by measuring the solvent mixture following equilibration with the MOF and subsequent removal (see the experimental section for more details). The relaxation times of the binary mixtures before and after contact with UiO-66 are different (Figure S3, in the Supplementary Materials). This indicates changes in the mass proportion of the two solvents in the mixture (Figure 4a). In particular, one observes that the content of both n-octane and cyclooctane increases in the mixture with 2-pentanone after separation. This indicates that UiO-66 has a preferential adsorption for 2-pentanone compared to the other two solvents, probably due

to a stronger interaction of the 2-pentanone with UiO-66. Furthermore, a partially removal of 2-pentanone from the mixture with TiPB was detected. Given that 2-pentanone should readily enter into UiO-66 and the kinetic diameter of TiPB of about 8.5 Å is much larger than the size of the UiO-66 window, a combination between a sieving mechanism and a blocking of the UiO66 windows by TiPB which prevents that 2-pentanone enters the pores can explain the observed behavior.

**Figure 3.** Structure of UiO-66(Zr) showing the carbon (gray), hydrogen (white), oxygen (red), zirconium (blue) and the unit cell (black outline). The tetrahedral and octahedral cavities are indicated by the green and orange spheres. Adapted from [48].

**Figure 4.** (**a**) Content of the first solvent before (filled symbols) and after (empty symbols) extraction by MOF as calculated based on the *T*2eff values given in Figure S3. For the n-hexane/cyclohexane a mixture with around 55 wt % cyclohexane was tested. The errors of the obtained values are lower than 0.5%. (**b**) Correlation of the solvent content in the mixture before and after separation as determined by low-field relaxometry and high-field liquid-state spectroscopy. For the sake of comparison, the results of all mixtures presented in Figure 4a are included. The continuous line is the linear fit result with a correlation factor of 0.997.

The proportion of n-octane and cyclooctane remains largely the same before and after the filtration indicating that the two isomers fail to be separated in the liquid phase under

static conditions by powdered UiO-66(Zr). This is an unexpected result because one can assume that n-octane can easily enter into the MOF given that the kinetic diameter of the n-octane is much smaller than the size of the UiO-66 window. Monte Carlo simulations of these two solvents inside the MOF indicate that at zero coverage, n-octane is proportionally distributed between the small and the large cavities and cyclooctane can fit even inside the small, tetrahedral, cavity [52]. However, the simulations give no hint if the cyclooctane, with his kinetic diameter of 8 Å can enter the MOF through the window of 6.5 Å. Given that, to our knowledge, no reports about the separation of the n-octane and cyclooctane by UiO66(Zr) in the liquid phase at room temperature are reported, the raisons behind our observations are not clear. Yet, it has been reported that n-alkanes have the same conformation in a pure liquid state and in a gas state, but they can change conformation in the presence of other solvents [55,56]. Thus, a possible explanation for our observations would be that n-octane changes conformation in the presence of cyclooctane towards a more coil structure and with this its kinetic diameter increases making thus difficult to pass through the MOF window. A further possible explanation of the observed behavior could be related to a solvent induced-breathing process of the MOF. This would lead to an increase in the size of the window such that also cyclooctane could enter the MOF. A similar solvent induced-breathing process had to be taken into account to explain the dependence of the self-diffusion coefficients of methane with the pressure in UiO-66(Zr) [57]. Additional studies are planned for the future to elucidate if a combination of both processes is involved in the observed behavior for this mixture or is largely due only to a change in conformation.

However, a small increase in the content of n-hexane compared to cyclohexane after separation was observed. This is consistent with the reported preferential adsorption of cyclic alkanes over the linear alkanes in UiO-66 measured using vapor phase breakthrough experiments on which the mixtures were diluted using carrier gases such as helium [51,52]. As the pore size of UiO-66 are large enough to accommodate both n-hexane and cyclohexane possible explanations of the much lower separation efficiency are a competitive co-adsorption of both components, the solvent-solvent interaction which in liquid state should play a non-negligible role as well as the particular experimental conditions [58].

The quantified mass proportions of all mixtures by low-field relaxometry approach show an excellent agreement with the results from liquid-state 1H spectroscopy. Proton NMR spectroscopy is another method which can be used to easily quantify the content of certain solvents in a mixture without the need of an a priori calibration or the use of advanced data analysis but requires more sophisticated equipment and for complicated solvent structures measurements at high-magnetic field. Furthermore, the spectra alone fail to give the needed information when applied to certain mixtures including linear alkanes as, for example, for n-hexane/n-octane (Figure 5a). The identical appearance of the spectra of the pure solvents and their mixtures prevents the quantification of the solvent content inside the mixture using solely the differences in the chemical shift of the functional groups. A differentiation between the two solvents and their mixtures can however very easily be achieved with relaxation measurements under the experimental conditions already described (Figure 5b).

The separation of a n-octane/n-hexane mixture by UiO-66 with initially 82 wt % n-octane as determined by weight was also tested. The *T*2eff of this mixture of 14.5 ms translates into 81.32 wt % n-octane according to the correlation equation, in good agreement with the weighted value. No separation could be observed for this mixture by UiO-66, probably due to raisons mentioned already before for other binary mixtures.

**Figure 5.** (**a**) Proton liquid-state spectra of pure n-octane, pure n-hexane, and two mixtures of them measured at room temperature. Both solvents show signals in the same range of chemical shifts. (**b**) Correlation of the low-field NMR relaxation times with the n-octane content in a binary mixture with n-hexane. The line depicts the fit result using the equation *T*2eff\_mixture = 5.03 × exp(content/113) + 4.17 with a correlation factor higher than 0.99.

#### **3. Materials and Methods**
